相关论文: Learning Mixtures of Plackett-Luce Models

Mixtures of Gaussian (or normal) distributions arise in a variety of application areas. Many heuristics have been proposed for the task of finding the component Gaussians given samples from the mixture, such as the EM algorithm, a…

Mixtures of linear dynamical systems (MoLDS) provide a path to model time-series data that exhibit diverse temporal dynamics across trajectories. However, its application remains challenging in complex and noisy settings, limiting its…

We study the problem of learning a mixture of multiple linear dynamical systems (LDSs) from unlabeled short sample trajectories, each generated by one of the LDS models. Despite the wide applicability of mixture models for time-series data,…

A natural Bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with Dirichlet weights, and put a prior on the number of components---that is, to use a mixture of finite mixtures…

Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in low-dimensional continuous space. In particular, mixtures of Gaussians can be fitted to data very quickly using an…

We study the problem of list-decodable Gaussian mean estimation and the related problem of learning mixtures of separated spherical Gaussians. We develop a set of techniques that yield new efficient algorithms with significantly improved…

The predominance of machine learning models in many spheres of human activity has led to a growing demand for their transparency. The transparency of models makes it possible to discern some factors, such as security or non-discrimination.…

This paper studies the application of the generalized method of moments (GMM) to multi-reference alignment (MRA): the problem of estimating a signal from its circularly-translated and noisy copies. We begin by proving that the GMM estimator…

Mixed-precision quantization improves the budget--accuracy trade-off for large language models (LLMs) by allocating more bits to sensitive modules. However, automating this allocation at LLM scale faces a unique combination of constraints:…

We consider estimation in moment condition models and show that under any bound on identification strength, asymptotically admissible (i.e. undominated) estimators in a wide class of estimation problems must be uniformly continuous in the…

We consider the problem of learning an unknown ReLU network with respect to Gaussian inputs and obtain the first nontrivial results for networks of depth more than two. We give an algorithm whose running time is a fixed polynomial in the…

The Expectation-Maximization (EM) algorithm has been predominantly used to approximate the maximum likelihood estimation of the location-scale Gaussian mixtures. However, when the models are over-specified, namely, the chosen number of…

Variance components estimation and mixed model analysis are central themes in statistics with applications in numerous scientific disciplines. Despite the best efforts of generations of statisticians and numerical analysts, maximum…

We study the complexity of learning mixtures of separated Gaussians with common unknown bounded covariance matrix. Specifically, we focus on learning Gaussian mixture models (GMMs) on $\mathbb{R}^d$ of the form $P= \sum_{i=1}^k w_i…

Generalized linear mixed models (GLMM) encompass large class of statistical models, with a vast range of applications areas. GLMM extends the linear mixed models allowing for different types of response variable. Three most common data…

Mixture modelling using elliptical distributions promises enhanced robustness, flexibility and stability over the widely employed Gaussian mixture model (GMM). However, existing studies based on the elliptical mixture model (EMM) are…

This paper studies the problem of model training under Federated Learning when clients exhibit cluster structure. We contextualize this problem in mixed regression, where each client has limited local data generated from one of $k$ unknown…

Mixture models serve as one fundamental tool with versatile applications. However, their training techniques, like the popular Expectation Maximization (EM) algorithm, are notoriously sensitive to parameter initialization and often suffer…

This paper is concerned with an important issue in finite mixture modelling, the selection of the number of mixing components. We propose a new penalized likelihood method for model selection of finite multivariate Gaussian mixture models.…

Motivated by problems in data clustering, we establish general conditions under which families of nonparametric mixture models are identifiable, by introducing a novel framework involving clustering overfitted \emph{parametric} (i.e.…