Related papers: Optimal Nonparametric Inference with Two-Scale Dis…
The problem of accurate nonparametric estimation of distributional functionals (integral functionals of one or more probability distributions) has received recent interest due to their wide applicability in signal processing, information…
In this paper, we aim at establishing an approximation theory and a learning theory of distribution regression via a fully connected neural network (FNN). In contrast to the classical regression methods, the input variables of distribution…
In a recently published paper [1], it is shown that deep neural networks (DNNs) with random Gaussian weights preserve the metric structure of the data, with the property that the distance shrinks more when the angle between the two data…
This paper studies the problem of distributed weighted least-squares (WLS) estimation for an interconnected linear measurement network with additive noise. Two types of measurements are considered: self measurements for individual nodes,…
Biased sampling and missing data complicates statistical problems ranging from causal inference to reinforcement learning. We often correct for biased sampling of summary statistics with matching methods and importance weighting. In this…
An Undirected Weighted Network (UWN) is commonly found in big data-related applications. Note that such a network's information connected with its nodes, and edges can be expressed as a Symmetric, High-Dimensional and Incomplete (SHDI)…
Nearest neighbor is a popular class of classification methods with many desirable properties. For a large data set which cannot be loaded into the memory of a single machine due to computation, communication, privacy, or ownership…
Modern datasets are characterized by a large number of features that may conceal complex dependency structures. To deal with this type of data, dimensionality reduction techniques are essential. Numerous dimensionality reduction methods…
Deep neural networks (DNNs) enable innovative applications of machine learning like image recognition, machine translation, or malware detection. However, deep learning is often criticized for its lack of robustness in adversarial settings…
Graph neural networks (GNN) have recently emerged as a vehicle for applying deep network architectures to graph and relational data. However, given the increasing size of industrial datasets, in many practical situations the message passing…
We propose a new weighted average estimator for the high dimensional parameters under the distributed learning system, in which the weight assigned to each coordinate is precisely proportional to the inverse of the variance of the local…
$k$-nearest neighbour ($k$-NN) is one of the simplest and most widely-used methods for supervised classification, that predicts a query's label by taking weighted ratio of observed labels of $k$ objects nearest to the query. The weights and…
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).…
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…
Motivated by a wide variety of applications, ranging from stochastic optimization to dimension reduction through variable selection, the problem of estimating gradients accurately is of crucial importance in statistics and learning theory.…
Meta learning of optimal classifier error rates allows an experimenter to empirically estimate the intrinsic ability of any estimator to discriminate between two populations, circumventing the difficult problem of estimating the optimal…
Gaussian process ($GP$) regression is a widely used non-parametric modeling tool, but its cubic complexity in the training size limits its use on massive data sets. A practical remedy is to predict using only the nearest neighbours of each…
The k-nearest neighbors (kNN) algorithm is a cornerstone of non-parametric classification in artificial intelligence, yet its deployment in large-scale applications is persistently constrained by the computational trade-off between…
Nonparametric learning is a fundamental concept in machine learning that aims to capture complex patterns and relationships in data without making strong assumptions about the underlying data distribution. Owing to simplicity and…
Artificial Neural Networks (ANNs) can be viewed as nonlinear sieves that can approximate complex functions of high dimensional variables more effectively than linear sieves. We investigate the performance of various ANNs in nonparametric…