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We develop a mixture-based approach to robust density modeling and outlier detection for experimental multivariate data that includes measurement error information. Our model is designed to infer atypical measurements that are not due to…

Gaussian processes (GP) for machine learning have been studied systematically over the past two decades and they are by now widely used in a number of diverse applications. However, GP kernel design and the associated hyper-parameter…

Differential privacy has become a cornerstone in the development of privacy-preserving learning algorithms. This work addresses optimizing differentially private kernel learning within the empirical risk minimization (ERM) framework. We…

Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…

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 consider the problem of system identification of partially observed linear time-invariant (LTI) systems. Given input-output data, we provide non-asymptotic guarantees for identifying the system parameters under general heavy-tailed noise…

This paper proposes a new algorithm for Gaussian process classification based on posterior linearisation (PL). In PL, a Gaussian approximation to the posterior density is obtained iteratively using the best possible linearisation of the…

Motivated by indirect measurements and applications from nanometrology with a mixed noise model, we develop a novel algorithm for jointly estimating the posterior and the noise parameters in Bayesian inverse problems. We propose to solve…

Persistent homology has become an important tool for extracting geometric and topological features from data, whose multi-scale features are summarized in a persistence diagram. From a statistical perspective, however, persistence diagrams…

Sequential neural posterior estimation (SNPE) techniques have been recently proposed for dealing with simulation-based models with intractable likelihoods. Unlike approximate Bayesian computation, SNPE techniques learn the posterior from…

Semi- and non-parametric mixture of regressions are a very useful flexible class of mixture of regressions in which some or all of the parameters are non-parametric functions of the covariates. These models are, however, based on the…

The data-centric machine learning aims to find effective ways to build appropriate datasets which can improve the performance of AI models. In this paper, we mainly focus on designing an efficient data-centric scheme to improve robustness…

Probabilistic point-set registration methods have been gaining more attention for their robustness to noise, outliers and occlusions. However, these methods tend to be much slower than the popular iterative closest point (ICP) algorithms,…

Many real-world applications involve the use of Optical Character Recognition (OCR) engines to transform handwritten images into transcripts on which downstream Natural Language Processing (NLP) models are applied. In this process, OCR…

The increased computerization in recent years has resulted in the production of a variety of different software, however measures need to be taken to ensure that the produced software isn't defective. Many researchers have worked in this…

Volterra series are especially useful for nonlinear system identification, also thanks to their capability to approximate a broad range of input-output maps. However, their identification from a finite set of data is hard, due to the curse…

Gaussian graphical modeling has been widely used to explore various network structures, such as gene regulatory networks and social networks. We often use a penalized maximum likelihood approach with the $L_1$ penalty for learning a…

We consider the problem of robust compressed sensing whose objective is to recover a high-dimensional sparse signal from compressed measurements corrupted by outliers. A new sparse Bayesian learning method is developed for robust compressed…

Classification of high-dimensional spectroscopic data is a common task in analytical chemistry. Well-established procedures like support vector machines (SVMs) and partial least squares discriminant analysis (PLS-DA) are the most common…

We propose a vector-valued regression problem whose solution is equivalent to the reproducing kernel Hilbert space (RKHS) embedding of the Bayesian posterior distribution. This equivalence provides a new understanding of kernel Bayesian…