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Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…

For highly skewed or fat-tailed distributions, mean or median-based methods often fail to capture the central tendencies in the data. Despite being a viable alternative, estimating the conditional mode given certain covariates (or mode…

This study proposes median consensus embedding (MCE) to address variability in low-dimensional embeddings caused by random initialization in nonlinear dimensionality reduction techniques such as $t$-distributed stochastic neighbor…

Statistical depth is the act of gauging how representative a point is compared to a reference probability measure. The depth allows introducing rankings and orderings to data living in multivariate, or function spaces. Though widely applied…

With the emergence of deep learning, metric learning has gained significant popularity in numerous machine learning tasks dealing with complex and large-scale datasets, such as information retrieval, object recognition and recommendation…

Global QCD analyses provide the primary framework for extracting hadron structure from experimental data, yet the mechanisms by which data constrain non-perturbative functions remain difficult to interpret due to the high dimensionality and…

In recent years, samples of time-varying object data such as time-varying networks that are not in a vector space have been increasingly collected. These data can be viewed as elements of a general metric space that lacks local or global…

Detecting distributional drift in high-dimensional data streams presents fundamental challenges: global comparison methods scale poorly, projection-based approaches lose geometric structure, and re-clustering methods suffer from identity…

Multi-objective evaluation is a necessary aspect when managing complex systems, as the intrinsic complexity of a system is generally closely linked to the potential number of optimization objectives. However, an evaluation makes no sense…

In fields such as hydrology and climatology, modelling the entire distribution of positive data is essential, as stakeholders require insights into the full range of values, from low to extreme. Traditional approaches often segment the…

Betweenness centrality is a popular centrality measure with applications in several domains, and whose exact computation is impractical for modern-sized networks. We present SILVAN, a novel, efficient algorithm to compute, with high…

The dispersive meshless method with scalar basis function has been successfully applied for analysis of frequency dependent media. However, as scalar based meshless methods are not always divergence-free in the absence of source,inaccurate…

We develop a Bayesian graphical modeling framework for functional data for correlated multivariate random variables observed over a continuous domain. Our method leads to graphical Markov models for functional data which allows the graphs…

A novel method is proposed for detecting changes in the covariance structure of moderate dimensional time series. This non-linear test statistic has a number of useful properties. Most importantly, it is independent of the underlying…

Here we present a new non-parametric approach to density estimation and classification derived from theory in Radon transforms and image reconstruction. We start by constructing a "forward problem" in which the unknown density is mapped to…

Distributionally robust optimization (DRO) has become a powerful framework for estimation under uncertainty, offering strong out-of-sample performance and principled regularization. In this paper, we propose a DRO-based method for linear…

We consider nonparametric estimation of a covariance function on the unit square, given a sample of discretely observed fragments of functional data. When each sample path is only observed on a subinterval of length $\delta<1$, one has no…

The ability to learn disentangled representations that split underlying sources of variation in high dimensional, unstructured data is important for data efficient and robust use of neural networks. While various approaches aiming towards…

Within the field of hierarchical modelling, little attention is paid to micro-macro models: those in which group-level outcomes are dependent on covariates measured at the level of individuals within groups. Although such models are perhaps…

In previous work the authors defined the k-th order simplicial distance between probability distributions which arises naturally from a measure of dispersion based on the squared volume of random simplices of dimension k. This theory is…