Related papers: HiMAP: Hilbert Mass-Aligned Parameterization for M…
Kernel dependence measures yield accurate estimates of nonlinear relations between random variables, and they are also endorsed with solid theoretical properties and convergence rates. Besides, the empirical estimates are easy to compute in…
Kernel mean embeddings, a widely used technique in machine learning, map probability distributions to elements of a reproducing kernel Hilbert space (RKHS). For supervised learning problems, where input-output pairs are observed, the…
Datasets containing both categorical and continuous variables are frequently encountered in many areas, and with the rapid development of modern measurement technologies, the dimensions of these variables can be very high. Despite the…
In practice, there often exist unobserved variables, also termed hidden variables, associated with both the response and covariates. Existing works in the literature mostly focus on linear regression with hidden variables. However, when the…
An algorithm for sampling from non-log-concave multivariate distributions is proposed, which improves the adaptive rejection Metropolis sampling (ARMS) algorithm by incorporating the hit and run sampling. It is not rare that the ARMS is…
In this work clustering schemes for uncertain and structured data are considered relying on the notion of Wasserstein barycenters, accompanied by appropriate clustering indices based on the intrinsic geometry of the Wasserstein space where…
Learning in the reproducing kernel Hilbert space (RKHS) such as the support vector machine has been recognized as a promising technique. It continues to be highly effective and competitive in numerous prediction tasks, particularly in…
Optimal transport is a notoriously difficult problem to solve numerically, with current approaches often remaining intractable for very large scale applications such as those encountered in machine learning. Wasserstein barycenters -- the…
In this paper, we propose Wasserstein Isometric Mapping (Wassmap), a nonlinear dimensionality reduction technique that provides solutions to some drawbacks in existing global nonlinear dimensionality reduction algorithms in imaging…
Learning from an imbalanced dataset is a tricky proposition. Because these datasets are biased towards one class, most existing classifiers tend not to perform well on minority class examples. Conventional classifiers usually aim to…
We propose a balanced coarsening scheme for multilevel hypergraph partitioning. In addition, an initial partitioning algorithm is designed to improve the quality of k-way hypergraph partitioning. By assigning vertex weights through the LPT…
Multivariate spatially-oriented data sets are prevalent in the environmental and physical sciences. Scientists seek to jointly model multiple variables, each indexed by a spatial location, to capture any underlying spatial association for…
In this paper first we give a partial answer to a question of L. Moln\'ar and W. Timmermann. Namely, we will describe those linear (not necessarily bijective) transformations on the set of self-adjoint matrices which preserve a unitarily…
The measure-multiplicity-invariant for masas in $\rm{II}_{1}$ factors was introduced in \cite{MR2261688} to distinguish masas that have the same Puk\'{a}nszky invariant. In this paper we study the measure class in the…
Traditional functional linear regression usually takes a one-dimensional functional predictor as input and estimates the continuous coefficient function. Modern applications often generate two-dimensional covariates, which become matrices…
Any image recovery algorithm attempts to achieve the highest quality reconstruction in a timely manner. The former can be achieved in several ways, among which are by incorporating Bayesian priors that exploit natural image tendencies to…
In this thesis, we consider the Wasserstein barycenter problem of discrete probability measures from computational and statistical sides. The statistical focus is estimating the sample size of measures necessary to calculate an…
Modern deep learning architectures increasingly contend with sophisticated signals that are natively infinite-dimensional, such as time series, probability distributions, or operators, and are defined over irregular domains. Yet, a unified…
We discuss the Heisenberg limit in the multiparameter metrology within two different paradigms -- the one, where the measurement is repeated many times (so the Cram\'er-Rao bound is guaranteed to be asymptotically saturable) and the second…
Non-Euclidean data that are indexed with a scalar predictor such as time are increasingly encountered in data applications, while statistical methodology and theory for such random objects are not well developed yet. To address the need for…