Existing work on differentially private linear regression typically assumes that end users can precisely set data bounds or algorithmic hyperparameters. End users often struggle to meet these requirements without directly examining the data (and violating privacy). Recent work has attempted to develop solutions that shift these burdens from users to algorithms, but they struggle to provide utility as the feature dimension grows. This work extends these algorithms to higher-dimensional problems by introducing a differentially private feature selection method based on Kendall rank correlation. We prove a utility guarantee for the setting where features are normally distributed and conduct experiments across 25 datasets. We find that adding this private feature selection step before regression significantly broadens the applicability of ``plug-and-play'' private linear regression algorithms at little additional cost to privacy, computation, or decision-making by the end user.

We present a differentially private algorithm for releasing the sequence of $k$ elements with the highest counts from a data domain of $d$ elements. The algorithm is a "joint" instance of the exponential mechanism, and its output space consists of all $O(d^k)$ length-$k$ sequences. Our main contribution is a method to sample this exponential mechanism in time $O(dk\log(k) + d\log(d))$ and space $O(dk)$. Experiments show that this approach outperforms existing pure differential privacy methods and improves upon even approximate differential privacy methods for moderate $k$.

Quantiles are often used for summarizing and understanding data. If that data is sensitive, it may be necessary to compute quantiles in a way that is differentially private, providing theoretical guarantees that the result does not reveal private information. However, when multiple quantiles are needed, existing differentially private algorithms fare poorly: they either compute quantiles individually, splitting the privacy budget, or summarize the entire distribution, wasting effort. In either case the result is reduced accuracy. In this work we propose an instance of the exponential mechanism that simultaneously estimates exactly $m$ quantiles from $n$ data points while guaranteeing differential privacy. The utility function is carefully structured to allow for an efficient implementation that returns estimates of all $m$ quantiles in time $O(mn\log(n) + m^2n)$. Experiments show that our method significantly outperforms the current state of the art on both real and synthetic data while remaining efficient enough to be practical.

Determinantal point processes (DPPs) are a good fit for modeling diversity in many machine learning applications. For instance, in recommender systems, one might have a basic DPP defined by item features, and a customized version of this DPP for each user with features re-weighted according to user preferences. While such models perform well, they are typically applied only to relatively small datasets, because existing maximum a posteriori (MAP) approximation algorithms are expensive. In this work, we propose a new MAP algorithm: we show that, by performing a one-time preprocessing step on a basic DPP, it is possible to run an approximate version of the standard greedy MAP approximation algorithm on any customized version of the DPP in time sublinear in the number of items. Our key observation is that the core computation can be written as a maximum inner product search (MIPS), which allows us to accelerate inference via approximate MIPS structures, e.g., trees or hash tables. We provide a theoretical analysis of the algorithm’s approximation quality, as well as empirical results on real-world datasets demonstrating that it is often orders of magnitude faster while sacrificing little accuracy.

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.

Many recommendation systems produce result sets with large numbers of highly similar items. Diversifying these results is often accomplished with heuristics, which are impoverished models of users' desire for diversity. However, integrating more complex statistical models of diversity into large-scale, mature systems is challenging. Without a good match between the model's definition of diversity and users' perception of diversity, the model can easily degrade users' perception of the recommendations. In this work we present a statistical model of diversity based on determinantal point processes (DPPs). We train this model from examples of user preferences with a simple procedure that can be integrated into large and complex production systems relatively easily. We use an approximate inference algorithm to serve the model at scale, and empirical results on live YouTube homepage traffic show that this model, coupled with a re-ranking algorithm, yields substantial short- and long-term increases in user engagement.

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.

We show that there is a largely unexplored class of functions (positive polymatroids) that can define proper discrete metrics over pairs of binary vectors and that are fairly tractable to optimize over. By exploiting submodularity, we are able to give hardness results and approximation algorithms for optimizing over such metrics. Additionally, we demonstrate empirically the effectiveness of these metrics and associated algorithms on both a metric minimization task (a form of clustering) and also a metric maximization task (generating diverse k-best lists).

Parsers have been shown to be helpful in information retrieval tasks because they are able to model long-span word dependencies efficiently. While previous work focused on using traditional syntactic parse trees, this paper proposes a new approach where, unlike previous work, the parser parameters are discriminatively trained to directly optimize a non-convex and non-smooth IR measure. The relevance between a document and a query is then modeled by the weighted tree edit distance between their parses. We evaluate our method on a large scale web search task consisting of a real world query set. Results show that the new parser is more effective for document retrieval than using traditional syntactic parse trees. It gives significant improvement, especially for long queries where proper modeling of long-span dependencies is crucial.

Determinantal point processes (DPPs) have recently been proposed as computationally efficient probabilistic models of diverse sets for a variety of applications, including document summarization, image search, and pose estimation. Many DPP inference operations, including normalization and sampling, are tractable; however, finding the most likely configuration (MAP), which is often required in practice for decoding, is NP-hard, so we must resort to approximate inference. Because DPP probabilities are log-submodular, greedy algorithms have been used in the past with some empirical success; however, these methods only give approximation guarantees in the special case of DPPs with monotone kernels. In this paper we propose a new algorithm for approximating the MAP problem based on continuous techniques for submodular function maximization. Our method involves a novel continuous relaxation of the log-probability function, which, in contrast to the multilinear extension used for general submodular functions, can be evaluated and differentiated exactly and efficiently. We obtain a practical algorithm with a 1/4-approximation guarantee for a general class of non-monotone DPPs. Our algorithm also extends to MAP inference under complex polytope constraints, making it possible to combine DPPs with Markov random fields, weighted matchings, and other models. We demonstrate that our approach outperforms greedy methods on both synthetic and real-world data.

Modern hardware description languages support code-generation constructs like generate/endgenerate in Verilog. These constructs are intended to describe regular or parameterized hardware designs and, when used effectively, can make hardware descriptions shorter, more understandable, and more reusable. In practice, however, designers avoid these constructs because it is difficult to understand and predict the properties of the generated code. Is the generated code even type safe? Is it synthesizable? What physical resources (e.g. combinatorial gates and flip-flops) does it require? It is often impossible to answer these questions without first generating the fully-expanded code. In the Verilog and VHDL communities, this generation process is referred to as elaboration.