We establish new exponential in dimension lower bounds for the Maximum Halfspace Discrepancy problem, which models linear classification. Both are fundamental problems in computational geometry and machine learning in their exact and approximate forms. However, only O(n^d) and respectively Õ(1/ε^d) upper bounds are known and complemented by polynomial lower bounds that do not support the exponential in dimension dependence. We close this gap up to polylogarithmic terms by reduction from widely-believed hardness conjectures for Affine Degeneracy testing and k-Sum problems. Our reductions yield matching lower bounds of Ω̃(n^d) and respectively Ω̃(1/ε^d) based on Affine Degeneracy testing, and Ω̃(n^{d/2}) and respectively Ω̃(1/ε^{d/2}) conditioned on k-Sum. The first bound also holds unconditionally if the computational model is restricted to make sidedness queries, which corresponds to a widely spread setting implemented and optimized in many contemporary algorithms and computing paradigms.

An important thread in the study of data-stream algorithms focuses on settings where stream items are active only for a limited time. We introduce a new expiration model, where each item arrives with its own arbitrary expiration time. The special case where items expire in the order that they arrive, which we call consistent expirations, contains the classical sliding-window model of Datar, Gionis, Indyk, and Motwani [SICOMP 2002] and its timestamp-based variant of Braverman and Ostrovsky [FOCS 2007]. Our first set of results explores the expiration streaming model and presents algorithms for several fundamental problems, including approximate counting, uniform sampling, and weighted sampling by efficiently tracking active items without explicitly storing them all. Naturally, these algorithms have many immediate applications, e.g., to range counting. Our second and main set of results for the expiration model designs algorithms for the diameter and k-center problems, where items are points in a metric space. Our results significantly extend those known for the special case of sliding-window streams by Cohen-Addad, Schwiegelshohn, and Sohler [ICALP 2016], and obtain a strictly better approximation factor for the diameter in the important special case of high-dimensional Euclidean metrics. We develop new decomposition and coordination techniques along with a geometric dominance framework to filter out redundant points based on both temporal and spatial proximity.

Modern simulations and observations generate vast amounts of data, fueling a growing interest in replacing discrete data with continuous surrogate models, such as functional models and implicit neural networks, to enhance data storage, transfer, analysis, and visualization. To that end, kernel regression is a well-known class of non-parametric techniques useful for surrogate modeling. In this paper, we propose a new framework to use coresets for kernel regression-a small dataset that is used as a proxy for the original data-in scientific visualization. Using kernel regression as a surrogate for scientific data, we construct an optimized coreset that is both compact and highly accurate, reducing errors from randomly-sampled and grid-based coresets by orders of magnitude. We evaluate our framework on large spatial datasets and demonstrate that it incurs negligible error while preserving the underlying topological features.

We study the estimation of Zipfian distributions under $L_1$ loss, and provide near minimax optimal bounds in several regimes. Specifically, we assume observations arrive from a known alphabet, and with a known decay rate parametrizing the Zipfian, but we do not know a priori which alphabet elements have larger probability than others. We present a novel Sort and Snap estimator, which uses the empirical proportions to sort the alphabet, and then snaps them to the associated term from the Zipfian distribution. For arbitrary decay rates and smaller alphabet sizes, as well as for large decay rates and large alphabet sizes, we show an exact or minor variant of this estimator is near minimax optimal and has exponential improvement over the standard empirical proportion estimator. However, for small decay rates and larger alphabet sizes a simulation study indicates the standard empirical proportion estimator is competitive with Sort and Snap procedures. In addition to providing nearly tight bounds for important high-dimensional estimation problems, we believe the Sort and Snap estimator, and its analysis, will have independent interest.

A long-standing belief holds that Bayesian Optimization (BO) with standard Gaussian processes (GP) --- referred to as standard BO --- underperforms in high-dimensional optimization problems. While this belief seems plausible, it lacks both robust empirical evidence and theoretical justification. To address this gap, we present a systematic investigation. First, through a comprehensive evaluation across twelve benchmarks, we found that while the popular Square Exponential (SE) kernel often leads to poor performance, using Mat\'ern kernels enables standard BO to consistently achieve top-tier results, frequently surpassing methods specifically designed for high-dimensional optimization. Second, our theoretical analysis reveals that the SE kernel’s failure primarily stems from improper initialization of the length-scale parameters, which are commonly used in practice but can cause gradient vanishing in training. We provide a probabilistic bound to characterize this issue, showing that Mat\'ern kernels are less susceptible and can robustly handle much higher dimensions. Third, we propose a simple robust initialization strategy that dramatically improves the performance of the SE kernel, bringing it close to state-of-the-art methods, without requiring additional priors or regularization. We prove another probabilistic bound that demonstrates how the gradient vanishing issue can be effectively mitigated with our method. Our findings advocate for a re-evaluation of standard BO’s potential in high-dimensional settings.

Linear probing-based hash tables offer high data locality and are considered among the fastest in real-world applications. However, they come with an inherent tradeoff between space efficiency and speed, i.e. when the hash table approaches full capacity, its performance tends to decline considerably due to an effect known as primary clustering. As a result they are only used at low load factors. Tombstones (markers for deleted elements) can help mitigate the effect of primary clustering in linear probing hash tables. However, tombstones require periodic redistribution, which, in turn, requires a complete halt of regular operations. This makes linear probing not suitable in practical applications where periodic halts are unacceptable. In this paper, we present a solution to forestall primary clustering in linear probing hash tables, ensuring high data locality and consistent performance even at high load factors. Our approach redistributes tombstones within small windows, deamortizing the cost of mitigating primary clustering and eliminating the need for periodic halts. We provide theoretical guarantees that our deamortization method is asymptotically optimal in efficiency and cost. We also design an efficient implementation within dominant linear-probing hash tables and show performance improvements. We introduce Zombie hashing in two variants: ordered (compact) and unordered (vectorized) linear probing hash tables. Both variants achieve consistent, high throughput and lowest variance in operation latency compared to other state-of-the-art hash tables across numerous churn cycles, while maintaining 95% space efficiency without downtime. Our results show that Zombie hashing overcomes the limitations of linear probing while preserving high data locality.

Scalar field comparison is a fundamental task in scientific visualization. In topological data analysis, we compare topological descriptors of scalar fields-such as persistence diagrams and merge trees-because they provide succinct and robust abstract representations. Several similarity measures for topological descriptors seem to be both asymptotically and practically efficient with polynomial time algorithms, but they do not scale well when handling large-scale, time-varying scientific data and ensembles. In this paper, we propose a new framework to facilitate the comparative analysis of merge trees, inspired by tools from locality sensitive hashing (LSH). LSH hashes similar objects into the same hash buckets with high probability. We propose two new similarity measures for merge trees that can be computed via LSH, using new extensions to Recursive MinHash and subpath signature, respectively. Our similarity measures are extremely efficient to compute and closely resemble the results of existing measures such as merge tree edit distance or geometric interleaving distance. Our experiments demonstrate the utility of our LSH framework in applications such as shape matching, clustering, key event detection, and ensemble summarization.

We refine and generalize what is known about coresets for classification problems via the sensitivity sampling framework. Such coresets seek the smallest possible subsets of input data, so one can optimize a loss function on the coreset and ensure approximation guarantees with respect to the original data. Our analysis provides the first no dimensional coresets, so the size does not depend on the dimension. Moreover, our results are general, apply for distributional input and can use iid samples, so provide sample complexity bounds, and work for a variety of loss functions. A key tool we develop is a Radamacher complexity version of the main sensitivity sampling approach, which can be of independent interest.

Ranking is at the core of many artificial intelligence (AI) applications, including search engines, recommender systems, etc. Modern ranking systems are often constructed with learning-to-rank (LTR) models built from user behavior signals. While previous studies have demonstrated the effectiveness of using user behavior signals (e.g., clicks) as both features and labels of LTR algorithms, we argue that existing LTR algorithms that indiscriminately treat behavior and non-behavior signals in input features could lead to suboptimal performance in practice. Because user behavior signals often have strong correlations with the ranking objective and can only be collected on items that have already been shown to users, directly using behavior signals in LTR could create an exploitation bias that hurts the system performance in the long run.

