High quality data is of vital importance for unlocking the full potential of AI for end users. Villalobos et al. stated in 2024 that finding new sources of such data is getting harder as most publicly-available human generated data will soon have been used. Additionally, publicly available data often is not representative of users of a particular system — for example, a research speech dataset of contractors interacting with an AI assistant will likely be more homogeneous, well articulated and self-censored that real world commands that end users will issue. Therefore unlocking high-quality data grounded in real user interactions is of vital interest to both system creators and end users themselves. However, the direct use of user data comes with significant privacy risks, which must be addressed before the data can be used. Differential Privacy (DP) is a well established framework for reasoning about and limiting information leakage, and is a gold standard for protecting user privacy. The focus of this work, Differentially Private Synthetic data, refers to synthetic data that preserves the overall trends of source data (often user-generated), while providing strong privacy guarantees to individuals that contributed to the source dataset. DP synthetic data can unlock the value of datasets that have previously been inaccessible due to privacy concerns. Additionally, DP synthetic data can replace the use of sensitive datasets that previously have only had rudimentary protections like ad-hoc rule-based anonymization. In this survey we explore the full suite of techniques surrounding DP synthetic data, the types of privacy protections different generation approaches can offer, and the state-of-the-art for various modalities including image, tabular, text and federated (decentralized) data. We outline all the components needed in a system that generates DP synthetic data, from sensitive data handling and preparation, to tracking the use of synthetic data and empirical privacy testing. We hope that work will result in increased adoption of DP synthetic data, spur additional research in still underexplored domains, and additionally increase trust in DP synthetic data approaches.

Scaling laws provide important insights that can guide the design of large language models (LLMs). Existing work has primarily focused on studying scaling laws for pretraining (upstream) loss. However, in transfer learning settings, in which LLMs are pretrained on an unsupervised dataset and then finetuned on a downstream task, we often also care about the downstream performance. In this work, we study the scaling behavior in a transfer learning setting, where LLMs are finetuned for machine translation tasks. Specifically, we investigate how the choice of the pretraining data and its size affect downstream performance (translation quality) as judged by: downstream cross-entropy and translation quality metrics such as BLEU and COMET scores. Our experiments indicate that the size of the finetuning dataset and the distribution alignment between the pretraining and downstream data significantly influence the scaling behavior. With sufficient alignment, both downstream cross-entropy and translation quality scores improve monotonically with more pretraining data. In such cases, we show that it is possible to predict the downstream translation quality metrics with good accuracy using a log-law. However, there are cases where moderate misalignment causes the downstream translation scores to fluctuate or get worse with more pretraining, whereas downstream cross-entropy monotonically improves. By analyzing these, we provide new practical insights for choosing appropriate pretraining data.

In this paper, we consider a new problem of portfolio optimization using stochastic information. In a setting where there is some uncertainty, we ask how to best select k potential solutions, with the goal of optimizing the value of the best solution. More formally, given a combinatorial problem Π, a set of value functions 𝒱 over the solutions of Π, and a distribution 𝒟 over 𝒱, our goal is to select k solutions of Π that maximize or minimize the expected value of the best of those solutions. For a simple example, consider the classic knapsack problem: given a universe of elements each with unit weight and a positive value, the task is to select r elements maximizing the total value. Now suppose that each element’s weight comes from a (known) distribution. How should we select k different solutions so that one of them is likely to yield a high value? In this work, we tackle this basic problem, and generalize it to the setting where the underlying set system forms a matroid. On the technical side, it is clear that the candidate solutions we select must be diverse and anti-correlated; however, it is not clear how to do so efficiently. Our main result is a polynomial-time algorithm that constructs a portfolio within a constant factor of the optimal.

The analysis of the privacy properties of Privacy-Preserving Ads APIs is an area of research that has received strong interest from academics, industry, and regulators.Despite this interest, the empirical study of these methods is severely hindered by the lack of publicly available data.Reliable empirical analysis of the privacy properties of an API, in fact, requires access to a dataset consisting of realistic API outputs for a large collection of users; however, privacy concerns prevent the general release of such data to the public.In this work, we address this problem by developing a novel methodology to construct synthetic API outputs that are simultaneously realistic enough to enable accurate study and provide strong privacy protections.We focus on one of the Privacy-Preserving Ads APIs: the Topics API, part of Google Chrome's Privacy Sandbox, which enables interest-based advertising without relying on third-party cookies.We developed a methodology to generate a differentially-private dataset that closely matches the re-identification risk properties of the real Topics API data.The use of differential privacy provides strong theoretical bounds on the leakage of private user information from this release.Our methodology is based on first computing a large number of differentially-private statistics describing how output API traces evolve over time.Then, we design a parameterized distribution over sequences of API traces and optimize its parameters so that they closely match the statistics obtained.Finally, we create the synthetic data by drawing from this distribution.Our work is complemented by an open-source release of the anonymized dataset obtained by this methodology.We hope this will enable external researchers to analyze the API in-depth and replicate prior and future work on a realistic large-scale dataset.

KDD ’25, Toronto, ON, Canada

Synthetically-generated data plays an increasingly larger role in training large language models. However, while synthetic data has been found to be useful, studies have also shown that without proper curation it can cause LLM performance to plateau, or even "collapse", after many training iterations. In this paper, we formalize this question and develop a theoretical framework to investigate how much curation is needed in order to ensure that LLM performance continually improves. Our analysis is inspired by boosting, a classic machine learning technique that leverages a very weak learning algorithm to produce an arbitrarily good classifier. The approach we analyze subsumes many recently proposed methods for training LLMs on synthetic data, and thus our analysis sheds light on why they are successful, and also suggests opportunities for future improvement. We present experiments that validate our theory, and show that dynamically focusing labeling resources on the most challenging examples --- in much the same way that boosting focuses the efforts of the weak learner --- leads to improved performance.

We study the Densest Subgraph (DSG) problem under the additional constraint of differential privacy. DSG is a fundamental theoretical question that plays a central role in graph analytics, and so privacy is a natural requirement. All known private algorithms for Densest Subgraph lose constant multiplicative factors, despite the existence of non-private exact algorithms. We show that, perhaps surprisingly, this loss is not necessary: in both the classic differential privacy model and the LEDP model (local edge differential privacy, introduced recently by Dhulipala et al. [FOCS 2022]), we give (ϵ, δ)-differentially private algorithms with no multiplicative loss whatsoever. In other words, the loss is purely additive. Moreover, our additive losses match or improve the previous state of the art additive loss (in any version of differential privacy) when 1/δ is polynomial in n, and are almost tight: in the centralized setting, our additive loss is O (log n/ϵ ) while there is a known lower bound of .

Push-Relabel is one of the most celebrated network flow algorithms. Maintaining a pre-flow that saturates a cut, it enjoys better theoretical and empirical running time than other flow algorithms, such as Ford-Fulkerson. In practice, Push-Relabel is even faster than what theoretical guarantees can promise, in part because of the use of good heuristics for seeding and updating the iterative algorithm. However, it remains unclear how to run Push-Relabel on an arbitrary initialization that is not necessarily a pre-flow or cut-saturating. We provide the first theoretical guarantees for warm-starting Push-Relabel with a predicted flow, where our learning-augmented version benefits from fast running time when the predicted flow is close to an optimal flow, while maintaining robust worst-case guarantees. Interestingly, our algorithm uses the gap relabeling heuristic, which has long been employed in practice, even though prior to our work there was no rigorous theoretical justification for why it can lead to run-time improvements. We then show our algorithmic framework works well in practice, as our warm-start version of Push-Relabel improves over the cold-start version by a larger and larger percentage as the size of the image increases.

Algorithms with (machine-learned) predictions is a powerful framework for combining traditional worst-case algorithms with modern machine learning. However, the vast majority of work in this space assumes that the prediction itself is non-probabilistic, even if it is generated by some stochastic process (such as a machine learning system). This is a poor fit for modern ML, particularly modern neural networks, which naturally generate a *distribution*. We initiate the study of algorithms with *distributional* predictions, where the prediction itself is a distribution. We focus on one of the simplest yet fundamental settings: binary search (or searching a sorted array). This setting has one of the simplest algorithms with a point prediction, but what happens if the prediction is a distribution? We show that this is a richer setting: there are simple distributions where using the classical prediction-based algorithm with any single prediction does poorly. Motivated by this, as our main result, we give an algorithm with query complexity $O(H(p) + \log \eta)$, where $H(p)$ is the entropy of the true distribution $p$ and $\eta$ is the earth mover's distance between $p$ and the predicted distribution $\hat p$. This also yields the first *distributionally-robust* algorithm for the classical problem of computing an optimal binary search tree given a distribution over target keys. We complement this with a lower bound showing that this query complexity is essentially optimal (up to constants), and experiments validating the practical usefulness of our algorithm.

The classical ski-rental problem admits a textbook 2-competitive deterministic algorithm, and a simple randomized algorithm that is e/e-1-competitive in expectation. The randomized algorithm, while optimal in expectation, has a large variance in its performance: it has more than a 37% chance of competitive ratio exceeding 2, and the change of the competitive ratio exceeding n is Θ(1/n)!

