Related papers: High-Dimensional Inference with the generalized Ho…

The gap between the huge volumes of data needed to train artificial neural networks and the relatively small amount of data needed by their biological counterparts is a central puzzle in machine learning. Here, inspired by biological…

Motivated by the problem of inferring the graph structure of functional connectivity networks from multi-level functional magnetic resonance imaging data, we develop a valid inference framework for high-dimensional graphical models that…

Interacting systems are prevalent in nature, from dynamical systems in physics to complex societal dynamics. The interplay of components can give rise to complex behavior, which can often be explained using a simple model of the system's…

Principal Components Analysis is a widely used technique for dimension reduction and characterization of variability in multivariate populations. Our interest lies in studying when and why the rotation to principal components can be used…

Network-linked data, where multivariate observations are interconnected by a network, are becoming increasingly prevalent in fields such as sociology and biology. These data often exhibit inherent noise and complex relational structures,…

We consider the demixing problem of two (or more) high-dimensional vectors from nonlinear observations when the number of such observations is far less than the ambient dimension of the underlying vectors. Specifically, we demonstrate an…

We address the problem of estimating a high-dimensional matrix from linear measurements, with a focus on designing optimal rank-adaptive algorithms. These algorithms infer the matrix by estimating its singular values and the corresponding…

A set of fixed points of the Hopfield type neural network is under investigation. Its connection matrix is constructed with regard to the Hebb rule from a highly symmetric set of the memorized patterns. Depending on the external parameter…

The set of the fixed points of the Hopfield type network is under investigation. The connection matrix of the network is constructed according the Hebb rule from the set of memorized patterns which are treated as distorted copies of the…

High-dimensional inference refers to problems of statistical estimation in which the ambient dimension of the data may be comparable to or possibly even larger than the sample size. We study an instance of high-dimensional inference in…

Factor analysis is a widely used statistical tool in many scientific disciplines, such as psychology, economics, and sociology. As observations linked by networks become increasingly common, incorporating network structures into factor…

Pairwise models like the Ising model or the generalized Potts model have found many successful applications in fields like physics, biology, and economics. Closely connected is the problem of inverse statistical mechanics, where the goal is…

Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional…

In this work, we consider causal inference in various high-dimensional treatment settings, including for single multi-valued treatments and vector treatments with binary or continuous components, when the number of treatments can be…

Causal inference from observation data is a core problem in many scientific fields. Here we present a general supervised deep learning framework that infers causal interactions by transforming the input vectors to an image-like…

Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the…

The Ising model is a celebrated example of a Markov random field, introduced in statistical physics to model ferromagnetism. This is a discrete exponential family with binary outcomes, where the sufficient statistic involves a quadratic…

Statistical inference is the science of drawing conclusions about some system from data. In modern signal processing and machine learning, inference is done in very high dimension: very many unknown characteristics about the system have to…

We consider statistical inference in factor analysis for ergodic and non-ergodic diffusion processes from discrete observations. Factor model based on high frequency time series data has been mainly discussed in the field of high…

Ising models with pairwise interactions are the least structured, or maximum-entropy, probability distributions that exactly reproduce measured pairwise correlations between spins. Here we use this equivalence to construct Ising models that…