Related papers: Misclassification excess risk bounds for 1-bit mat…

Risk bounds for Classification and Regression Trees (CART, Breiman et. al. 1984) classifiers are obtained under a margin condition in the binary supervised classification framework. These risk bounds are obtained conditionally on the…

The vast majority of statistical theory on binary classification characterizes performance in terms of accuracy. However, accuracy is known in many cases to poorly reflect the practical consequences of classification error, most famously in…

A primary concern of excessive reuse of test datasets in machine learning is that it can lead to overfitting. Multiclass classification was recently shown to be more resistant to overfitting than binary classification. In an open problem of…

On the heels of compressed sensing, a remarkable new field has very recently emerged. This field addresses a broad range of problems of significant practical interest, namely, the recovery of a data matrix from what appears to be…

We study the problem of the identification of m arms with largest means under a fixed error rate $\delta$ (fixed-confidence Top-m identification), for misspecified linear bandit models. This problem is motivated by practical applications,…

In this paper, we consider the problem of binary classification with a class of general deep convolutional neural networks, which includes fully-connected neural networks and fully convolutional neural networks as special cases. We…

The problem of predicting unobserved entries in a binary matrix, known as 1-bit matrix completion, has found diverse applications in fields such as recommendation systems. In this study, we develop an empirical Bayes method for 1-bit matrix…

We study the completion of approximately low rank matrices with entries missing not at random (MNAR). In the context of typical large-dimensional statistical settings, we establish a framework for the performance analysis of the nuclear…

Matrix completion focuses on recovering missing or incomplete information in matrices. This problem arises in various applications, including image processing and network analysis. Previous research proposed Poisson matrix completion for…

Always-valid concentration inequalities are increasingly used as performance measures for online statistical learning, notably in the learning of generative models and supervised learning. Such inequality advances the online learning…

In this work, we consider the matrix completion problem, where the objective is to reconstruct a low-rank matrix from a few observed entries. A commonly employed approach involves nuclear norm minimization. For this method to succeed, the…

PAC-Bayesian bounds have proven to be a valuable tool for deriving generalization bounds and for designing new learning algorithms in machine learning. However, it typically focus on providing generalization bounds with respect to a chosen…

This paper considers the problem of matrix completion when some number of the columns are completely and arbitrarily corrupted, potentially by a malicious adversary. It is well-known that standard algorithms for matrix completion can return…

We consider a general statistical learning problem where an unknown fraction of the training data is corrupted. We develop a robust learning method that only requires specifying an upper bound on the corrupted data fraction. The method…

The forecasting of credit default risk has been an active research field for several decades. Historically, logistic regression has been used as a major tool due to its compliance with regulatory requirements: transparency, explainability,…

In massive data analysis, training and testing data often come from very different sources, and their probability distributions are not necessarily identical. A feature example is nonparametric classification in posterior drift model where…

Many classification applications require accurate probability estimates in addition to good class separation but often classifiers are designed focusing only on the latter. Calibration is the process of improving probability estimates by…

We consider a high dimensional binary classification problem and construct a classification procedure by minimizing the empirical misclassification risk with a penalty on the number of selected features. We derive non-asymptotic probability…

The literature on "benign overfitting" in overparameterized models has been mostly restricted to regression or binary classification; however, modern machine learning operates in the multiclass setting. Motivated by this discrepancy, we…

This article studies the achievable guarantees on the error rates of certain learning algorithms, with particular focus on refining logarithmic factors. Many of the results are based on a general technique for obtaining bounds on the error…