Related papers: The problem of perfect predictors in statistical s…
In recent years, methods of approximate parameter estimation have attracted considerable interest in complex problems where exact likelihoods are hard to obtain. In their most basic form, Bayesian methods such as Approximate Bayesian…
Estimating the matrix of connections probabilities is one of the key questions when studying sparse networks. In this work, we consider networks generated under the sparse graphon model and the in-homogeneous random graph model with missing…
We introduce the spiked mixture model (SMM) to address the problem of estimating a set of signals from many randomly scaled and noisy observations. Subsequently, we design a novel expectation-maximization (EM) algorithm to recover all…
Capturing aleatoric uncertainty is a critical part of many machine learning systems. In deep learning, a common approach to this end is to train a neural network to estimate the parameters of a heteroscedastic Gaussian distribution by…
Gridless methods show great superiority in line spectral estimation. These methods need to solve an atomic $l_0$ norm (i.e., the continuous analog of $l_0$ norm) minimization problem to estimate frequencies and model order. Since this…
In this paper, we develop asymptotic theories for a class of latent variable models for large-scale multi-relational networks. In particular, we establish consistency results and asymptotic error bounds for the (penalized) maximum…
Although a generalized spike population model has been actively studied in random matrix theory, its application to real data has been rarely explored. We find that most methods for determining the number of spikes based on the Johnstone's…
For regression model selection via maximum likelihood estimation, we adopt a vector representation of candidate models and study the likelihood ratio confidence region for the regression parameter vector of a full model. We show that when…
We discuss an approach to signal recovery in Generalized Linear Models (GLM) in which the signal estimation problem is reduced to the problem of solving a stochastic monotone variational inequality (VI). The solution to the stochastic VI…
Bidimensional spiking models currently gather a lot of attention for their simplicity and their ability to reproduce various spiking patterns of cortical neurons, and are particularly used for large network simulations. These models…
This paper considers a general class of parameter-driven models for time series of counts. A comprehensive simulation study is conducted to evaluate the accuracy and efficiency of three estimators: the maximum likelihood estimators of the…
Consider the nonparametric logistic regression problem. In the logistic regression, we usually consider the maximum likelihood estimator, and the excess risk is the expectation of the Kullback-Leibler (KL) divergence between the true and…
We study the law of the iterated logarithm (LIL) for the maximum likelihood estimation of the parameters (as a convex optimization problem) in the generalized linear models with independent or weakly dependent ($\rho$-mixing, $m$-dependent)…
Optimal planning with respect to learned neural network (NN) models in continuous action and state spaces using mixed-integer linear programming (MILP) is a challenging task for branch-and-bound solvers due to the poor linear relaxation of…
The computation of the maximum likelihood (ML) estimator for heteroscedastic regression models is considered. The traditional Newton algorithms for the problem require matrix multiplications and inversions, which are bottlenecks in modern…
This paper derives central limit theorems (CLTs) for general linear spectral statistics (LSS) of three important multi-spiked Hermitian random matrix ensembles. The first is the most common spiked scenario, proposed by Johnstone, which is a…
Joint peak detection is a central problem when comparing samples in genomic data analysis, but current algorithms for this task are unsupervised and limited to at most 2 sample types. We propose PeakSegJoint, a new constrained maximum…
We consider regression problems with binary weights. Such optimization problems are ubiquitous in quantized learning models and digital communication systems. A natural approach is to optimize the corresponding Lagrangian using variants of…
We consider the matrix completion problem under a form of row/column weighted entrywise sampling, including the case of uniform entrywise sampling as a special case. We analyze the associated random observation operator, and prove that with…
It is increasingly common to encounter time-varying random fields on networks (metabolic networks, sensor arrays, distributed computing, etc.). This paper considers the problem of optimal, nonlinear prediction of these fields, showing from…