Related papers: Learning High-dimensional Gaussians from Censored …

As in standard linear regression, in truncated linear regression, we are given access to observations $(A_i, y_i)_i$ whose dependent variable equals $y_i= A_i^{\rm T} \cdot x^* + \eta_i$, where $x^*$ is some fixed unknown vector of interest…

We study the problem of lossless feature selection for a $d$-dimensional feature vector $X=(X^{(1)},\dots ,X^{(d)})$ and label $Y$ for binary classification as well as nonparametric regression. For an index set $S\subset \{1,\dots ,d\}$,…

While it is commonly observed in practice that pruning networks to a certain level of sparsity can improve the quality of the features, a theoretical explanation of this phenomenon remains elusive. In this work, we investigate this by…

The detection of hidden two-dimensional Gauss-Markov random fields using sensor networks is considered. Under a conditional autoregressive model, the error exponent for the Neyman-Pearson detector satisfying a fixed level constraint is…

We describe a general technique that yields the first {\em Statistical Query lower bounds} for a range of fundamental high-dimensional learning problems involving Gaussian distributions. Our main results are for the problems of (1) learning…

Consider observation of a phenomenon of interest subject to selective sampling due to a censoring mechanism regulated by some other variable. In this context, an extensive literature exists linked to the so-called Heckman selection model. A…

In truncated linear regression, samples $(x,y)$ are shown only when the outcome $y$ falls inside a certain survival set $S^\star$ and the goal is to estimate the unknown $d$-dimensional regressor $w^\star$. This problem has a long history…

We study the task of high-dimensional entangled mean estimation in the subset-of-signals model. Specifically, given $N$ independent random points $x_1,\ldots,x_N$ in $\mathbb{R}^D$ and a parameter $\alpha \in (0, 1)$ such that each $x_i$ is…

Gaussian distributions are commonly used as a key building block in many generative models. However, their applicability has not been well explored in deep networks. In this paper, we propose a novel deep generative model named as Normal…

The Sampled Gaussian Mechanism (SGM)---a composition of subsampling and the additive Gaussian noise---has been successfully used in a number of machine learning applications. The mechanism's unexpected power is derived from privacy…

High-dimensional auto-regressive models provide a natural way to model influence between $M$ actors given multi-variate time series data for $T$ time intervals. While there has been considerable work on network estimation, there is limited…

In distributed statistical learning, $N$ samples are split across $m$ machines and a learner wishes to use minimal communication to learn as well as if the examples were on a single machine. This model has received substantial interest in…

High dimensional data analysis is known to be as a challenging problem. In this article, we give a theoretical analysis of high dimensional classification of Gaussian data which relies on a geometrical analysis of the error measure. It…

A novel framework of compressed sensing, namely statistical compressed sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution, and achieving accurate reconstruction on average, is…

We study the problem of learning mixtures of $k$ Gaussians in $d$ dimensions. We make no separation assumptions on the underlying mixture components: we only require that the covariance matrices have bounded condition number and that the…

Neural networks excel at discovering statistical patterns in high-dimensional data sets. In practice, higher-order cumulants, which quantify the non-Gaussian correlations between three or more variables, are particularly important for the…

A good measure of similarity between data points is crucial to many tasks in machine learning. Similarity and metric learning methods learn such measures automatically from data, but they do not scale well respect to the dimensionality of…

The estimation of the generalization error of classifiers often relies on a validation set. Such a set is hardly available in few-shot learning scenarios, a highly disregarded shortcoming in the field. In these scenarios, it is common to…

We consider the following basic inference problem: there is an unknown high-dimensional vector $w \in \mathbb{R}^n$, and an algorithm is given access to labeled pairs $(x,y)$ where $x \in \mathbb{R}^n$ is a measurement and $y = w \cdot x +…

This paper addresses the problem of learning a sparse structure Bayesian network from high-dimensional discrete data. Compared to continuous Bayesian networks, learning a discrete Bayesian network is a challenging problem due to the large…