相关论文: Sampling via Gaussian Mixture Approximations

In this paper, we study convergence properties of the gradient Expectation-Maximization algorithm \cite{lange1995gradient} for Gaussian Mixture Models for general number of clusters and mixing coefficients. We derive the convergence rate…

This paper proposes a new framework to regularize the highly ill-posed and non-linear phase retrieval problem through deep generative priors using simple gradient descent algorithm. We experimentally show effectiveness of proposed algorithm…

The estimation of normalizing constants is a fundamental step in probabilistic model comparison. Sequential Monte Carlo methods may be used for this task and have the advantage of being inherently parallelizable. However, the standard…

A framework for adaptive and non-adaptive statistical compressive sensing is developed, where a statistical model replaces the standard sparsity model of classical compressive sensing. We propose within this framework optimal task-specific…

We propose two novel approaches to the recovery of an (approximately) sparse signal from noisy linear measurements in the case that the signal is a priori known to be non-negative and obey given linear equality constraints, such as simplex…

We study the estimation of the latent variable Gaussian graphical model (LVGGM), where the precision matrix is the superposition of a sparse matrix and a low-rank matrix. In order to speed up the estimation of the sparse plus low-rank…

Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques, such as Markov chain Monte Carlo (MCMC) and particle filters, have become very popular in signal processing over the last years. However, in many…

Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…

Gaussian Probability Path based Generative Models (GPPGMs) generate data by reversing a stochastic process that progressively corrupts samples with Gaussian noise. Despite state-of-the-art results in 3D molecular generation, their…

Density estimation, which estimates the distribution of data, is an important category of probabilistic machine learning. A family of density estimators is mixture models, such as Gaussian Mixture Model (GMM) by expectation maximization.…

We investigate a Gaussian mixture model (GMM) with component means constrained in a pre-selected subspace. Applications to classification and clustering are explored. An EM-type estimation algorithm is derived. We prove that the subspace…

We study the gradient Expectation-Maximization (EM) algorithm for Gaussian Mixture Models (GMM) in the over-parameterized setting, where a general GMM with $n>1$ components learns from data that are generated by a single ground truth…

We consider the problem of estimating the parameters a Gaussian Mixture Model with K components of known weights, all with an identity covariance matrix. We make two contributions. First, at the population level, we present a sharper…

This paper studies the optimization of the KL functional on the Wasserstein space of probability measures, and develops a sampling framework based on Wasserstein gradient descent (WGD). We identify two important subclasses of the…

We consider nonparametric Bayesian estimation inference using a rescaled smooth Gaussian field as a prior for a multidimensional function. The rescaling is achieved using a Gamma variable and the procedure can be viewed as choosing an…

We consider sampling from a Gibbs distribution by evolving a finite number of particles using a particular score estimator rather than Brownian motion. To accelerate the particles, we consider a second-order score-based ODE, similar to…

The upcoming gravitational wave (GW) observatory LISA will measure the parameters of sources like extreme-mass-ratio inspirals (EMRIs) to exquisite precision. These measurements will also be sensitive to perturbations to the vacuum,…

Contextual optimization enhances decision quality by leveraging side information to improve predictions of uncertain parameters. However, existing approaches face significant challenges when dealing with multimodal or mixtures of…

Modern ultra-high-resolution image synthesis relies heavily on the robust generative capacity of large-scale pre-trained Latent Diffusion Models (LDMs). While recent representation alignment methods have proven effective by distilling…

We study model evaluation and model selection from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. We believe that GA is one way formally to address…