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The Levenberg-Marquardt algorithm is a flexible iterative procedure used to solve non-linear least squares problems. In this work we study how a class of possible adaptations of this procedure can be used to solve maximum likelihood…

We introduce Exponential Family Discriminant Analysis (EFDA), a unified generative framework that extends classical Linear Discriminant Analysis (LDA) beyond the Gaussian setting to any member of the exponential family. Under the assumption…

Doubly stochastic learning algorithms are scalable kernel methods that perform very well in practice. However, their generalization properties are not well understood and their analysis is challenging since the corresponding learning…

The matrix completion problem consists in reconstructing a matrix from a sample of entries, possibly observed with noise. A popular class of estimator, known as nuclear norm penalized estimators, are based on minimizing the sum of a data…

Kernel methods provide a flexible and powerful framework for nonparametric statistical testing by embedding probability distributions into a reproducing kernel Hilbert space (RKHS). In this work, we study the kernel two-sample testing…

Minimum Description Length (MDL) estimators, using two-part codes for universal coding, are analyzed. For general parametric families under certain regularity conditions, we introduce a two-part code whose regret is close to the minimax…

Stochastic processes are random variables with values in some space of paths. However, reducing a stochastic process to a path-valued random variable ignores its filtration, i.e. the flow of information carried by the process through time.…

We propose a novel kernel-based two-sample test that leverages the spectral decomposition of the maximum mean discrepancy (MMD) statistic to identify and utilize well-estimated directional components in reproducing kernel Hilbert space…

A theoretical framework for non-negative matrix factorization based on generalized dual Kullback-Leibler divergence, which includes members of the exponential family of models, is proposed. A family of algorithms is developed using this…

Sequential hypothesis testing is a desirable decision making strategy in any time sensitive scenario. Compared with fixed sample-size testing, sequential testing is capable of achieving identical probability of error requirements using less…

We study strictly proper scoring rules in the Reproducing Kernel Hilbert Space. We propose a general Kernel Scoring rule and associated Kernel Divergence. We consider conditions under which the Kernel Score is strictly proper. We then…

We consider the segmentation problem of univariate distributions from the exponential family with multiple parameters. In segmentation, the choice of the number of segments remains a difficult issue due to the discrete nature of the…

We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…

Conditional density estimation is a general framework for solving various problems in machine learning. Among existing methods, non-parametric and/or kernel-based methods are often difficult to use on large datasets, while methods based on…

We employ a parameter-free distribution estimation framework where estimators are random distributions and utilize the Kullback-Leibler (KL) divergence as a loss function. Wu and Vos [J. Statist. Plann. Inference 142 (2012) 1525-1536] show…

In recent years, there have been significant efforts on mitigating unethical demographic biases in machine learning methods. However, very little is done for kernel methods. In this paper, we propose a new fair kernel regression method via…

In this paper we suggest two statistical hypothesis tests for the regression function of binary classification based on conditional kernel mean embeddings. The regression function is a fundamental object in classification as it determines…

To accelerate kernel methods, we propose a near input sparsity time algorithm for sampling the high-dimensional feature space implicitly defined by a kernel transformation. Our main contribution is an importance sampling method for…

We introduce a new deal of kernel density estimation using an exponentiated form of kernel density estimators. The density estimator has two hyperparameters flexibly controlling the smoothness of the resulting density. We tune them in a…

Tensor-based discrete density estimation requires flexible modeling and proper divergence criteria to enable effective learning; however, traditional approaches using $\alpha$-divergence face analytical challenges due to the $\alpha$-power…