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We consider global efficiency of algorithms for minimizing a sum of a convex function and a composition of a Lipschitz convex function with a smooth map. The basic algorithm we rely on is the prox-linear method, which in each iteration…
Randomized algorithms, such as randomized sketching or stochastic optimization, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs,…
Due to the drastic gap in complexity between sequential and batch statistical learning, recent work has studied a smoothed sequential learning setting, where Nature is constrained to select contexts with density bounded by 1/{\sigma} with…
Matrix trace estimation is ubiquitous in machine learning applications and has traditionally relied on Hutchinson's method, which requires $O(\log(1/\delta)/\epsilon^2)$ matrix-vector product queries to achieve a $(1 \pm…
We consider the problem of finding anomalies in high-dimensional data using popular PCA based anomaly scores. The naive algorithms for computing these scores explicitly compute the PCA of the covariance matrix which uses space quadratic in…
We establish rates of convergences in time series forecasting using the statistical learning approach based on oracle inequalities. A series of papers extends the oracle inequalities obtained for iid observations to time series under weak…
Many geometric estimation problems take the form of synchronization over the special Euclidean group: estimate the values of a set of poses given noisy measurements of a subset of their pairwise relative transforms. This problem is…
Recent work in theoretical computer science and scientific computing has focused on nearly-linear-time algorithms for solving systems of linear equations. While introducing several novel theoretical perspectives, this work has yet to lead…
This work considers the problem of learning the Markov parameters of a linear system from observed data. Recent non-asymptotic system identification results have characterized the sample complexity of this problem in the single and…
We derive a high-resolution formula for the quantization problem under Orlicz norm distortion. In this setting, the optimal point density solves a variational problem which comprises a function $g:\mathbb{R}_+\to[0,\infty)$ characterizing…
Linear regression without correspondences is the problem of performing a linear regression fit to a dataset for which the correspondences between the independent samples and the observations are unknown. Such a problem naturally arises in…
Generalized matrix approximation plays a fundamental role in many machine learning problems, such as CUR decomposition, kernel approximation, and matrix low rank approximation. Especially with today's applications involved in larger and…
For the \textsc{Minkowski Sum Selection} problem with linear objective functions, we obtain the following results: (1) optimal $O(n\log n)$ time algorithms for $\lambda=1$; (2) $O(n\log^2 n)$ time deterministic algorithms and expected…
Estimating symmetric properties of a distribution, e.g. support size, coverage, entropy, distance to uniformity, are among the most fundamental problems in algorithmic statistics. While each of these properties have been studied extensively…
In this paper we present algorithms for a number of problems in geometric pattern matching where the input consist of a collections of segments in the plane. Our work consists of two main parts. In the first, we address problems and…
Overparametrization often helps improve the generalization performance. This paper presents a dual view of overparametrization suggesting that downsampling may also help generalize. Focusing on the proportional regime $m\asymp n \asymp p$,…
In stochastic optimization, the population risk is generally approximated by the empirical risk. However, in the large-scale setting, minimization of the empirical risk may be computationally restrictive. In this paper, we design an…
Linear bandits have become a cornerstone of online learning and sequential decision-making, providing solid theoretical foundations for balancing exploration and exploitation. Within this domain, matrix sketching serves as a critical…
We obtain estimation error rates and sharp oracle inequalities for regularization procedures of the form \begin{equation*} \hat f \in argmin_{f\in F}\left(\frac{1}{N}\sum_{i=1}^N\ell(f(X_i), Y_i)+\lambda \|f\|\right) \end{equation*} when…
We consider the problem of approximating and learning disjunctions (or equivalently, conjunctions) on symmetric distributions over $\{0,1\}^n$. Symmetric distributions are distributions whose PDF is invariant under any permutation of the…