Related papers: Unsupervised learning of binary vectors: a Gaussia…

The theory of two projections is utilized to study two-component Gibbs samplers. Through this theory, previously intractable problems regarding the asymptotic variances of two-component Gibbs samplers are reduced to elementary matrix…

Self-training is a classical approach in semi-supervised learning which is successfully applied to a variety of machine learning problems. Self-training algorithm generates pseudo-labels for the unlabeled examples and progressively refines…

We study the sparse high-dimensional Gaussian mixture model when the number of clusters is allowed to grow with the sample size. A minimax lower bound for parameter estimation is established, and we show that a constrained maximum…

Unsupervised representation learning has recently received lots of interest due to its powerful generalizability through effectively leveraging large-scale unlabeled data. There are two prevalent approaches for this, contrastive learning…

In settings where only unlabelled speech data is available, speech technology needs to be developed without transcriptions, pronunciation dictionaries, or language modelling text. A similar problem is faced when modelling infant language…

Bayesian inference for graphical models has received much attention in the literature in recent years. It is well known that when the graph G is decomposable, Bayesian inference is significantly more tractable than in the general…

Bayesian inference on structured models typically relies on the ability to infer posterior distributions of underlying hidden variables. However, inference in implicit models or complex posterior distributions is hard. A popular tool for…

We consider a binary classification problem when the data comes from a mixture of two rotationally symmetric distributions satisfying concentration and anti-concentration properties enjoyed by log-concave distributions among others. We show…

Recently there has been increased interest in semi-supervised classification in the presence of graphical information. A new class of learning models has emerged that relies, at its most basic level, on classifying the data after first…

Self supervised learning (SSL) is a machine learning paradigm where models learn to understand the underlying structure of data without explicit supervision from labeled samples. The acquired representations from SSL have demonstrated…

Symmetry is ubiquitous in many real-world phenomena and tasks, such as physics, images, and molecular simulations. Empirical studies have demonstrated that incorporating symmetries into generative models can provide better generalization…

The Gaussian mixture model is widely used in unsupervised learning, owing to its simplicity and interpretability. However, a fundamental limitation of the classical Gaussian mixture model is that it forces each observation to belong to…

Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…

It is of fundamental importance to find algorithms obtaining optimal performance for learning of statistical models in distributed and communication limited systems. Aiming at characterizing the optimal strategies, we consider learning of…

This paper is about variable selection, clustering and estimation in an unsupervised high-dimensional setting. Our approach is based on fitting constrained Gaussian mixture models, where we learn the number of clusters $K$ and the set of…

Real world learning scenarios involve a nonstationary distribution of classes with sequential dependencies among the samples, in contrast to the standard machine learning formulation of drawing samples independently from a fixed, typically…

Deep reinforcement learning systems often suffer from unstable training dynamics due to non-stationarity, where learning objectives and data distributions evolve over time. We show that under non-stationary targets, isotropic Gaussian…

We investigate the influence of different kinds of structure on the learning behaviour of a perceptron performing a classification task defined by a teacher rule. The underlying pattern distribution is permitted to have spatial…

We use the maximum a posteriori estimation principle for learning representations distributed on the unit sphere. We propose to use the angular Gaussian distribution, which corresponds to a Gaussian projected on the unit-sphere and derive…

For binary classification we establish learning rates up to the order of $n^{-1}$ for support vector machines (SVMs) with hinge loss and Gaussian RBF kernels. These rates are in terms of two assumptions on the considered distributions:…