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The Lopsided Lov\'{a}sz Local Lemma (LLLL) is a powerful probabilistic principle which has been used in a variety of combinatorial constructions. While originally a general statement about probability spaces, it has recently been…

To achieve scalable and accurate inference for latent Gaussian processes, we propose a variational approximation based on a family of Gaussian distributions whose covariance matrices have sparse inverse Cholesky (SIC) factors. We combine…

We consider stochastic approximations of sampling algorithms, such as Stochastic Gradient Langevin Dynamics (SGLD) and the Random Batch Method (RBM) for Interacting Particle Dynamcs (IPD). We observe that the noise introduced by the…

The high communication cost of sending model updates from the clients to the server is a significant bottleneck for scalable federated learning (FL). Among existing approaches, state-of-the-art bitrate-accuracy tradeoffs have been achieved…

A number of researchers have independently introduced topologies on the set of laws of stochastic processes that extend the usual weak topology. Depending on the respective scientific background this was motivated by applications and…

Transfer learning, or domain adaptation, is concerned with machine learning problems in which training and testing data come from possibly different probability distributions. In this work, we give an information-theoretic analysis of the…

Empirical risk minimization, a cornerstone in machine learning, is often hindered by the Optimizer's Curse stemming from discrepancies between the empirical and true data-generating distributions.To address this challenge, the robust…

Variational inference (VI) is a popular approach in Bayesian inference, that looks for the best approximation of the posterior distribution within a parametric family, minimizing a loss that is typically the (reverse) Kullback-Leibler (KL)…

Regression by composition provides a flexible framework for constructing conditional distributions through sequential group actions. However, when multiple flows act on the same distribution, the model becomes non-identifiable, leading to…

In knowledge distillation, a primary focus has been on transforming and balancing multiple distillation components. In this work, we emphasize the importance of thoroughly examining each distillation component, as we observe that not all…

In this paper, we derive a useful lower bound for the Kullback-Leibler divergence (KL-divergence) based on the Hammersley-Chapman-Robbins bound (HCRB). The HCRB states that the variance of an estimator is bounded from below by the…

We provide full theoretical guarantees for the convergence behaviour of diffusion-based generative models under the assumption of strongly log-concave data distributions while our approximating class of functions used for score estimation…

The generalized Kullback-Leibler divergence (K-Ld) in Tsallis statistics [constrained by the additive duality of generalized statistics (dual generalized K-Ld)] is here reconciled with the theory of Bregman divergences for expectations…

This paper introduces and analyses interacting underdamped Langevin algorithms, termed Kinetic Interacting Particle Langevin Monte Carlo (KIPLMC) methods, for statistical inference in latent variable models. We propose a diffusion process…

We study the fundamental and timely problem of learning long sequences in autoregressive modeling and next-token prediction under model misspecification, measured by the joint Kullback--Leibler (KL) divergence. Our goal is to characterize…

We decompose the Kullback--Leibler generalization error (GE) -- the expected KL divergence from the data distribution to the trained model -- of unsupervised learning into three non-negative components: model error, data bias, and variance.…

Understanding the dimension dependency of computational complexity in high-dimensional sampling problem is a fundamental problem, both from a practical and theoretical perspective. Compared with samplers with unbiased stationary…

Gaussian mixture models (GMM) are powerful parametric tools with many applications in machine learning and computer vision. Expectation maximization (EM) is the most popular algorithm for estimating the GMM parameters. However, EM…

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…

flip is an extremely simple and maximally local classical decoder which has been used to great effect in certain classes of classical codes. When applied to quantum codes there exist constant-weight errors (such as half of a stabiliser)…