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The increased availability of massive data sets provides a unique opportunity to discover subtle patterns in their distributions, but also imposes overwhelming computational challenges. To fully utilize the information contained in big…
In this paper we present the Markov variation, a smoothness measure which offers a probabilistic interpretation of graph signal smoothness. This measure is then used to develop an optimization framework for graph signal interpolation. Our…
Diffusion kernels over graphs have been widely utilized as effective tools in various applications due to their ability to accurately model the flow of information through nodes and edges. However, there is a notable gap in the literature…
We study diffusive mixing in the presence of thermal fluctuations under the assumption of large Schmidt number. In this regime we obtain a limiting equation that contains a diffusive thermal drift term with diffusion coefficient obeying a…
We propose a valid and consistent test for the hypothesis that two latent distance random graphs on the same vertex set have the same generating latent positions, up to some unidentifiable similarity transformations. Our test statistic is…
In this thesis we consider the problem of information hiding in the scenarios of interactive systems, statistical disclosure control, and refinement of specifications. We apply quantitative approaches to information flow in the first two…
This paper proposes a physical-statistical modeling approach for spatio-temporal data arising from a class of stochastic convection-diffusion processes. Such processes are widely found in scientific and engineering applications where…
Graph matching finds the correspondence of nodes across two correlated graphs and lies at the core of many applications. When graph side information is not available, the node correspondence is estimated on the sole basis of network…
We study the asymptotic behavior of empirical processes generated by measurable bounded functions of an infinite source Poisson transmission process when the session length have infinite variance. In spite of the boundedness of the…
We derive central limit theorems for the Wasserstein distance between the empirical distributions of Gaussian samples. The cases are distinguished whether the underlying laws are the same or different. Results are based on the (quadratic)…
We provide a means of computing and estimating the asymptotic distributions of statistics based on an outer minimization of an inner maximization. Such test statistics, which arise frequently in moment models, are of special interest in…
We propose a new class of semiparametric exponential family graphical models for the analysis of high dimensional mixed data. Different from the existing mixed graphical models, we allow the nodewise conditional distributions to be…
Graph models are widely used to study diffusion processes in contact networks. Recent data-driven research has highlighted the significance of indirect links, where interactions are possible when two nodes visit the same place at different…
The non-contact heat transfer between two bodies is more efficient than the Stefan-Boltzmann law, when the distances are on the nanometer scale (shorter than Wien's wavelength), due to contributions of thermally excited near fields. This is…
Statisticians increasingly face the problem to reconsider the adaptability of classical inference techniques. In particular, divers types of high-dimensional data structures are observed in various research areas; disclosing the boundaries…
Diffusion maps approximate the generator of Langevin dynamics from simulation data. They afford a means of identifying the slowly-evolving principal modes of high-dimensional molecular systems. When combined with a biasing mechanism,…
Probabilistic breadth-first traversals (BPTs) are used in many network science and graph machine learning applications. In this paper, we are motivated by the application of BPTs in stochastic diffusion-based graph problems such as…
In this paper we compare two regression curves by measuring their difference by the area between the two curves, represented by their $L^1$-distance. We develop asymptotic confidence intervals for this measure and statistical tests to…
Modeling functions that are sequentially observed as functional time series is becoming increasingly common. In such models, it is often crucial to ensure data homogeneity. We investigate the sensitivity of graph-based change point…
This paper presents a novel method for analyzing the latent space geometry of generative models, including statistical physics models and diffusion models, by reconstructing the Fisher information metric. The method approximates the…