Related papers: Compositional Active Inference I: Bayesian Lenses.…

Active inference is a state-of-the-art framework in neuroscience that offers a unified theory of brain function. It is also proposed as a framework for planning in AI. Unfortunately, the complex mathematics required to create new models --…

Inspired by empirical work in neuroscience for Bayesian approaches to brain function, we give a unified probabilistic account of various types of symbolic reasoning from data. We characterise them in terms of formal logic using the…

Bayesian statistical models allow us to formalise our knowledge about the world and reason about our uncertainty, but there is a need for better procedures to accurately encode its complexity. One way to do so is through compositional…

Bayesian inference is an effective approach for solving statistical learning problems especially with uncertainty and incompleteness. However, inference efficiencies are physically limited by the bottlenecks of conventional computing…

Multivariate functional data arise in a wide range of applications. One fundamental task is to understand the causal relationships among these functional objects of interest, which has not yet been fully explored. In this article, we…

The idea that the brain is a probabilistic (Bayesian) inference machine, continuously trying to figure out the hidden causes of its inputs, has become very influential in cognitive (neuro)science over recent decades. Here I present a…

Machine learning methods for computational imaging require uncertainty estimation to be reliable in real settings. While Bayesian models offer a computationally tractable way of recovering uncertainty, they need large data volumes to be…

Bayesian network is a complete model for the variables and their relationships, it can be used to answer probabilistic queries about them. A Bayesian network can thus be considered a mechanism for automatically applying Bayes' theorem to…

Categories of polymorphic lenses in computer science, and of open games in compositional game theory, have a curious structure that is reminiscent of compact closed categories, but differs in some crucial ways. Specifically they have a…

We formulate, and present a numerical method for solving, an inverse problem for inferring parameters of a deterministic model from stochastic observational data (quantities of interest). The solution, given as a probability measure, is…

Data assimilation, in its most comprehensive form, addresses the Bayesian inverse problem of identifying plausible state trajectories that explain noisy or incomplete observations of stochastic dynamical systems. Various approaches have…

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…

This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…

There is currently a renewed interest in the Bayesian predictive approach to statistics. This paper offers a review on foundational concepts and focuses on predictive modeling, which by directly reasoning on prediction, bypasses inferential…

We study active structure learning of Bayesian networks in an observational setting, in which there are external limitations on the number of variable values that can be observed from the same sample. Random samples are drawn from the joint…

Beyond the conventional trial-and-error method, machine learning offers a great opportunity to accelerate the discovery of functional materials, but still often suffers from difficulties such as limited materials data and unbalanced…

Probabilistic Graphical Bayesian models of causation have continued to impact on strategic analyses designed to help evaluate the efficacy of different interventions on systems. However, the standard causal algebras upon which these…

We present a framework for the efficient computation of optimal Bayesian decisions under intractable likelihoods, by learning a surrogate model for the expected utility (or its distribution) as a function of the action and data spaces. We…

Bayesian active learning relies on the precise quantification of predictive uncertainty to explore unknown function landscapes. While Gaussian process surrogates are the standard for such tasks, an underappreciated fact is that their…

We provide a new flexible framework for inference with the instrumental variable model. Rather than using linear specifications, functions characterizing the effects of instruments and other explanatory variables are estimated using machine…