We study differentially private mechanisms for sharing training data in machine learning settings. Our goal is to enable learning of an accurate predictive model while protecting the privacy of each user's label. Previous work established privacy guarantees that assumed the features are public and given exogenously, a setting known as label differential privacy. In some scenarios, this can be a strong assumption that removes the interplay between features and labels from the privacy analysis. We relax this approach and instead assume the features are drawn from a distribution that depends on the private labels. We first show that simply adding noise to the label, as in previous work, can lead to an arbitrarily weak privacy guarantee, and also present methods for estimating this privacy loss from data. We then present a new mechanism that replaces some training examples with synthetically generated data, and show that our mechanism has a much better privacy-utility tradeoff if the synthetic data is ‘realistic’, in a certain quantifiable sense. Finally, we empirically validate our theoretical analysis.

Recent work has shown that leveraging learned predictions can improve the running time of algorithms for bipartite matching and similar combinatorial problems. In this work, we build on this idea to improve the performance of the widely used Ford-Fulkerson algorithm for computing maximum flows by seeding Ford-Fulkerson with predicted flows. Our proposed method offers strong theoretical performance in terms of the quality of the prediction. We then consider image segmentation, a common use-case of flows in computer vision, and complement our theoretical analysis with strong empirical results.

When applying differential privacy to sensitive data, we can often improve performance using external information such as other sensitive data, public data, or human priors. We propose to use the learning-augmented algorithms (or algorithms with predictions) framework---previously applied largely to improve time complexity or competitive ratios---as a powerful way of designing and analyzing privacy-preserving methods that can take advantage of such external information to improve utility. This idea is instantiated on the important task of multiple quantile release, for which we derive error guarantees that scale with a natural measure of prediction quality while (almost) recovering state-of-the-art prediction-independent guarantees. Our analysis enjoys several advantages, including minimal assumptions about the data, a natural way of adding robustness, and the provision of useful surrogate losses for two novel ''meta'' algorithms that learn predictions from other (potentially sensitive) data. We conclude with experiments on challenging tasks demonstrating that learning predictions across one or more instances can lead to large error reductions while preserving privacy.

The Bellman-Ford algorithm is a basic primitive for computing single source shortest paths in graphs with negative weight edges. Its running time is governed by the order the algorithm examines vertices for iterative updates on the value of their shortest path. In this work we study this problem through the lens of ’Algorithms with predictions,’ and show how to leverage auxiliary information from similar instances to improve the running time. We do this by identifying the key problem of Minimum Violation Permutations, and give algorithms with strong approximation guarantees as well as formal lower bounds. We complement the theoretical analysis with an empirical evaluation, showing that this approach can lead to a significant speed up in practice.

The streaming model of computation is a popular approach for working with large-scale data. In this setting, there is a stream of items and the goal is to compute the desired quantities (usually data statistics) while making a single pass through the stream and using as little space as possible. Motivated by the importance of data privacy, we develop differentially private streaming algorithms under the continual release setting, where the union of outputs of the algorithm at every timestamp must be differentially private. Specifically, we study the fundamental $\ell_p$ $(p\in [0,+\infty))$ frequency moment estimation problem under this setting, and give an $\varepsilon$-DP algorithm that achieves $(1+η)$-relative approximation $(\forall η\in(0,1))$ with $\mathrm{poly}\log(Tn)$ additive error and uses $\mathrm{poly}\log(Tn)\cdot \max(1, n^{1-2/p})$ space, where $T$ is the length of the stream and $n$ is the size of the universe of elements. Our space is near optimal up to poly-logarithmic factors even in the non-private setting. To obtain our results, we first reduce several primitives under the differentially private continual release model, such as counting distinct elements, heavy hitters and counting low frequency elements, to the simpler, counting/summing problems in the same setting. Based on these primitives, we develop a differentially private continual release level set estimation approach to address the $\ell_p$ frequency moment estimation problem. We also provide a simple extension of our results to the harder sliding window model, where the statistics must be maintained over the past $W$ data items.

Machine Learning (ML) models are ubiquitous in real world applications and are a constant focus of research. At the same time, the community has started to realize the importance of protecting the privacy of models' training data.

Machine Learning (ML) models are ubiquitous in real-world applications and are a constant focus of research. Modern ML models have become more complex, deeper, and harder to reason about. At the same time, the community has started to realize the importance of protecting the privacy of the training data that goes into these models. Differential Privacy (DP) has become a gold standard for making formal statements about data anonymization. However, while some adoption of DP has happened in industry, attempts to apply DP to real world complex ML models are still few and far between. The adoption of DP is hindered by limited practical guidance of what DP protection entails, what privacy guarantees to aim for, and the difficulty of achieving good privacy-utility-computation trade-offs for ML models. Tricks for tuning and maximizing performance are scattered among papers or stored in the heads of practitioners, particularly with respect to the challenging task of hyperparameter tuning. Furthermore, the literature seems to present conflicting evidence on how and whether to apply architectural adjustments and which components are “safe” to use with DP. In this survey paper, we attempt to create a self-contained guide that gives an in-depth overview of the field of DP ML. We aim to assemble information about achieving the best possible DP ML model with rigorous privacy guarantees. Our target audience is both researchers and practitioners. Researchers interested in DP for ML will benefit from a clear overview of current advances and areas for improvement. We also include theory-focused sections that highlight important topics such as privacy accounting and convergence. For a practitioner, this survey provides a background in DP theory and a clear step-by-step guide for choosing an appropriate privacy definition and approach, implementing DP training, potentially updating the model architecture, and tuning hyperparameters. For both researchers and practitioners, consistently and fully reporting privacy guarantees is critical, so we propose a set of specific best practices for stating guarantees. With sufficient computation and a sufficiently large training set or supplemental nonprivate data, both good accuracy (that is, almost as good as a non-private model) and good privacy can often be achievable. And even when computation and dataset size are limited, there are advantages to training with even a weak (but still finite) formal DP guarantee. Hence, we hope this work will facilitate more widespread deployments of DP ML models.

Compact user representations (such as embeddings) form the backbone of personalization services. In this work, we present a new theoretical framework to measure re-identification risk in such user representations. Our framework, based on hypothesis testing, formally bounds the probability that an attacker may be able to obtain the identity of a user from their representation. As an application, we show how our framework is general enough to model important real-world applications such as the Chrome's Topics API for interest-based advertising. We complement our theoretical bounds by showing provably good attack algorithms for re-identification that we use to estimate the re-identification risk in the Topics API. We believe this work provides a rigorous and interpretable notion of re-identification risk and a framework to measure it that can be used to inform real-world applications.

We present new mechanisms for label differential privacy, a relaxation of differentially private machine learning that only protects the privacy of the labels in the training set. Our mechanisms cluster the examples in the training set using their (non-private) feature vectors, randomly re-sample each label from examples in the same cluster, and output a training set with noisy labels as well as a modified version of the true loss function. We prove that when the clusters are both large and high-quality, the model that minimizes the modified loss on the noisy training set converges to small excess risk at a rate that is comparable to the rate for non-private learning. We also describe a learning problem in which large clusters are necessary to achieve both strong privacy and either good precision or good recall. Our experiments show that randomizing the labels within each cluster significantly improves the privacy vs. accuracy trade-off compared to applying uniform randomized response to the labels, and also compared to learning a model via DP-SGD.

We study the private k-median and k-means clustering problem in d dimensional Euclidean space. By leveraging tree embeddings, we give an efficient and easy to implement algorithm, that is empirically competitive with state of the art non private methods. We prove that our method computes a solution with cost at most O(d3/2 log n)⁆ OPT + O(kd2 log2 n/ε2), where ε is the privacy guarantee. (The dimension term, d, can be replaced with O(log k) using standard dimension reduction techniques.) Although the worst-case guarantee is worse than that of state of the art private clustering methods, the algorithm we propose is practical, runs in near-linear, Õ (nkd), time and scales to tens of millions of points. We also show that our method is amenable to parallelization in large-scale distributed computing environments. In particular we show that our private algorithms can be implemented in logarithmic number of MPC rounds in the sublinear memory regime. Finally, we complement our theoretical analysis with an empirical evaluation demonstrating the algorithm's efficiency and accuracy in comparison to other privacy clustering baselines.

The research area of algorithms with predictions has seen recent success showing how to incorporate machine learning into algorithm design to improve performance when the predictions are correct, while retaining worst-case guarantees when they are not. Most previous work has assumed that the algorithm has access to a single predictor. However, in practice, there are many machine learning methods available, often with incomparable generalization guarantees, making it hard to pick a best method a priori. In this work we consider scenarios where multiple predictors are available to the algorithm and the question is how to best utilize them. Ideally, we would like the algorithm's performance to depend on the quality of the {\em best} predictor. However, utilizing more predictions comes with a cost, since we now have to identify which prediction is best. We study the use of multiple predictors for a number of fundamental problems, including matching, load balancing, and non-clairvoyant scheduling, which have been well-studied in the single predictor setting. For each of these problems we introduce new algorithms that take advantage of multiple predictors, and prove bounds on the resulting performance.

A burgeoning paradigm in algorithm design is the field of algorithms with predictions, in which algorithms can take advantage of a possibly-imperfect prediction of some aspect of the problem. While much work has focused on using predictions to improve competitive ratios, running times, or other performance measures, less effort has been devoted to the question of how to obtain the predictions themselves, especially in the critical online setting. We introduce a general design approach for algorithms that learn predictors: (1) identify a functional dependence of the performance measure on the prediction quality and (2) apply techniques from online learning to learn predictors, tune robustness-consistency trade-offs, and bound the sample complexity. We demonstrate the effectiveness of our approach by applying it to bipartite matching, ski-rental, page migration, and job scheduling. In several settings we improve upon multiple existing results while utilizing a much simpler analysis, while in the others we provide the first learning-theoretic guarantees.