In linear distance metric learning, we are given data in one Euclidean metric space and the goal is to find an appropriate linear map to another Euclidean metric space which respects certain distance conditions as much as possible. In this paper, we formalize a simple and elegant method which reduces to a general continuous convex loss optimization problem, and for different noise models we derive the corresponding loss functions. We show that even if the data is noisy, the ground truth linear metric can be learned with any precision provided access to enough samples, and we provide a corresponding sample complexity bound. Moreover, we present an effective way to truncate the learned model to a low-rank model that can provably maintain the accuracy in the loss function and in parameters -- the first such results of this type. Several experimental observations on synthetic and real data sets support and inform our theoretical results.

Word vector embeddings have been shown to contain and amplify biases in the data they are extracted from. Consequently, many techniques have been proposed to identify, mitigate, and attenuate these biases in word representations. In this article, we utilize interactive visualization to increase the interpretability and accessibility of a collection of state-of-the-art debiasing techniques. To aid this, we present the Visualization of Embedding Representations for deBiasing (VERB) system, an open-source web-based visualization tool that helps users gain a technical understanding and visual intuition of the inner workings of debiasing techniques, with a focus on their geometric properties. In particular, VERB offers easy-to-follow examples that explore the effects of these debiasing techniques on the geometry of high-dimensional word vectors. To help understand how various debiasing techniques change the underlying geometry, VERB decomposes each technique into interpretable sequences of primitive transformations and highlights their effect on the word vectors using dimensionality reduction and interactive visual exploration. VERB is designed to target natural language processing (NLP) practitioners who are designing decision-making systems on top of word embeddings and researchers working with the fairness and ethics of machine learning systems in NLP. It can also serve as a visual medium for education, which helps an NLP novice understand and mitigate biases in word embeddings.

Time series discords are a useful primitive for time series anomaly detection, and the matrix profile is capable of capturing discord effectively. There exist many research efforts to improve the scalability of discord discovery with respect to the length of time series. However, there is surprisingly little work focused on reducing the time complexity of matrix profile computation associated with dimensionality of a multidimensional time series. In this work, we propose a sketch for discord mining among multi-dimensional time series. After an initial pre-processing of the sketch as fast as reading the data, the discord mining has runtime independent of the dimensionality of the original data. On several real world examples from water treatment and transportation, the proposed algorithm improves the throughput by at least an order of magnitude (50X) and only has minimal impact on the quality of the approximated solution. Additionally, the proposed method can handle the dynamic addition or deletion of dimensions inconsequential overhead. This allows a data analyst to consider “what-if” scenarios in real time while exploring the data.

A Content-based Time Series Retrieval (CTSR) system is an information retrieval system for users to interact with time series emerged from multiple domains, such as finance, healthcare, and manufacturing. For example, users seeking to learn more about the source of a time series can submit the time series as a query to the CTSR system and retrieve a list of relevant time series with associated metadata. By analyzing the retrieved metadata, users can gather more information about the source of the time series. Because the CTSR system is required to work with time series data from diverse domains, it needs a high-capacity model to effectively measure the similarity between different time series. On top of that, the model within the CTSR system has to compute the similarity scores in an efficient manner as the users interact with the system in real-time. In this paper, we propose an effective and efficient CTSR model that outperforms alternative models, while still providing reasonable inference runtimes. To demonstrate the capability of the proposed method in solving business problems, we compare it against alternative models using our in-house transaction data. Our findings reveal that the proposed model is the most suitable solution compared to others for our transaction data problem.

Abstract How do we ensure the veracity of science? The act of manipulating or fabricating scientific data has led to many high‐profile fraud cases and retractions. Detecting manipulated data, however, is a challenging and time‐consuming endeavor. Automated detection methods are limited due to the diversity of data types and manipulation techniques. Furthermore, patterns automatically flagged as suspicious can have reasonable explanations. Instead, we propose a nuanced approach where experts analyze tabular datasets, e.g., as part of the peer‐review process, using a guided, interactive visualization approach. In this paper, we present an analysis of how manipulated datasets are created and the artifacts these techniques generate. Based on these findings, we propose a suite of visualization methods to surface potential irregularities. We have implemented these methods in Ferret, a visualization tool for data forensics work. Ferret makes potential data issues salient and provides guidance on spotting signs of tampering and differentiating them from truthful data.

Oblivious RAMs (ORAMs) are proposed to completely hide access patterns. However, most ORAM constructions are expensive and not suitable to deploy in a database for supporting query processing over large data. In this work, we design a practical oblivious query processing framework to enable efficient query processing over a cloud database. In particular, we focus on processing multiple range and kNN queries asynchronously and concurrently with high throughput. The key idea is to integrate indices into ORAM which leverages a suite of optimization techniques (e.g., oblivious batch processing and caching). Our construction shows an order of magnitude speedup in comparison with other baselines over large datasets.

Learning functions with high-dimensional outputs is critical in many applications, such as physical simulation and engineering design. However, collecting training examples for these applications is often costly, e.g., by running numerical solvers. The recent work (Li et al., 2022) proposes the first multi-fidelity active learning approach for high-dimensional outputs, which can acquire examples at different fidelities to reduce the cost while improving the learning performance. However, this method only queries at one pair of fidelity and input at a time, and hence has a risk of bringing in strongly correlated examples to reduce the learning efficiency. In this paper, we propose Batch Multi-Fidelity Active Learning with Budget Constraints (BMFAL-BC), which can promote the diversity of training examples to improve the benefit-cost ratio, while respecting a given budget constraint for batch queries. Hence, our method can be more practically useful. Specifically, we propose a novel batch acquisition function that measures the mutual information between a batch of multi-fidelity queries and the target function, so as to penalize highly correlated queries and encourages diversity. The optimization of the batch acquisition function is challenging in that it involves a combinatorial search over many fidelities while subject to the budget constraint. To address this challenge, we develop a weighted greedy algorithm that can sequentially identify each (fidelity, input) pair, while achieving a near $(1 - 1/e)$-approximation of the optimum. We show the advantage of our method in several computational physics and engineering applications.

Increasingly, individuals and companies adopt a cloud service provider as a primary data and IT infrastructure platform. The remote access of the data inevitably brings the issue of trust. Data encryption is necessary to keep sensitive information secure and private on the cloud. Yet adversaries can still learn valuable information regarding encrypted data by observing data access patterns. To solve such problem, Oblivious RAMs (ORAMs) are proposed to completely hide access patterns. However, most ORAM constructions are expensive and not suitable to deploy in a database for supporting query processing over large data. Furthermore, an ORAM processes queriessynchronously, hence, does not provide high throughput forconcurrent query processing. In this article, we design a practicaloblivious query processing frameworkto enable efficient query processing over a cloud database. In particular, we focus on processing multiple range and$k$NN queriesasynchronously and concurrently with high throughput. The key idea is to integrate indices into ORAM which leverages a suite of optimization techniques (e.g., oblivious batch processing and caching). The effectiveness and efficiency of our oblivious query processing framework is demonstrated through extensive evaluations over large datasets. Our construction shows an order of magnitude speedup in comparison with other baselines.

We provide a deterministic space-efficient algorithm for estimating ridge regression. For n data points with d features and a large enough regularization parameter, we provide a solution within eps L_2 error using only O(d/eps) space. This is the first o(d^2) space deterministic streaming algorithm with guaranteed solution error and risk bound for this classic problem. The algorithm sketches the covariance matrix by variants of Frequent Directions, which implies it can operate in insertion-only streams and a variety of distributed data settings. In comparisons to randomized sketching algorithms on synthetic and real-world datasets, our algorithm has less empirical error using less space and similar time.

