Related papers: Statistical Learning Theory: Models, Concepts, and…

Machine learning (ML) has emerged as a powerful tool for tackling complex regression and classification tasks, yet its success often hinges on the quality of training data. This study introduces an ML paradigm inspired by domain knowledge…

Although principles of neuroscience like reinforcement learning, visual perception and attention have been applied in machine learning models, there is a huge gap between machine learning and mammalian learning. Based on the advances in…

Learning representations of data is an important problem in statistics and machine learning. While the origin of learning representations can be traced back to factor analysis and multidimensional scaling in statistics, it has become a…

Transfer learning, also referred as knowledge transfer, aims at reusing knowledge from a source dataset to a similar target one. While many empirical studies illustrate the benefits of transfer learning, few theoretical results are…

This article serves as an introduction to the study of networks of social systems. First, we introduce the reader to key mathematical tools to study social networks, including mathematical representations of networks and essential…

These notes gather recent results on robust statistical learning theory. The goal is to stress the main principles underlying the construction and theoretical analysis of these estimators rather than provide an exhaustive account on this…

Statistical learning theory provides the foundation to applied machine learning, and its various successful applications in computer vision, natural language processing and other scientific domains. The theory, however, does not take into…

Supervised machine learning and predictive models have achieved an impressive standard today, enabling us to answer questions that were inconceivable a few years ago. Besides these successes, it becomes clear, that beyond pure prediction,…

This textbook provides a systematic treatment of statistical machine learning for astronomical research through the lens of Bayesian inference, developing a unified framework that reveals connections between modern data analysis techniques…

The progress of machine learning over the past decade is undeniable. In retrospect, it is both remarkable and unsettling that this progress was achievable with little to no rigorous theory to guide experimentation. Despite this fact,…

We survey current developments in the approximation theory of sequence modelling in machine learning. Particular emphasis is placed on classifying existing results for various model architectures through the lens of classical approximation…

Based on limited observations, machine learning discerns a dependence which is expected to hold in the future. What makes it possible? Statistical learning theory imagines indefinitely increasing training sample to justify its approach. In…

Statistical learning theory under independent and identically distributed (iid) sampling and online learning theory for worst case individual sequences are two of the best developed branches of learning theory. Statistical learning under…

Latent space models are powerful statistical tools for modeling and understanding network data. While the importance of accounting for uncertainty in network analysis has been well recognized, the current literature predominantly focuses on…

Several authors, including the American Statistician (ASA), have noted the challenges facing statisticians when attacking large, complex, unstructured problems, as opposed to well-defined textbook problems. Clearly, the standard paradigm of…

In the era of big data, analysts usually explore various statistical models or machine learning methods for observed data in order to facilitate scientific discoveries or gain predictive power. Whatever data and fitting procedures are…

Predictive inference is a fundamental task in statistics, traditionally addressed using parametric assumptions about the data distribution and detailed analyses of how models learn from data. In recent years, conformal prediction has…

This paper introduces a novel measure-theoretic theory for machine learning that does not require statistical assumptions. Based on this theory, a new regularization method in deep learning is derived and shown to outperform previous…

We present a simple theoretical framework, and corresponding practical procedures, for comparing probabilistic models on real data in a traditional machine learning setting. This framework is based on the theory of proper scoring rules, but…

In this article, we review the literature on statistical theories of neural networks from three perspectives: approximation, training dynamics and generative models. In the first part, results on excess risks for neural networks are…