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Large language models (LLMs) have achieved remarkable performance but face critical challenges: hallucinations and high inference costs. Leveraging multiple experts offers a solution: deferring uncertain inputs to more capable experts…

We describe a complete method that learns a neural network which is guaranteed to overestimate a reference function on a given domain. The neural network can then be used as a surrogate for the reference function. The method involves two…

(Partial) ranking loss is a commonly used evaluation measure for multi-label classification, which is usually optimized with convex surrogates for computational efficiency. Prior theoretical work on multi-label ranking mainly focuses on…

Surrogate models are statistical or conceptual approximations for more complex simulation models. In this context, it is crucial to propagate the uncertainty induced by limited simulation budget and surrogate approximation error to…

Optimization in machine learning typically deals with the minimization of empirical objectives defined by training data. However, the ultimate goal of learning is to minimize the error on future data (test error), for which the training…

Classification is often the first problem described in introductory machine learning classes. Generalization guarantees of classification have historically been offered by Vapnik-Chervonenkis theory. Yet those guarantees are based on…

Invariance (defined in a general sense) has been one of the most effective priors for representation learning. Direct factorization of parametric models is feasible only for a small range of invariances, while regularization approaches,…

In this paper I propose a generative model of supervised learning that unifies two approaches to supervised learning, using a concept of a correct loss function. Addressing two measurability problems, which have been ignored in statistical…

The increasing penetration of renewable energy sources introduces significant uncertainty in power system operations, making traditional deterministic unit commitment approaches computationally expensive. This paper presents a machine…

Many real-world systems are modelled using complex ordinary differential equations (ODEs). However, the dimensionality of these systems can make them challenging to analyze. Dimensionality reduction techniques like Proper Orthogonal…

We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design…

PAC-Bayesian bounds have proven to be a valuable tool for deriving generalization bounds and for designing new learning algorithms in machine learning. However, it typically focus on providing generalization bounds with respect to a chosen…

Recent works in learning-integrated optimization have shown promise in settings where the optimization problem is only partially observed or where general-purpose optimizers perform poorly without expert tuning. By learning an optimizer…

We introduce a conditional pseudo-reversible normalizing flow for constructing surrogate models of a physical model polluted by additive noise to efficiently quantify forward and inverse uncertainty propagation. Existing surrogate modeling…

Inverse modeling for computing a high-dimensional spatially-varying property field from indirect sparse and noisy observations is a challenging problem. This is due to the complex physical system of interest often expressed in the form of…

The existing matrix completion methods focus on optimizing the relaxation of rank function such as nuclear norm, Schatten-p norm, etc. They usually need many iterations to converge. Moreover, only the low-rank property of matrices is…

Classical learning of the expectation values of observables for quantum states is a natural variant of learning quantum states or channels. While learning-theoretic frameworks establish the sample complexity and the number of measurement…

Recent advancements in Markov chain Monte Carlo (MCMC) sampling and surrogate modelling have significantly enhanced the feasibility of Bayesian analysis across engineering fields. However, the selection and integration of surrogate models…

Data-driven surrogate models offer quick approximations to complex numerical and experimental systems but typically lack uncertainty quantification, limiting their reliability in safety-critical applications. While Bayesian methods provide…

Surrogate regret bounds, also known as excess risk bounds, bridge the gap between the convergence rates of surrogate and target losses. The regret transfer is lossless if the surrogate regret bound is linear. While convex smooth surrogate…