Related papers: Local nearest neighbour classification with applic…
We study the effect of imperfect training data labels on the performance of classification methods. In a general setting, where the probability that an observation in the training dataset is mislabelled may depend on both the feature vector…
We derive the probability that a randomly chosen NL-node over $S$ gets localized as a function of a variety of parameters. Then, we derive the probability that the whole network of NL-nodes over $S$ gets localized. In connection with the…
Learning a good distance metric in feature space potentially improves the performance of the KNN classifier and is useful in many real-world applications. Many metric learning algorithms are however based on the point estimation of a…
The practical success of deep learning has led to the discovery of several surprising phenomena. One of these phenomena, that has spurred intense theoretical research, is ``benign overfitting'': deep neural networks seem to generalize well…
Multi-class classification with a very large number of classes, or extreme classification, is a challenging problem from both statistical and computational perspectives. Most of the classical approaches to multi-class classification,…
This article considers a semi-supervised classification setting on a Gaussian mixture model, where the data is not labeled strictly as usual, but instead with uncertain labels. Our main aim is to compute the Bayes risk for this model. We…
We consider the classical problem of learning, with arbitrary accuracy, the natural parameters of a $k$-parameter truncated \textit{minimal} exponential family from i.i.d. samples in a computationally and statistically efficient manner. We…
Estimating expected polynomials of density functions from samples is a basic problem with numerous applications in statistics and information theory. Although kernel density estimators are widely used in practice for such functional…
We revisit the framework of Smart PAC learning, which seeks supervised learners which compete with semi-supervised learners that are provided full knowledge of the marginal distribution on unlabeled data. Prior work has shown that such…
Despite the wide use of $k$-Nearest Neighbors as classification models, their explainability properties remain poorly understood from a theoretical perspective. While nearest neighbors classifiers offer interpretability from a ``data…
This paper describes a new form of unsupervised learning, whose input is a set of unlabeled points that are assumed to be local maxima of an unknown value function v in an unknown subset of the vector space. Two functions are learned: (i) a…
Minimax problems have achieved success in machine learning such as adversarial training, robust optimization, reinforcement learning. For theoretical analysis, current optimal excess risk bounds, which are composed by generalization error…
Bayesian optimization has attracted huge attention from diverse research areas in science and engineering, since it is capable of efficiently finding a global optimum of an expensive-to-evaluate black-box function. In general, a…
In the panoply of pattern classification techniques, few enjoy the intuitive appeal and simplicity of the nearest neighbor rule: given a set of samples in some metric domain space whose value under some function is known, we estimate the…
Motivated by social network analysis and network-based recommendation systems, we study a semi-supervised community detection problem in which the objective is to estimate the community label of a new node using the network topology and…
We propose a theoretical framework to analyze semi-supervised classification under the low density separation assumption in a high-dimensional regime. In particular, we introduce QLDS, a linear classification model, where the low density…
Clustered sampling is prevalent in empirical regression discontinuity (RD) designs, but it has not received much attention in the theoretical literature. In this paper, we introduce a general model-based framework for such settings and…
There is a large body of work on convergence rates either in passive or active learning. Here we outline some of the results that have been obtained, more specifically in a nonparametric setting under assumptions about the smoothness and…
Universal anomaly detection still remains a challenging problem in machine learning and medical image analysis. It is possible to learn an expected distribution from a single class of normative samples, e.g., through epistemic uncertainty…
Classifiers built with neural networks handle large-scale high dimensional data, such as facial images from computer vision, extremely well while traditional statistical methods often fail miserably. In this paper, we attempt to understand…