arXiv research

MixTS uses a mixture prior to analyze Thompson Sampling in multi-task learning.

Study on Dirichlet process mixtures for clustering consistency.

We give tight concentration bounds for mixtures of martingales that are simultaneously uniform over (a) mixture distributions, in a PAC-Bayes sense; and (b) all finite times. These bounds are proved in terms of the martingale variance, extending classical Bernstein inequalities, and sharpening and simplifying prior wor…

Concentration of infinitely exchangeable sequences with bounded-difference constants

Robustly clusters mixtures of Gaussians even with outliers.

Self-training improves weak classifiers in mixture models.

New method certifies anti-concentration for various non-Gaussian distributions.

Private estimation with public data reduces sample complexity.

X in R^D has mean zero and finite second moments. We show that there is a precise sense in which almost all linear projections of X into R^d (for d < D) look like a scale-mixture of spherical Gaussians -- specifically, a mixture of distributions N(0, sigma^2 I_d) where the weight of the particular sigma component is P …

In this paper, we study the spectrum and the eigenvectors of radial kernels for mixtures of distributions in $\mathbb{R}^n$. Our approach focuses on high dimensions and relies solely on the concentration properties of the components in the mixture. We give several results describing of the structure of kernel matrices …

A new distance metric for vMF distributions simplifies spherical data analysis.

Robust clustering of high-dimensional data is an important topic because clusters in real datasets are often heavy-tailed and/or asymmetric. Traditional approaches to model-based clustering often fail for high dimensional data, e.g., due to the number of free covariance parameters. A parametrization of the component sc…

In many applications, a finite mixture is a natural model, but it can be difficult to choose an appropriate number of components. To circumvent this choice, investigators are increasingly turning to Dirichlet process mixtures (DPMs), and Pitman-Yor process mixtures (PYMs), more generally. While these models may be well…

Phase segregation, the process by which the components of a binary mixture spontaneously separate, is a key process in the evolution and design of many chemical, mechanical, and biological systems. In this work, we present a data-driven approach for the learning, modeling, and prediction of phase segregation. A direct …

We study the concentration of random kernel matrices around their mean. We derive nonasymptotic exponential concentration inequalities for Lipschitz kernels assuming that the data points are independent draws from a class of multivariate distributions on $\mathbb R^d$, including the strongly log-concave distributions u…

Paper proposes a method to efficiently cluster stretched mixtures.

In this paper, we are concerned with obtaining distribution-free concentration inequalities for mixture of independent Bernoulli variables that incorporate a notion of variance. Missing mass is the total probability mass associated to the outcomes that have not been seen in a given sample which is an important quantity…

New analysis proves sketching operators' RIP guarantees for mixture models without importance sampling.

Improved concentration inequalities for sub-Weibull variables enhance statistical and machine learning applications.

This paper shows that deep learning (DL) representations of data produced by generative adversarial nets (GANs) are random vectors which fall within the class of so-called \textit{concentrated} random vectors. Further exploiting the fact that Gram matrices, of the type $G = X^T X$ with $X=[x_1,\ldots,x_n]\in \mathbb{R}…

The study assesses sensitivity to prior choices in Bayesian nonparametric models.

This paper considers statistical estimation problems where the probability distribution of the observed random variable is invariant with respect to actions of a finite topological group. It is shown that any such distribution must satisfy a restricted finite mixture representation. When specialized to the case of dist…

We develop a sequential low-complexity inference procedure for Dirichlet process mixtures of Gaussians for online clustering and parameter estimation when the number of clusters are unknown a-priori. We present an easily computable, closed form parametric expression for the conditional likelihood, in which hyperparamet…

New framework models uncertainty in classification debates.

The paper proposes methods to identify and sample from mixtures of Mallows models for top-k rankings.

Algorithm learns Gaussian mixtures robust to outliers.

New algorithm learns halfspaces with noise using Forster decomposition.

A new model CDTM improves text classification by concentrating document topics.

Paper addresses concentration of distances for fractional quasi p-norms, identifying conditions for concentration and anti-concentration.

Study calculates tail risk for various mixture distributions.

Quantum ML predicts data with improved speed and accuracy.

Modelling highly multi-modal data is a challenging problem in machine learning. Most algorithms are based on maximizing the likelihood, which corresponds to the M(oment)-projection of the data distribution to the model distribution. The M-projection forces the model to average over modes it cannot represent. In contras…

uMoE trains NNs with uncertain data by embedding uncertainty into training.

The problem of Hybrid Linear Modeling (HLM) is to model and segment data using a mixture of affine subspaces. Different strategies have been proposed to solve this problem, however, rigorous analysis justifying their performance is missing. This paper suggests the Theoretical Spectral Curvature Clustering (TSCC) algori…

Sharp concentration results for sums of heavy-tailed random variables.

The paper explores how data geometry influences generalization in neural networks.

Understanding proper distance measures between distributions is at the core of several learning tasks such as generative models, domain adaptation, clustering, etc. In this work, we focus on mixture distributions that arise naturally in several application domains where the data contains different sub-populations. For …

New algorithm reduces reinforcement learning regret for linear MDPs with unknown transitions.

Detecting and recovering labels in binomial logistic mixtures is challenging due to an information gap.

Heavy-tailed distributions are widely used in robust mixture modelling due to possessing thick tails. As a computationally tractable subclass of the stable distributions, sub-Gaussian $α$-stable distribution received much interest in the literature. Here, we introduce a type of expectation maximization algorithm that e…

New methods correct spectral distortions using known analyte concentrations.

We provide guarantees for learning latent variable models emphasizing on the overcomplete regime, where the dimensionality of the latent space can exceed the observed dimensionality. In particular, we consider multiview mixtures, spherical Gaussian mixtures, ICA, and sparse coding models. We provide tight concentration…

Understanding separation effects on parameter estimation in finite Gaussian mixtures

AdaPT-GMM improves multiple testing power with covariates.

Improved bounds for estimating discrete distributions in KL divergence.

New concentration inequalities for tensors with heavy-tailed coefficients.

Conditional Value-at-Risk (CVaR) is a widely used risk metric in applications such as finance. We derive concentration bounds for CVaR estimates, considering separately the cases of light-tailed and heavy-tailed distributions. In the light-tailed case, we use a classical CVaR estimator based on the empirical distributi…

Consistent estimator for mixtures of nonparametric elliptical distributions helps cluster analysis.