Related papers: Random Function Priors for Correlation Modeling
The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…
We introduce a new approach to probabilistic unsupervised learning based on the recognition-parametrised model (RPM): a normalised semi-parametric hypothesis class for joint distributions over observed and latent variables. Under the key…
For each $n$, let $U_n$ be Haar distributed on the group of $n\times n$ unitary matrices. Let $\bfx_{n,1},\ldots,\bfx_{n,m} $ denote orthogonal nonrandom unit vectors in ${\Bbb C}^n$ and let $\text{\bf…
We study certain probability measures on partitions of n=1,2,..., originated in representation theory, and demonstrate their connections with random matrix theory and multivariate hypergeometric functions. Our measures depend on three…
Bayesian predictive densities when the observed data $x$ and the target variable $y$ to be predicted have different distributions are investigated by using the framework of information geometry. The performance of predictive densities is…
We introduce a sharpness functional for probabilistic models that quantifies sharpness as an intrinsic property of the probability distribution. The measure is derived based on a rank-based concentration principle that tracks upward…
We introduce a random graph model based on k-trees, which can be generated by applying a probabilistic preferential attachment rule, but which also has a simple combinatorial description. We carry out a precise distributional analysis of…
We investigate the concept of Best Approximation for Feedforward Neural Networks (FNN) and explore their convergence properties through the lens of Random Projection (RPNNs). RPNNs have predetermined and fixed, once and for all, internal…
This paper presents an approach to the modeling of degree-degree correlation in complex networks. Thus, a simple function, \Delta(k', k), describing specific degree-to- degree correlations is considered. The function is well suited to…
Koopman theory studies dynamical systems in terms of operator theoretic properties of the Perron-Frobenius operator $\mathcal{P}$ and Koopman operator $\mathcal{U}$ respectively. In this paper, we derive the rates of convergence of…
Deep latent variable models have achieved significant empirical successes in model-based reinforcement learning (RL) due to their expressiveness in modeling complex transition dynamics. On the other hand, it remains unclear theoretically…
Non-holonomic vehicle motion has been studied extensively using physics-based models. Common approaches when using these models interpret the wheel/ground interactions using a linear tire model and thus may not fully capture the nonlinear…
There are so many models in the literature that it is difficult for practitioners to decide which combinations are likely to be effective for a new task. This paper attempts to address this question by capturing relationships among…
In statistical relational learning, the link prediction problem is key to automatically understand the structure of large knowledge bases. As in previous studies, we propose to solve this problem through latent factorization. However, here…
A new class of general exponential ranking models is introduced which we label angle-based models for ranking data. A consensus score vector is assumed, which assigns scores to a set of items, where the scores reflect a consensus view of…
We introduce sparse random projection, an important dimension-reduction tool from machine learning, for the estimation of discrete-choice models with high-dimensional choice sets. Initially, high-dimensional data are compressed into a…
We investigate the extent to which verb alternation classes, as described by Levin (1993), are encoded in the embeddings of Large Pre-trained Language Models (PLMs) such as BERT, RoBERTa, ELECTRA, and DeBERTa using selectively constructed…
This paper considers the topic of finding prior distributions when a major component of the statistical model depends on a nonlinear function. Using results on how to construct uniform distributions in general metric spaces, we propose a…
Challenging research in various fields has driven a wide range of methodological advances in variable selection for regression models with high-dimensional predictors. In comparison, selection of nonlinear functions in models with additive…
Linear mixed-effects models are widely used in analyzing clustered or repeated measures data. We propose a quasi-likelihood approach for estimation and inference of the unknown parameters in linear mixed-effects models with high-dimensional…