Related papers: Interpolating Discriminant Functions in High-Dimen…
The paper proposes a latent variable model for binary data coming from an unobserved heterogeneous population. The heterogeneity is taken into account by replacing the traditional assumption of Gaussian distributed factors by a finite…
A central topic in functional data analysis is how to design an optimaldecision rule, based on training samples, to classify a data function. We exploit the optimal classification problem when data functions are Gaussian processes. Sharp…
This paper considers the problem of reconstructing missing parts of functions based on their observed segments. It provides, for Gaussian processes and arbitrary bijective transformations thereof, theoretical expressions for the…
Deep learning is a hierarchical inference method formed by subsequent multiple layers of learning able to more efficiently describe complex relationships. In this work, Deep Gaussian Mixture Models are introduced and discussed. A Deep…
Deep neural networks (DNNs) typically involve a large number of parameters and are trained to achieve zero or near-zero training error. Despite such interpolation, they often exhibit strong generalization performance on unseen data, a…
This work investigates theoretically the interplay between interpolation and aggregation in regression. We establish that the $\gamma$-graph dimension characterizes learnability for a broad class of natural aggregation procedures.…
Tensor classification is gaining importance across fields, yet handling partially observed data remains challenging. In this paper, we introduce a novel approach to tensor classification with incomplete data, framed within high-dimensional…
Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…
Finite mixture regression models are useful for modeling the relationship between response and predictors, arising from different subpopulations. In this article, we study high-dimensional predic- tors and high-dimensional response, and…
Missing values with mixed data types is a common problem in a large number of machine learning applications such as processing of surveys and in different medical applications. Recently, Gaussian copula models have been suggested as a means…
When approximating a function that depends on a parameter, one encounters many practical examples where linear interpolation or linear approximation with respect to the parameters prove ineffective. This is particularly true for responses…
The selection of optimal designs for generalized linear mixed models is complicated by the fact that the Fisher information matrix, on which most optimality criteria depend, is computationally expensive to evaluate. Our focus is on the…
This work presents a new procedure for obtaining predictive distributions in the context of Gaussian process (GP) modeling, with a relaxation of the interpolation constraints outside ranges of interest: the mean of the predictive…
We introduce a very general method for sparse and large-scale variable selection. The large-scale regression settings is such that both the number of parameters and the number of samples are extremely large. The proposed method is based on…
Deep learning has been applied to various tasks in the field of machine learning and has shown superiority to other common procedures such as kernel methods. To provide a better theoretical understanding of the reasons for its success, we…
We derive minimax testing errors in a distributed framework where the data is split over multiple machines and their communication to a central machine is limited to $b$ bits. We investigate both the $d$- and infinite-dimensional signal…
Function approximation from input and output data is one of the most investigated problems in signal processing. This problem has been tackled with various signal processing and machine learning methods. Although tensors have a rich history…
Many high dimensional integrals can be reduced to the problem of finding the relative measures of two sets. Often one set will be exponentially larger than the other, making it difficult to compare the sizes. A standard method of dealing…
For many expensive deterministic computer simulators, the outputs do not have replication error and the desired metamodel (or statistical emulator) is an interpolator of the observed data. Realizations of Gaussian spatial processes (GP) are…
High-dimensional classification is a fundamentally important research problem in high-dimensional data analysis. In this paper, we derive a nonasymptotic rate for the minimax excess misclassification risk when feature dimension…