Related papers: Statistical Learning Theory of Quasi-Regular Cases

Symmetry is a cornerstone of much of mathematics, and many probability distributions possess symmetries characterized by their invariance to a collection of group actions. Thus, many mathematical and statistical methods rely on such…

Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of…

Pattern recognition is a central topic in Learning Theory with numerous applications such as voice and text recognition, image analysis, computer diagnosis. The statistical set-up in classification is the following: we are given an i.i.d.…

Mixed effects regression models are widely used by language researchers. However, these regressions are implemented with an algorithm which may not converge on a solution. While convergence issues in linear mixed effects models can often be…

Variational methods for parameter estimation are an active research area, potentially offering computationally tractable heuristics with theoretical performance bounds. We build on recent work that applies such methods to network data, and…

Building invariance to non-meaningful transformations is essential to building efficient and generalizable machine learning models. In practice, the most common way to learn invariance is through data augmentation. There has been recent…

We consider the problem of learning a non-deterministic probabilistic system consistent with a given finite set of positive and negative tree samples. Consistency is defined with respect to strong simulation conformance. We propose learning…

The distribution regression problem encompasses many important statistics and machine learning tasks, and arises in a large range of applications. Among various existing approaches to tackle this problem, kernel methods have become a method…

When we use the normal mixture model, the optimal number of the components describing the data should be determined. Testing homogeneity is good for this purpose; however, to construct its theory is challenging, since the test statistic…

In this paper, we consider mixtures of multinomial logistic models (MNL), which are known to $\epsilon$-approximate any random utility model. Despite its long history and broad use, rigorous results are only available for learning a uniform…

Symmetry is one of the most central concepts in physics, and it is no surprise that it has also been widely adopted as an inductive bias for machine-learning models applied to the physical sciences. This is especially true for models…

The Restricted Boltzmann Machine (RBM), an important tool used in machine learning in particular for unsupervized learning tasks, is investigated from the perspective of its spectral properties. Starting from empirical observations, we…

A finite point process is characterized by the distribution of the number of points (the size) of the process. In some applications, for example, in the context of packet flows in modern communication networks, it is of interest to infer…

A significant obstacle in the development of robust machine learning models is covariate shift, a form of distribution shift that occurs when the input distributions of the training and test sets differ while the conditional label…

We directly combine ideas of the quasiclassical approximation with random matrix theory and apply them to the study of the spectrum, in particular to the two-level correlator. Bogomolny's transfer operator T, quasiclassically an NxN unitary…

Errors of approximations of the quasi-stationary distribution (the QSD) of the logistic SIS model are evaluated numerically. The results are used to derive asymptotic approximations of the approximation errors for large populations. We show…

Domain generalization is the problem of machine learning when the training data and the test data come from different data domains. We present a simple theoretical model of learning to generalize across domains in which there is a…

In this paper, a mathematical theory of learning is proposed that has many parallels with information theory. We consider Vapnik's General Setting of Learning in which the learning process is defined to be the act of selecting a hypothesis…

It has been demonstrated earlier that universal computation is 'almost surely' chaotic. Machine learning is a form of computational fixed point iteration, iterating over the computable function space. We showcase some properties of this…

Typical neural network trainings have substantial variance in test-set performance between repeated runs, impeding hyperparameter comparison and training reproducibility. In this work we present the following results towards understanding…