Related papers: On the Minimax Optimality of the EM Algorithm for …
Softmax mixture models (SMMs) are discrete $K$-mixtures introduced to model the probability of choosing an attribute $x_j \in \RR^L$ from $p$ candidates, in heterogeneous populations. They have been known as mixed multinomial logits in the…
We study super-resolution multi-reference alignment, the problem of estimating a signal from many circularly shifted, down-sampled, and noisy observations. We focus on the low SNR regime, and show that a signal in $\mathbb{R}^M$ is uniquely…
Since its development, the minimax framework has been one of the corner stones of theoretical statistics, and has contributed to the popularity of many well-known estimators, such as the regularized M-estimators for high-dimensional…
Learning Gaussian Mixture Models (GMMs) is a fundamental problem in machine learning, with the Expectation-Maximization (EM) algorithm and its popular variant gradient EM being arguably the most widely used algorithms in practice. In the…
Usually, hearing impaired people use hearing aids which are implemented with speech enhancement algorithms. Estimation of speech and estimation of nose are the components in single channel speech enhancement system. The main objective of…
Several approximate inference algorithms have been proposed to minimize an alpha-divergence between an approximating distribution and a target distribution. Many of these algorithms introduce bias, the magnitude of which becomes problematic…
Any clustering algorithm must synchronously learn to model the clusters and allocate data to those clusters in the absence of labels. Mixture model-based methods model clusters with pre-defined statistical distributions and allocate data to…
Diffractive neural networks leverage the high-dimensional characteristics of electromagnetic (EM) fields for high-throughput computing. However, the existing architectures face challenges in integrating large-scale multidimensional…
We propose self-adaptive training---a new training algorithm that dynamically corrects problematic training labels by model predictions without incurring extra computational cost---to improve generalization of deep learning for potentially…
Meta-learning synthesizes and leverages the knowledge from a given set of tasks to rapidly learn new tasks using very little data. Meta-learning of linear regression tasks, where the regressors lie in a low-dimensional subspace, is an…
We address the problem of signal denoising via transform-domain shrinkage based on a novel $\textit{risk}$ criterion called the minimum probability of error (MPE), which measures the probability that the estimated parameter lies outside an…
Empirical risk minimization (ERM) is ubiquitous in machine learning and underlies most supervised learning methods. While there has been a large body of work on algorithms for various ERM problems, the exact computational complexity of ERM…
Distributed stochastic optimization algorithms can simultaneously process large-scale datasets, significantly accelerating model training. However, their effectiveness is often hindered by the sparsity of distributed networks and data…
This paper investigates the optimal ergodic sublinear convergence rate of the relaxed proximal point algorithm for solving monotone variational inequality problems. The exact worst case convergence rate is computed using the performance…
Expectation Maximization (EM) algorithm is a parameter estimation method from incomplete observations. In this paper, an implementation of this method to the calibration of HKS spectrometer at Jefferson Lab is described. We show that the…
We investigate regularized algorithms combining with projection for least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space. We prove convergence results with respect…
We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first…
Recent research shows the susceptibility of machine learning models to adversarial attacks, wherein minor but maliciously chosen perturbations of the input can significantly degrade model performance. In this paper, we theoretically analyse…
Multi-layer feedforward networks have been used to approximate a wide range of nonlinear functions. An important and fundamental problem is to understand the learnability of a network model through its statistical risk, or the expected…
We consider an $\ell_2$-regularized non-convex optimization problem for recovering signals from their noisy phaseless observations. We design and study the performance of a message passing algorithm that aims to solve this optimization…