Related papers: Exact Lower Bounds for the Agnostic Probably-Appro…
We propose an active-learning method for nonlinear minimax regression. Given a nonlinear function that can be arbitrarily evaluated over a compact set, we fit a surrogate model, such as a feedforward neural network, by minimizing the…
This paper establishes problem-specific sample complexity lower bounds for linear system identification problems. The sample complexity is defined in the PAC framework: it corresponds to the time it takes to identify the system parameters…
Probably Approximately Correct (PAC) bounds are widely used to derive probabilistic guarantees for the generalisation of machine learning models. They highlight the components of the model which contribute to its generalisation capacity.…
We study the high-dimensional asymptotics of empirical risk minimization (ERM) in over-parametrized two-layer neural networks with quadratic activations trained on synthetic data. We derive sharp asymptotics for both training and test…
In risk-sensitive learning, one aims to find a hypothesis that minimizes a risk-averse (or risk-seeking) measure of loss, instead of the standard expected loss. In this paper, we propose to study the generalization properties of…
Approximate model-predictive control (AMPC) aims to imitate an MPC's behavior with a neural network, removing the need to solve an expensive optimization problem at runtime. However, during deployment, the parameters of the underlying MPC…
In this article, we investigate certain asymptotic optimality properties of a very broad class of one-group continuous shrinkage priors for simultaneous estimation and testing of a sparse normal mean vector. Asymptotic optimality of Bayes…
An agnostic PAC learning algorithm finds a predictor that is competitive with the best predictor in a benchmark hypothesis class, where competitiveness is measured with respect to a given loss function. However, its predictions might be…
This paper presents an empirical study regarding training probabilistic neural networks using training objectives derived from PAC-Bayes bounds. In the context of probabilistic neural networks, the output of training is a probability…
We consider the problem of estimating the mean of a sequence of random elements $f(X_1, \theta)$ $, \ldots, $ $f(X_n, \theta)$ where $f$ is a fixed scalar function, $S=(X_1, \ldots, X_n)$ are independent random variables, and $\theta$ is a…
Missing values arise in most real-world data sets due to the aggregation of multiple sources and intrinsically missing information (sensor failure, unanswered questions in surveys...). In fact, the very nature of missing values usually…
The goal of a learning algorithm is to receive a training data set as input and provide a hypothesis that can generalize to all possible data points from a domain set. The hypothesis is chosen from hypothesis classes with potentially…
We propose a novel method for closed-form predictive distribution modeling with neural nets. In quantifying prediction uncertainty, we build on Evidential Deep Learning, which has been impactful as being both simple to implement and giving…
Currently, machine learning plays an important role in the lives and individual activities of numerous people. Accordingly, it has become necessary to design machine learning algorithms to ensure that discrimination, biased views, or unfair…
We develop minimax optimal risk bounds for the general learning task consisting in predicting as well as the best function in a reference set G up to the smallest possible additive term, called the convergence rate. When the reference set…
An important challenge facing modern machine learning is how to rigorously quantify the uncertainty of model predictions. Conveying uncertainty is especially important when there are changes to the underlying data distribution that might…
A general lower bound is developed for the minimax risk when estimating an arbitrary functional. The bound is based on testing two composite hypotheses and is shown to be effective in estimating the nonsmooth functional…
Recent advances in the binary classification setting by Hanneke [2016b] and Larsen [2023] have resulted in optimal PAC learners. These learners leverage, respectively, a clever deterministic subsampling scheme and the classic heuristic of…
Recently, there has been a significant focus on exploring the theoretical aspects of deep learning, especially regarding its performance in classification tasks. Bayesian deep learning has emerged as a unified probabilistic framework,…
In statistical learning theory, determining the sample complexity of realizable binary classification for VC classes was a long-standing open problem. The results of Simon and Hanneke established sharp upper bounds in this setting. However,…