Hierarchical clustering is a widely used data analysis method, but suffers from scalability issues, requiring quadratic time in general metric spaces. In this work, we demonstrate how approximate nearest neighbor (ANN) queries can be used to improve the running time of the popular single-linkage and average-linkage methods. Our proposed algorithms are the first subquadratic time algorithms for non-Euclidean metrics. We complement our theoretical analysis with an empirical evaluation showcasing our methods’ efficiency and accuracy.

We study the problem of differentially private optimization with linear constraints when the right-hand-side of the constraints depends on private data. This type of problem appears in many applications, especially resource allocation. Previous research provided solutions that retained privacy but sometimes violated the constraints. In many settings, however, the constraints cannot be violated under any circumstances. To address this hard requirement, we present an algorithm that releases a nearly-optimal solution satisfying the constraints with probability 1. We also prove a lower bound demonstrating that the difference between the objective value of our algorithm’s solution and the optimal solution is tight up to logarithmic factors among all differentially private algorithms. We conclude with experiments demonstrating that our algorithm can achieve nearly optimal performance while preserving privacy.

We study the problem of designing privacy-enhanced solutions for interest-based advertisement (IBA). IBA is a key component of the online ads ecosystem and provides a better ad experience to users. Indeed, IBA enables advertisers to show users impressions that are relevant to them. Nevertheless, the current way ad tech companies achieve this is by building detailed interest profiles for individual users. In this work we ask whether such fine grained personalization is required, and present mechanisms that achieve competitive performance while giving privacy guarantees to the end users. More precisely we present the first detailed exploration of how to implement Chrome's Federated Learning of Cohorts (FLoC) API. We define the privacy properties required for the API and evaluate multiple hashing and clustering algorithms discussing the trade-offs between utility, privacy, and ease of implementation.

A recent line of research investigates how algorithms can be augmented with machine-learned predictions to overcome worst case lower bounds. This area has revealed interesting algorithmic insights into problems, with particular success in the design of competitive online algorithms. However, the question of improving algorithm running times with predictions has largely been unexplored. We take a first step in this direction by combining the idea of machine-learned predictions with the idea of ``warm-starting" primal-dual algorithms. We consider one of the most important primitives in combinatorial optimization: weighted bipartite matching and its generalization to $b$-matching. We identify three key challenges when using learned dual variables in a primal-dual algorithm. First, predicted duals may be infeasible, so we give an algorithm that efficiently maps predicted infeasible duals to nearby feasible solutions. Second, once the duals are feasible, they may not be optimal, so we show that they can be used to quickly find an optimal solution. Finally, such predictions are useful only if they can be learned, so we show that the problem of learning duals for matching has low sample complexity. We validate our theoretical findings through experiments on both real and synthetic data. As a result we give a rigorous, practical, and empirically effective method to compute bipartite matchings.

In correlation clustering we are given a set of points along with recommendations whether each pair of points should be placed in the same cluster or into separate clusters. The goal cluster the points to minimize disagreements from the recommendations. We study the correlation clustering problem in the online setting., where points arrive one at a time, and upon arrival the algorithm must make an irrevocable cluster assignment decision. While the online version is natural, there is a simple lower bound that rules out any algorithm with a non-trivial competitive ratio. In this work we go beyond worst case analysis, and show that the celebrated Pivot algorithm performs well when given access to a small number of random samples from the input. Moreover, we prove that Pivot is robust to additional adversarial perturbations of the sample set in this setting. We conclude with an empirical analysis validating our theoretical findings.

The secretary problem is probably the purest model of decision making under uncertainty. In this paper, we ask which advice we can give the algorithm to improve its success probability. We propose a general model that unifies a broad range of problems: from the classic secretary problem with no advice to the variant where the quality of a secretary is drawn from a known distribution and the algorithm learns each candidate’s quality on arrival, more modern versions of advice in the form of samples, and a machine-learning inspired model where a classifier gives us a noisy signal about whether the current secretary is the best on the market. Our main technique is a factor-revealing linear program (LP) that captures all of these problems. We use this LP formulation to gain structural insight into the optimal policy. Using tools from linear programming, we present a tight analysis of optimal algorithms for secretaries with samples, optimal algorithms when secretaries’ qualities are drawn from a known distribution, and optimal algorithms for a new noisy binary advice model.

Traditional online algorithms encapsulate decision making under uncertainty, and give ways to hedge against all possible future events, while guaranteeing a nearly optimal solution, as compared to an offline optimum. On the other hand, machine learning algorithms are in the business of extrapolating patterns found in the data to predict the future, and usually come with strong guarantees on the expected generalization error. In this work, we develop a framework for augmenting online algorithms with a machine learned predictor to achieve competitive ratios that provably improve upon unconditional worst-case lower bounds when the predictor has low error. Our approach treats the predictor as a complete black box and is not dependent on its inner workings or the exact distribution of its errors. We apply this framework to the traditional caching problem—creating an eviction strategy for a cache of size k . We demonstrate that naively following the oracle’s recommendations may lead to very poor performance, even when the average error is quite low. Instead, we show how to modify the Marker algorithm to take into account the predictions and prove that this combined approach achieves a competitive ratio that both (i) decreases as the predictor’s error decreases and (ii) is always capped by O (log k ), which can be achieved without any assistance from the predictor. We complement our results with an empirical evaluation of our algorithm on real-world datasets and show that it performs well empirically even when using simple off-the-shelf predictions.

As machine learning has become more prevalent, researchers have begun to recognize the necessity of ensuring machine learning systems are fair. Recently, there has been an interest in defining a notion of fairness that mitigates over-representation in traditional clustering. In this paper we extend this notion to hierarchical clustering, where the goal is to recursively partition the data to optimize a specific objective. For various natural objectives, we obtain simple, efficient algorithms to find a provably good fair hierarchical clustering. Empirically, we show that our algorithms can find a fair hierarchical clustering, with only a negligible loss in the objective.

The sliding window model of computation captures scenarios in which data is arriving continuously, but only the latest $w$ elements should be used for analysis. The goal is to design algorithms that update the solution efficiently with each arrival rather than recomputing it from scratch. In this work, we focus on $k$-clustering problems such as $k$-means and $k$-median. In this setting, we provide simple and practical algorithms that offer stronger performance guarantees than previous results. Empirically, we show that our methods store only a small fraction of the data, are orders of magnitude faster, and find solutions with costs only slightly higher than those returned by algorithms with access to the full dataset.

Online algorithms are a hallmark of worst case optimization under uncertainty. On the other hand, in practice, the input is often far from worst case, and has some predictable characteristics. A recent line of work has shown how to use machine learned predictions to circumvent strong lower bounds on competitive ratios in classic online problems such as ski rental and caching. We study how predictive techniques can be used to break through worst case barriers in online scheduling. The makespan minimization problem with restricted assignments is a classic problem in online scheduling theory. Worst case analysis of this problem gives Ω(log m) lower bounds on the competitive ratio in the online setting. We identify a robust quantity that can be predicted and then used to guide online algorithms to achieve better performance. Our predictions are compact in size, having dimension linear in the number of machines, and can be learned using standard off the shelf methods. The performance guarantees of our algorithms depend on the accuracy of the predictions, given predictions with error η, we show how to construct O(log η) competitive fractional assignments. We then give an online algorithm that rounds any fractional assignment into an integral schedule. Our algorithm is O((log log m)3)-competitive and we give a nearly matching Ω(log log m) lower bound for online rounding algorithms.1 Altogether, we give algorithms that, equipped with predictions with error η, achieve O(log η (log log m)3) competitive ratios, breaking the Ω(log m) lower bound even for moderately accurate predictions.

The need for fairness in machine learning algorithms is increasingly critical. A recent focus has been on developing fair versions of classical algorithms, such as those for bandit learning, regression, and clustering. In this work we extend this line of work to include algorithms for optimization subject to one or multiple matroid constraints. We map out a series of results, showing optimal solutions, approximation algorithms, and hardness proofs depending on the specific flavor of the problem. Our algorithms are efficient and empirical experiments demonstrate that fairness can be achieved with a modest compromise to the overall objective value.

Modern online learning algorithms achieve low (sublinear) regret in a variety of diverse settings. These algorithms, however, update their solution at every time step. While these updates are computationally efficient, the very requirement of frequent updates makes the algorithms untenable in some practical applications. In this work we develop online learning algorithms that update a sublinear number of times. We give a meta algorithm based on non-homogeneous Poisson Processes that gives a smooth trade-off between regret and frequency of updates. Empirically, we show that in many cases, we can significantly reduce updates at a minimal increase in regret.

We propose online algorithms for Column Subset Selection (CSS) and Principal Component Analysis (PCA), two methods that are widely employed for data analysis, summarization, and visualization. Given a data matrix A that is revealed one column at a time, the online CSS problems asks to keep a small set of columns, S, that best approximates the space spanned by the columns of A. As each column arrives, the algorithm must irrevocably decide whether to add it to S, or to ignore it. In the online PCA problem, the goal is to output a projection of each column to a low dimensional subspace. In other words, the algorithm must provide an embedding for each column as it arrives, which cannot be changed as new columns arrive. While both of these problems have been studied in the online setting, only additive approximations were known prior to our work. The core of our approach is an adaptive sampling technique that gives a practical and efficient algorithm for both of these problems. We prove that by sampling columns using their 'residual norm'' (i.e. their norm orthogonal to directions sampled so far), we end up with a significantly better dependence between the number of columns sampled, and the desired error in the approximation. We further show how to combine our algorithm "in series'' with prior algorithms. In particular, using the results of Boutsidis et al. and Frieze et al. that have additive guarantees, we show how to improve the bounds on the error of our algorithm.

