Related papers: Estimating a Polya frequency function_2

Estimating the normalizing constant of an unnormalized probability distribution has important applications in computer science, statistical physics, machine learning, and statistics. In this work, we consider the problem of estimating the…

We consider nonparametric maximum-likelihood estimation of a log-concave density in case of interval-censored, right-censored and binned data. We allow for the possibility of a subprobability density with an additional mass at $+\infty$,…

We propose a new algorithm---Stochastic Proximal Langevin Algorithm (SPLA)---for sampling from a log concave distribution. Our method is a generalization of the Langevin algorithm to potentials expressed as the sum of one stochastic smooth…

Convex nonsmooth optimization problems, whose solutions live in very high dimensional spaces, have become ubiquitous. To solve them, the class of first-order algorithms known as proximal splitting algorithms is particularly adequate: they…

We investigate a class of composite nonconvex functions, where the outer function is the sum of univariate extended-real-valued convex functions and the inner function is the limit of difference-of-convex functions. A notable feature of…

We show that there is an intimate connection between the theory of nonparametric (smoothed) maximum likelihood estimators for certain inverse problems and integral equations. This is illustrated by estimators for interval censoring and…

The maximum likelihood amplitude estimation algorithm (MLAE) is a practical solution to the quantum amplitude estimation problem with Heisenberg limit error convergence. We improve MLAE by using random depths to avoid the so-called critical…

We propose a new randomized algorithm for solving convex optimization problems that have a large number of constraints (with high probability). Existing methods like interior-point or Newton-type algorithms are hard to apply to such…

Minimizing a convex risk function is the main step in many basic learning algorithms. We study protocols for convex optimization which provably leak very little about the individual data points that constitute the loss function.…

We investigate the behavior of the nonparametric maximum likelihood estimator $\hat{f}_n$ for a decreasing density $f$ near the boundaries of the support of $f$. We establish the limiting distribution of $\hat{f}_n(n^{-\alpha})$, where we…

In this paper, we will generate a convex iterative FP thresholding algorithm to solve the problem $(FP^{\lambda}_{a})$. Two schemes of convex iterative FP thresholding algorithms are generated. One is convex iterative FP thresholding…

For the task of sampling from a density $\pi \propto \exp(-V)$ on $\mathbb{R}^d$, where $V$ is possibly non-convex but $L$-gradient Lipschitz, we prove that averaged Langevin Monte Carlo outputs a sample with $\varepsilon$-relative Fisher…

Particle filtering algorithms have enabled practical solutions to problems in autonomous robotics (self-driving cars, UAVs, warehouse robots), target tracking, and econometrics, with further applications in speech processing and medicine…

Many data-fitting applications require the solution of an optimization problem involving a sum of large number of functions of high dimensional parameter. Here, we consider the problem of minimizing a sum of $n$ functions over a convex…

We consider polyhedral approximations of strictly convex compacta in finite dimensional Euclidean spaces (such compacta are also uniformly convex). We obtain the best possible estimates for errors of considered approximations in the…

The problem of phase synchronization is to estimate the phases (angles) of a complex unit-modulus vector $z$ from their noisy pairwise relative measurements $C = zz^* + \sigma W$, where $W$ is a complex-valued Gaussian random matrix. The…

Motivated by problems of anomaly detection, this paper implements the Neyman-Pearson paradigm to deal with asymmetric errors in binary classification with a convex loss. Given a finite collection of classifiers, we combine them and obtain a…

Probabilistic programming uses programs to express generative models whose posterior probability is then computed by built-in inference engines. A challenging goal is to develop general purpose inference algorithms that work out-of-the-box…

In this paper we consider regression problems subject to arbitrary noise in the operator or design matrix. This characterization appropriately models many physical phenomena with uncertainty in the regressors. Although the problem has been…

We study three fundamental statistical-learning problems: distribution estimation, property estimation, and property testing. We establish the profile maximum likelihood (PML) estimator as the first unified sample-optimal approach to a wide…