Related papers: A new approach to locally adaptive polynomial regr…
We propose a computationally efficient method to construct nonparametric, heteroscedastic prediction bands for uncertainty quantification, with or without any user-specified predictive model. Our approach provides an alternative to the…
In this paper we introduce a new methodology to determine an optimal coefficient of penalized functional regression. We assume the dependent, independent variables and the regression coefficients are functions of time and error dynamics…
We consider the problem of adaptation to the margin in binary classification. We suggest a penalized empirical risk minimization classifier that adaptively attains, up to a logarithmic factor, fast optimal rates of convergence for the…
We consider the problem of estimating a $d$-dimensional discrete distribution from its samples observed under a $b$-bit communication constraint. In contrast to most previous results that largely focus on the global minimax error, we study…
We introduce adaptive sampling methods for stochastic programs with deterministic constraints. First, we propose and analyze a variant of the stochastic projected gradient method where the sample size used to approximate the reduced…
Elliptical slice sampling is a widely used gradient-free Markov chain Monte Carlo algorithm that is tuning-free and capable of adapting to local characteristics of the target distribution. However, its primary limitation is that sampling…
We investigate and extend the conformal prediction method due to Vovk,Gammerman and Shafer (2005) to construct nonparametric prediction regions. These regions have guaranteed distribution free, finite sample coverage, without any…
The local least squares estimator for a regression curve cannot provide optimal results when non-Gaussian noise is present. Both theoretical and empirical evidence suggests that residuals often exhibit distributional properties different…
In this article we consider the problem of choosing an optimal sampling scheme for the regression problem simultaneously with that of model selection. We consider a batch type approach and an on-line approach following algorithms recently…
In this paper we initiate a study of non parametric contextual bandits under shape constraints on the mean reward function. Specifically, we study a setting where the context is one dimensional, and the mean reward function is isotonic with…
Nonparametric regression models with locally stationary covariates have received increasing interest in recent years. As a nice relief of "curse of dimensionality" induced by large dimension of covariates, additive regression model is…
The graphical Lasso (GLASSO) is a widely used algorithm for learning high-dimensional undirected Gaussian graphical models (GGM). Given i.i.d. observations from a multivariate normal distribution, GLASSO estimates the precision matrix by…
Kernel density estimation is a key component of a wide variety of algorithms in machine learning, Bayesian inference, stochastic dynamics and signal processing. However, the unsupervised density estimation technique requires tuning a…
Deep neural network is a state-of-art method in modern science and technology. Much statistical literature have been devoted to understanding its performance in nonparametric estimation, whereas the results are suboptimal due to a redundant…
We consider the problem of estimating the parameters of a Gaussian or binary distribution in such a way that the resulting undirected graphical model is sparse. Our approach is to solve a maximum likelihood problem with an added l_1-norm…
This paper studies the distributed adaptiveestimation problems for stochastic large regression modelswith an infinite number of parameters. By constructing a re-cursive local cost function, we propose a novel distributedrecursive least…
In this note, we introduce a general version of the well-known elliptical potential lemma that is a widely used technique in the analysis of algorithms in sequential learning and decision-making problems. We consider a stochastic linear…
Random forests are a powerful method for non-parametric regression, but are limited in their ability to fit smooth signals, and can show poor predictive performance in the presence of strong, smooth effects. Taking the perspective of random…
For many algorithms, parameter tuning remains a challenging and critical task, which becomes tedious and infeasible in a multi-parameter setting. Multi-penalty regularization, successfully used for solving undetermined sparse regression of…
This paper develops a general asymptotic theory of local polynomial (LP) regression for spatial data observed at irregularly spaced locations in a sampling region $R_n \subset \mathbb{R}^d$. We adopt a stochastic sampling design that can…