arXiv research

Algorithm samples composite logconcave densities efficiently.

New algorithms sample convex bodies using Markov chains and restricted Gaussian oracles.

New algorithms sample structured logconcave families with improved efficiency.

Algorithm samples from composite log-concave distributions using gradient evaluations and restricted Gaussian oracles.

New study shows Gaussian samplers struggle with heavy-tailed targets, while stable samplers excel.

Develops new oracle inequalities for Gaussian ranking estimators.

Oracle inequalities and variable selection properties for the Lasso in linear models have been established under a variety of different assumptions on the design matrix. We show in this paper how the different conditions and concepts relate to each other. The restricted eigenvalue condition (Bickel et al., 2009) or the…

There has been considerable advance in understanding the properties of sparse regularization procedures in high-dimensional models. In time series context, it is mostly restricted to Gaussian autoregressions or mixing sequences. We study oracle properties of LASSO estimation of weakly sparse vector-autoregressive model…

Paper develops methods for non-quadratic loss low-rank matrix recovery.

This paper investigates the supervised learning problem with observations drawn from certain general stationary stochastic processes. Here by \emph{general}, we mean that many stationary stochastic processes can be included. We show that when the stochastic processes satisfy a generalized Bernstein-type inequality, a u…

We study graph estimation and density estimation in high dimensions, using a family of density estimators based on forest structured undirected graphical models. For density estimation, we do not assume the true distribution corresponds to a forest; rather, we form kernel density estimates of the bivariate and univaria…

The paper improves count data regression models for overdispersed data.

We consider the problem of learning high-dimensional Gaussian graphical models. The graphical lasso is one of the most popular methods for estimating Gaussian graphical models. However, it does not achieve the oracle rate of convergence. In this paper, we propose the graphical nonconvex optimization for optimal estimat…

New characterization limits sampling with inexact scores.

RPI combines imitation and reinforcement learning to improve policies efficiently.

We study the Nonparametric Maximum Likelihood Estimator (NPMLE) for estimating Gaussian location mixture densities in $d$-dimensions from independent observations. Unlike usual likelihood-based methods for fitting mixtures, NPMLEs are based on convex optimization. We prove finite sample results on the Hellinger accurac…

Study on tradeoffs between mistakes and ERM oracle calls in online and transductive learning.

Bayesian-guided method selects optimal design from large candidate pool.

Oracle-efficient algorithm for offline RL with partial data coverage.

Method selects valid IVs from a large set using clustering and test of overidentifying restrictions.

Multi-view data have been routinely collected in various fields of science and engineering. A general problem is to study the predictive association between multivariate responses and multi-view predictor sets, all of which can be of high dimensionality. It is likely that only a few views are relevant to prediction, an…

High throughput genetic sequencing arrays with thousands of measurements per sample and a great amount of related censored clinical data have increased demanding need for better measurement specific model selection. In this paper we establish strong oracle properties of nonconcave penalized methods for nonpolynomial (N…

Paper introduces structured sparsity estimators for Generalized Linear Models.

Improved sampling algorithm with state-of-the-art complexity bounds.

Probabilistic Bisection Algorithm performs root finding based on knowledge acquired from noisy oracle responses. We consider the generalized PBA setting (G-PBA) where the statistical distribution of the oracle is unknown and location-dependent, so that model inference and Bayesian knowledge updating must be performed s…

Data de-duplication is the task of detecting multiple records that correspond to the same real-world entity in a database. In this work, we view de-duplication as a clustering problem where the goal is to put records corresponding to the same physical entity in the same cluster and putting records corresponding to diff…

Nonparametric empirical Bayes denoising on Riemannian manifolds

Improved sampling from high-dimensional Gaussians using smoothed scores.

Adaptive Bayesian learning aggregates experts to improve performance.

RS-NSGD improves SGD convergence for heavy-tailed noise.

New algorithm achieves small-loss bounds in online learning with improved rates.

The paper analyzes the efficiency of gradient estimation methods in noisy function evaluations.

Study phase transitions in shuffled regression problems.

A scalable method for estimating spatial data using VREML.

New protocol identifies impossible edge orientations in causal graphs.

Approximate Message Passing (AMP) has been shown to be an excellent statistical approach to signal inference and compressed sensing problem. The AMP framework provides modularity in the choice of signal prior; here we propose a hierarchical form of the Gauss-Bernouilli prior which utilizes a Restricted Boltzmann Machin…

This article is concerned with the Bridge Regression, which is a special family in penalized regression with penalty function $\sum_{j=1}^{p}|β_j|^q$ with $q>0$, in a linear model with linear restrictions. The proposed restricted bridge (RBRIDGE) estimator simultaneously estimates parameters and selects important varia…

Paper relaxes assumptions for non-parametric estimation in pairwise learning.

Study improves sampling from non-log-concave distributions using Fisher information.

Thompson Sampling tackles noisy context in stochastic bandits.

RBM models reveal how hidden unit tail behavior affects pattern reconstruction.

Develops a framework for distributional Granger causality

Filtered conformal ellipsoids for graph-native time series

This paper proposes a Lasso-type estimator for a high-dimensional sparse parameter identified by a single index conditional moment restriction (CMR). In addition to this parameter, the moment function can also depend on a nuisance function, such as the propensity score or the conditional choice probability, which we es…

A Gaussian restricted Boltzmann machine (GRBM) is a Boltzmann machine defined on a bipartite graph and is an extension of usual restricted Boltzmann machines. A GRBM consists of two different layers: a visible layer composed of continuous visible variables and a hidden layer composed of discrete hidden variables. In th…

Paper analyzes holdout cross-validation for large non-Gaussian covariance estimation.

Low-rank tensor regression, a new model class that learns high-order correlation from data, has recently received considerable attention. At the same time, Gaussian processes (GP) are well-studied machine learning models for structure learning. In this paper, we demonstrate interesting connections between the two, espe…

The paper derives Cramer-Rao bounds for Laplacian matrix estimation under various constraints.