Related papers: A Gaussian Comparison Theorem for Training Dynamic…

In this letter, we propose a Gaussian mixture model (GMM)-based channel estimator which is learned on imperfect training data, i.e., the training data are solely comprised of noisy and sparsely allocated pilot observations. In a practical…

Model selection criteria are one of the most important tools in statistics. Proofs showing a model selection criterion is asymptotically optimal are tailored to the type of model (linear regression, quantile regression, penalized…

We propose a class of structured diffusion models, in which the prior distribution is chosen as a mixture of Gaussians, rather than a standard Gaussian distribution. The specific mixed Gaussian distribution, as prior, can be chosen to…

Characterizing precisely the asymptotic generalization error of neural networks using parameters that can be estimated efficiently is a crucial problem in machine learning, which relies heavily on heuristics and practitioners' intuition to…

Multi-task learning leverages shared information among data sets to improve the learning performance of individual tasks. The paper applies this framework for data where each task is a phase-shifted periodic time series. In particular, we…

Dynamic paired comparison models, such as Elo and Glicko, are frequently used for sports prediction and ranking players or teams. We present an alternative dynamic paired comparison model which uses a Gaussian Process (GP) as a prior for…

In this paper, a distributed learning leader-follower consensus protocol based on Gaussian process regression for a class of nonlinear multi-agent systems with unknown dynamics is designed. We propose a distributed learning approach to…

In this paper, we focus on the data-driven discovery of a general second-order particle-based model that contains many state-of-the-art models for modeling the aggregation and collective behavior of interacting agents of similar size and…

We study a random dynamical system such that one transformation is randomly selected from a family of transformations and then applied on each iteration. For such random dynamical systems, we consider estimates of absolutely continuous…

The performance of state-of-the-art machine learning models often deteriorates when testing on demographics that are under-represented in the training dataset. This problem has predominately been studied in a supervised learning setting…

Generative adversarial networks (GANs) are powerful tools for learning generative models. In practice, the training may suffer from lack of convergence. GANs are commonly viewed as a two-player zero-sum game between two neural networks.…

We apply a general theory describing the dynamics of supervised learning in layered neural networks in the regime where the size p of the training set is proportional to the number of inputs N, as developed in a previous paper, to several…

Gaussian processes (GPs) are Bayesian nonparametric generative models that provide interpretability of hyperparameters, admit closed-form expressions for training and inference, and are able to accurately represent uncertainty. To model…

Score matching is an estimation procedure that has been developed for statistical models whose probability density function is known up to proportionality but whose normalizing constant is intractable, so that maximum likelihood is…

We consider estimation of a deterministic unknown parameter vector in a linear model with non-Gaussian noise. In the Gaussian case, dimensionality reduction via a linear matched filter provides a simple low dimensional sufficient statistic…

Match-and-copy is a core retrieval primitive used at inference time by large language models to retrieve a matching token from the context then copy its successor. Yet, understanding how this behavior emerges on natural data is challenging…

We propose a nonparametric density estimator based on the Gaussian process (GP) and derive three novel closed form learning algorithms based on Fisher divergence (FD) score matching. The density estimator is formed by multiplying a base…

In this paper, we study the problem of learning multi-dimensional Gaussian Mixture Models (GMMs), with a specific focus on model order selection and efficient mixing distribution estimation. We first establish an information-theoretic lower…

Using a result of Behrend concerning sets without arithmetic progressions, we construct some examples of dynamical systems with slow time of multiple recurrence. Our theorem is a quatitative analog of Furstenberg's Correspondence Principle.

This paper studies a training method to jointly estimate an energy-based model and a flow-based model, in which the two models are iteratively updated based on a shared adversarial value function. This joint training method has the…