Related papers: Random Function Priors for Correlation Modeling

We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…

Probabilistic models learned as density estimators can be exploited in representation learning beside being toolboxes used to answer inference queries only. However, how to extract useful representations highly depends on the particular…

We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological…

We propose a new framework for 2-D interpreting (features and samples) black-box machine learning models via a metamodeling technique, by which we study the output and input relationships of the underlying machine learning model. The…

Bayesian deep learning approaches assume model parameters to be latent random variables and infer posterior distributions to quantify uncertainty, increase safety and trust, and prevent overconfident and unpredictable behavior. However,…

Individual events at high-energy colliders like the LHC can be represented by a sequence of measurements, or 'point patterns' in an observable space. Starting from this data representation, we build a simple Bayesian probabilistic model for…

We introduce probabilistic embeddings using Laplacian priors (PELP). The proposed model enables incorporating graph side-information into static word embeddings. We theoretically show that the model unifies several previously proposed…

We introduce a latent 3D representation that models 3D surfaces as probability density functions in 3D, i.e., p(x,y,z), with flow-matching. Our representation is specifically designed for consumption by machine learning models, offering…

We introduce the notion of hidden quantum correlations. We present the mean values of observables depending on one classical random variable described by the probability distribution in the form of correlation functions of two (three, etc.)…

We study mixture of linear regression (random coefficient) models, which capture population heterogeneity by allowing the regression coefficients to follow an unknown distribution $G^*$. In contrast to common parametric methods that fix the…

Let $\mathbf{Q}=(Q_1,\ldots,Q_n)$ be a random vector drawn from the uniform distribution on the set of all $n!$ permutations of $\{1,2,\ldots,n\}$. Let $\mathbf{Z}=(Z_1,\ldots,Z_n)$, where $Z_j$ is the mean zero variance one random variable…

Semiparametric mixture models are parametric models with latent variables. They are defined kernel, $p_\theta(x | z)$, where z is the unknown latent variable, and $\theta$ is the parameter of interest. We assume that the latent variables…

Bayesian inference for statistical models with a hierarchical structure is often characterized by specification of priors for parameters at different levels of the hierarchy. When higher level parameters are functions of the lower level…

As we deploy reinforcement learning agents to solve increasingly challenging problems, methods that allow us to inject prior knowledge about the structure of the world and effective solution strategies becomes increasingly important. In…

In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…

We present a method for modelling the covariance structure of tensor-variate data, with the ulterior aim of learning an unknown model parameter vector using such data. We express the high-dimensional observable as a function of this sought…

In a mixture of linear regression model, the regression coefficients are treated as random vectors that may follow either a continuous or discrete distribution. We propose two Expectation-Maximization (EM) algorithms to estimate this prior…

This paper investigates the generalisability of Koopman-based representations for chaotic dynamical systems, focusing on their transferability across prediction and control tasks. Using the Lorenz system as a testbed, we propose a…

Robot kinematics data, despite being a high dimensional process, is highly correlated, especially when considering motions grouped in certain primitives. These almost linear correlations within primitives allow us to interpret the motions…

Let $\alpha_n(\cdot)=P\bigl(X_{n+1}\in\cdot\mid X_1,\ldots,X_n\bigr)$ be the predictive distributions of a sequence $(X_1,X_2,\ldots)$ of $p$-dimensional random vectors. Suppose $$\alpha_n= \mathcal{N} _p (M_n,Q_n)$$ where…