Related papers: Estimating multi-index models with response-condit…
Expectation propagation is a general prescription for approximation of integrals in statistical inference problems. Its literature is mainly concerned with Bayesian inference scenarios. However, expectation propagation can also be used to…
Distribution shifts are ubiquitous in real-world machine learning applications, posing a challenge to the generalization of models trained on one data distribution to another. We focus on scenarios where data distributions vary across…
Missing value is a very common and unavoidable problem in sensors, and researchers have made numerous attempts for missing value imputation, particularly in deep learning models. However, for real sensor data, the specific data distribution…
The problem of adaptive multivariate function estimation in the single-index regression model with random design and weak assumptions on the noise is investigated. A novel estimation procedure that adapts simultaneously to the unknown index…
In this article, we extend predictor envelope models to settings with multivariate outcomes and multiple, functional predictors. We propose a two-step estimation strategy, which first projects the function onto a finite-dimensional…
We study the properties of nonparametric least squares regression using deep neural networks. We derive non-asymptotic upper bounds for the prediction error of the empirical risk minimizer of feedforward deep neural regression. Our error…
This paper proposes a novel diffusion-index model for forecasting when predictors are high-dimensional matrix-valued time series. We apply an $\alpha$-PCA method to extract low-dimensional matrix factors and build a bilinear regression…
We develop an approach for estimating models described via conditional moment restrictions, with a prototypical application being non-parametric instrumental variable regression. We introduce a min-max criterion function, under which the…
In the framework of nonparametric multivariate function estimation we are interested in structural adaptation. We assume that the function to be estimated possesses the single-index structure where neither the link function nor the index…
This paper proposes a novel non-parametric multidimensional convex regression estimator which is designed to be robust to adversarial perturbations in the empirical measure. We minimize over convex functions the maximum (over Wasserstein…
We show that the way inference is performed in few-shot segmentation tasks has a substantial effect on performances -- an aspect often overlooked in the literature in favor of the meta-learning paradigm. We introduce a transductive…
We present large sample results for partitioning-based least squares nonparametric regression, a popular method for approximating conditional expectation functions in statistics, econometrics, and machine learning. First, we obtain a…
We consider fitting a bivariate spline regression model to data using a weighted least-squares cost function, with weights that sum to one to form a discrete probability distribution. By applying the principle of maximum entropy, the weight…
In partially linear single-index models, we obtain the semiparametrically efficient profile least-squares estimators of regression coefficients. We also employ the smoothly clipped absolute deviation penalty (SCAD) approach to…
Single Index Models (SIMs) are simple yet flexible semi-parametric models for classification and regression. Response variables are modeled as a nonlinear, monotonic function of a linear combination of features. Estimation in this context…
We study a functional linear regression model that deals with functional responses and allows for both functional covariates and high-dimensional vector covariates. The proposed model is flexible and nests several functional regression…
This paper introduces an efficient multi-linear nonparametric (kernel-based) approximation framework for data regression and imputation, and its application to dynamic magnetic-resonance imaging (dMRI). Data features are assumed to reside…
In the framework of nonparametric multivariate function estimation we are interested in structural adaptation. We assume that the function to be estimated has the "single-index" structure where neither the link function nor the index vector…
For the past two decades, single-index model, a special case of projection pursuit regression, has proven to be an efficient way of coping with the high dimensional problem in nonparametric regression. In this paper, based on weakly…
In some cases, computational benefit can be gained by exploring the hyper parameter space using a deterministic set of grid points instead of a Markov chain. We view this as a numerical integration problem and make three unique…