Consciousness is originarily not an “I think that,” but rather an “I can.”1
Probabilistic modeling has particular abilities to sense, and the capacities of these, like any form of perception, are both constrained by and flourish from the friction of their limits. First thematized in mathematics as the “frequency with which a proposition similar to the one in question is found true in the course of experience”2, and now permeating media landscapes and theories of mind, the mathematical pragmatics of these models often remain unexamined in their phenomenological detail. This paper turns to the problems of statistical modelling and conjugate priors as part of a “body schema” of perceptual ability that graphical probabilistic modeling entails, specifically within undirected models and their parametrization, and the problems this poses for exact and even approximate inference.
This phenomenological study focuses on a small partition of these models — the move from image segmentation to object recognition using markov networks and conditional random fields. In this small frame, it examines at a minimal scale concepts such as conditioning, dependencies, cliques and factor reduction. It aims to return the problem of probability to that of experience; but within mathematical modelling practices themselves rather than the mediated experiences of their outputs. This research focuses on the idea of movement as essential to cognition, as outlined in Husserl and Merleau-Ponty, and applies this problem to some of the formal necessities of statistical conjugacy in graphical probabilistic modelling.
Conjugacy here is regarded as not just a computational problem, but a phenomenon that requires both a certain amount of formal necessity and also a slippery motility. Basic tenets of category theory are applied to the usage of these models to ascertain the hardwired shape of these models. The phenomenological consideration is focused on the formal assumptions involved in the mechanics of mathematics that underlie this approach, and the way that these structures move in the world of their existence, as opposed to a user interface level wherein experience is theorized on a virtual scale.
Under the aegis of Husserl’s formation of perception as an apparatus that can do something, the foremost question that this project asks is, what can inference do? And what does this tell us about its overall schema of perception?
1 Merleau-Ponty, Phenomenology of Perception, 22G
2 Abraham de Moivre, The Doctrine of Chances, ch 7, 1718
https://bit.ly/SYMPSem170425
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