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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…
We assume the direct sum <A> o <B> for the signal subspace. As a result of post- measurement, a number of operational contexts presuppose the a priori knowledge of the LB -dimensional "interfering" subspace <B> and the goal is to estimate…
In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…
We study the problem of optimizing a function under a \emph{budgeted number of evaluations}. We only assume that the function is \emph{locally} smooth around one of its global optima. The difficulty of optimization is measured in terms of…
This article studies the behavior of regularized Tyler estimators (RTEs) of scatter matrices. The key advantages of these estimators are twofold. First, they guarantee by construction a good conditioning of the estimate and second, being a…
Recently, the stochastic asymptotical regularization (SAR) has been developed in (\emph{Inverse Problems}, 39: 015007, 2023) for the uncertainty quantification of the stable approximate solution of linear ill-posed inverse problems. In this…
Modern computational models in supervised machine learning are often highly parameterized universal approximators. As such, the value of the parameters is unimportant, and only the out of sample performance is considered. On the other hand…
We investigate regularized algorithms combining with projection for least-squares regression problem over a Hilbert space, covering nonparametric regression over a reproducing kernel Hilbert space. We prove convergence results with respect…
Quantum machine learning with quantum kernels for classification problems is a growing area of research. Recently, quantum kernel alignment techniques that parameterise the kernel have been developed, allowing the kernel to be trained and…
Through one decade's development, the kernel-based regularization method (KRM) has become a complement to the classical maximum likelihood/prediction error method and an emerging new system identification paradigm. One recent example is its…
In recent years, kernel density estimation has been exploited by computer scientists to model machine learning problems. The kernel density estimation based approaches are of interest due to the low time complexity of either O(n) or…
Dataset bias has attracted increasing attention recently for its detrimental effect on the generalization ability of fine-tuned models. The current mainstream solution is designing an additional shallow model to pre-identify biased…
Adjustable hyperparameters of machine learning models typically impact various key trade-offs such as accuracy, fairness, robustness, or inference cost. Our goal in this paper is to find a configuration that adheres to user-specified limits…
The problem of establishing out-of-sample bounds for the values of an unkonwn ground-truth function is considered. Kernels and their associated Hilbert spaces are the main formalism employed herein along with an observational model where…
A variety of algorithms have been proposed to address the power system state estimation problem in the presence of uncertainties in the data. However, less emphasis has been given to handling perturbations in the model. In the context of…
We study the convergence rates of the EM algorithm for learning two-component mixed linear regression under all regimes of signal-to-noise ratio (SNR). We resolve a long-standing question that many recent results have attempted to tackle:…
We consider the estimation of a scalar parameter, when two estimators are available. The first is always consistent. The second is inconsistent in general, but has a smaller asymptotic variance than the first, and may be consistent if an…
In the context of kernel density estimation, we give a characterization of the kernels for which the parametric mean integrated squared error rate $n^{-1}$ may be obtained, where $n$ is the sample size. Also, for the cases where this rate…
The kernel smoothing with large bandwidth values causes oversmoothing or underfitting in general. However, when irrelevant variables are included, the corresponding large bandwidth values are known to have an effect of shrinking them. This…
We investigate the choice of tuning parameters for a Bayesian multi-level group lasso model developed for the joint analysis of neuroimaging and genetic data. The regression model we consider relates multivariate phenotypes consisting of…