Related papers: Statistical Hypothesis Testing Based on Machine Le…
Consider a setting with $N$ independent individuals, each with an unknown parameter, $p_i \in [0, 1]$ drawn from some unknown distribution $P^\star$. After observing the outcomes of $t$ independent Bernoulli trials, i.e., $X_i \sim…
The general approach taken when training deep learning classifiers is to save the parameters after every few iterations, train until either a human observer or a simple metric-based heuristic decides the network isn't learning anymore, and…
Neural Networks are being integrated into safety critical systems, e.g., perception systems for autonomous vehicles, which require trained networks to perform safely in novel scenarios. It is challenging to verify neural networks because…
This paper considers maximum likelihood (ML) estimation in a large class of models with hidden Markov regimes. We investigate consistency of the ML estimator and local asymptotic normality for the models under general conditions which allow…
Statistical inverse learning aims at recovering an unknown function $f$ from randomly scattered and possibly noisy point evaluations of another function $g$, connected to $f$ via an ill-posed mathematical model. In this paper we blend…
Large language models (LLMs) are a type of machine learning tool that economists have started to apply in their empirical research. One such application is macroeconomic forecasting with backtesting of LLMs, even though they are trained on…
In this article we quantify almost sure martingale convergence theorems in terms of the tradeoff between asymptotic almost sure rates of convergence (error tolerance) and the respective modulus of convergence. For this purpose we generalize…
The rapid recent progress in machine learning (ML) has raised a number of scientific questions that challenge the longstanding dogma of the field. One of the most important riddles is the good empirical generalization of overparameterized…
When estimating a proportion and only a sample of triplets is given, dependencies within the triplets are to be accounted for. Without assuming a distribution for the success count of the triplet, together with the proportion, as second and…
Deep learning models require a large amount of data to perform well. When data is scarce for a target task, we can transfer the knowledge gained by training on similar tasks to quickly learn the target. A successful approach is…
The last decade has seen blossoming research in deep learning theory attempting to answer, "Why does deep learning generalize?" A powerful shift in perspective precipitated this progress: the study of overparametrized models in the…
Given observations from a stationary time series, permutation tests allow one to construct exactly level $\alpha$ tests under the null hypothesis of an i.i.d. (or, more generally, exchangeable) distribution. On the other hand, when the null…
This paper investigates the asymptotic behavior of the soft-margin and hard-margin support vector machine (SVM) classifiers for simultaneously high-dimensional and numerous data (large $n$ and large $p$ with $n/p\to\delta$) drawn from a…
Hypothesis testing in high dimensional data is a notoriously difficult problem without direct access to competing models' likelihood functions. This paper argues that statistical divergences can be used to quantify the difference between…
Machine learning models are increasingly used in practice. However, many machine learning methods are sensitive to test or operational data that is dissimilar to training data. Out-of-distribution (OOD) data is known to increase the…
Continual learning (CL), which aims to learn a sequence of tasks, has attracted significant recent attention. However, most work has focused on the experimental performance of CL, and theoretical studies of CL are still limited. In…
Deep Metric Learning (DML) learns a non-linear semantic embedding from input data that brings similar pairs together while keeping dissimilar data away from each other. To this end, many different methods are proposed in the last decade…
Machine learning software, deep neural networks (DNN) software in particular, discerns valuable information from a large dataset, a set of data. Outcomes of such DNN programs are dependent on the quality of both learning programs and…
Machine learning (ML) formalizes the problem of getting computers to learn from experience as optimization of performance according to some metric(s) on a set of data examples. This is in contrast to requiring behaviour specified in advance…
Machine Learning (ML) is an expressive framework for turning data into computer programs. Across many problem domains -- both in industry and policy settings -- the types of computer programs needed for accurate prediction or optimal…