Differentially private learning algorithms protect individual participants in the training dataset by guaranteeing that their presence does not significantly change the resulting model. In order to make this promise, such algorithms need to know the maximum contribution that can be made by a single user: the more data an individual can contribute, the more noise will need to be added to protect them. While most existing analyses assume that the maximum contribution is known and fixed in advance{—}indeed, it is often assumed that each user contributes only a single example{—}we argue that in practice there is a meaningful choice to be made. On the one hand, if we allow users to contribute large amounts of data, we may end up adding excessive noise to protect a few outliers, even when the majority contribute only modestly. On the other hand, limiting users to small contributions keeps noise levels low at the cost of potentially discarding significant amounts of excess data, thus introducing bias. Here, we characterize this trade-off for an empirical risk minimization setting, showing that in general there is a “sweet spot” that depends on measurable properties of the dataset, but that there is also a concrete cost to privacy that cannot be avoided simply by collecting more data.

It is often desirable in recommender systems and other information retrieval applications to provide diverse results, and determinantal point processes (DPPs) have become a popular way to capture the trade-off between the quality of individual results and the diversity of the overall set. However, sampling from a DPP is inherently expensive: if the underlying collection contains N items, then generating each DPP sample requires time linear in N following a one-time preprocessing phase. Additionally, results often need to be personalized to a user, but standard approaches to personalization invalidate the preprocessing, making personalized samples especially expensive. In this work we address both of these shortcomings. First, we propose a new algorithm for generating DPP samples in time logarithmic in N, following a slightly more expensive preprocessing phase. We then extend the algorithm to support arbitrary query-time feature weights, allowing us to generate samples customized to individual users while still retaining logarithmic runtime; experiments show our approach runs over 300 times faster than traditional DPP sampling on collections of 100,000 items for samples of size 10.

The covariance matrix of a dataset is a fundamental statistic that can be used for calculating optimum regression weights as well as in many other learning and data analysis settings. For datasets containing private user information, we often want to estimate the covariance matrix in a way that preserves differential privacy. While there are known methods for privately computing the covariance matrix, they all have one of two major shortcomings. Some, like the Gaussian mechanism, only guarantee (epsilon, delta)-differential privacy, leaving a non-trivial probability of privacy failure. Others give strong epsilon-differential privacy guarantees, but are impractical, requiring complicated sampling schemes, and tend to perform poorly on real data. In this work we propose a new epsilon-differentially private algorithm for computing the covariance matrix of a dataset that addresses both of these limitations. We show that it has lower error than existing state-of-the-art approaches, both analytically and empirically. In addition, the algorithm is significantly less complicated than other methods and can be efficiently implemented with rejection sampling.

The streaming computation model is a standard model for large-scale data analysis: the input arrives one element at a time, and the goal is to maintain an approximately optimal solution using only a constant, or, at worst, polylogarithmic space.

The rollout of new versions of a feature in modern applications is a manual multi-stage process, as the feature is released to ever larger groups of users, while its performance is carefully monitored. This kind of A/B testing is ubiquitous, but suboptimal, as the monitoring requires heavy human intervention, is not guaranteed to capture consistent, but short-term fluctuations in performance, and is inefficient, as better versions take a long time to reach the full population.

We develop a framework for augmenting online algorithms with a machine learned oracle to achieve competitive ratios that provably improve upon unconditional worst case lower bounds when the oracle has low error. Our approach treats the oracle as a complete black box, and is not dependent on its inner workings, or the exact distribution of its errors. We apply this framework to the traditional caching problem {—} creating an eviction strategy for a cache of size k. We demonstrate that naively following the oracle’s recommendations may lead to very poor performance, even when the average error is quite low. Instead we show how to modify the Marker algorithm to take into account the oracle’s predictions, and prove that this combined approach achieves a competitive ratio that both (i) decreases as the oracle’s error decreases, and (ii) is always capped by O(log k), which can be achieved without any oracle input. We complement our results with an empirical evaluation of our algorithm on real world datasets, and show that it performs well empirically even using simple off the shelf predictions.

Determinantal point processes (DPPs) are well-suited to recommender systems where the goal is to generate collections of diverse, high-quality items. In the existing literature this is usually formulated as finding the mode of the DPP (the so-called MAP set). However, the MAP objective inherently assumes that the DPP models "optimal" recommendation sets, and yet obtaining such a DPP is nontrivial when there is no ready source of example optimal sets. In this paper we advocate an alternative framework for applying DPPs to recommender systems. Our approach assumes that the DPP simply models user engagements with recommended items, which is more consistent with how DPPs for recommender systems are typically trained. With this assumption, we are able to formulate a metric that measures the expected number of items that a user will engage with. We formalize this optimization of this metric as the Maximum Induced Cardinality (MIC) problem. Although the MIC objective is not submodular, we show that it can be approximated by a submodular function, and that empirically it is well-optimized by a greedy algorithm.

Consider a buyer participating in a repeated auction, such as those prevalent in display advertising. How would she test whether the auction is incentive compatible? To bid effectively, she is interested in whether the auction is single-shot incentive compatible---a pure second-price auction, with fixed reserve price---and also dynamically incentive compatible---her bids are not used to set future reserve prices. In this work we develop tests based on simple bid perturbations that a buyer can use to answer these questions, with a focus on dynamic incentive compatibility. There are many potential A/B testing setups that one could use, but we find that many natural experimental designs are, in fact, flawed. For instance, we show that additive perturbations can lead to paradoxical results, where higher bids lead to lower optimal reserve prices. We precisely characterize this phenomenon and show that reserve prices are only guaranteed to be monotone for distributions satisfying the Monotone Hazard Rate (MHR) property. The experimenter must also decide how to split traffic to apply systematic perturbations. It is tempting to have this split be randomized, but we demonstrate empirically that unless the perturbations are aligned with the partitions used by the seller to compute reserve prices, the results are guaranteed to be inconclusive. We validate our results with experiments on real display auction data and show that a buyer can quantify both single-shot and dynamic incentive compatibility even under realistic conditions where only the cost of the impression is observed (as opposed to the exact reserve price). We analyze the cost of running such experiments, exposing trade-offs between test accuracy, cost, and underlying market dynamics.

The goal of this article is to identify fundamental limitations on how efficiently algorithms implemented on platforms such as MapReduce and Hadoop can compute the central problems in motivating application domains, such as graph connectivity problems. We introduce an abstract model of massively parallel computation, where essentially the only restrictions are that the “fan-in” of each machine is limited to s bits, where s is smaller than the input size n , and that computation proceeds in synchronized rounds, with no communication between different machines within a round. Lower bounds on the round complexity of a problem in this model apply to every computing platform that shares the most basic design principles of MapReduce-type systems. We prove that computations in our model that use few rounds can be represented as low-degree polynomials over the reals. This connection allows us to translate a lower bound on the (approximate) polynomial degree of a Boolean function to a lower bound on the round complexity of every (randomized) massively parallel computation of that function. These lower bounds apply even in the “unbounded width” version of our model, where the number of machines can be arbitrarily large. As one example of our general results, computing any nontrivial monotone graph property—such as connectivity—requires a super-constant number of rounds when every machine receives only a subpolynomial (in n ) number of input bits s . Finally, we prove that, in two senses, our lower bounds are the best one could hope for. For the unbounded-width model, we prove a matching upper bound. Restricting to a polynomial number of machines, we show that asymptotically better lower bounds would separate P from NC 1 .

Many enterprises have migrated their data from an on-site database to a cloud-based database-as-a-service that handles all database-related administrative tasks while providing a simple SQL interface to the end user. Businesses are also increasingly relying on machine learning to understand their customers and develop new products. Given these converging trends, there is a pressing need for database-as-a-service providers to add support for sophisticated machine learning algorithms to the core functionality of their products.

The study of online algorithms and competitive analysis provides a solid foundation for studying the quality of irrevocable decision making when the data arrives in an online manner. While in some scenarios the decisions are indeed irrevocable, there are many practical situations when changing a previous decision is not impossible, but simply expensive. In this work we formalize this notion and introduce the consistent k-clustering problem. With points arriving online, the goal is to maintain a constant approximate solution, while minimizing the number of reclusterings necessary. We prove a lower bound, showing that $\Omega(k \log n)$ changes are necessary in the worst case for a wide range of objective functions. On the positive side, we give an algorithm that needs only $O(k^2 \log^4n)$ changes to maintain a constant competitive solution, an exponential improvement on the naive solution of reclustering at every time step. Finally, we show experimentally that our approach performs much better than the theoretical bound, with the number of changes growing approximately as $O(\log n)$.

We study the cost sharing problem for cooperative games in situations where the cost function C is not available via oracle queries, but must instead be learned from samples drawn from a distribution, represented as tuples (S, C(S)), for different subsets S of players. We formalize this approach, which we call statistical cost sharing, and consider the computation of the core and the Shapley value. Expanding on the work by Balcan et al, we give precise sample complexity bounds for computing cost shares that satisfy the core property with high probability for any function with a non-empty core. For the Shapley value, which has never been studied in this setting, we show that for submodular cost functions with curvature bounded curvature kappa it can be approximated from samples from the uniform distribution to a sqrt{1 - kappa} factor, and that the bound is tight. We then define statistical analogues of the Shapley axioms, and derive a notion of statistical Shapley value and that these can be approximated arbitrarily well from samples from any distribution and for any function.

