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We present a framework for the theoretical analysis of ensembles of low-complexity empirical risk minimisers trained on independent random compressions of high-dimensional data. First we introduce a general distribution-dependent…
The minimax risk is often considered as a gold standard against which we can compare specific statistical procedures. Nevertheless, as has been observed recently in robust and heavy-tailed estimation problems, the inherent reduction of the…
A widely recognized difficulty in federated learning arises from the statistical heterogeneity among clients: local datasets often originate from distinct yet not entirely unrelated probability distributions, and personalization is,…
We study a localized notion of uniform convergence known as an "optimistic rate" (Panchenko 2002; Srebro et al. 2010) for linear regression with Gaussian data. Our refined analysis avoids the hidden constant and logarithmic factor in…
This paper investigates robust versions of the general empirical risk minimization algorithm, one of the core techniques underlying modern statistical methods. Success of the empirical risk minimization is based on the fact that for a…
Population risk is always of primary interest in machine learning; however, learning algorithms only have access to the empirical risk. Even for applications with nonconvex nonsmooth losses (such as modern deep networks), the population…
Machine learning algorithms in high-dimensional settings are highly susceptible to the influence of even a small fraction of structured outliers, making robust optimization techniques essential. In particular, within the…
We study the problem of learning classification functions from noiseless training samples, under the assumption that the decision boundary is of a certain regularity. We establish universal lower bounds for this estimation problem, for…
We investigate the problem of minimizing the excess generalization error with respect to the best expert prediction in a finite family in the stochastic setting, under limited access to information. We assume that the learner only has…
We study the sequential general online regression, known also as the sequential probability assignments, under logarithmic loss when compared against a broad class of experts. We focus on obtaining tight, often matching, lower and upper…
In analyses with severe data-limitations, augmenting the target dataset with information from ancillary datasets in the application domain, called source datasets, can lead to significantly improved statistical procedures. However, existing…
We develop a general framework for estimating function-valued parameters under equality or inequality constraints in infinite-dimensional statistical models. Such constrained learning problems are common across many areas of statistics and…
We propose a lower bound on the log marginal likelihood of Gaussian process regression models that can be computed without matrix factorisation of the full kernel matrix. We show that approximate maximum likelihood learning of model…
Supervised learning typically optimizes the expected value risk functional of the loss, but in many cases, we want to optimize for other risk functionals. In full-batch gradient descent, this is done by taking gradients of a risk functional…
This paper studies the problem of learning an unknown function $f$ from given data about $f$. The learning problem is to give an approximation $\hat f$ to $f$ that predicts the values of $f$ away from the data. There are numerous settings…
We extend the notion of minimax fairness in supervised learning problems to its natural conclusion: lexicographic minimax fairness (or lexifairness for short). Informally, given a collection of demographic groups of interest, minimax…
We propose a general approach for supervised learning with structured output spaces, such as combinatorial and polyhedral sets, that is based on minimizing estimated conditional risk functions. Given a loss function defined over pairs of…
In the field of reinforcement learning there has been recent progress towards safety and high-confidence bounds on policy performance. However, to our knowledge, no practical methods exist for determining high-confidence policy performance…
In large-scale learning algorithms, the momentum term is usually included in the stochastic sub-gradient method to improve the learning speed because it can navigate ravines efficiently to reach a local minimum. However, step-size and…
This paper surveys recent developments at the intersection of operator learning, statistical learning theory, and approximation theory. First, it reviews error bounds for empirical risk minimization with a focus on holomorphic operators and…