Related papers: Information-theoretic limits and approximate messa…
Various alignment problems arising in cryo-electron microscopy, community detection, time synchronization, computer vision, and other fields fall into a common framework of synchronization problems over compact groups such as Z/L, U(1), or…
Inferring missing facts in temporal knowledge graphs (TKGs) is a fundamental and challenging task. Previous works have approached this problem by augmenting methods for static knowledge graphs to leverage time-dependent representations.…
Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…
This paper proposes Graph Signal Adaptive Message Passing (GSAMP), a novel message passing method that simultaneously conducts online prediction, missing data imputation, and noise removal on time-varying graph signals. Unlike conventional…
Spatio-temporal point process models play a central role in the analysis of spatially distributed systems in several disciplines. Yet, scalable inference remains computa- tionally challenging both due to the high resolution modelling…
Recently we extended Approximate message passing (AMP) algorithm to be able to handle general invariant matrix ensembles. In this contribution we extend our S-AMP approach to non-linear observation models. We obtain generalized AMP (GAMP)…
Although the standard formulations of prediction problems involve fully-observed and noiseless data drawn in an i.i.d. manner, many applications involve noisy and/or missing data, possibly involving dependence, as well. We study these…
Approximate Message Passing (AMP) algorithms enable precise characterization of certain classes of random objects in the high-dimensional limit, and have found widespread applications in fields such as signal processing, statistics, and…
Debiasing is a fundamental concept in high-dimensional statistics. While degrees-of-freedom adjustment is the state-of-the-art technique in high-dimensional linear regression, it is limited to i.i.d. samples and sub-Gaussian covariates.…
For regression model selection via maximum likelihood estimation, we adopt a vector representation of candidate models and study the likelihood ratio confidence region for the regression parameter vector of a full model. We show that when…
Sparse Group LASSO (SGL) is a regularized model for high-dimensional linear regression problems with grouped covariates. SGL applies $l_1$ and $l_2$ penalties on the individual predictors and group predictors, respectively, to guarantee…
We propose an orthogonal approximate message passing (OAMP) algorithm for signal estimation in the rectangular spiked matrix model with general rotationally invariant (RI) noise. We establish a rigorous state evolution that exactly…
In a regression setting we propose algorithms that reduce the dimensionality of the features while simultaneously maximizing a statistical measure of dependence known as distance correlation between the low-dimensional features and a…
We derive an approximate expression for mutual information in a broad class of discrete-time stationary channels with continuous input, under the constraint of vanishing input amplitude or power. The approximation describes the input by its…
This article studies bootstrap inference for high dimensional weakly dependent time series in a general framework of approximately linear statistics. The following high dimensional applications are covered: (1) uniform confidence band for…
This paper studies methods for testing and estimating change-points in the covariance structure of a high-dimensional linear time series. The assumed framework allows for a large class of multivariate linear processes (including vector…
Message passing algorithms, whose iterative nature captures well complicated interactions among interconnected variables in complex systems and extracts information from the fixed point of iterated messages, provide a powerful toolkit in…
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…
These lecture notes provide an overview of existing methodologies and recent developments for estimation and inference with high dimensional time series regression models. First, we present main limit theory results for high dimensional…
Approximate Message Passing (AMP) is a general framework for iterative algorithms, originally developed for compressed sensing and later extended to a wide range of high-dimensional inference problems. Although recent work has advanced…