We study the question of fair clustering under the {\em disparate impact} doctrine, where each protected class must have approximately equal representation in every cluster. We formulate the fair clustering problem under both the k-center and the k-median objectives, and show that even with two protected classes the problem is challenging, as the optimum solution can violate common conventions---for instance a point may no longer be assigned to its nearest cluster center! En route we introduce the concept of fairlets, which are minimal sets that satisfy fair representation while approximately preserving the clustering objective. We show that any fair clustering problem can be decomposed into first finding good fairlets, and then using existing machinery for traditional clustering algorithms. While finding good fairlets can be NP-hard, we proceed to obtain efficient approximation algorithms based on minimum cost flow. We empirically demonstrate the \emph{price of fairness} by quantifying the value of fair clustering on real-world datasets with sensitive attributes.

In the context of advertising auctions, finding good reserve prices is a notoriously challenging learning problem. This is due to the heterogeneity of ad opportunity types, and the non-convexity of the objective function. In this work, we show how to reduce reserve price optimization to the standard setting of prediction under squared loss, a well understood problem in the learning community. We further bound the gap between the expected bid and revenue in terms of the average loss of the predictor. This is the first result that formally relates the revenue gained to the quality of a standard machine learned model.

We consider the reachability indexing problem for private-public directed graphs. In these graphs nodes come in three flavors: public--nodes visible to all users, private--nodes visible to a specific set of users, and protected--nodes visible to any user who can see at least one of the node's parents. We are interested in computing the set of nodes visible to a specific user online. There are two obvious algorithms: precompute the result for every user, or run a reachability algorithm at query time. This paper explores the trade-off between these two strategies.

Maximizing submodular functions under cardinality constraints lies at the core of numerous data mining and machine learning applications, including data diversification, data summarization, and coverage problems. In this work, we study this question in the context of data streams, where elements arrive one at a time, and we want to design low-memory and fast update-time algorithms that maintain a good solution. Specifically, we focus on the sliding window model, where we are asked to maintain a solution that considers only the last W items.

We study the problem of k -means clustering in the presence of outliers. The goal is to cluster a set of data points to minimize the variance of the points assigned to the same cluster, with the freedom of ignoring a small set of data points that can be labeled as outliers. Clustering with outliers has received a lot of attention in the data processing community, but practical, efficient, and provably good algorithms remain unknown for the most popular k -means objective. Our work proposes a simple local search-based algorithm for k -means clustering with outliers. We prove that this algorithm achieves constant-factor approximate solutions and can be combined with known sketching techniques to scale to large data sets. Using empirical evaluation on both synthetic and large-scale real-world data, we demonstrate that the algorithm dominates recently proposed heuristic approaches for the problem.

In this paper we show how to embed information distances like the χ^2 and Jensen-Shannon divergences efficiently in low dimensional spaces while preserving all pairwise distances. We then prove a dimensionality reduction result for the Hellinger, Jensen–Shannon, and χ^2 divergences that preserves the information geometry of the distributions, specifically, by retaining the simplex structure of the space. While our first result already implies these divergences can be explicitly embedded in the Euclidean space, retaining the simplex structure is important because it allows us to do inferences in the reduced space. We also show that these divergences can be sketched efficiently (i.e., up to a multiplicative error in sublinear space) in the aggregate streaming model. This result is exponentially stronger than known upper bounds for sketching these distances in the strict turnstile streaming model.

As the number of ad exchanges has grown, publishers have turned to low regret learning algorithms to decide which exchange offers the best price for their inventory. This in turn opens the following question for the exchange: how to set prices to attract as many sellers as possible and maximize revenue. In this work we formulate this precisely as a learning problem, and present algorithms showing that by simply knowing that the counterparty is using a low regret algorithm is enough for the exchange to have its own low regret learning algorithm to find the optimal price.

We study the problem of reconstructing a mixture of Markov chains from the trajectories generated by random walks through the state space. Under mild non-degeneracy conditions, we show that we can uniquely reconstruct the underlying chains by only considering trajectories of length three, which represent triples of states. Our algorithm is spectral in nature, and is easy to implement.

The goal of this paper is to identify fundamental limitations on how efficiently algorithms implemented on platforms such as MapReduce and Hadoop can compute the central problems in the motivating application domains, such as graph connectivity problems.

We study the question of setting and testing reserve prices in single item auctions when the bidders are not identical. At a high level, there are two generalizations of the standard second price auction: in the lazy version we first determine the winner, and then apply reserve prices; in the eager version we first discard the bidders not meeting their reserves, and then determine the winner among the rest. We show that the two versions have dramatically different properties: lazy reserves are easy to optimize, and A/B test in production, whereas eager reserves always lead to higher welfare, but their optimization is NP-complete, and naive A/B testing will lead to incorrect conclusions. Despite their different characteristics, we show that the overall revenue for the two scenarios is always within a factor of 2 of each other, even in the presence of correlated bids. Moreover, we prove that the eager auction dominates the lazy auction on revenue whenever the bidders are independent or symmetric. We complement our theoretical results with simulations on real world data that show that even suboptimally set eager reserve prices are preferred from a revenue standpoint.

We study the problem of selecting a set of points of interest (POIs) to show on a map. We begin with a formal model of the setting, noting that the utility of a POI may be discounted by (i) the presence of competing businesses nearby as well as (ii) its position in the set of establishments ordered by distance from the user. We present simple, approximately optimal selection algorithms, coupled with incentive compatible pricing schemes in case of advertiser supplied points of interest. Finally, we evaluate our algorithms on real data sets and show that they outperform simple baselines.

In this work we study the dynamics of geographic choice, i.e., how users choose one from a set of objects in a geographic region. We postulate a model in which an object is selected from a slate of candidates with probability that depends on how far it is (distance) and how many closer alternatives exist (rank). Under a discrete choice formulation, we argue that there exists a factored form in which unknown functions of rank and distance may be combined to produce an accurate estimate of the likelihood that a user will select each alternative. We then learn these hidden functions and show that each can be closely approximated by an appropriately parameterized lognormal, even though the respective marginals look quite different. We give a theoretical justification to support the presence of lognormal distributions.

We consider the problem of inferring choices made by users based only on aggregate data containing the relative popularity of each item. We propose a framework that models the problem as that of inferring a Markov chain given a stationary distribution. Formally, we are given a graph and a target steady-state distribution on its nodes. We are also give a mapping from per-node scores to a transition matrix, from a broad family of such mappings. The goal is to set the scores of each node such that the resulting transition matrix induces the desired steady state. We prove sufficient conditions under which this problem is feasible and, for the feasible instances, obtain a simple algorithm for a generic version of the problem. This iterative algorithm provably finds the unique solution to this problem and has a polynomial rate of convergence; in practice we find that the algorithm converges after fewer than ten iterations. We then apply this framework to choice problems in online settings and show that our algorithm is able to explain the observed data and predict the user choices much better than other competing baselines across a variety of diverse datasets.

Computing connected components of a graph lies at the core of many data mining algorithms, and is a fundamental subroutine in graph clustering. This problem is well studied, yet many of the algorithms with good theoretical guarantees perform poorly in practice, especially when faced with graphs with hundreds of billions of edges. In this paper, we design improved algorithms based on traditional MapReduce architecture for large scale data analysis. We also explore the effect of augmenting MapReduce with a distributed hash table (DHT) service. We show that these algorithms have provable theoretical guarantees, and easily outperform previously studied algorithms, sometimes by more than an order of magnitude. In particular, our iterative MapReduce algorithms run 3 to 15 times faster than the best previously studied algorithms, and the MapReduce implementation using a DHT is 10 to 30 times faster than the best previously studied algorithms. These are the fastest algorithms that easily scale to graphs with hundreds of billions of edges.

The k-means clustering algorithm has a long history and a proven practical performance, however it does not scale to clustering millions of data points into thousands of clusters in high dimensional spaces. The main computational bottleneck is the need to recompute the nearest centroid for every data point at every iteration, aprohibitive cost when the number of clusters is large. In this paper we show how to reduce the cost of the k-means algorithm by large factors by adapting ranked retrieval techniques. Using a combination of heuristics, on two real life data sets the wall clock time per iteration is reduced from 445 minutes to less than 4, and from 705 minutes to 1.4, while the clustering quality remains within 0.5% of the k-means quality.

We study the patterns by which a user consumes the same item repeatedly over time, in a wide variety domains ranging from check-ins at the same business location to re-watches of the same video. We find that recency of consumption is the strongest predictor of repeat consumption. Based on this, we develop a model by which the item from $t$ timesteps ago is reconsumed with a probability proportional to a function of t. We study theoretical properties of this model, develop algorithms to learn reconsumption likelihood as a function of t, and show a strong fit of the resulting inferred function via a power law with exponential cutoff. We then introduce a notion of item quality, show that it alone underperforms our recency-based model, and develop a hybrid model that predicts user choice based on a combination of recency and quality. We show how the parameters of this model may be jointly estimated, and show that the resulting scheme outperforms other alternatives.