Language representations are known to carry certain associations (e.g., gendered connotations) which may lead to invalid and harmful predictions in downstream tasks.While existing methods are effective at mitigating such unwanted associations by linear projection, we argue that they are too aggressive: not only do they remove such associations, they also erase information that should be retained.To address this issue, we propose OS-CAR (Orthogonal Subspace Correction and Rectification), a balanced approach of mitigation that focuses on disentangling associations between concepts that are deemed problematic, instead of removing concepts wholesale.We develop new measurements for evaluating information retention relevant to the debiasing goal.Our experiments on genderoccupation associations show that OSCAR is a well-balanced approach that ensures that semantic information is retained in the embeddings and unwanted associations are also effectively mitigated.

Content Warning: This paper contains examples of stereotypes and associations, misgendering, erasure, and other harms that could be offensive and triggering to trans and nonbinary individuals.Gender is widely discussed in the context of language tasks and when examining the stereotypes propagated by language models.However, current discussions primarily treat gender as binary, which can perpetuate harms such as the cyclical erasure of non-binary gender identities.These harms are driven by model and dataset biases, which are consequences of the non-recognition and lack of understanding of non-binary genders in society.In this paper, we explain the complexity of gender and language around it, and survey non-binary persons to understand harms associated with the treatment of gender as binary in English language technologies.We also detail how current language representations (e.g., GloVe, BERT) capture and perpetuate these harms and related challenges that need to be acknowledged and addressed for representations to equitably encode gender information.

Embeddings are one of the fundamental building blocks for data analysis tasks. Embeddings are already essential tools for large language models and image analysis, and their use is being extended to many other research domains. The generation of these distributed representations is often a data-and computation-expensive process; yet the holistic analysis and adjustment of them after they have been created is still a developing area. In this paper, we first propose a very general quantitatively measure for the presence of features in the embedding data based on if it can be learned. We then devise a method to remove or alleviate undesired features in the embedding while retaining the essential structure of the data. We use a Domain Adversarial Network (DAN) to generate a non-affine transformation, but we add constraints to ensure the essential structure of the embedding is preserved. Our empirical results demonstrate that the proposed algorithm significantly outperforms the state-of-art unsupervised algorithm on several data sets, including novel applications from the industry.

Consider the geometric range space $(X, \mathcal{H}_d)$ where $X \subset \mathbb{R}^d$ and $\mathcal{H}_d$ is the set of ranges defined by $d$-dimensional halfspaces. In this setting we consider that $X$ is the disjoint union of a red and blue set. For each halfspace $h \in \mathcal{H}_d$ define a function $Φ(h)$ that measures the "difference" between the fraction of red and fraction of blue points which fall in the range $h$. In this context the maximum discrepancy problem is to find the $h^* = \arg \max_{h \in (X, \mathcal{H}_d)} Φ(h)$. We aim to instead find an $\hat{h}$ such that $Φ(h^*) - Φ(\hat{h}) \le \varepsilon$. This is the central problem in linear classification for machine learning, in spatial scan statistics for spatial anomaly detection, and shows up in many other areas. We provide a solution for this problem in $O(|X| + (1/\varepsilon^d) \log^4 (1/\varepsilon))$ time, which improves polynomially over the previous best solutions. For $d=2$ we show that this is nearly tight through conditional lower bounds. For different classes of $Φ$ we can either provide a $Ω(|X|^{3/2 - o(1)})$ time lower bound for the exact solution with a reduction to APSP, or an $Ω(|X| + 1/\varepsilon^{2-o(1)})$ lower bound for the approximate solution with a reduction to 3SUM. A key technical result is a $\varepsilon$-approximate halfspace range counting data structure of size $O(1/\varepsilon^d)$ with $O(\log (1/\varepsilon))$ query time, which we can build in $O(|X| + (1/\varepsilon^d) \log^4 (1/\varepsilon))$ time.

Word vector embeddings have been shown to contain and amplify biases in data they are extracted from. Consequently, many techniques have been proposed to identify, mitigate, and attenuate these biases in word representations. In this tutorial, we will review a collection of state-of-the-art debiasing techniques. To aid this, we provide an open source web-based visualization tool and offer hands-on experience in exploring the effects of these debiasing techniques on the geometry of high-dimensional word vectors. To help understand how various debiasing techniques change the underlying geometry, we decompose each technique into interpretable sequences of primitive operations, and study their effect on the word vectors using dimensionality reduction and interactive visual exploration.

Many applications involve multi-type event data. Understanding the complex influences of the events on each other is critical to discover useful knowledge and to predict future events and their types. Existing methods either ignore or partially account for these influences. Recent works use recurrent neural networks to model the event rate. While being highly expressive, they couple all the temporal dependencies in a black-box and can hardly extract meaningful knowledge. More important, most methods assume an exponential time decay of the influence strength, which is over-simplified and can miss many important strength varying patterns. To overcome these limitations, we propose SPRITE, a $\underline{S}$elf-adaptable $\underline{P}$oint p$\underline{R}$ocess w$\underline{I}$th nonparametric $\underline{T}$ime d$\underline{E}$cays, which can decouple the influences between every pair of the events and capture various time decays of the influence strengths. Specifically, we use an embedding to represent each event type and model the event influence as an unknown function of the embeddings and time span. We derive a general construction that can cover all possible time decaying functions. By placing Gaussian process (GP) priors over the latent functions and using Gauss-Legendre quadrature to obtain the integral in the construction, we can flexibly estimate all kinds of time-decaying influences, without restricting to any specific form or imposing derivative constraints that bring learning difficulties. We then use weight space augmentation of GPs to develop an efficient stochastic variational learning algorithm. We show the advantages of our approach in both the ablation study and real-world applications.

Thanks to the wide adoption of GPS-equipped devices, the volume of collected spatial data is exploding. To achieve interactive exploration and analysis over big spatial data, people are willing to trade off accuracy for performance through approximation. As a foundation in many approximate algorithms, data sampling now requires more flexibility and better performance. In this paper, we study the spatial independent range sampling (SIRS) problem aiming at retrieving random samples with independence over points residing in a query region. Specifically, we have designed concise index structures with careful data layout based on various space decomposition strategies. Moreover, we propose novel algorithms for both uniform and weighted SIRS queries with low theoretical cost and complexity as well as excellent practical performance. Last but not least, we demonstrate how to support data updates and trade-offs between different sampling methods in practice. According to comprehensive evaluations conducted on real-world datasets, our methods achieve orders of magnitude performance improvement against baselines derived by existing works.

In the era of big data, more and more applications require the information of historical data to support rich analytics, learning, and mining operations. In these cases, it is highly desirable to retrieve information of previous versions of data. Traditionally, multi-version databases can be used to store all historical values of the data in order to support historical queries. However, storing all the historical data can be impractical due to its large space consumption. In this paper, we propose the concept of at-the-time persistent (ATTP) and back-in-time persistent (BITP) sketches, which are sketches that approximately answer queries on previous versions of data with small space. We then provide several implementations of ATTP/BITP sketches which are shown to be more efficient compared to existing state-of-the-art solutions in our empirical studies.

Abstract The Vapnik–Chervonenkis dimension provides a notion of complexity for systems of sets. If the VC dimension is small, then knowing this can drastically simplify fundamental computational tasks such as classification, range counting, and density estimation through the use of sampling bounds. We analyze set systems where the ground set X is a set of polygonal curves in $$\mathbb {R}^d$$ R d and the sets $$\mathcal {R}$$ R are metric balls defined by curve similarity metrics, such as the Fréchet distance and the Hausdorff distance, as well as their discrete counterparts. We derive upper and lower bounds on the VC dimension that imply useful sampling bounds in the setting that the number of curves is large, but the complexity of the individual curves is small. Our upper and lower bounds are either near-quadratic or near-linear in the complexity of the curves that define the ranges and they are logarithmic in the complexity of the curves that define the ground set.

