Related papers: High-Dimensional Inference with the generalized Ho…
Several recent experiments in biology study systems composed of several interacting elements, for example neuron networks. Normally, measurements describe only the collective behavior of the system, even if in most cases we would like to…
This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter,…
We investigate the problem of statistical inference for logistic regression with high-dimensional covariates in settings where dependence among individuals is induced by an underlying Markov random field. Going beyond the pairwise…
Through a redefinition of patterns in an Hopfield-like model, we introduce and develop an approach to model discrete systems made up of many, interacting components with inner degrees of freedom. Our approach clarifies the intrinsic…
The problem of infering the top component of a noisy sample covariance matrix with prior information about the distribution of its entries is considered, in the framework of the spiked covariance model. Using the replica method of…
The problem of inferring pair-wise and higher-order interactions in complex systems involving large numbers of interacting variables, from observational data, is fundamental to many fields. Known to the statistical physics community as the…
This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We…
Modeling the complex interactions of systems of particles or agents is a fundamental scientific and mathematical problem that is studied in diverse fields, ranging from physics and biology, to economics and machine learning. In this work,…
A statistical inference method is developed and tested for pairwise interacting systems whose degrees of freedom are continuous angular variables, such as planar spins in magnetic systems or wave phases in optics and acoustics. We…
Using a hierarchical construction, we develop methods for a wide and flexible class of models by taking a fully parametric approach to generalized linear mixed models with complex covariance dependence. The Laplace approximation is used to…
Logistic regression is key method for modeling the probability of a binary outcome based on a collection of covariates. However, the classical formulation of logistic regression relies on the independent sampling assumption, which is often…
There have been two separate lines of work on estimating Ising models: (1) estimating them from multiple independent samples under minimal assumptions about the model's interaction matrix; and (2) estimating them from one sample in…
Many visual scenes can be described as compositions of latent factors. Effective recognition, reasoning, and editing often require not only forming such compositional representations, but also solving the decomposition problem. One popular…
Dynamical behaviors of complex interacting systems, including brain activities, financial price movements, and physical collective phenomena, are associated with underlying interactions between the system's components. The issue of…
The interactions between holes in the Hubbard model, in the low density, intermediate to strong coupling limit, are investigated by systematically improving mean field calculations. The Configuration Interaction basis set is constructed by…
This article considers a novel and widely applicable approach to modeling high-dimensional dependent data when a large number of explanatory variables are available and the signal-to-noise ratio is low. We postulate that a $p$-dimensional…
We study parameter estimation in Nonlinear Factor Analysis (NFA) where the generative model is parameterized by a deep neural network. Recent work has focused on learning such models using inference (or recognition) networks; we identify a…
Empirical complex systems can be characterized not only by pairwise interactions, but also by higher-order (group) interactions influencing collective phenomena, from metabolic reactions to epidemics. Nevertheless, higher-order networks'…
This paper develops an inferential theory for high-dimensional matrix-variate factor models with missing observations. We propose an easy-to-use all-purpose method that involves two straightforward steps. First, we perform principal…
We discuss how inference can be performed when data are sampled from the non-ergodic phase of systems with multiple attractors. We take as model system the finite connectivity Hopfield model in the memory phase and suggest a cavity method…