Related papers: Statistical Hypothesis Testing Based on Machine Le…

Distance metric learning (DML) is to learn the embeddings where examples from the same class are closer than examples from different classes. It can be cast as an optimization problem with triplet constraints. Due to the vast number of…

Deep learning algorithms have been applied very successfully in recent years to a range of problems out of reach for classical solution paradigms. Nevertheless, there is no completely rigorous mathematical error and convergence analysis…

Selective classification techniques (also known as reject option) have not yet been considered in the context of deep neural networks (DNNs). These techniques can potentially significantly improve DNNs prediction performance by trading-off…

Deep metric learning (DML) aims to minimize empirical expected loss of the pairwise intra-/inter- class proximity violations in the embedding space. We relate DML to feasibility problem of finite chance constraints. We show that minimizer…

We study the behavior of error bounds for multiclass classification under suitable margin conditions. For a wide variety of methods we prove that the classification error under a hard-margin condition decreases exponentially fast without…

Machine learning algorithms have grown in sophistication over the years and are increasingly deployed for real-life applications. However, when using machine learning techniques in practical settings, particularly in high-risk applications…

Machine learning is transforming materials discovery by providing rapid predictions of material properties, which enables large-scale screening for target materials. However, such models require training data. While automated data…

Large-margin classifiers are popular methods for classification. We derive the asymptotic expression for the generalization error of a family of large-margin classifiers in the limit of both sample size $n$ and dimension $p$ going to…

The mainstream AI community has seen a rise in large-scale open-source classifiers, often pre-trained on vast datasets and tested on standard benchmarks; however, users facing diverse needs and limited, expensive test data may be…

Deep neural network training often involves stochastic optimization, meaning each run will produce a different model. This implies that hyperparameters of the training process, such as the random seed itself, can potentially have…

In this work, we explore the theoretical properties of conditional deep generative models under the statistical framework of distribution regression where the response variable lies in a high-dimensional ambient space but concentrates…

In this work, we study statistical learning with dependent ($\beta$-mixing) data and square loss in a hypothesis class $\mathscr{F}\subset L_{\Psi_p}$ where $\Psi_p$ is the norm $\|f\|_{\Psi_p} \triangleq \sup_{m\geq 1} m^{-1/p} \|f\|_{L^m}…

This paper studies the generalization performance of multi-class classification algorithms, for which we obtain, for the first time, a data-dependent generalization error bound with a logarithmic dependence on the class size, substantially…

We show that for unconstrained Deep Linear Discriminant Analysis (LDA) classifiers, maximum-likelihood training admits pathological solutions in which class means drift together, covariances collapse, and the learned representation becomes…

The main question is: why and how can we ever predict based on a finite sample? The question is not answered by statistical learning theory. Here, I suggest that prediction requires belief in "predictability" of the underlying dependence,…

Machine learning is vital in high-stakes domains, yet conventional validation methods rely on averaging metrics like mean squared error (MSE) or mean absolute error (MAE), which fail to quantify extreme errors. Worst-case prediction…

In this letter, we consider multiple statistical classification problem where a sequence of n independent and identically distributed observations, that are generated by one of M discrete sources, need to be classified. The source…

Machine learning models can make critical errors that are easily hidden within vast amounts of data. Such errors often run counter to rules based on human intuition. However, rules based on human knowledge are challenging to scale or to…

We derive an (almost) guaranteed upper bound on the error of deep neural networks under distribution shift using unlabeled test data. Prior methods either give bounds that are vacuous in practice or give estimates that are accurate on…

As big data continues to grow, statistical inference for multivariate functional data (MFD) has become crucial. Although recent advancements have been made in testing the equality of mean functions, research on testing linear hypotheses for…