Related papers: Regression with reject option and application to k…
Consider a multinomial regression model where the response, which indicates a unit's membership in one of several possible unordered classes, is associated with a set of predictor variables. Such models typically involve a matrix of…
Rejection sampling is a technique for sampling from difficult distributions. However, its use is limited due to a high rejection rate. Common adaptive rejection sampling methods either work only for very specific distributions or without…
The earth system is exceedingly complex and often chaotic in nature, making prediction incredibly challenging: we cannot expect to make perfect predictions all of the time. Instead, we look for specific states of the system that lead to…
The $k$-nearest neighbor algorithm ($k$-NN) is a widely used non-parametric method for classification and regression. We study the mean squared error of the $k$-NN estimator when $k$ is chosen by leave-one-out cross-validation (LOOCV).…
Nonparametric regression with random design is considered. Estimates are defined by minimzing a penalized empirical $L_2$ risk over a suitably chosen class of neural networks with one hidden layer via gradient descent. Here, the gradient…
We consider a nonparametric regression setup, where the covariate is a random element in a complete separable metric space, and the parameter of interest associated with the conditional distribution of the response lies in a separable…
We propose a kernel regression method to predict a target signal lying over a graph when an input observation is given. The input and the output could be two different physical quantities. In particular, the input may not be a graph signal…
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…
This paper presents a new estimator of the intercept of a linear regression model in cases where the outcome varaible is observed subject to a selection rule. The intercept is often in this context of inherent interest; for example, in a…
We introduce a new principle for model selection in regression and classification. Many regression models are controlled by some smoothness or flexibility or complexity parameter c, e.g. the number of neighbors to be averaged over in k…
Adversarial machine learning challenges the assumption that the underlying distribution remains consistent throughout the training and implementation of a prediction model. In particular, adversarial evasion considers scenarios where…
Reinforcement Learning (RL) has shown great empirical success in various application domains. The theoretical aspects of the problem have been extensively studied over past decades, particularly under tabular and linear Markov Decision…
In the nonparametric regression setting, we construct an estimator which is a continuous function interpolating the data points with high probability, while attaining minimax optimal rates under mean squared risk on the scale of H\"older…
Decisions are increasingly taken by both humans and machine learning models. However, machine learning models are currently trained for full automation -- they are not aware that some of the decisions may still be taken by humans. In this…
Recent results in nonparametric regression show that for deep learning, i.e., for neural network estimates with many hidden layers, we are able to achieve good rates of convergence even in case of high-dimensional predictor variables,…
We introduce an algorithm which, in the context of nonlinear regression on vector-valued explanatory variables, chooses those combinations of vector components that provide best prediction. The algorithm devotes particular attention to…
Recent theoretical studies illustrated that kernel ridgeless regression can guarantee good generalization ability without an explicit regularization. In this paper, we investigate the statistical properties of ridgeless regression with…
Kernel methods, particularly kernel ridge regression (KRR), are time-proven, powerful nonparametric regression techniques known for their rich capacity, analytical simplicity, and computational tractability. The analysis of their predictive…
In this article we study the asymptotic predictive optimality of a model selection criterion based on the cross-validatory predictive density, already available in the literature. For a dependent variable and associated explanatory…
This book chapter introduces regression approaches and regression adjustment for Approximate Bayesian Computation (ABC). Regression adjustment adjusts parameter values after rejection sampling in order to account for the imperfect match…