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Motivated by recently emerging problems in machine learning and statistics, we propose data models which relax the familiar i.i.d. assumption. In essence, we seek to understand what it means for data to come from a set of probability…
We explore the probabilistic foundations of shared control in complex dynamic environments. In order to do this, we formulate shared control as a random process and describe the joint distribution that governs its behavior. For…
We study the statistical inference of nonlinear stochastic approximation algorithms utilizing a single trajectory of Markovian data. Our methodology has practical applications in various scenarios, such as Stochastic Gradient Descent (SGD)…
General hypergeometric distribution (GHGD) definition: from a finite space $N$ containing $n$ elements, randomly select totally $T$ subsets $M_i$ (each contains $m_i$ elements, $1 \geq i \geq T$), what is the probability that exactly $x$…
The rapid evolution of generative AI, from GANs to modern diffusion models, has resulted in increasingly subtle discriminative clues. These fine-grained signals are often overshadowed by dominant, high-fidelity image content (e.g., the main…
The Random Geometric Graph (RGG) is a random graph model for network data with an underlying spatial representation. Geometry endows RGGs with a rich dependence structure and often leads to desirable properties of real-world networks such…
State-space models (SSMs) are a powerful statistical tool for modelling time-varying systems via a latent state. In these models, the latent state is never directly observed. Instead, a sequence of observations related to the state is…
In many fields of science, generalized likelihood ratio tests are established tools for statistical inference. At the same time, it has become increasingly common that a simulator (or generative model) is used to describe complex processes…
Functional Gaussian graphical models (GGM) used for analyzing multivariate functional data customarily estimate an unknown graphical model representing the conditional relationships between the functional variables. However, in many…
Continuous determinantal point processes (DPPs) are a class of repulsive point processes on $\mathbb{R}^d$ with many statistical applications. Although an explicit expression of their density is known, it is too complicated to be used…
Hypergraphs are structures that can be decomposed or described; in other words they are recursively countable. Here, we get exact and asymptotic enumeration results on hypergraphs by means of exponential generating functions. The number of…
Symbolic data analysis has been proposed as a technique for summarising large and complex datasets into a much smaller and tractable number of distributions -- such as random rectangles or histograms -- each describing a portion of the…
A random algebraic graph is defined by a group $G$ with a uniform distribution over it and a connection $\sigma:G\longrightarrow[0,1]$ with expectation $p,$ satisfying $\sigma(g)=\sigma(g^{-1}).$ The random graph…
Lifting uses a representative of indistinguishable individuals to exploit symmetries in probabilistic relational models, denoted as parametric factor graphs, to speed up inference while maintaining exact answers. In this paper, we show how…
We propose a probabilistic model for inferring the multivariate function from multiple areal data sets with various granularities. Here, the areal data are observed not at location points but at regions. Existing regression-based models can…
In the context of dynamic emission tomography, the conventional processing pipeline consists of independent image reconstruction of single time frames, followed by the application of a suitable kinetic model to time activity curves (TACs)…
In this study, we focus on the graph representation learning (a.k.a. network embedding) in attributed graphs. Different from existing embedding methods that treat the incorporation of graph structure and semantic as the simple combination…
This paper presents exact formulas for the probability distribution function (PDF) and moment generating function (MGF) of the sum-product of statistically independent but not necessarily identically distributed (i.n.i.d.) Nakagami-$m$…
Gaussian Graphical Models (GGM) are often used to describe the conditional correlations between the components of a random vector. In this article, we compare two families of GGM inference methods: nodewise edge selection and penalised…
Gaussian processes (GPs) provide flexible distributions over functions, with inductive biases controlled by a kernel. However, in many applications Gaussian processes can struggle with even moderate input dimensionality. Learning a low…