Related papers: Copy-composition for Probabilistic Graphical Model…
We characterize a number of well known systems of approximate inference as loss models: lax sections of 2-fibrations of statistical games, constructed by attaching internally-defined loss functions to Bayesian lenses. Our examples include…
General results from statistical learning theory suggest to understand not only brain computations, but also brain plasticity as probabilistic inference. But a model for that has been missing. We propose that inherently stochastic features…
Widely used closed product-form networks have emerged recently as a primary model of stochastic growth of sub-cellular structures, e.g., cellular filaments. In the baseline model, homogeneous monomers attach and detach stochastically to…
We propose a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics. In contrast to existing techniques which are based on a fine-to-coarse map, we adopt the opposite strategy by prescribing a…
There has been an increased interest in applying machine learning techniques on relational structured-data based on an observed graph. Often, this graph is not fully representative of the true relationship amongst nodes. In these settings,…
Inference is a fundamental reasoning technique in probability theory. When applied to a large joint distribution, it involves updating with evidence (conditioning) in one or more components (variables) and computing the outcome in other…
Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The…
We present a theory for slicing probabilistic imperative programs -- containing random assignments, and ``observe'' statements (for conditioning) -- represented as probabilistic control-flow graphs (pCFGs) whose nodes modify probability…
This paper presents an introduction to the stochastic concepts of \emph{coupling} and \emph{copula}. Coupling means the construction of a joint distribution of two or more random variables that need not be defined on one and the same…
Decomposable models and Bayesian networks can be defined as sequences of oligo-dimensional probability measures connected with operators of composition. The preliminary results suggest that the probabilistic models allowing for effective…
In the process of building (structural learning) a probabilistic graphical model from a set of observed data, the directional, cyclic dependencies between the random variables of the model are often found. Existing graphical models such as…
Stochastic models share many characteristics with generic parametric models. In some ways they can be regarded as a special case. But for stochastic models there is a notion of weak distribution or generalised random variable, and the same…
Copulas are a powerful tool for modeling multivariate distributions as they allow to separately estimate the univariate marginal distributions and the joint dependency structure. However, known parametric copulas offer limited flexibility…
Composition of low-dimensional distributions, whose foundations were laid in the papaer published in the Proceeding of UAI'97 (Jirousek 1997), appeared to be an alternative apparatus to describe multidimensional probabilistic models. In…
An inductive probabilistic classification rule must generally obey the principles of Bayesian predictive inference, such that all observed and unobserved stochastic quantities are jointly modeled and the parameter uncertainty is fully…
This dissertation reports some first steps towards a compositional account of active inference and the Bayesian brain. Specifically, we use the tools of contemporary applied category theory to supply functorial semantics for approximate…
A steadily increasing body of evidence suggests that the brain performs probabilistic inference to interpret and respond to sensory input and that trial-to-trial variability in neural activity plays an important role. The neural sampling…
Stochastic localization is a pathwise analysis technique originating from convex geometry. This paper explores certain algorithmic aspects of stochastic localization as a computational tool. First, we unify various existing stochastic…
We propose a graphical model for representing networks of stochastic processes, the minimal generative model graph. It is based on reduced factorizations of the joint distribution over time. We show that under appropriate conditions, it is…
Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…