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High-fidelity simulations are essential for predicting material behavior under high-velocity impact (HVI), but their accuracy depends on material models and parameters that are often calibrated by manual fitting to multiple costly…
We study the problem of extracting a small subset of representative items from a large data stream. In many data mining and machine learning applications such as social network analysis and recommender systems, this problem can be…
We provide algorithms that learn simple auctions whose revenue is approximately optimal in multi-item multi-bidder settings, for a wide range of valuations including unit-demand, additive, constrained additive, XOS, and subadditive. We…
Retrieving points based on proximity in a high-dimensional vector space is a crucial step in information retrieval applications. The approximate nearest neighbor search (ANNS) problem, which identifies the $k$ nearest neighbors for a query,…
We consider the problem of estimating the mean of a sequence of random elements $f(X_1, \theta)$ $, \ldots, $ $f(X_n, \theta)$ where $f$ is a fixed scalar function, $S=(X_1, \ldots, X_n)$ are independent random variables, and $\theta$ is a…
Accurately extracting patterns that appear frequently only within specific time intervals, together with their dense intervals, is important in many applications such as understanding seasonal demand and detecting anomalous…
VC-dimension and $\varepsilon$-nets are key concepts in Statistical Learning Theory. Intuitively, VC-dimension is a measure of the size of a class of sets. The famous $\varepsilon$-net theorem, a fundamental result in Discrete Geometry,…
Estimating similarity between vertices is a fundamental issue in network analysis across various domains, such as social networks and biological networks. Methods based on common neighbors and structural contexts have received much…
We develop a framework for algorithms finding the diameter in graphs of bounded distance Vapnik-Chervonenkis dimension, in (parameterized) subquadratic time complexity. The class of bounded distance VC-dimension graphs is wide, including,…
For a $d$-dimensional log-concave distribution $\pi(\theta) \propto e^{-f(\theta)}$ constrained to a convex body $K$, the problem of outputting samples from a distribution $\nu$ which is $\varepsilon$-close in infinity-distance…
Approximate functional dependencies (AFDs) relax exact functional dependencies by tolerating a bounded degree of violation, making them suited for data quality auditing. Threshold-based discovery returns all dependencies above a…
For any family of measurable sets in a probability space, we show that either (i) the family has infinite Vapnik-Chervonenkis (VC) dimension or (ii) for every epsilon > 0 there is a finite partition pi such the pi-boundary of each set has…
We consider the problem of inferring constraints on a high-dimensional parameter space with a computationally expensive likelihood function. We propose a machine learning algorithm that maps out the Frequentist confidence limit on parameter…
We investigate the approximation of high-dimensional target measures as low-dimensional updates of a dominating reference measure. This approximation class replaces the associated density with the composition of: (i) a feature map that…
We develop a general framework for estimating the $L_\infty(\mathbb{T}^d)$ error for the approximation of multivariate periodic functions belonging to specific reproducing kernel Hilbert spaces (RHKS) using approximants that are…
Randomized subspace approximation with "matrix sketching" is an effective approach for constructing approximate partial singular value decompositions (SVDs) of large matrices. The performance of such techniques has been extensively…
Support Vector Data Description (SVDD) is a popular one-class classifiers for anomaly and novelty detection. But despite its effectiveness, SVDD does not scale well with data size. To avoid prohibitive training times, sampling methods…
Recently, there has been significant progress in understanding reinforcement learning in discounted infinite-horizon Markov decision processes (MDPs) by deriving tight sample complexity bounds. However, in many real-world applications, an…
The Vapnik-Chervonenkis dimension is a combinatorial parameter that reflects the "complexity" of a set of sets (a.k.a. concept classes). It has been introduced by Vapnik and Chervonenkis in their seminal 1971 paper and has since found many…
Let $p$ be an unknown and arbitrary probability distribution over $[0,1)$. We consider the problem of {\em density estimation}, in which a learning algorithm is given i.i.d. draws from $p$ and must (with high probability) output a…