Related papers: Statistical Query Lower Bounds for Learning Trunca…
We study the algorithmic task of learning Boolean disjunctions in the distribution-free agnostic PAC model. The best known agnostic learner for the class of disjunctions over $\{0, 1\}^n$ is the $L_1$-polynomial regression algorithm,…
We propose a stochastic approximation (SA) based method with randomization of samples for policy evaluation using the least squares temporal difference (LSTD) algorithm. Our proposed scheme is equivalent to running regular temporal…
In this paper we present a method for learning the parameters of a mixture of $k$ identical spherical Gaussians in $n$-dimensional space with an arbitrarily small separation between the components. Our algorithm is polynomial in all…
We revisit the problem of learning mixtures of spherical Gaussians. Given samples from mixture $\frac{1}{k}\sum_{j=1}^{k}\mathcal{N}(\mu_j, I_d)$, the goal is to estimate the means $\mu_1, \mu_2, \ldots, \mu_k \in \mathbb{R}^d$ up to a…
We present a general approach, based on exponential inequalities, to derive bounds on the generalization error of randomized learning algorithms. Using this approach, we provide bounds on the average generalization error as well as bounds…
We study the following fundamental hypothesis testing problem, which we term Gaussian mean testing. Given i.i.d. samples from a distribution $p$ on $\mathbb{R}^d$, the task is to distinguish, with high probability, between the following…
We systematically investigate quantum algorithms and lower bounds for mean estimation given query access to non-identically distributed samples. On the one hand, we give quantum mean estimators with quadratic quantum speed-up given samples…
The article starts with generalizations of some classical results and new truncation error upper bounds in the sampling theorem for bandlimited stochastic processes. Then, it investigates $L_p([0,T])$ and uniform approximations of…
Graphon estimation has been one of the most fundamental problems in network analysis and has received considerable attention in the past decade. From the statistical perspective, the minimax error rate of graphon estimation has been…
This paper establishes a statistical versus computational trade-off for solving a basic high-dimensional machine learning problem via a basic convex relaxation method. Specifically, we consider the {\em Sparse Principal Component Analysis}…
We study sequential prediction of real-valued, arbitrary and unknown sequences under the squared error loss as well as the best parametric predictor out of a large, continuous class of predictors. Inspired by recent results from…
The generalization error of a learning algorithm refers to the discrepancy between the loss of a learning algorithm on training data and that on unseen testing data. Various information-theoretic bounds on the generalization error have been…
While several papers have investigated computationally and statistically efficient methods for learning Gaussian mixtures, precise minimax bounds for their statistical performance as well as fundamental limits in high-dimensional settings…
We address the problem of learning of continuous exponential family distributions with unbounded support. While a lot of progress has been made on learning of Gaussian graphical models, we still lack scalable algorithms for reconstructing…
We provide efficient algorithms for the problem of distribution learning from high-dimensional Gaussian data where in each sample, some of the variable values are missing. We suppose that the variables are missing not at random (MNAR). The…
We consider the problem of sparse normal means estimation in a distributed setting with communication constraints. We assume there are $M$ machines, each holding $d$-dimensional observations of a $K$-sparse vector $\mu$ corrupted by…
This work represents a natural coalescence of two important lines of work: learning mixtures of Gaussians and algorithmic robust statistics. In particular we give the first provably robust algorithm for learning mixtures of any constant…
This paper presents an efficient variational inference framework for deriving a family of structured gaussian process regression network (SGPRN) models. The key idea is to incorporate auxiliary inducing variables in latent functions and…
To simulate bosons on a qubit- or qudit-based quantum computer, one has to regularize the theory by truncating infinite-dimensional local Hilbert spaces to finite dimensions. In the search for practical quantum applications, it is important…
We introduce a fast and easy-to-implement simulation algorithm for a multivariate normal distribution truncated on the intersection of a set of hyperplanes, and further generalize it to efficiently simulate random variables from a…