Related papers: Inference via low-dimensional couplings

We propose a new driving scheme, when different parts of a system are driven with different, generally incommensurate, frequencies. Such driving provides a flexible handle to control various properties of the system and to obtain new types…

In this work, we study scaling limits of shallow Bayesian neural networks (BNNs) via their connection to Gaussian processes (GPs), with an emphasis on statistical modeling, identifiability, and scalable inference. We first establish a…

We study the statistical properties of piecewise expanding maps in the general setting of metric measure spaces. We provide sufficient conditions for exponential mixing of such systems with explicit estimates on the constants. We also…

The interface between stochastic analysis and machine learning is a rapidly evolving field, with path signatures - iterated integrals that provide faithful, hierarchical representations of paths - offering a principled and universal feature…

Large scale neural recordings have established that the transformation of sensory stimuli into motor outputs relies on low-dimensional dynamics at the population level, while individual neurons exhibit complex selectivity. Understanding how…

Inferring dependence structure through undirected graphs is crucial for uncovering the major modes of multivariate interaction among high-dimensional genomic markers that are potentially associated with cancer. Traditionally, conditional…

We introduce a new framework for efficient sampling from complex probability distributions, using a combination of optimal transport maps and the Metropolis-Hastings rule. The core idea is to use continuous transportation to transform…

This paper studies the problem of statistical inference for genetic relatedness between binary traits based on individual-level genome-wide association data. Specifically, under the high-dimensional logistic regression models, we define…

Learning systems often expand their ambient features or latent representations over time, embedding earlier representations into larger spaces with limited new latent structure. We study transfer learning for structured matrix estimation…

This article focuses on drawing computationally-efficient predictive inference from Gaussian process (GP) regressions with a large number of features when the response is conditionally independent of the features given the projection to a…

A fundamental task in AI is providing performance guarantees for predictions made in unseen domains. In practice, there can be substantial uncertainty about the distribution of new data, and corresponding variability in the performance of…

This work presents a low-rank tensor model for multi-dimensional Markov chains. A common approach to simplify the dynamical behavior of a Markov chain is to impose low-rankness on the transition probability matrix. Inspired by the success…

We consider the fundamental problem of sampling the optimal transport coupling between given source and target distributions. In certain cases, the optimal transport plan takes the form of a one-to-one mapping from the source support to the…

In this note we prove that in a metric measure space $(X, d, m)$ verifying the measure contraction property with parameters $K \in \mathbb{R}$ and $1< N< \infty$, any optimal transference plan between two marginal measures is induced by an…

Many recent invertible neural architectures are based on coupling block designs where variables are divided in two subsets which serve as inputs of an easily invertible (usually affine) triangular transformation. While such a transformation…

Causal models seek to unravel the cause-effect relationships among variables from observed data, as opposed to mere mappings among them, as traditional regression models do. This paper introduces a novel causal discovery algorithm designed…

In the course of evolution, proteins show a remarkable conservation of their three-dimensional structure and their biological function, leading to strong evolutionary constraints on the sequence variability between homologous proteins. Our…

Despite advances in representation learning, high-dimensional classification remains challenging in low-sample-size regimes, where the dominant signal may vary across applications and labeled data are often limited. We propose a…

Flexible Bayesian models are typically constructed using limits of large parametric models with a multitude of parameters that are often uninterpretable. In this article, we offer a novel alternative by constructing an exponentially tilted…

We examine an analytic variational inference scheme for the Gaussian Process State Space Model (GPSSM) - a probabilistic model for system identification and time-series modelling. Our approach performs variational inference over both the…