We develop a family of techniques to align word embeddings which are derived from different source datasets or created using different mechanisms (e.g., GloVe or word2vec). Our methods are simple and have a closed form to optimally rotate, translate, and scale to minimize root mean squared errors or maximize the average cosine similarity between two embeddings of the same vocabulary into the same dimensional space. Our methods extend approaches known as Absolute Orientation, which are popular for aligning objects in three-dimensions, and generalize an approach by Smith et al. (ICLR 2017). We prove new results for optimal scaling and for maximizing cosine similarity. Then we demonstrate how to evaluate the similarity of embeddings from different sources or mechanisms, and that certain properties like synonyms and analogies are preserved across the embeddings and can be enhanced by simply aligning and averaging ensembles of embeddings.

The size of large, geo-located datasets has reached scales where visualization of all data points is inefficient. Random sampling is a method to reduce the size of a dataset, yet it can introduce unwanted errors. We describe a method for subsampling of spatial data suitable for creating kernel density estimates from very large data and demonstrate that it results in less error than random sampling. We also introduce a method to ensure that thresholding of low values based on sampled data does not omit any regions above the desired threshold when working with sampled data. We demonstrate the effectiveness of our approach using both, artificial and real-world large geospatial datasets.

Abstract The available spatial data are rapidly growing and also diversifying. One may obtain in large quantities information such as annotated point/place of interest (POIs), check-in comments on those POIs, geo-tagged microblog comments, and demarked regions of interest (ROI). All sources interplay with each other, and together build a more complete picture of the spatial and social dynamics at play in a region. However, building a single fused representation of these data entries has been mainly rudimentary, such as allowing spatial joins. In this paper, we extend the concept of semantic embedding for POIs (points of interests) and devise the first semantic embedding of ROIs, and in particular ones that captures both its spatial and its semantic components. To accomplish this, we develop a multipart network model capturing the relationships between the diverse components, and through random-walk-based approaches, use this to embed the ROIs. We demonstrate the effectiveness of this embedding at simultaneously capturing both the spatial and semantic relationships between ROIs through extensive experiments. Applications like popularity region prediction demonstrate the benefit of using ROI embedding as features in comparison with baselines.

Word embeddings carry stereotypical connotations from the text they are trained on, which can lead to invalid inferences in downstream models that rely on them. We use this observation to design a mechanism for measuring stereotypes using the task of natural language inference. We demonstrate a reduction in invalid inferences via bias mitigation strategies on static word embeddings (GloVe). Further, we show that for gender bias, these techniques extend to contextualized embeddings when applied selectively only to the static components of contextualized embeddings (ELMo, BERT).

We introduce two versions of a new sketch for approximately embedding the Gaussian kernel into Euclidean inner product space. These work by truncating infinite expansions of the Gaussian kernel, and carefully invoking the RecursiveTensorSketch [Ahle et al. SODA 2020]. After providing concentration and approximation properties of these sketches, we use them to approximate the kernel distance between points sets. These sketches yield almost (1+ε)-relative error, but with a small additive α term. In the first variants the dependence on 1/α is poly-logarithmic, but has higher degree of polynomial dependence on the original dimension d. In the second variant, the dependence on 1/α is still poly-logarithmic, but the dependence on d is linear.

We consider sketch vectors of geometric objects $J$ through the \mindist function \[ v_i(J) = \inf_{p \in J} \|p-q_i\| \] for $q_i \in Q$ from a point set $Q$. Collecting the vector of these sketch values induces a simple, effective, and powerful distance: the Euclidean distance between these sketched vectors. This paper shows how large this set $Q$ needs to be under a variety of shapes and scenarios. For hyperplanes we provide direct connection to the sensitivity sample framework, so relative error can be preserved in $d$ dimensions using $Q = O(d/\varepsilon^2)$. However, for other shapes, we show we need to enforce a minimum distance parameter $ρ$, and a domain size $L$. For $d=2$ the sample size $Q$ then can be $\tilde{O}((L/ρ) \cdot 1/\varepsilon^2)$. For objects (e.g., trajectories) with at most $k$ pieces this can provide stronger \emph{for all} approximations with $\tilde{O}((L/ρ)\cdot k^3 / \varepsilon^2)$ points. Moreover, with similar size bounds and restrictions, such trajectories can be reconstructed exactly using only these sketch vectors.

We construct near-optimal coresets for kernel density estimates for points in $${\mathbb {R}}^d$$ when the kernel is positive definite. Specifically we provide a polynomial time construction for a coreset of size $$O(\sqrt{d}/\varepsilon \cdot \sqrt{\log 1/\varepsilon } )$$ , and we show a near-matching lower bound of size $$\Omega (\min \{\sqrt{d}/\varepsilon , 1/\varepsilon ^2\})$$ . When $$d\ge 1/\varepsilon ^2$$ , it is known that the size of coreset can be $$O(1/\varepsilon ^2)$$ . The upper bound is a polynomial-in- $$(1/\varepsilon )$$ improvement when $$d \in [3,1/\varepsilon ^2)$$ and the lower bound is the first known lower bound to depend on d for this problem. Moreover, the upper bound restriction that the kernel is positive definite is significant in that it applies to a wide variety of kernels, specifically those most important for machine learning. This includes kernels for information distances and the sinc kernel which can be negative.

We define several new models for how to define anomalous regions among enormous sets of trajectories. These are based on spatial scan statistics, and identify a geometric region which captures a subset of trajectories which are significantly different in a measured characteristic from the background population. The model definition depends on how much a geometric region is contributed to by some overlapping trajectory. This contribution can be the full trajectory, proportional to the length within the spatial region, or dependent on the flux across the boundary of that spatial region. Our methods are based on and significantly extend a recent two-level sampling approach which provides high accuracy at enormous scales of data. We support these new models and algorithms with extensive experiments on millions of trajectories and also theoretical guarantees.

Word vector representations are well developed tools for various NLP and Machine Learning tasks and are known to retain significant semantic and syntactic structure of languages. But they are prone to carrying and amplifying bias which can perpetrate discrimination in various applications. In this work, we explore new simple ways to detect the most stereotypically gendered words in an embedding and remove the bias from them. We verify how names are masked carriers of gender bias and then use that as a tool to attenuate bias in embeddings. Further, we extend this property of names to show how names can be used to detect other types of bias in the embeddings such as bias based on race, ethnicity, and age.

We revisit the range sampling problem: the input is a set of points where each point is associated with a real-valued weight. The goal is to store them in a structure such that given a query range and an integer $k$, we can extract $k$ independent random samples from the points inside the query range, where the probability of sampling a point is proportional to its weight. This line of work was initiated in 2014 by Hu, Qiao, and Tao and it was later followed up by Afshani and Wei. The first line of work mostly studied unweighted but dynamic version of the problem in one dimension whereas the second result considered the static weighted problem in one dimension as well as the unweighted problem in 3D for halfspace queries. We offer three main results and some interesting insights that were missed by the previous work: We show that it is possible to build efficient data structures for range sampling queries if we allow the query time to hold in expectation (the first result), or obtain efficient worst-case query bounds by allowing the sampling probability to be approximately proportional to the weight (the second result). The third result is a conditional lower bound that shows essentially one of the previous two concessions is needed. For instance, for the 3D range sampling queries, the first two results give efficient data structures with near-linear space and polylogarithmic query time whereas the lower bound shows with near-linear space the worst-case query time must be close to $n^{2/3}$, ignoring polylogarithmic factors. Up to our knowledge, this is the first such major gap between the expected and worst-case query time of a range searching problem.

Kulldorff's (1997) seminal paper on spatial scan statistics (SSS) has led to many methods considering different regions of interest, different statistical models, and different approximations while also having numerous applications in epidemiology, environmental monitoring, and homeland security. SSS provides a way to rigorously test for the existence of an anomaly and provide statistical guarantees as to how "anomalous" that anomaly is. However, these methods rely on defining specific regions where the spatial information a point contributes is limited to binary 0 or 1, of either inside or outside the region, while in reality anomalies will tend to follow smooth distributions with decaying density further from an epicenter. In this work, we propose a method that addresses this shortcoming through a continuous scan statistic that generalizes SSS by allowing the point contribution to be defined by a kernel. We provide extensive experimental and theoretical results that shows our methods can be computed efficiently while providing high statistical power for detecting anomalous regions.

