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The study of networks leads to a wide range of high dimensional inference problems. In many practical applications, one needs to draw inference from one or few large sparse networks. The present paper studies hypothesis testing of graphs in…

In this paper we study minimax and adaptation rates in general isotonic regression. For uniform deterministic and random designs in $[0,1]^d$ with $d\ge 2$ and $N(0,1)$ noise, the minimax rate for the $\ell_2$ risk is known to be bounded…

We consider the problem of estimating Ising models over $n$ variables in Total Variation (TV) distance, given $l$ independent samples from the model. While the statistical complexity of the problem is well-understood [DMR20], identifying…

We give upper and lower bounds on the information-theoretic threshold for community detection in the stochastic block model. Specifically, let $k$ be the number of groups, $d$ be the average degree, the probability of edges between vertices…

The criterion commonly used in directed acyclic graphs (dags) for testing graphical independence is the well-known d-separation criterion. It allows us to build graphical representations of dependency models (usually probabilistic…

Change point detection in time series aims to identify moments when the probability distribution of time series changes. It is widely applied in many areas, such as human activity sensing and medical science. In the context of multivariate…

We establish optimal Statistical Query (SQ) lower bounds for robustly learning certain families of discrete high-dimensional distributions. In particular, we show that no efficient SQ algorithm with access to an $\epsilon$-corrupted binary…

Consider the Gaussian vector model with mean value {\theta}. We study the twin problems of estimating the number |{\theta}|_0 of non-zero components of {\theta} and testing whether |{\theta}|_0 is smaller than some value. For testing, we…

This paper is motivated by the comparison of genetic networks based on microarray samples. The aim is to test whether the differences observed between two inferred Gaussian graphical models come from real differences or arise from…

We consider linear regression in the high-dimensional regime where the number of observations $n$ is smaller than the number of parameters $p$. A very successful approach in this setting uses $\ell_1$-penalized least squares (a.k.a. the…

We propose a distributed Bayesian quickest change detection algorithm for sensor networks, based on a random gossip inter-sensor communication structure. Without a control or fusion center, each sensor executes its local change detection…

This paper investigates a change-point estimation problem in the context of high-dimensional Markov Random Field models. Change-points represent a key feature in many dynamically evolving network structures. The change-point estimate is…

Gaussian Bayesian networks (a.k.a. linear Gaussian structural equation models) are widely used to model causal interactions among continuous variables. In this work, we study the problem of learning a fixed-structure Gaussian Bayesian…

We introduce a new method to identify phase boundaries in physical systems. It is based on training a predictive model such as a neural network to infer a physical system's parameters from its state. The deviation of the inferred parameters…

Changepoint models typically assume the data within each segment are independent and identically distributed conditional on some parameters which change across segments. This construction may be inadequate when data are subject to local…

This paper studies the classification of high-dimensional Gaussian signals from low-dimensional noisy, linear measurements. In particular, it provides upper bounds (sufficient conditions) on the number of measurements required to drive the…

A weighted Shiryaev-Roberts change detection procedure is shown to approximately minimize the expected delay to detection as well as higher moments of the detection delay among all change-point detection procedures with the given low…

We consider models for molecular sequence evolution in which the transition rates at each site depend on the local sequence context, giving rise to a time-inhomogeneous Markov process in which sites evolve under a complex dependency…

Change point estimation is often formulated as a search for the maximum of a gain function describing improved fits when segmenting the data. Searching through all candidates requires $O(n)$ evaluations of the gain function for an interval…

Estimation and prediction problems for dense signals are often framed in terms of minimax problems over highly symmetric parameter spaces. In this paper, we study minimax problems over l2-balls for high-dimensional linear models with…