Related papers: Classification with High-Dimensional Sparse Sample…

The fundamental theorem of statistical learning states that for binary classification problems, any Empirical Risk Minimization (ERM) learning rule has close to optimal sample complexity. In this paper we seek for a generic optimal learner…

We consider selection of random predictors for high-dimensional regression problem with binary response for a general loss function. Important special case is when the binary model is semiparametric and the response function is misspecified…

In supervised learning, we often face with ambiguous (A) samples that are difficult to label even by domain experts. In this paper, we consider a binary classification problem in the presence of such A samples. This problem is substantially…

Let $p$ be an unknown and arbitrary probability distribution over $[0,1)$. We consider the problem of {\em density estimation}, in which a learning algorithm is given i.i.d. draws from $p$ and must (with high probability) output a…

We study the performance of machine learning binary classification techniques in terms of error probabilities. The statistical test is based on the Data-Driven Decision Function (D3F), learned in the training phase, i.e., what is…

Sparse linear discriminant analysis via penalized optimal scoring is a successful tool for classification in high-dimensional settings. While the variable selection consistency of sparse optimal scoring has been established, the…

Most existing binary classification methods target on the optimization of the overall classification risk and may fail to serve some real-world applications such as cancer diagnosis, where users are more concerned with the risk of…

We consider high-dimensional multiclass classification by sparse multinomial logistic regression. Unlike binary classification, in the multiclass setup one can think about an entire spectrum of possible notions of sparsity associated with…

The statistics and machine learning communities have recently seen a growing interest in classification-based approaches to two-sample testing. The outcome of a classification-based two-sample test remains a rejection decision, which is not…

We consider the problem of identifying, from its first $m$ noisy moments, a probability distribution on $[0,1]$ of support $k<\infty$. This is equivalent to the problem of learning a distribution on $m$ observable binary random variables…

We consider two independent binary i.i.d. random strings $X$ and $Y$ of equal length $n$ and the optimal alignments according to a symmetric scoring functions only. We decompose the space of scoring functions into five components. Two of…

We consider pairs of finite-length individual sequences that are realizations of unknown, finite alphabet, stationary sources in a clas M of sources with vanishing memory (e.g. stationary Markov sources). The task of a universal classifier…

One of the central problems in the classification of individual test sequences (e.g. genetic analysis), is that of checking for the similarity of sample test sequences as compared with a set of much longer training sequences. This is done…

Many binary classification problems minimize misclassification above (or below) a threshold. We show that instances of ranking problems, accuracy at the top or hypothesis testing may be written in this form. We propose a general framework…

A common approach to statistical learning with big-data is to randomly split it among $m$ machines and learn the parameter of interest by averaging the $m$ individual estimates. In this paper, focusing on empirical risk minimization, or…

When data analysts train a classifier and check if its accuracy is significantly different from chance, they are implicitly performing a two-sample test. We investigate the statistical properties of this flexible approach in the…

The objective of the paper is to study accuracy of multi-class classification in high-dimensional setting, where the number of classes is also large ("large $L$, large $p$, small $n$" model). While this problem arises in many practical…

We study distribution testing without direct access to a source of relevant data, but rather to one where only a tiny fraction is relevant. To enable this, we introduce the following verification query model. The goal is to perform a…

We consider the problem of fitting the parameters of a high-dimensional linear regression model. In the regime where the number of parameters $p$ is comparable to or exceeds the sample size $n$, a successful approach uses an…

When the competing classes in a classification problem are not of comparable size, many popular classifiers exhibit a bias towards larger classes, and the nearest neighbor classifier is no exception. To take care of this problem, we develop…