One of the most important innovations of social networking websites is the notion of a "feed", a sequence of news items presented to the user as a stream that expands as the user scrolls down. The common method for monetizing such streams is to insert ads in between news items. In this paper, we model this setting, and observe that allocation and pricing of ad insertions in a stream poses interesting algorithmic and mechanism design challenges. In particular, we formulate an optimization problem that captures a typical stream ad placement setting. We give an approximation algorithm for this problem that provably achieves a value close to the optimal, and show how this algorithm can be turned into an incentive compatible mechanism. Finally, we conclude with a simple practical algorithm that makes the allocation decisions in an online fashion. We prove this algorithm to be approximately welfare-maximizing and show that it also has good incentive properties.

We propose a new method for unsupervised tagging that finds minimal models which are then further improved by Expectation Maximization training. In contrast to previous approaches that rely on manually specified and multi-step heuristics for model minimization, our approach is a simple greedy approximation algorithm DMLC (Distributed-Minimum-Label-Cover) that solves this objective in a single step. We extend the method and show how to efficiently parallelize the algorithm on modern parallel computing platforms while preserving approximation guarantees. The new method easily scales to large data and grammar sizes, overcoming the memory bottleneck in previous approaches. We demonstrate the power of the new algorithm by evaluating on various sequence labeling tasks: Part-of-Speech tagging for multiple languages (including low-resource languages), with complete and incomplete dictionaries, and supertagging, a complex sequence labeling task, where the grammar size alone can grow to millions of entries. Our results show that for all of these settings, our method achieves state-of-the-art scalable performance that yields high quality tagging outputs.

Multi-fold cross-validation is an established practice to estimate the error rate of a learning algorithm. Quantifying the variance reduction gains due to cross-validation has been challenging due to the inherent correlations introduced by the folds. In this work we introduce a new and weak measure of stability called \emphloss stability and relate the cross-validation performance to loss stability; we also establish that this relationship is near-optimal. Our work thus quantitatively improves the current best bounds on cross-validation.

Greedy algorithms are practitioners' best friends - they are intuitive, simple to implement, and often lead to very good solutions. However, implementing greedy algorithms in a distributed setting is challenging since the greedy choice is inherently sequential, and it is not clear how to take advantage of the extra processing power.

Online social networking platforms regularly support hundreds of millions of users, who in aggregate generate substantially more data than can be stored on any single physical server. As such, user data are distributed, or sharded, across many machines. A key requirement in this setting is rapid retrieval not only of a given user's information, but also of all data associated with his or her social contacts, suggesting that one should consider the topology of the social network in selecting a sharding policy. In this paper we formalize the problem of efficiently sharding large social network databases, and evaluate several sharding strategies, both analytically and empirically. We find that random sharding---the de facto standard---results in provably poor performance even when frequently accessed nodes are replicated to many shards. By contrast, we demonstrate that one can substantially reduce querying costs by identifying and assigning tightly knit communities to shards. In particular, our theoretical analysis motivates a novel, scalable sharding algorithm that outperforms both random and location-based sharding schemes.

We study the problem of aggregating and summarizing partial orders, on a large scale. Our motivation is two-fold: to discover elements at similar preference levels and to reduce the number of bits needed to store an element's position in a full ranking.We proceed in two steps: first, we find a total order by linearizing the rankings induced by the multiple partial orders and removing potentially inconsistent pairwise preferences. Next, given a total order, we introduce and formalize the rank quantization problem, which intuitively aims to bucketize the total order in a manner that mostly preserves the relations appearing in the partial orders. We show an exact quadratic-time quantization algorithm, as well as a greedy 2/3-approximation algorithm whose running is substantially faster on sparse instances. As an application, we aggregate rankings of top-10 search results over millions of search engine queries, approximately reproducing and then efficiently encoding the underlying static ranks used by the engine. We evaluate the performance of our algorithms on a web dataset of 12 million(2^{23.5}) unique pages and show that we can quantize the pages' static ranks using as few as eight bits, with only a minor degradation in search quality.

Motivated by the problem of optimizing allocation in guaranteed display advertising, we develop an efficient, lightweight method of generating a compact allocation plan that can be used to guide ad server decisions. The plan itself uses just O(1) state per guaranteed contract, is robust to noise, and allows us to serve (provably) nearly optimally.

A large fraction of online display advertising is sold via guaranteed contracts: a publisher guarantees to the advertiser a certain number of user visits satisfying the targeting predicates of the contract. The publisher is then tasked with solving the ad serving problem ---given a user visit, which of the thousands of matching contracts should be displayed, so that by the expiration time every contract has obtained the requisite number of user visits. The challenges of the problem come from (1) the sheer size of the problem being solved, with tens of thousands of contracts and billions of user visits, (2) the unpredictability of user behavior, since these contracts are sold months ahead of time, when only a forecast of user visits is available and (3) the minute amount of resources available online, as an ad server must respond with a matching contract in a fraction of a second.

Modern online advertising increasingly relies on the availability of user tracking technology called cookie-matching to increase efficiency in ad allocations. Web publishers today use this technology to share information about the websites a user has visited, making it possible to target advertisements to users based on their prior history. This begs the question: do publishers (who are competitors for advertising money) always have the incentive to share online information? Intuitive arguments as well as anecdotal evidence suggest that sometimes a premium publisher might suffer from information sharing through an effect called information leakage: by sharing user information with the advertiser, the advertiser will be able to target the same user elsewhere on cheaper publishers, leading to a dilution of the value of the supply on the premium publishers.

Most of the online advertising today is sold via an auction, which requires the advertiser to respond with a valid bid within a fraction of a second. As such, most advertisers employ bidding agents to submit bids on their behalf. The architecture of such agents typically has (1) an offline optimization phase which incorporates the bidder's knowledge about the market and (2) an online bidding strategy which simply executes the offline strategy. The online strategy is typically highly dependent on both supply and expected price distributions, both of which are forecast using traditional machine learning methods. In this work we investigate the optimum strategy of the bidding agent when faced with incorrect forecasts. At a high level, the agent can invest resources in improving the forecasts, or can tighten the loop between successive offline optimization cycles in order to detect errors more quickly. We show analytically that the latter strategy, while simple, is extremely effective in dealing with forecast errors, and confirm this finding with experimental evaluations.

The problem of finding locally dense components of a graph is an important primitive in data analysis, with wide-ranging applications from community mining to spam detection and the discovery of biological network modules. In this paper we present new algorithms for finding the densest subgraph in the streaming model. For any ε > 0, our algorithms make O (log 1+ε n ) passes over the input and find a subgraph whose density is guaranteed to be within a factor 2(1 + ε) of the optimum. Our algorithms are also easily parallelizable and we illustrate this by realizing them in the MapReduce model. In addition we perform extensive experimental evaluation on massive real-world graphs showing the performance and scalability of our algorithms in practice.

Over half a century old and showing no signs of aging, k -means remains one of the most popular data processing algorithms. As is well-known, a proper initialization of k -means is crucial for obtaining a good final solution. The recently proposed k -means++ initialization algorithm achieves this, obtaining an initial set of centers that is provably close to the optimum solution. A major downside of the k -means++ is its inherent sequential nature, which limits its applicability to massive data: one must make k passes over the data to find a good initial set of centers. In this work we show how to drastically reduce the number of passes needed to obtain, in parallel, a good initialization. This is unlike prevailing efforts on parallelizing k -means that have mostly focused on the post-initialization phases of k -means. We prove that our proposed initialization algorithm k -means|| obtains a nearly optimal solution after a logarithmic number of passes, and then show that in practice a constant number of passes suffices. Experimental evaluation on real-world large-scale data demonstrates that k -means|| outperforms k -means++ in both sequential and parallel settings.

Many large-scale Web applications that require ranked top-k retrieval are implemented using inverted indices. An inverted index represents a sparse term-document matrix, where non-zero elements indicate the strength of term-document associations. In this work, we present an approach for lossless compression of inverted indices. Our approach maps terms in a document corpus to a new term space in order to reduce the number of non-zero elements in the term-document matrix, resulting in a more compact inverted index. We formulate the problem of selecting a new term space as a matrix factorization problem, and prove that finding the optimal solution is an NP-hard problem. We develop a greedy algorithm for finding an approximate solution. A side effect of our approach is increasing the number of terms in the index, which may negatively affect query evaluation performance. To eliminate such effect, we develop a methodology for modifying query evaluation algorithms by exploiting specific properties of our compression approach.

Precomputation of common term co-occurrences has been successfully applied to improve query performance in large scale search engines based on inverted indexes. The results of such precomputations are traditionally stored as additional posting lists in the index. During query evaluation, these precomputed lists are used to reduce the number of query terms, as the results for multiple terms can be accessed through a single precomputed list. In this paper, we expand this paradigm by considering an alternative method for storing term co-occurrences in inverted indexes. For a selected set of terms in the index, we store bitmaps that encode term co-occurrences. A bitmap of size k for term t augments each posting to store the co-occurrences of t with k other terms, across every document in the index. At query evaluation, size k bitmaps can be used to answer queries that involve any of the 2^k combinations of the additional terms. In contrast, a precomputed list, although typically shorter, can only be used to evaluate queries containing all of its terms. We evaluate the bitmaps technique we propose, and the baseline of adding precomputed posting lists and show that they are complementary, as they capture different aspects of the query evaluation cost. We perform an experimental evaluation on the TREC WT10g corpus and show that a hybrid strategy combining both methods significantly lowers the cost of query evaluation compared to each method separately.

