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We present a distributed (non-Bayesian) learning algorithm for the problem of parameter estimation with Gaussian noise. The algorithm is expressed as explicit updates on the parameters of the Gaussian beliefs (i.e. means and precision). We…
Bayesian optimisation has gained great popularity as a tool for optimising the parameters of machine learning algorithms and models. Somewhat ironically, setting up the hyper-parameters of Bayesian optimisation methods is notoriously hard.…
We revisit the problem of distribution learning within the framework of learning-augmented algorithms. In this setting, we explore the scenario where a probability distribution is provided as potentially inaccurate advice on the true,…
Nonparametric regression for massive numbers of samples (n) and features (p) is an increasingly important problem. In big n settings, a common strategy is to partition the feature space, and then separately apply simple models to each…
Subspace learning and matrix factorization problems have great many applications in science and engineering, and efficient algorithms are critical as dataset sizes continue to grow. Many relevant problem formulations are non-convex, and in…
Solving the generalized eigenvalue problem is a useful method for finding energy eigenstates of large quantum systems. It uses projection onto a set of basis states which are typically not orthogonal. One needs to invert a matrix whose…
In this paper we consider the statistical inference of the unknown parameter of an exponential distribution based on the time truncated data. The time truncated data occurs quite often in the reliability analysis for type-I or hybrid…
Given a Gaussian Markov random field, we consider the problem of selecting a subset of variables to observe which minimizes the total expected squared prediction error of the unobserved variables. We first show that finding an exact…
This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…
We study the problem of learning general (i.e., not necessarily homogeneous) halfspaces with Random Classification Noise under the Gaussian distribution. We establish nearly-matching algorithmic and Statistical Query (SQ) lower bound…
We provide an algorithm for properly learning mixtures of two single-dimensional Gaussians without any separability assumptions. Given $\tilde{O}(1/\varepsilon^2)$ samples from an unknown mixture, our algorithm outputs a mixture that is…
We study the problem of learning an unknown function using random feature models. Our main contribution is an exact asymptotic analysis of such learning problems with Gaussian data. Under mild regularity conditions for the feature matrix,…
The Gaussian graphical model, a popular paradigm for studying relationship among variables in a wide range of applications, has attracted great attention in recent years. This paper considers a fundamental question: When is it possible to…
We study the problem of learning latent variables in Gaussian graphical models. Existing methods for this problem assume that the precision matrix of the observed variables is the superposition of a sparse and a low-rank component. In this…
Many problems arising in applications result in the need to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become…
A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is…
We consider the reconstruction of a bandlimited function from its finite localized sample data. Truncating the classical Shannon sampling series results in an unsatisfactory convergence rate due to the slow decay of the sinc function. To…
We study the problem of high-dimensional linear regression in a robust model where an $\epsilon$-fraction of the samples can be adversarially corrupted. We focus on the fundamental setting where the covariates of the uncorrupted samples are…
Sparse linear regression is a central problem in high-dimensional statistics. We study the correlated random design setting, where the covariates are drawn from a multivariate Gaussian $N(0,\Sigma)$, and we seek an estimator with small…
Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…