Related papers: Sample Complexity Using Infinite Multiview Models
Explainability models are now prevalent within machine learning to address the black-box nature of neural networks. The question now is which explainability model is most effective. Probabilistic Lipschitzness has demonstrated that the…
Image segmentation is an important median level vision topic. Accurate and efficient multiphase segmentation for images with intensity inhomogeneity is still a great challenge. We present a new two-stage multiphase segmentation method…
We initiate the study of nonsmooth optimization problems under bounded local subgradient variation, which postulates bounded difference between (sub)gradients in small local regions around points, in either average or maximum sense. The…
Theoretical estimates of the convergence rate of many well-known gradient-type optimization methods are based on quadratic interpolation, provided that the Lipschitz condition for the gradient is satisfied. In this article we obtain a…
We introduce and analyse a new nonparametric estimator of a multi-dimensional density. Our smooth projection estimator (SPE) is defined by a least squares projection of the sample onto an infinite dimensional mixture class via an…
An important estimation problem that is closely related to large-scale multiple testing is that of estimating the null density and the proportion of nonnull effects. A few estimators have been introduced in the literature; however, several…
Nearest neighbor (NN) matching as a tool to align data sampled from different groups is both conceptually natural and practically well-used. In a landmark paper, Abadie and Imbens (2006) provided the first large-sample analysis of NN…
We study the problem of efficiently computing the derivative of the fixed-point of a parametric nondifferentiable contraction map. This problem has wide applications in machine learning, including hyperparameter optimization, meta-learning…
The likelihood calculation of a vast number of particles is the computational bottleneck for the particle filter in applications where the observation information is rich. For fast computing the likelihood of particles, a numerical fitting…
We provide finite-sample analysis of a general framework for using k-nearest neighbor statistics to estimate functionals of a nonparametric continuous probability density, including entropies and divergences. Rather than plugging a…
We present a novel model for text complexity analysis which can be fitted to ordered categorical data measured on multiple scales, e.g. a corpus with binary responses mixed with a corpus with more than two ordered outcomes. The multiple…
We study norm-based uniform convergence bounds for neural networks, aiming at a tight understanding of how these are affected by the architecture and type of norm constraint, for the simple class of scalar-valued one-hidden-layer networks,…
We consider a non-parametric Bayesian model for conditional densities. The model is a finite mixture of normal distributions with covariate dependent multinomial logit mixing probabilities. A prior for the number of mixture components is…
In this paper, we systematically study the regularity theory of the linear system of nearly incompressible elasticity. In the setting of stochastic homogenization, we develop new techniques to establish the large-scale estimates of…
In this manuscript, we consider a finite nonparametric mixture model with non-independent marginal density functions. Dependence between the marginal densities is modeled using a copula device. Until recently, no deterministic algorithms…
Although continuous density estimation has received abundant attention in the Bayesian nonparametrics literature, there is limited theory on multivariate mixed scale density estimation. In this note, we consider a general framework to…
Stochastic proximal point methods have recently garnered renewed attention within the optimization community, primarily due to their desirable theoretical properties. Notably, these methods exhibit a convergence rate that is independent of…
We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the margin-adapted dimension, which is a simple function of the second order statistics of…
Shape-constrained density estimation is an important topic in mathematical statistics. We focus on densities on $\mathbb{R}^d$ that are log-concave, and we study geometric properties of the maximum likelihood estimator (MLE) for weighted…
In the present paper, a systematic study is made of quantitative semicontinuity (a.k.a. Lipschitzian) properties of certain multifunctions, which are defined as a solution map associated to a family of parameterized ``split" feasibility…