The secretary problem lies at the core of mechanism design for online auctions. In this work we study the generalization of the classical secretary problem in a setting where there is only a partial order between the elements and the goal of the algorithm is to return one of the maximal elements of the poset. This is equivalent to the auction setting where the seller has a multidimensional objective function with only a partial order among the outcomes. We obtain an algorithm that succeeds with probability at least k-k/(k-1)((1 + log k1/(k-1))k - 1), where k is the number of maximal elements in the poset and is the only information about the poset that is known to the algorithm; the success probability approaches the classical bound of 1/e as k -> 1. On the other hand, we prove an almost matching upper bound of k-1/(k-1) on the success probability of any algorithm for this problem; this upper bound holds even if the algorithm knows the complete structure of the poset.

The MapReduce framework is currently the de facto standard used throughout both industry and academia for petabyte scale data analysis. As the input to a typical MapReduce computation is large, one of the key requirements of the framework is that the input cannot be stored on a single machine and must be processed in parallel. In this paper we describe a general algorithmic design technique in the MapReduce framework called filtering. The main idea behind filtering is to reduce the size of the input in a distributed fashion so that the resulting, much smaller, problem instance can be solved on a single machine. Using this approach we give new algorithms in the MapReduce framework for a variety of fundamental graph problems for sufficiently dense graphs. Specifically, we present algorithms for minimum spanning trees, maximal matchings, approximate weighted matchings, approximate vertex and edge covers and minimum cuts. In all of these cases, we parameterize our algorithms by the amount of memory available on the machines allowing us to show tradeoffs between the memory available and the number of MapReduce rounds. For each setting we will show that even if the machines are only given substantially sublinear memory, our algorithms run in a constant number of MapReduce rounds. To demonstrate the practical viability of our algorithms we implement the maximal matching algorithm that lies at the core of our analysis and show that it achieves a significant speedup over the sequential version.

We introduce the problem of evaluating graph constraints in content-based publish/subscribe (pub/sub) systems. This problem formulation extends traditional content-based pub/sub systems in the following manner: publishers and subscribers are connected via a (logical) directed graph G with node and edge constraints, which limits the set of valid paths between them. Such graph constraints can be used to model a Web advertising exchange (where there may be restrictions on how advertising networks can connect advertisers and publishers) and content delivery problems in social networks (where there may be restrictions on how information can be shared via the social graph). In this context, we develop efficient algorithms for evaluating graph constraints over arbitrary directed graphs G. We also present experimental results that demonstrate the effectiveness and scalability of the proposed algorithms using a realistic dataset from Yahoo!'s Web advertising exchange.

The clustering coefficient of a node in a social network is a fundamental measure that quantifies how tightly-knit the community is around the node. Its computation can be reduced to counting the number of triangles incident on the particular node in the network. In case the graph is too big to fit into memory, this is a non-trivial task, and previous researchers showed how to estimate the clustering coefficient in this scenario. A different avenue of research is to to perform the computation in parallel, spreading it across many machines. In recent years MapReduce has emerged as a de facto programming paradigm for parallel computation on massive data sets. The main focus of this work is to give MapReduce algorithms for counting triangles which we use to compute clustering coefficients. Our contributions are twofold. First, we describe a sequential triangle counting algorithm and show how to adapt it to the MapReduce setting. This algorithm achieves a factor of 10-100 speed up over the naive approach. Second, we present a new algorithm designed specifically for the MapReduce framework. A key feature of this approach is that it allows for a smooth tradeoff between the memory available on each individual machine and the total memory available to the algorithm, while keeping the total work done constant. Moreover, this algorithm can use any triangle counting algorithm as a black box and distribute the computation across many machines. We validate our algorithms on real world datasets comprising of millions of nodes and over a billion edges. Our results show both algorithms effectively deal with skew in the degree distribution and lead to dramatic speed ups over the naive implementation.

We study the unit-demand envy-free pricing problem faced by a profit-maximizing seller with unlimited supply when there is metric substitutability among the items—consumer i's value for item j is $v_i-c_{i,j}$, and the substitution costs, $\{c_{i,j}\}$, form a metric. Our model is motivated by the observation that sellers often sell the same product at different prices in different locations, and rational consumers optimize the tradeoff between prices and substitution costs. While the general envy-free pricing problem is hard to approximate, we show that the problem of maximizing revenue with metric substitutability among items can be solved exactly in polynomial time. We do this by first showing that in any optimal price vector, the set of nodes that pay exactly their value uniquely determines which nodes buy an item and what price they pay, and therefore the revenue. We transform the problem of finding an optimal set of such nodes to an instance of weighted independent set on a perfect graph which can be solved in polynomial time by the strong perfect graph theorem, proving the result. We then analyze the computational tractability of various extensions to our model. We begin with relaxing the metric substitutability requirement and show that when the substitution costs do not form a metric, even if a $(1+\epsilon)$-approximate triangle inequality holds, the problem becomes NP-hard. Thus the triangle inequality characterizes the threshold at which the problem goes from “tractable” to “hard.” We then relax assumptions on the supply and demand. We consider restricting supplies to a subset of locations, or the amount of supplies, or allowing buyers to demand more than one unit. In all cases, the problem becomes NP-hard. In addition, the multiunit demand case illustrates an interesting paradoxical nonmonotonicity: The optimal revenue the seller can extract can actually decrease when consumers' demands increase. We show the revenue maximization problem with multiunit demand is APX-hard even for the simplest valuations with equal marginal values for all items up to the demand constraint, and demands of at most 3.

Motivated by the allocation problem facing publishers in display advertising we formulate the online assignment with forecast problem, a version of the online allocation problem where the algorithm has access to random samples from the future set of arriving vertices. We provide a solution that allows us to serve Internet users in an online manner that is provably nearly optimal. Our technique applies to the forecast version of a large class of online assignment problems, such as online bipartite matching, allocation, and budgeted bidders, in which we wish to minimize the value of some convex objective function subject to a set of linear supply and demand constraints.

The problem of efficiently evaluating a large collection of complex Boolean expressions - beyond simple conjunctions and Disjunctive/Conjunctive Normal Forms (DNF/CNF) - occurs in many emerging online advertising applications such as advertising exchanges and automatic targeting. The simple solution of normalizing complex Boolean expressions to DNF or CNF form, and then using existing methods for evaluating such expressions is not always effective because of the exponential blow-up in the size of expressions due to normalization. We thus propose a novel method for evaluating complex expressions, which leverages existing techniques for evaluating leaf-level conjunctions, and then uses a bottom-up evaluation technique to only process the relevant parts of the complex expressions that contain the matching conjunctions. We develop two such bottom-up evaluation techniques, one based on Dewey IDs and another based on mapping Boolean expressions to one-dimensional intervals. Our experimental evaluation based on data obtained from an online advertising exchange shows that the proposed techniques are efficient and scalable, both with respect to space usage as well as evaluation time.

The median problem in the weighted Jaccard metric was analyzed by Späth in 1981. Up until now, only an exponential-time exact algorithm was known. We (a) obtain a PTAS for the weighted Jaccard median problem and (b) show that the problem does not admit a FPTAS (assuming P ≠ NP), even when restricted to binary vectors. The PTAS is built on a number of different algorithmic ideas and the hardness result makes use of an especially interesting gadget.

In recent years the MapReduce framework has emerged as one of the most widely used parallel computing platforms for processing data on terabyte and petabyte scales.Used daily at companies such as Yahoo!, Google, Amazon, and Facebook, and adopted more recently by several universities, it allows for easy parallelization of data intensive computations over many machines.One key feature of MapReduce that differentiates it from previous models of parallel computation is that it interleaves sequential and parallel computation.We propose a model of efficient computation using the MapReduce paradigm.Since MapReduce is designed for computations over massive data sets, our model limits the number of machines and the memory per machine to be substantially sublinear in the size of the input.On the other hand, we place very loose restrictions on the computational power of of any individual machineour model allows each machine to perform sequential computations in time polynomial in the size of the original input.We compare MapReduce to the PRAM model of computation.We prove a simulation lemma showing that a large class of PRAM algorithms can be efficiently simulated via MapReduce.The strength of MapReduce, however, lies in the fact that it uses both sequential and parallel computation.We demonstrate how algorithms can take advantage of this fact to compute an MST of a dense graph in only two rounds, as opposed to Ω(log(n)) rounds needed in the standard PRAM model.We show how to evaluate a wide class of functions using the MapReduce framework.We conclude by applying this result to show how to compute some basic algorithmic problems such as undirected s-t connectivity in the MapReduce framework.

Spearman's footrule and Kendall's tau are two well established distances between rankings. They, however, fail to take into account concepts crucial to evaluating a result set in information retrieval: element relevance and positional information. That is, changing the rank of a highly-relevant document should result in a higher penalty than changing the rank of an irrelevant document; a similar logic holds for the top versus the bottom of the result ordering. In this work, we extend both of these metrics to those with position and element weights, and show that a variant of the Diaconis-Graham inequality still holds - the generalized two measures remain within a constant factor of each other for all permutations.

We introduce the similarity caching problem, a variant of classical caching in which an algorithm can return an element from the cache that is similar, but not necessarily identical, to the query element. We are motivated by buffer management questions in approximate nearest-neighbor applications, especially in the context of caching targeted advertisements on the web. Formally, we assume the queries lie in a metric space, with distance function d(.,.). A query p is considered a cache hit if there is a point q in the cache that is sufficiently close to p, i.e., for a threshold radius r, we have d(p,q) ≤ r. The goal is then to minimize the number of cache misses, vis-à-vis the optimal algorithm. As with classical caching, we use the competitive ratio to measure the performance of different algorithms.

