
Internal Category with Families in Presheaves
In this note, we review a construction of category with families (CwF) i...
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Lenses and Learners
Lenses are a wellestablished structure for modelling bidirectional tran...
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Incremental Monoidal Grammars
In this work we define formal grammars in terms of free monoidal categor...
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Category Theory for Modeling OOP
An outline and summary of four new potential applications of category th...
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Backprop as Functor: A compositional perspective on supervised learning
A supervised learning algorithm searches over a set of functions A → B p...
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A Category Theoretic Interpretation of Gandy's Principles for Mechanisms
Based on Gandy's principles for models of computation we give categoryt...
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Network Models from Petri Nets with Catalysts
Petri networks and network models are two frameworks for the composition...
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Categorical Stochastic Processes and Likelihood
In this work we take a Category Theoretic perspective on the relationship between probabilistic modeling and function approximation. We begin by defining two extensions of function composition to stochastic process subordination: one based on the coKleisli category under the comonad (Omega x ) and one based on the parameterization of a category with a Lawvere theory. We show how these extensions relate to the category Stoch and other Markov Categories. Next, we apply the Para construction to extend stochastic processes to parameterized statistical models and we define a way to compose the likelihood functions of these models. We conclude with a demonstration of how the Maximum Likelihood Estimation procedure defines an identityonobjects functor from the category of statistical models to the category of Learners. Code to accompany this paper can be found at https://github.com/dshieble/Categorical_Stochastic_Processes_and_Likelihood
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