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The notion of metric plays a key role in machine learning problems such as classification, clustering or ranking. However, it is worth noting that there is a severe lack of theoretical guarantees that can be expected on the generalization…

Empirical analysis serves as an important complement to theoretical analysis for studying practical Bayesian optimization. Often empirical insights expose strengths and weaknesses inaccessible to theoretical analysis. We define two metrics…

We study consistency of learning algorithms for a multi-class performance metric that is a non-decomposable function of the confusion matrix of a classifier and cannot be expressed as a sum of losses on individual data points; examples of…

A variety of different performance metrics are commonly used in the machine learning literature for the evaluation of classification systems. Some of the most common ones for measuring quality of hard decisions are standard and balanced…

The ultimate goal of a supervised learning algorithm is to produce models constructed on the training data that can generalize well to new examples. In classification, functional margin maximization -- correctly classifying as many training…

We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on…

One of the most critical issues in machine learning is the selection of appropriate hyper parameters for training models. Machine learning models may be able to reach the best training performance and may increase the ability to generalize…

This paper proposes several novel optimization algorithms for minimizing a nonlinear objective function. The algorithms are enlightened by the optimal state trajectory of an optimal control problem closely related to the minimized objective…

Parameter-free stochastic optimization aims to design algorithms that are agnostic to the underlying problem parameters while still achieving convergence rates competitive with optimally tuned methods. While some parameter-free methods do…

Bayesian Optimization (BO) has shown great promise for the global optimization of functions that are expensive to evaluate, but despite many successes, standard approaches can struggle in high dimensions. To improve the performance of BO,…

Model explainability is crucial for human users to be able to interpret how a proposed classifier assigns labels to data based on its feature values. We study generalized linear models constructed using sets of feature value rules, which…

This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…

In this paper, we propose a metric on the space of finite sets of trajectories for assessing multi-target tracking algorithms in a mathematically sound way. The main use of the metric is to compare estimates of trajectories from different…

Recently there has been sustained interest in modifying prediction algorithms to satisfy fairness constraints. These constraints are typically complex nonlinear functionals of the observed data distribution. Focusing on the path-specific…

Machine learning models are increasingly used in critical decision-making applications. However, these models are susceptible to replicating or even amplifying bias present in real-world data. While there are various bias mitigation methods…

Majorization-minimization algorithms consist of iteratively minimizing a majorizing surrogate of an objective function. Because of its simplicity and its wide applicability, this principle has been very popular in statistics and in signal…

We use the PAC-Bayesian theory for the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-Bayesian bounds) and explicit…

A general Bayesian framework for model selection on random network models regarding their features is considered. The goal is to develop a principle Bayesian model selection approach to compare different fittable, not necessarily nested,…

Realizing high-throughput aberration-corrected Scanning Transmission Electron Microscopy (STEM) exploration of atomic structures requires rapid tuning of multipole probe correctors while compensating for the inevitable drift of the optical…

Bayesian optimisation (BO) algorithms have shown remarkable success in applications involving expensive black-box functions. Traditionally BO has been set as a sequential decision-making process which estimates the utility of query points…