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Markov decision processes (MDPs) are a well studied framework for solving sequential decision making problems under uncertainty. Exact methods for solving MDPs based on dynamic programming such as policy iteration and value iteration are…

A first proposal of a sparse and cellwise robust PCA method is presented. Robustness to single outlying cells in the data matrix is achieved by substituting the squared loss function for the approximation error by a robust version. The…

Every day, we experience the effects of the global warming: extreme weather events, major forest fires, storms, global warming, etc.The scientific community acknowledges that this crisis is a consequence of human activities where…

All machine learning algorithms use a loss, cost, utility or reward function to encode the learning objective and oversee the learning process. This function that supervises learning is a frequently unrecognized hyperparameter that…

The top-k classification accuracy is one of the core metrics in machine learning. Here, k is conventionally a positive integer, such as 1 or 5, leading to top-1 or top-5 training objectives. In this work, we relax this assumption and…

The Extreme Learning Machine (ELM) is a growing statistical technique widely applied to regression problems. In essence, ELMs are single-layer neural networks where the hidden layer weights are randomly sampled from a specific distribution,…

In artificial neural networks, learning from data is a computationally demanding task in which a large number of connection weights are iteratively tuned through stochastic-gradient-based heuristic processes over a cost-function. It is not…

Conformal prediction has shown spurring performance in constructing statistically rigorous prediction sets for arbitrary black-box machine learning models, assuming the data is exchangeable. However, even small adversarial perturbations…

The random matrix ensembles (RME) of quantum statistical Hamiltonian operators, e.g. Gaussian random matrix ensembles (GRME) and Ginibre random matrix ensembles (Ginibre RME), are applied to following quantum statistical systems: nuclear…

Quantum machine learning is a rapidly evolving field of research that could facilitate important applications for quantum computing and also significantly impact data-driven sciences. In our work, based on various arguments from complexity…

Information theory provides principled ways to analyze different inference and learning problems such as hypothesis testing, clustering, dimensionality reduction, classification, among others. However, the use of information theoretic…

Although large language models (LLMs) perform well in general tasks, domain-specific applications suffer from hallucinations and accuracy limitations. Continual Pre-Training (CPT) approaches encounter two key issues: (1) domain-biased data…

This paper characterizes the maximum mean discrepancies (MMD) that metrize the weak convergence of probability measures for a wide class of kernels. More precisely, we prove that, on a locally compact, non-compact, Hausdorff space, the MMD…

Least squares kernel based methods have been widely used in regression problems due to the simple implementation and good generalization performance. Among them, least squares support vector regression (LS-SVR) and extreme learning machine…

We derive the mapping between two of the most pervasive utility functions, the mean square error ($MSE$) and the concordance correlation coefficient (CCC, $\rho_c$). Despite its drawbacks, $MSE$ is one of the most popular performance…

Modal linear regression (MLR) is a method for obtaining a conditional mode predictor as a linear model. We study kernel selection for MLR from two perspectives: "which kernel achieves smaller error?" and "which kernel is computationally…

In this work we study the quality of low-dimensional embeddings from an explicitly information-theoretic perspective. We begin by noting that classical evaluation metrics such as stress, rank-based neighborhood criteria, or Local Procrustes…

Recent end-to-end deep neural networks for disparity regression have achieved the state-of-the-art performance. However, many well-acknowledged specific properties of disparity estimation are omitted in these deep learning algorithms.…

Multi-label learning draws great interests in many real world applications. It is a highly costly task to assign many labels by the oracle for one instance. Meanwhile, it is also hard to build a good model without diagnosing discriminative…

Distributional assumptions have been shown to be necessary for the robust learnability of concept classes when considering the exact-in-the-ball robust risk and access to random examples by Gourdeau et al. (2019). In this paper, we study…