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Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the…
Traditional nonparametric estimation methods often lead to a slow convergence rate in large dimensions and require unrealistically enormous sizes of datasets for reliable conclusions. We develop an approach based on partial derivatives,…
Conditional Neural Processes~(CNPs) formulate distributions over functions and generate function observations with exact conditional likelihoods. CNPs, however, have limited expressivity for high-dimensional observations, since their…
We consider data transmission across discrete memoryless channels (DMCs) using variable-length codes with feedback. We consider the family of such codes whose rates are $\rho_N$ below the channel capacity $C$, where $\rho_N$ is a positive…
In this paper, we consider the unconstrained submodular maximization problem. We propose the first algorithm for this problem that achieves a tight $(1/2-\varepsilon)$-approximation guarantee using $\tilde{O}(\varepsilon^{-1})$ adaptive…
Response-adaptive randomization has recently attracted a lot of attention in the literature. In this paper, we propose a new and simple family of response-adaptive randomization procedures that attain the Cramer--Rao lower bounds on the…
Finding a maximum-cardinality or maximum-weight matching in (edge-weighted) undirected graphs is among the most prominent problems of algorithmic graph theory. For $n$-vertex and $m$-edge graphs, the best known algorithms run in…
We consider the framework of non-stationary stochastic optimization [Besbes et al, 2015] with squared error losses and noisy gradient feedback where the dynamic regret of an online learner against a time varying comparator sequence is…
We study the problem of computing an approximate maximum cardinality matching in the semi-streaming model when edges arrive in a \emph{random} order. In the semi-streaming model, the edges of the input graph G = (V,E) are given as a stream…
In the presence of large sets of labeled data, Deep Learning (DL) has accomplished extraordinary triumphs in the avenue of computer vision, particularly in object classification and recognition tasks. However, DL cannot always perform well…
We study alternating minimization for matrix completion in the simplest possible setting: completing a rank-one matrix from a revealed subset of the entries. We bound the asymptotic convergence rate by the variational characterization of…
Spurious correlations pose a major challenge for robust machine learning. Models trained with empirical risk minimization (ERM) may learn to rely on correlations between class labels and spurious attributes, leading to poor performance on…
Stochastic coordinate descent algorithms are efficient methods in which each iterate is obtained by fixing most coordinates at their values from the current iteration, and approximately minimizing the objective with respect to the remaining…
We revisit the problem of computing submatrices of the Cram\'er-Rao bound (CRB), which lower bounds the variance of any unbiased estimator of a vector parameter $\vth$. We explore iterative methods that avoid direct inversion of the Fisher…
Phase retrieval aims at recovering a complex-valued signal from magnitude-only measurements, which attracts much attention since it has numerous applications in many disciplines. However, phase recovery involves solving a system of…
This paper is concerned with normal approximation under relaxed moment conditions using Stein's method. We obtain the explicit rates of convergence in the central limit theorem for (i) nonlinear statistics with finite absolute moment of…
The Expectation-Maximization (EM) algorithm is an iterative method to maximize the log-likelihood function for parameter estimation. Previous works on the convergence analysis of the EM algorithm have established results on the asymptotic…
A determinantal approximation is obtained for the permanent of a doubly stochastic matrix. For moderate-deviation matrix sequences, the asymptotic relative error is of order $O(n^{-1})$.
We study a new parametric approach for hidden discrete-time diffusion models. This method is based on contrast minimization and deconvolution and leads to estimate a large class of stochastic models with nonlinear drift and nonlinear…
We consider the stochastic approximation problem where a convex function has to be minimized, given only the knowledge of unbiased estimates of its gradients at certain points, a framework which includes machine learning methods based on…