We examine the case of over-specialization in recommender systems, which results from returning items that are too similar to those previously rated by the user. We propose Outside-The-Box (otb) recommendation, which takes some risk to help users make fresh discoveries, while maintaining high relevance. The proposed formalization relies on item regions and attempts to identify regions that are under-exposed to the user. We develop a recommendation algorithm which achieves a compromise between relevance and risk to find otb items. We evaluate this approach on the MovieLens data set and compare our otb recommendations against conventional recommendation strategies.

There has been considerable past work on efficiently computing top k objects by aggregating information from multiple ranked lists of these objects. An important instance of this problem is query processing in search engines: One has to combine information from several different posting lists (rankings) of web pages (objects) to obtain the top k web pages to answer user queries. Two particularly well-studied approaches to achieve efficiency in top-k aggregation include early-termination algorithms (e.g., TA and NRA) and preaggregation of some of the input lists. However, there has been little work on a rigorous treatment of combining these approaches.

Motivated by the emergence of auction-based marketplaces for display ads such as the Right Media Exchange, we study the design of a bidding agent that implements a display advertising campaign by bidding in such a marketplace. The bidding agent must acquire a given number of impressions with a given target spend, when the highest external bid in the marketplace is drawn from an unknown distribution P. The quantity and spend constraints arise from the fact that display ads are usually sold on a CPM basis. We consider both the full information setting, where the winning price in each auction is announced publicly, and the partially observable setting where only the winner obtains information about the distribution; these differ in the penalty incurred by the agent while attempting to learn the distribution. We provide algorithms for both settings, and prove performance guarantees using bounds on uniform closeness from statistics, and techniques from online learning. We experimentally evaluate these algorithms: both algorithms perform very well with respect to both target quantity and spend; further, our algorithm for the partially observable case performs nearly as well as that for the fully observable setting despite the higher penalty incurred during learning.

Motivated by contextual advertising systems and other web applications involving efficiency-accuracy tradeoffs, we study similarity caching. Here, a cache hit is said to occur if the requested item is similar but not necessarily equal to some cached item. We study two objectives that dictate the efficiency-accuracy tradeoff and provide our caching policies for these objectives. By conducting extensive experiments on real data we show similarity caching can significantly improve the efficiency of contextual advertising systems, with minimal impact on accuracy. Inspired by the above, we propose a simple generative model that embodies two fundamental characteristics of page requests arriving to advertising systems, namely, long-range dependences and similarities. We provide theoretical bounds on the gains of similarity caching in this model and demonstrate these gains empirically by fitting the actual data to the model. Copyright is held by the International World Wide Web Conference Committee (IW3C2).

We consider the problem of efficiently indexing Disjunctive Normal Form (DNF) and Conjunctive Normal Form (CNF) Boolean expressions over a high-dimensional multi-valued attribute space. The goal is to rapidly find the set of Boolean expressions that evaluate to true for a given assignment of values to attributes. A solution to this problem has applications in online advertising (where a Boolean expression represents an advertiser's user targeting requirements, and an assignment of values to attributes represents the characteristics of a user visiting an online page) and in general any publish/subscribe system (where a Boolean expression represents a subscription, and an assignment of values to attributes represents an event). All existing solutions that we are aware of can only index a specialized sub-set of conjunctive and/or disjunctive expressions, and cannot efficiently handle general DNF and CNF expressions (including NOTs) over multi-valued attributes. In this paper, we present a novel solution based on the inverted list data structure that enables us to index arbitrarily complex DNF and CNF Boolean expressions over multi-valued attributes. An interesting aspect of our solution is that, by virtue of leveraging inverted lists traditionally used for ranked information retrieval, we can efficiently return the top-N matching Boolean expressions. This capability enables emerging applications such as ranked publish/subscribe systems [16], where only the top subscriptions that match an event are desired. For example, in online advertising there is a limit on the number of advertisements that can be shown on a given page and only the "best" advertisements can be displayed. We have evaluated our proposed technique based on data from an online advertising application, and the results show a dramatic performance improvement over prior techniques.

We show a worst-case lower bound and a smoothed upper bound on the number of iterations performed by the Iterative Closest Point (ICP) algorithm. First proposed by Besl and McKay, the algorithm is widely used in computational geometry, where it is known for its simplicity and its observed speed. The theoretical study of ICP was initiated by Ezra, Sharir, and Efrat, who showed that the worst-case running time to align two sets of n points in $\mathbb{R}^d$ is between $\Omega(n\log n)$ and $O(n^2d)^d$. We substantially tighten this gap by improving the lower bound to $\Omega(n/d)^{d+1}$. To help reconcile this bound with the algorithm's observed speed, we also show that the smoothed complexity of ICP is polynomial, independent of the dimensionality of the data. Using similar methods, we improve the best known smoothed upper bound for the popular k-means method to $n^{O(k)}$, once again independent of the dimension.

We introduce the hiring problem, in which a growing company continuously interviews and decides whether to hire applicants. This problem is similar in spirit but quite different from the well-studied secretary problem. Like the secretary problem, it captures fundamental aspects of decision making under uncertainty and has many possible applications. We analyze natural strategies of hiring above the current average, considering both the mean and the median averages; we call these Lake Wobegon strategies. Like the hiring problem itself, our strategies are intuitive, simple to describe, and amenable to mathematically and economically significant modifications. We demonstrate several intriguing behaviors of the two strategies. Specifically, we show dramatic differences between hiring above the mean and above the median. We also show that both strategies are intrinsically connected to the lognormal distribution, leading to only very weak concentration results, and the marked importance of the first few hires on the overall outcome.

We study the envy-free pricing problem faced by a profit maximizing seller when there is metric substitutability among the items --- consumer i's value for item j is vi -- ci,j, and the substitution costs, {ci,j}, form a metric. Our model is motivated from the observation that sellers often sell the same product at different prices in different locations, and rational consumers optimize the tradeoff between prices and substitution costs. While the general envy-free pricing problem is hard to approximate, the addition of metric substitutability constraints allows us to solve the problem exactly in polynomial time by reducing it to an instance of weighted independent set on a perfect graph.

In this paper we propose a novel document retrieval model in which text queries are augmented with multi-dimensional taxonomy restrictions. These restrictions may be relaxed at a cost to result quality. This new model may be applicable in many arenas, including multifaceted, product, and local search, where documents are augmented with hierarchical metadata such as topic or location. We present efficient algorithms for indexing and query processing in this new retrieval model. We decompose query processing into two sub-problems: first, an online search problem to determine the correct overall level of relaxation cost that must be incurred to generate the top k results; and second, a budgeted relaxation search problem in which all results at a particular relaxation cost must be produced at minimal cost. We show the latter problem is solvable exactly in two hierarchical dimensions, is NP-hard in three or more dimensions, but admits efficient approximation algorithms with provable guarantees. We present experimental results evaluating our algorithms on both synthetic and real data, showing order of magnitude improvements over the baseline algorithm.

Motivated by the role of incentives in large-scale information systems, Kleinberg and Raghavan (FOCS 2005) studied strategic games in decentralized information networks. Given a branching process that specifies the network, the rarity of answers to a specific question, and a desired probability of success, how much reward does the root node need to offer so that it receives an answer with this probability, when all of the nodes are playing strategically? For a specific family of branching processes and a constant failure probability, they showed that the reward function exhibited a threshold behavior that depends on the branching parameter b.

The k-means method is an old but popular clustering algorithm known for its observed speed and its simplicity. Until recently, however, no meaningful theoretical bounds were known on its running time. In this paper, we demonstrate that the worst-case running time of k-means is superpolynomial by improving the best known lower bound from Ω(n) iterations to 2Ω(√n).

We show a worst-case lower bound and a smoothed upper bound on the number of iterations performed by the iterative closest point (ICP) algorithm. First proposed by Besl and McKay, the algorithm is widely used in computational geometry where it is known for its simplicity and its observed speed. The theoretical study of ICP was initiated by Ezra, Sharir and Efrat, who bounded its worst-case running time between Omega(n log n) and O(n2d)d. We substantially tighten this gap by improving the lower bound to Omega(n/d)d+1. To help reconcile this bound with the algorithm's observed speed, we also show the smoothed complexity of ICP is polynomial, independent of the dimensionality of the data. Using similar methods, we improve the best known smoothed upper bound for the popular k-means method to nO(k)once again independent of the dimension

We study the effect of user supplied relevance feedback in improving web search results. Rather than using query refinement or document similarity measures to rerank results, we show that the web-graph distance between two documents is a robust measure of their relative relevancy. We demonstrate how the use of this metric can improve the rankings of result URLs, even when the user only rates one document in the dataset. Our research suggests that such interactive systems can significantly improve search results.

We discuss the theoretical limitations for reconfiguration of metamorphic robots made up of Telecubes, six degree of freedom cube shaped modules currently being developed at Xerox PARC. We show that by using meta-modules composed of 8 individual modules as a backbone for building the desired shape, we can establish completeness for the reconfiguration as well as time and space bounds for the process. Finally we present several open problems in the field of reconfiguration.

We present a complete, local, and parallel reconfiguration algorithm for metamorphic robots made up of Telecubes, six degree of freedom cube shaped modules currently being developed at PARC. We show that by using 2 /spl times/ 2 /spl times/ 2 meta-modules we can achieve completeness of reconfiguration space using only local rules. Furthermore, this reconfiguration can be done in place and massively in parallel with many simultaneous module movements. Finally we present a loose quadratic upper bound on the total number of module movements required by the algorithm.