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The kernel mean embedding of probability distributions is commonly used in machine learning as an injective mapping from distributions to functions in an infinite dimensional Hilbert space. It allows us, for example, to define a distance…

These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…

Recent studies have demonstrated that correntropy is an efficient tool for analyzing higher-order statistical moments in nonGaussian noise environments. Although it has been used with complex data, some adaptations were then necessary…

Extreme learning machine (ELM) is an extremely fast learning method and has a powerful performance for pattern recognition tasks proven by enormous researches and engineers. However, its good generalization ability is built on large numbers…

Contrastive learning has emerged as a powerful method in deep learning, excelling at learning effective representations through contrasting samples from different distributions. However, dimensional collapse, where embeddings converge into…

In this paper, we propose and study a Nystr\"om based approach to efficient large scale kernel principal component analysis (PCA). The latter is a natural nonlinear extension of classical PCA based on considering a nonlinear feature map or…

Existing statistical learning guarantees for general kernel regressors often yield loose bounds when used with finite-rank kernels. Yet, finite-rank kernels naturally appear in several machine learning problems, e.g.\ when fine-tuning a…

We study risk-sensitive reinforcement learning (RL) based on an entropic risk measure in episodic non-stationary Markov decision processes (MDPs). Both the reward functions and the state transition kernels are unknown and allowed to vary…

A foundational assumption in complex-system collapse studies is that critical transitions are second-order, preceded by early-warning signals like rising autocorrelation, variance, and critical slowing down (Scheffer, 2009). We show this…

Quantum machine learning is a growing research field that aims to perform machine learning tasks assisted by a quantum computer. Kernel-based quantum machine learning models are paradigmatic examples where the kernel involves quantum…

As quantum computers become increasingly practical, so does the prospect of using quantum computation to improve upon traditional algorithms. Kernel methods in machine learning is one area where such improvements could be realized in the…

Safe reinforcement learning is extremely challenging--not only must the agent explore an unknown environment, it must do so while ensuring no safety constraint violations. We formulate this safe reinforcement learning (RL) problem using the…

Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…

Recursive learning -- where models are trained on data generated by previous versions of themselves -- is increasingly common in large language models, autonomous agents, and self-supervised systems. However, standard performance metrics…

In this paper, we propose a general framework to learn a robust large-margin binary classifier when corrupt measurements, called anomalies, caused by sensor failure might be present in the training set. The goal is to minimize the…

Continuous-time reinforcement learning (CTRL) provides a natural framework for sequential decision-making in dynamic environments where interactions evolve continuously over time. While CTRL has shown growing empirical success, its ability…

The paper addresses the multiple kernel learning (MKL) problem for one-class classification (OCC). For this purpose, based on the Fisher null-space one-class classification principle, we present a multiple kernel learning algorithm where a…

While robust parameter estimation has been well studied in parametric density estimation, there has been little investigation into robust density estimation in the nonparametric setting. We present a robust version of the popular kernel…

Kernel Principal Component Analysis (KPCA) is a key machine learning algorithm for extracting nonlinear features from data. In the presence of a large volume of high dimensional data collected in a distributed fashion, it becomes very…

Maximum entropy has become a mainstream off-policy reinforcement learning (RL) framework for balancing exploitation and exploration. However, two bottlenecks still limit further performance improvement: (1) non-stationary Q-value estimation…