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Self-Supervised Learning (SSL) is crucial for real-world applications, especially in data-hungry domains such as healthcare and self-driving cars. In addition to a lack of labeled data, these applications also suffer from distributional…
The increasing adoption of Artificial Intelligence (AI) in engineering problems calls for the development of calibration methods capable of offering robust statistical reliability guarantees. The calibration of black box AI models is…
Statistical learning theory provides bounds on the necessary number of training samples needed to reach a prescribed accuracy in a learning problem formulated over a given target class. This accuracy is typically measured in terms of a…
We present a distributional approach to theoretical analyses of reinforcement learning algorithms for constant step-sizes. We demonstrate its effectiveness by presenting simple and unified proofs of convergence for a variety of…
We study the problem of estimating, in the sense of optimal transport metrics, a measure which is assumed supported on a manifold embedded in a Hilbert space. By establishing a precise connection between optimal transport metrics, optimal…
In this work, we study the asymptotic randomness of an algorithmic estimator of the saddle point of a globally convex-concave and locally strongly-convex strongly-concave objective. Specifically, we show that the averaged iterates of a…
Many machine learning approaches are characterized by information constraints on how they interact with the training data. These include memory and sequential access constraints (e.g. fast first-order methods to solve stochastic…
Semi-supervised learning (SSL) constructs classifiers from datasets in which only a subset of observations is labelled, a situation that naturally arises because obtaining labels often requires expert judgement or costly manual effort. This…
A crucial assumption underlying the most current theory of machine learning is that the training distribution is identical to the test distribution. However, this assumption may not hold in some real-world applications. In this paper, we…
Recent works have proposed various explanations for the ability of modern large language models (LLMs) to perform in-context prediction. We propose an alternative conceptual viewpoint from an information-geometric and statistical…
Spiking Neural Networks (SNNs) offer a novel computational paradigm that captures some of the efficiency of biological brains by processing through binary neural dynamic activations. Probabilistic SNN models are typically trained to…
Machine learning typically presupposes classical probability theory which implies that aggregation is built upon expectation. There are now multiple reasons to motivate looking at richer alternatives to classical probability theory as a…
Risk prediction models are widely used to guide real-world decision-making in areas such as healthcare and economics, and they also play a key role in estimating nuisance parameters in semiparametric inference. The super learner is a…
This paper deals with a class of neural SDEs and studies the limiting behavior of the associated sampled optimal control problems as the sample size grows to infinity. The neural SDEs with $N$ samples can be linked to the $N$-particle…
The aim of this paper is to provide several novel upper bounds on the excess risk with a primal focus on classification problems. We suggest two approaches and the obtained bounds are represented via the distribution dependent local…
For a given distribution, learning algorithm, and performance metric, the rate of convergence (or data-scaling law) is the asymptotic behavior of the algorithm's test performance as a function of number of train samples. Many learning…
We present an algorithm for the statistical learning setting with a bounded exp-concave loss in $d$ dimensions that obtains excess risk $O(d \log(1/\delta)/n)$ with probability at least $1 - \delta$. The core technique is to boost the…
We develop, discuss, and compare several inference techniques to constrain theory parameters in collider experiments. By harnessing the latent-space structure of particle physics processes, we extract extra information from the simulator.…
A fundamental tool in network information theory is the covering lemma, which lower bounds the probability that there exists a pair of random variables, among a give number of independently generated candidates, falling within a given set.…
We develop a new theoretical framework to analyze the generalization error of deep learning, and derive a new fast learning rate for two representative algorithms: empirical risk minimization and Bayesian deep learning. The series of…