We develop a new class of distances for trajectories, based on the distance to a set of landmarks. These distances easily and interpretably map objects to a Euclidean space, are simple to compute, and perform well in data analysis tasks. For trajectories, they match and in some cases significantly out-perform all state-of-the-art other metrics, can effortlessly be used in k-means clustering, and directly plugged into approximate nearest neighbor approaches which immediately out-perform the best recent advances in trajectory similarity search by several orders of magnitude. These distances do not require complicated alignment (common in trajectory case). We show reasonable and often simple conditions under which these distances are metrics.

Robust estimators, like the median of a point set, are important for data analysis in the presence of outliers. We study robust estimators for locationally uncertain points with discrete distributions. That is, each point in a data set has a discrete probability distribution describing its location. The probabilistic nature of uncertain data makes it challenging to compute such estimators, since the true value of the estimator is now described by a distribution rather than a single point. We show how to construct and estimate the distribution of the median of a point set. Building the approximate support of the distribution takes near-linear time, and assigning probability to that support takes quadratic time. We also develop a general approximation technique for distributions of robust estimators with respect to ranges with bounded VC dimension. This includes the geometric median for high dimensions and the Siegel estimator for linear regression.

Consider a geometric range space (X,A) where X is comprised of the union of a red set R and blue set B. Let Phi(A) define the absolute difference between the fraction of red and fraction of blue points which fall in the range A. The maximum discrepancy range A^* = arg max_{A in (X,A)} Phi(A). Our goal is to find some A^ in (X,A) such that Phi(A^*) - Phi(A^) <= epsilon. We develop general algorithms for this approximation problem for range spaces with bounded VC-dimension, as well as significant improvements for specific geometric range spaces defined by balls, halfspaces, and axis-aligned rectangles. This problem has direct applications in discrepancy evaluation and classification, and we also show an improved reduction to a class of problems in spatial scan statistics.

With the popularity of portable wireless devices it is important to model and predict how information or contagions spread by natural human mobility - for understanding the spreading of deadly infectious diseases and for improving delay tolerant communication schemes. Formally, we model this problem by considering M moving agents, where each agent initially carries a distinct bit of information. When two agents are at the same location or in close proximity to one another, they share all their information with each other. We would like to know the time it takes until all bits of information reach all agents, called the flood time, and how it depends on the way agents move, the size and shape of the network and the number of agents moving in the network.

Consider a geometric range space (X,A) where X is comprised of the union of a red set R and blue set B. Let Phi(A) define the absolute difference between the fraction of red and fraction of blue points which fall in the range A. The maximum discrepancy range A^* = arg max_{A in (X,A)} Phi(A). Our goal is to find some A^ in (X,A) such that Phi(A^*) - Phi(A^) <= epsilon. We develop general algorithms for this approximation problem for range spaces with bounded VC-dimension, as well as significant improvements for specific geometric range spaces defined by balls, halfspaces, and axis-aligned rectangles. This problem has direct applications in discrepancy evaluation and classification, and we also show an improved reduction to a class of problems in spatial scan statistics.

We study the construction of coresets for kernel density estimates. That is we show how to approximate the kernel density estimate described by a large point set with another kernel density estimate with a much smaller point set. For characteristic kernels (including Gaussian and Laplace kernels), our approximation preserves the L∞ error between kernel density estimates within error ε, with coreset size 4/ε2, but no other aspects of the data, including the dimension, the diameter of the point set, or the bandwidth of the kernel common to other approximations. When the dimension is unrestricted, we show this bound is tight for these kernels as well as a much broader set. This work provides a careful analysis of the iterative Frank-Wolfe algorithm adapted to this context, an algorithm called kernel herding. This analysis unites a broad line of work that spans statistics, machine learning, and geometry. When the dimension d is constant, we demonstrate much tighter bounds on the size of the coreset specifically for Gaussian kernels, showing that it is bounded by the size of the coreset for axis-aligned rectangles. Currently the best known constructive bound is , and non-constructively, this can be improved by . This improves the best constant dimension bounds polynomially for d ≥ 3.

A reproducing kernel defines an embedding of a data point into an infinite dimensional reproducing kernel Hilbert space (RKHS). The norm in this space describes a distance, which we call the kernel distance. The random Fourier features (of Rahimi and Recht) describe an oblivious approximate mapping into finite dimensional Euclidean space that behaves similar to the RKHS. We show in this paper that for the Gaussian kernel the Euclidean norm between these mapped to features has $(1+\varepsilon)$-relative error with respect to the kernel distance. When there are $n$ data points, we show that $O((1/\varepsilon^2) \log n)$ dimensions of the approximate feature space are sufficient and necessary. Without a bound on $n$, but when the original points lie in $\mathbb{R}^d$ and have diameter bounded by $\mathcal{M}$, then we show that $O((d/\varepsilon^2) \log \mathcal{M})$ dimensions are sufficient, and that this many are required, up to $\log(1/\varepsilon)$ factors. We empirically confirm that relative error is indeed preserved for kernel PCA using these approximate feature maps.

Kernel regression is an essential and ubiquitous tool for non-parametric data analysis, particularly popular among time series and spatial data. However, the central operation which is performed many times, evaluating a kernel on the data set, takes linear time. This is impractical for modern large data sets.

Mobile and sensing devices have already become ubiquitous. They have made tracking moving objects an easy task. As a result, mobile applications like Uber and many IoT projects have generated massive amounts of trajectory data that can no longer be processed by a single machine efficiently. Among the typical query operations over trajectories, similarity search is a common yet expensive operator in querying trajectory data. It is useful for applications in different domains such as traffic and transportation optimizations, weather forecast and modeling, and sports analytics. It is also a fundamental operator for many important mining operations such as clustering and classification of trajectories. In this paper, we propose a distributed query framework to process trajectory similarity search over a large set of trajectories. We have implemented the proposed framework in Spark, a popular distributed data processing engine, by carefully considering different design choices. Our query framework supports both the Hausdorff distance the Fréchet distance. Extensive experiments have demonstrated the excellent scalability and query efficiency achieved by our design, compared to other methods and design alternatives.

Kernel principal component analysis (KPCA) provides a concise set of basis vectors which capture non-linear structures within large data sets, and is a central tool in data analysis and learning. To allow for non-linear relations, typically a full n x n kernel matrix is constructed over n data points, but this requires too much space and time for large values of n. Techniques such as the Nystrom method and random feature maps can help towards this goal, but they do not explicitly maintain the basis vectors in a stream and take more space than desired. We propose a new approach for streaming KPCA which maintains a small set of basis elements in a stream, requiring space only logarithmic in n, and also improves the dependence on the error parameter. Our technique combines together random feature maps with recent advances in matrix sketching, it has guaranteed spectral norm error bounds with respect to the original kernel matrix, and it compares favorably in practice to state-of-the-art approaches.

With the dramatic growth in the number of application domains that generate probabilistic, noisy and uncertain data, there has been an increasing interest in designing algorithms for geometric or combinatorial optimization problems over such data. In this paper, we initiate the study of constructing epsilon-kernel coresets for uncertain points. We consider uncertainty in the existential model where each point's location is fixed but only occurs with a certain probability, and the locational model where each point has a probability distribution describing its location. An epsilon-kernel coreset approximates the width of a point set in any direction. We consider approximating the expected width (an epsilon-EXP-KERNEL), as well as the probability distribution on the width (an (epsilon, tau)-QUANT-KERNEL) for any direction. We show that there exists a set of O(epsilon^{-(d-1)/2}) deterministic points which approximate the expected width under the existential and locational models, and we provide efficient algorithms for constructing such coresets. We show, however, it is not always possible to find a subset of the original uncertain points which provides such an approximation. However, if the existential probability of each point is lower bounded by a constant, an epsilon-EXP-KERNEL is still possible. We also provide efficient algorithms for construct an (epsilon, tau)-QUANT-KERNEL coreset in nearly linear time. Our techniques utilize or connect to several important notions in probability and geometry, such as Kolmogorov distances, VC uniform convergence and Tukey depth, and may be useful in other geometric optimization problem in stochastic settings. Finally, combining with known techniques, we show a few applications to approximating the extent of uncertain functions, maintaining extent measures for stochastic moving points and some shape fitting problems under uncertainty.

