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We extend our earlier work on the compositional structure of cybernetic systems in order to account for the embodiment of such systems. All their interactions proceed through their bodies' boundaries: sensations impinge on their surfaces,…

This article presents a heuristic view that shows that the inner states of consciousness experienced by every human being have a physical but imaginary hypercomplex basis. The hypercomplex description is necessary because certain processes…

We consider an agent who represents uncertainty about the environment via a possibly misspecified model. Each period, the agent takes an action, observes a consequence, and uses Bayes' rule to update her belief about the environment. This…

This paper considers neural representation through the lens of active inference, a normative framework for understanding brain function. It delves into how living organisms employ generative models to minimize the discrepancy between…

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…

In the subjective Bayesian approach uncertainty is described by a prior distribution chosen by the statistician. Fuzzy set theory is another way of representing uncertainty. Here we give a decision theoretic approach which allows a Bayesian…

A method for sequential Bayesian inference of the static parameters of a dynamic state space model is proposed. The method is based on the observation that many dynamic state space models have a relatively small number of static parameters…

Recent advances in computational cognitive science (i.e., simulation-based probabilistic programs) have paved the way for significant progress in formal, implementable models of pragmatics. Rather than describing a pragmatic reasoning…

Bayesian inference is limited in scope because it cannot be applied in idealized contexts where none of the hypotheses under consideration is true and because it is committed to always using the likelihood as a measure of evidential…

Statistical inference is the science of drawing conclusions about some system from data. In modern signal processing and machine learning, inference is done in very high dimension: very many unknown characteristics about the system have to…

We introduce structured active inference, a large generalization and formalization of active inference using the tools of categorical systems theory. We cast generative models formally as systems "on an interface", with the latter being a…

We study a dynamic model of Bayesian persuasion in sequential decision-making settings. An informed principal observes an external parameter of the world and advises an uninformed agent about actions to take over time. The agent takes…

Physicists have, hitherto, mostly adopted a frequentist conception of probability, according to which probability statements apply only to ensembles. It is argued that we should, instead, adopt an epistemic, or Bayesian conception, in which…

This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space,…

Non-Bayesian social learning theory provides a framework that models distributed inference for a group of agents interacting over a social network. In this framework, each agent iteratively forms and communicates beliefs about an unknown…

We propose a general solution to the problem of robust Bayesian inference in complex settings where outliers may be present. In practice, the automation of robust Bayesian analyses is important in the many applications involving large and…

Phenomenology is the rigorous descriptive study of conscious experience. Recent attempts to formalize Husserlian phenomenology provide us with a mathematical model of perception as a function of prior knowledge and expectation. In this…

In a published paper [Sengupta, 2016], we have proposed that the brain (and other self-organized biological and artificial systems) can be characterized via the mathematical apparatus of a gauge theory. The picture that emerges from this…

In earlier work, we introduced flexible inference and decision-theoretic metareasoning to address the intractability of normative inference. Here, rather than pursuing the task of computing beliefs and actions with decision models composed…

We propose a new approach to explain Bayesian Networks. The approach revolves around a new definition of a probabilistic argument and the evidence it provides. We define a notion of independent arguments, and propose an algorithm to extract…