Related papers: On deconvolution of distribution functions
A linear functional of an object from a convex symmetric set can be optimally estimated, in a worst-case sense, by a linear functional of observations made on the object. This well-known fact is extended here to a nonlinear setting: other…
Two-sample feature selection is the problem of finding features that describe a difference between two probability distributions, which is a ubiquitous problem in both scientific and engineering studies. However, existing methods have…
Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments.…
In this paper, we propose a new way to obtain optimal convergence rates for smooth stochastic (strong) convex optimization tasks. Our approach is based on results for optimization tasks where gradients have nonrandom noise. In contrast to…
We develop a distributed algorithm for convex Empirical Risk Minimization, the problem of minimizing large but finite sum of convex functions over networks. The proposed algorithm is derived from directly discretizing the second-order…
We investigate minimax results for the anisotropic functional deconvolution model when observations are affected by the presence of long-memory. Under specific conditions about the covariance matrices of the errors, we follow a standard…
The authors consider the problem of estimating the density $g$ of independent and identically distributed variables $X\_i$, from a sample $Z\_1, ..., Z\_n$ where $Z\_i=X\_i+\sigma\epsilon\_i$, $i=1, ..., n$, $\epsilon$ is a noise…
M-estimation, aka empirical risk minimization, is at the heart of statistics and machine learning: Classification, regression, location estimation, etc. Asymptotic theory is well understood when the loss satisfies some smoothness…
This paper studies the problem of nonparametric estimation of a smooth function with data distributed across multiple machines. We assume an independent sample from a white noise model is collected at each machine, and an estimator of the…
The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence…
Let $(Y_i,\theta_i)$, $i=1,...,n$, be independent random vectors distributed like $(Y,\theta) \sim G^*$, where the marginal distribution of $\theta$ is completely unknown, and the conditional distribution of $Y$ conditional on $\theta$ is…
We consider the problem of estimating the regression function in functional linear regression models by proposing a new type of projection estimators which combine dimension reduction and thresholding. The introduction of a threshold rule…
We consider a non-convex constrained Lagrangian formulation of a fundamental bi-criteria optimization problem for variable selection in statistical learning; the two criteria are a smooth (possibly) nonconvex loss function, measuring the…
We consider robust optimization problems, where the goal is to optimize in the worst case over a class of objective functions. We develop a reduction from robust improper optimization to Bayesian optimization: given an oracle that returns…
A new maximum likelihood method for deconvoluting a continuous density with a positive lower bound on a known compact support in additive measurement error models with known error distribution using the approximate Bernstein type polynomial…
We consider a class of hypothesis testing problems where the null hypothesis postulates $M$ distributions for the observed data, and there is only one possible distribution under the alternative. We show that one can use a stochastic mirror…
So-called functional error estimators provide a valuable tool for reliably estimating the discretization error for a sum of two convex functions. We apply this concept to Tikhonov regularization for the solution of inverse problems for…
We propose a formulation for nonlinear recurrent models that includes simple parametric models of recurrent neural networks as a special case. The proposed formulation leads to a natural estimator in the form of a convex program. We provide…
The paper deals with the problem of nonparametric estimating the $L_p$--norm, $p\in (1,\infty)$, of a probability density on $R^d$, $d\geq 1$ from independent observations. The unknown density %to be estimated is assumed to belong to a ball…
In this paper we consider a class of nonparametric estimators of a distribution function F, with compact support, based on the theory of IFSs. The estimator of F is tought as the fixed point of a contractive operator T defined in terms of a…