Finding anomalous regions within spatial data sets is a central task for biosurveillance, homeland security, policy making, and many other important areas. These communities have mainly settled on spatial scan statistics as a rigorous way to discover regions where a measured quantity (e.g., crime) is statistically significant in its difference from a baseline population. However, most common approaches are inefficient and thus, can only be run with very modest data sizes (a few thousand data points) or make assumptions on the geographic distributions of the data.

This paper describes Sparse Frequent Directions, a variant of Frequent Directions for sketching sparse matrices. It resembles the original algorithm in many ways: both receive the rows of an input matrix An x d one by one in the streaming setting and compute a small sketch B ∈ Rl x d. Both share the same strong (provably optimal) asymptotic guarantees with respect to the space-accuracy tradeoff in the streaming setting. However, unlike Frequent Directions which runs in O(ndl) time regardless of the sparsity of the input matrix A, Sparse Frequent Directions runs in Õ(nnz(A)l + nl2) time. Our analysis loosens the dependence on computing the Singular Value Decomposition (SVD) as a black box within the Frequent Directions algorithm. Our bounds require recent results on the properties of fast approximate SVD computations. Finally, we empirically demonstrate that these asymptotic improvements are practical and significant on real and synthetic data.

We formalize notions of robustness for composite estimators via the notion of a breakdown point. A composite estimator successively applies two (or more) estimators: on data decomposed into disjoint parts, it applies the first estimator on each part, then the second estimator on the outputs of the first estimator. And so on, if the composition is of more than two estimators. Informally, the breakdown point is the minimum fraction of data points which if significantly modified will also significantly modify the output of the estimator, so it is typically desirable to have a large breakdown point. Our main result shows that, under mild conditions on the individual estimators, the breakdown point of the composite estimator is the product of the breakdown points of the individual estimators. We also demonstrate several scenarios, ranging from regression to statistical testing, where this analysis is easy to apply, useful in understanding worst case robustness, and sheds powerful insights onto the associated data analysis.

We describe a new algorithm called FrequentDirections for deterministic matrix sketching in the row-update model. The algorithm is presented an arbitrary input matrix A \in \mathbb{R}^{n \times d} one row at a time. It performs O(d\ell) operations per row and maintains a sketch matrix B \in \mathbb{R}^{\ell \times d} such that for any k < \ell, \|A^TA - B^TB \|_2 \leq \|A - A_k\|_F^2 / (\ell-k) {\;and\;} \|A - \pi_{B_k}(A)\|_F^2 \leq (1 + \frac{k}{\ell-k}) \|A-A_k\|_F^2. Here, A_k stands for the minimizer of \|A - A_k\|_F over all rank k matrices (similarly for B_k) and \pi_{B_k}(A) is the rank k matrix resulting from projecting A on the row span of B_k. We show that both of these bounds are the best possible for the space allowed. The summary is mergeable and hence trivially parallelizable. Moreover, FrequentDirections outperforms exemplar implementations of existing streaming algorithms in the space-error tradeoff. This paper combines, simplifies, and extends the results of Liberty [Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2013], Ghashami and Phillips [Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, 2014], and Woodruff [Proceedings of the 27th Annual Conference on Advances in Neural Information Processing Systems, 2014].

In this paper we prove lower bounds on randomized multiparty communication complexity, mainly in the message-passing model, where messages are sent player-to-player. Some of our results apply to the blackboard model, where each message is written on a blackboard for all players to see. We introduce a new technique for proving such bounds, called symmetrization, which is natural, intuitive, and often easy to use. For example, for the problem where each of $k$ players gets a bit-vector of length $n$, and the goal is to compute the coordinatewise XOR of these vectors, we prove a tight lower bound of $\Omega(nk)$ in the blackboard model. For the same problem with AND instead of XOR, we prove a lower bound of roughly $\Omega(nk)$ in the message-passing model (assuming $k \le n/3200$) and $\Omega(n \log k)$ in the blackboard model. We also prove lower bounds for bitwise majority, for a graph-connectivity problem, and for other problems; the technique seems applicable to a wide range of other problems as well. All of our lower bounds allow randomized communication protocols with two-sided error. We also use the symmetrization technique to prove several direct-sum-like results for multiparty communication.

Nearest-neighbor search, which returns the nearest neighbor of a query point in a set of points, is an important and widely studied problem in many fields, and it has a wide range of applications. In many of them, such as sensor databases, location-based services, face recognition, and mobile data, the location of data is imprecise. We therefore study nearest-neighbor queries in a probabilistic framework in which the location of each input point is specified as a probability distribution function. We present efficient algorithms for (i) computing all points that are nearest neighbors of a query point with nonzero probability and (ii) estimating the probability of a point being the nearest neighbor of a query point, either exactly or within a specified additive error.

Matrices have become essential data representations for many large-scale problems in data analytics, and hence matrix sketching is a critical task. Although much research has focused on improving the error/size tradeoff under various sketching paradigms, the many forms of error bounds make these approaches hard to compare in theory and in practice. This paper attempts to categorize and compare the most known methods under row-wise streaming updates with provable guarantees, and then to tweak some of these methods to gain practical improvements while retaining guarantees. For instance, we observe that a simple heuristic iSVD, with no guarantees, tends to outperform all known approaches in terms of size/error trade-off. We modify the best performing method with guarantees, FREQUENTDIRECTIONS, under the size/error trade-off to match the performance of iSVD and retain its guarantees. We also demonstrate some adversarial datasets where iSVD performs quite poorly. In comparing techniques in the time/error trade-off, techniques based on hashing or sampling tend to perform better. In this setting, we modify the most studied sampling regime to retain error guarantee but obtain dramatic improvements in the time/error trade-off. Finally, we provide easy replication of our studies on APT, a new testbed which makes available not only code and datasets, but also a computing platform with fixed environmental settings.

Presents the introductory editorial for this issue of the publication.

We show that geometric inference of a point cloud can be calculated by examining its kernel density estimate with a Gaussian kernel. This allows one to consider kernel density estimates, which are robust to spatial noise, subsampling, and approximate computation in comparison to raw point sets. This is achieved by examining the sublevel sets of the kernel distance, which isomorphically map to superlevel sets of the kernel density estimate. We prove new properties about the kernel distance, demonstrating stability results and allowing it to inherit reconstruction results from recent advances in distance-based topological reconstruction. Moreover, we provide an algorithm to estimate its topology using weighted Vietoris-Rips complexes.

Kernel density estimates are a robust way to reconstruct a continuous distribution from a discrete point set. Typically their effectiveness is measured either in L1 or L2 error. In this paper we investigate the challenges in using L∞ (or worst case) error, a stronger measure than L1 or L2. We present efficient solutions to two linked challenges: how to evaluate the L∞ error between two kernel density estimates and how to choose the bandwidth parameter for a kernel density estimate built on a subsample of a large data set.

We describe a new algorithm called FrequentDirections for deterministic matrix sketching in the row-update model. The algorithm is presented an arbitrary input matrix A \in \mathbb{R}^{n \times d} one row at a time. It performs O(d\ell) operations per row and maintains a sketch matrix B \in \mathbb{R}^{\ell \times d} such that for any k < \ell, \|A^TA - B^TB \|_2 \leq \|A - A_k\|_F^2 / (\ell-k) {\;and\;} \|A - \pi_{B_k}(A)\|_F^2 \leq (1 + \frac{k}{\ell-k}) \|A-A_k\|_F^2. Here, A_k stands for the minimizer of \|A - A_k\|_F over all rank k matrices (similarly for B_k) and \pi_{B_k}(A) is the rank k matrix resulting from projecting A on the row span of B_k. We show that both of these bounds are the best possible for the space allowed. The summary is mergeable and hence trivially parallelizable. Moreover, FrequentDirections outperforms exemplar implementations of existing streaming algorithms in the space-error tradeoff. This paper combines, simplifies, and extends the results of Liberty [Proceedings of the 19th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2013], Ghashami and Phillips [Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, 2014], and Woodruff [Proceedings of the 27th Annual Conference on Advances in Neural Information Processing Systems, 2014].

Tracking and approximating data matrices in streaming fashion is a fundamental challenge. The problem requires more care and attention when data comes from multiple distributed sites, each receiving a stream of data. This paper considers the problem of "tracking approximations to a matrix" in the distributed streaming model. In this model, there are m distributed sites each observing a distinct stream of data (where each element is a row of a distributed matrix) and has a communication channel with a coordinator, and the goal is to track an ε-approximation to the norm of the matrix along any direction. To that end, we present novel algorithms to address the matrix approximation problem. Our algorithms maintain a smaller matrix B , as an approximation to a distributed streaming matrix A , such that for any unit vector x : ||| Ax || 2 − || Bx || 2 | ≤ ε|| A || 2 F . Our algorithms work in streaming fashion and incur small communication, which is critical for distributed computation. Our best method is deterministic and uses only O (( m /ε) log(β N )) communication, where N is the size of stream (at the time of the query) and β is an upperbound on the squared norm of any row of the matrix. In addition to proving all algorithmic properties theoretically, extensive experiments with real large datasets demonstrate the efficiency of these protocols.

We study coresets for various types of range counting queries on uncertain data. In our model each uncertain point has a probability density describing its location, sometimes defined as k distinct locations. Our goal is to construct a subset of the uncertain points, including their locational uncertainty, so that range counting queries can be answered by just examining this subset. We study three distinct types of queries. RE queries return the expected number of points in a query range. RC queries return the number of points in the range with probability at least a threshold. RQ queries returns the probability that fewer than some threshold fraction of the points are in the range. In both RC and RQ coresets the threshold is provided as part of the query. And for each type of query we provide coreset constructions with approximation-size tradeoffs. We show that random sampling can be used to construct each type of coreset, and we also provide significantly improved bounds using discrepancy-based approaches on axis-aligned range queries.

Network radio frequency (RF) environment sensing (NRES) systems pinpoint and track people in buildings using changes in the signal strength measurements made by a wireless sensor network. It has been shown that such systems can locate people who do not participate in the system by wearing any radio device, even through walls, because of the changes that moving people cause to the static wireless sensor network. However, many such systems cannot locate stationary people. We present and evaluate a system which can locate stationary or moving people, without calibration, by using kernel distance to quantify the difference between two histograms of signal strength measurements. From five experiments, we show that our kernel distance-based radio tomographic localization system performs better than the state-of-the-art NRES systems in different non line-of-sight environments.

Nearest-neighbor (NN) search, which returns the nearest neighbor of a query point in a set of points, is an important and widely studied problem in many fields, and it has wide range of applications. In many of them, such as sensor databases, location-based services, face recognition, and mobile data, the location of data is imprecise. We therefore study nearest neighbor queries in a probabilistic framework in which the location of each input point is specified as a probability distribution function. We present efficient algorithms for (i) computing all points that are nearest neighbors of a query point with nonzero probability; (ii) estimating, within a specified additive error, the probability of a point being the nearest neighbor of a query point; (iii) using it to return the point that maximizes the probability being the nearest neighbor, or all the points with probabilities greater than some threshold to be the NN. We also present some experimental results to demonstrate the effectiveness of our approach.

Kernel density estimates are important for a broad variety of applications. Their construction has been well-studied, but existing techniques are expensive on massive datasets and/or only provide heuristic approximations without theoretical guarantees. We propose randomized and deterministic algorithms with quality guarantees which are orders of magnitude more efficient than previous algorithms. Our algorithms do not require knowledge of the kernel or its bandwidth parameter and are easily parallelizable. We demonstrate how to implement our ideas in a centralized setting and in MapReduce, although our algorithms are applicable to any large-scale data processing framework. Extensive experiments on large real datasets demonstrate the quality, efficiency, and scalability of our techniques.

We study the worst case error of kernel density estimates via subset approximation. A kernel density estimate of a distribution is the convolution of that distribution with a fixed kernel (e.g. Gaussian kernel). Given a subset (i.e. a point set) of the input distribution, we can compare the kernel density estimates of the input distribution with that of the subset and bound the worst case error. If the maximum error is ε, then this subset can be thought of as an ε-sample (aka an ε-approximation) of the range space defined with the input distribution as the ground set and the fixed kernel representing the family of ranges. Interestingly, in this case the ranges are not binary, but have a continuous range (for simplicity we focus on kernels with range of [0, 1]); these allow for smoother notions of range spaces. It turns out, the use of this smoother family of range spaces has an added benefit of greatly decreasing the size required for ε-samples. For instance, in the plane the size is O((1/ε4/3) log 2/3 (1/ε)) for disks (based on VC-dimension arguments) but is only for Gaussian kernels and for kernels with bounded slope that only affect a bounded domain. These bounds are accomplished by studying the discrepancy of these “kernel” range spaces, and here the improvement in bounds are even more pronounced. In the plane, we show the discrepancy is for these kernels, whereas for balls there is a lower bound of Ω(n1/4).

We study the mergeability of data summaries. Informally speaking, mergeability requires that, given two summaries on two datasets, there is a way to merge the two summaries into a single summary on the two datasets combined together, while preserving the error and size guarantees. This property means that the summaries can be merged in a way akin to other algebraic operators such as sum and max, which is especially useful for computing summaries on massive distributed data. Several data summaries are trivially mergeable by construction, most notably all the sketches that are linear functions of the datasets. But some other fundamental ones, like those for heavy hitters and quantiles, are not (known to be) mergeable. In this article, we demonstrate that these summaries are indeed mergeable or can be made mergeable after appropriate modifications. Specifically, we show that for ε-approximate heavy hitters, there is a deterministic mergeable summary of size O (1/ε); for ε-approximate quantiles, there is a deterministic summary of size O ((1/ε) log(ε n )) that has a restricted form of mergeability, and a randomized one of size O ((1/ε) log 3/2 (1/ε)) with full mergeability. We also extend our results to geometric summaries such as ε-approximations which permit approximate multidimensional range counting queries. While most of the results in this article are theoretical in nature, some of the algorithms are actually very simple and even perform better than the previously best known algorithms, which we demonstrate through experiments in a simulated sensor network. We also achieve two results of independent interest: (1) we provide the best known randomized streaming bound for ε-approximate quantiles that depends only on ε, of size O ((1/ε) log 3/2 (1/ε)), and (2) we demonstrate that the MG and the SpaceSaving summaries for heavy hitters are isomorphic.

In this paper, we propose a new and accurate technique for uncertainty analysis and uncertainty visualization based on fiber orientation distribution function (ODF) glyphs, associated with high angular resolution diffusion imaging (HARDI). Our visualization applies volume rendering techniques to an ensemble of 3D ODF glyphs, which we call SIP functions of diffusion shapes, to capture their variability due to underlying uncertainty. This rendering elucidates the complex heteroscedastic structural variation in these shapes. Furthermore, we quantify the extent of this variation by measuring the fraction of the volume of these shapes, which is consistent across all noise levels, the certain volume ratio. Our uncertainty analysis and visualization framework is then applied to synthetic data, as well as to HARDI human-brain data, to study the impact of various image acquisition parameters and background noise levels on the diffusion shapes.

In distributed data management, a primary concern is monitoring the distributed data and generating an alarm when a user specified constraint is violated. A particular useful instance is the threshold based constraint, which is commonly known as the distributed threshold monitoring problem [4], [16], [19], [29]. This work extends this useful and fundamental study to distributed probabilistic data that emerge in a lot of applications, where uncertainty naturally exists when massive amounts of data are produced at multiple sources in distributed, networked locations. Examples include distributed observing stations, large sensor fields, geographically separate scientific institutes/units and many more. When dealing with probabilistic data, there are two thresholds involved, the score and the probability thresholds. One must monitor both simultaneously, as such, techniques developed for deterministic data are no longer directly applicable. This work presents a comprehensive study to this problem. Our algorithms have significantly outperformed the baseline method in terms of both the communication cost (number of messages and bytes) and the running time, as shown by an extensive experimental evaluation using several, real large datasets.

We study the mergeability of data summaries. Informally speaking, mergeability requires that, given two summaries on two data sets, there is a way to merge the two summaries into a single summary on the union of the two data sets, while preserving the error and size guarantees. This property means that the summaries can be merged in a way like other algebraic operators such as sum and max, which is especially useful for computing summaries on massive distributed data. Several data summaries are trivially mergeable by construction, most notably all the sketches that are linear functions of the data sets. But some other fundamental ones like those for heavy hitters and quantiles, are not (known to be) mergeable. In this paper, we demonstrate that these summaries are indeed mergeable or can be made mergeable after appropriate modifications. Specifically, we show that for ε-approximate heavy hitters, there is a deterministic mergeable summary of size O(1/ε) for ε-approximate quantiles, there is a deterministic summary of size O(1 over ε log(εn))that has a restricted form of mergeability, and a randomized one of size O(1 over ε log 3/21 over ε) with full mergeability. We also extend our results to geometric summaries such as ε-approximations and εkernels.

In this paper we prove lower bounds on randomized multiparty communication complexity, both in the blackboard model (where each message is written on a blackboard for all players to see) and (mainly) in the message-passing model, where messages are sent player-to-player. We introduce a new technique for proving such bounds, called symmetrization, which is natural, intuitive, and often easy to use. For example, for the problem where each of k players gets a bit-vector of length n, and the goal is to compute the coordinate-wise XOR of these vectors, we prove a tight lower bounds of Ω(nk) in the blackboard model. For the same problem with AND instead of XOR, we prove a lower bounds of roughly Ω(nk) in the message-passing model (assuming k ≤ n/3200) and Ω(n log k) in the blackboard model. We also prove lower bounds for bit-wise majority, for a graphconnectivity problem, and for other problems; the technique seems applicable to a wide range of other problems as well. The obtained communication lower bounds imply new lower bounds in the functional monitoring model [11] (also called the distributed streaming model). All of our lower bounds allow randomized communication protocols with two-sided error. We also use the symmetrization technique to prove several direct-sum-like results for multiparty communication.

Ranking temporal data has not been studied until recently, even though ranking is an important operator (being promoted as a first-class citizen) in database systems. However, only the instant top- k queries on temporal data were studied in, where objects with the k highest scores at a query time instance t are to be retrieved. The instant top- k definition clearly comes with limitations (sensitive to outliers, difficult to choose a meaningful query time t ). A more flexible and general ranking operation is to rank objects based on the aggregation of their scores in a query interval, which we dub the aggregate top- k query on temporal data. For example, return the top-10 weather stations having the highest average temperature from 10/01/2010 to 10/07/2010; find the top-20 stocks having the largest total transaction volumes from 02/05/2011 to 02/07/2011. This work presents a comprehensive study to this problem by designing both exact and approximate methods (with approximation quality guarantees). We also provide theoretical analysis on the construction cost, the index size, the update and the query costs of each approach. Extensive experiments on large real datasets clearly demonstrate the efficiency, the effectiveness, and the scalability of our methods compared to the baseline methods.

Starting with a similarity function between objects, it is possible to define a distance metric (the kernel distance) on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis and geometric measure theory, and have a rich structure that includes an isometric embedding into a Hilbert space. They have recently been applied to numerous problems in machine learning and shape analysis.

Given a set of points with uncertain locations, we consider the problem of computing the probability of each point lying on the skyline, that is, the probability that it is not dominated by any other input point. If each point's uncertainty is described as a probability distribution over a discrete set of locations, we improve the best known exact solution. We also suggest why we believe our solution might be optimal. Next, we describe simple, near-linear time approximation algorithms for computing the probability of each point lying on the skyline. In addition, some of our methods can be adapted to construct data structures that can efficiently determine the probability of a query point lying on the skyline.

This paper proposes a new distance metric between clusterings that incorporates information about the spatial distribution of points and clusters. Our approach builds on the idea of a Hilbert space-based representation of clusters as a combination of the representations of their constituent points. We use this representation and the underlying metric to design a spatially-aware consensus clustering procedure. This consensus procedure is implemented via a novel reduction to Euclidean clustering, and is both simple and efficient. All of our results apply to both soft and hard clusterings. We accompany these algorithms with a detailed experimental evaluation that demonstrates the efficiency and quality of our techniques.

In this paper, we propose a unified algorithmic framework for solving many known variants of MDS. Our algorithm is a simple iterative scheme with guaranteed convergence, and is modular; by changing the internals of a single subroutine in the algorithm, we can switch cost functions and target spaces easily. In addition to the formal guarantees of convergence, our algorithms are accurate; in most cases, they converge to better quality solutions than existing methods in comparable time. Moreover, they have a small memory footprint and scale effectively for large data sets. We expect that this framework will be useful for a number of MDS variants that have not yet been studied.

In this paper, we present a measure associated with detection and inference of statistically anomalous clusters of a graph based on the likelihood test of observed and expected edges in a subgraph.This measure is adapted from spatial scan statistics for point sets and provides quantitative assessment for clusters.We discuss some important properties of this statistic and its relation to modularity and Bregman divergences.We apply a simple clustering algorithm to find clusters with large values of this measure in a variety of real-world data sets, and we illustrate its ability to identify statistically significant clusters of selected granularity.

Spatial scan statistics are used to determine hotspots in spatial data, and are widely used in epidemiology and biosurveillance. In recent years, there has been much effort invested in designing efficient algorithms for finding such "high discrepancy" regions, with methods ranging from fast heuristics for special cases, to general grid-based methods, and to efficient approximation algorithms with provable guarantees on performance and quality.In this paper, we make a number of contributions to the computational study of spatial scan statistics. First, we describe a simple exact algorithm for finding the largest discrepancy region in a domain. Second, we propose a new approximation algorithm for a large class of discrepancy functions (including the Kulldorff scan statistic) that improves the approximation versus run time trade-off of prior methods. Third, we extend our simple exact and our approximation algorithms to data sets which lie naturally on a grid or are accumulated onto a grid. Fourth, we conduct a detailed experimental comparison of these methods with a number of known methods, demonstrating that our approximation algorithm has far superior performance in practice to prior methods, and exhibits a good performance-accuracy trade-off.All extant methods (including those in this paper) are suitable for data sets that are modestly sized; if data sets are of the order of millions of data points, none of these methods scale well. For such massive data settings, it is natural to examine whether small-space streaming algorithms might yield accurate answers. Here, we provide some negative results, showing that any streaming algorithms that even provide approximately optimal answers to the discrepancy maximization problem must use space linear in the input.

Motion planning for systems with constraints on controls or the need for relatively straight paths for real-time actions presents challenges for modern planners. This paper presents an approach which addresses these types of systems by building on existing motion planning approaches. Guided Expansive Spaces Trees are introduced to search for a low cost and relatively straight path in a space with motion constraints. Path Gradient Descent, which builds on the idea of Elastic Strips, finds the locally optimal path for an existing path. These techniques are tested on simulations of rendezvous and docking of the space shuttle to the International Space Station and of a 4-foot fan-controlled blimp in a factory setting.

Applications such as suturing in medical simulations require the modeling of knot tying in physically realistic rope. The paper describes the design and implementation of such a system. Our model uses a spline of linear springs, adaptive subdivision and a dynamics simulation. Collisions are discrete event simulated and follow the impulse model. Although some care must be taken to maintain stable knots, we demonstrate our simple model is sufficient for this task. In particular, we do not use friction or explicit constraints to maintain the knot. As examples, we tie an overhand knot and a reef knot.