Cameron E. Freer
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View article: Forcing with Invariant Measures
Forcing with Invariant Measures Open
This paper introduces a model-theoretic generalization of the notion of forcing with random reals, in which forcing gives rise to random generic structures . Specifically, we consider forcing with $$\kappa $$ -Borel probability measures …
View article: GenSQL: A Probabilistic Programming System for Querying Generative Models of Database Tables
GenSQL: A Probabilistic Programming System for Querying Generative Models of Database Tables Open
This article presents GenSQL, a probabilistic programming system for querying probabilistic generative models of database tables. By augmenting SQL with only a few key primitives for querying probabilistic models, GenSQL enables complex Ba…
View article: Probabilistic Programming Interfaces for Random Graphs: Markov Categories, Graphons, and Nominal Sets
Probabilistic Programming Interfaces for Random Graphs: Markov Categories, Graphons, and Nominal Sets Open
We study semantic models of probabilistic programming languages over graphs, and establish a connection to graphons from graph theory and combinatorics. We show that every well-behaved equational theory for our graph probabilistic programm…
View article: Probabilistic programming interfaces for random graphs: Markov categories, graphons, and nominal sets
Probabilistic programming interfaces for random graphs: Markov categories, graphons, and nominal sets Open
We study semantic models of probabilistic programming languages over graphs, and establish a connection to graphons from graph theory and combinatorics. We show that every well-behaved equational theory for our graph probabilistic programm…
View article: On computable learning of continuous features
On computable learning of continuous features Open
We introduce definitions of computable PAC learning for binary classification over computable metric spaces. We provide sufficient conditions for learners that are empirical risk minimizers (ERM) to be computable, and bound the strong Weih…
View article: On computable aspects of algebraic and definable closure
On computable aspects of algebraic and definable closure Open
We investigate the computability of algebraic closure and definable closure with respect to a collection of formulas. We show that for a computable collection of formulas of quantifier rank at most $n$, in any given computable structure, b…
View article: Deep Involutive Generative Models for Neural MCMC
Deep Involutive Generative Models for Neural MCMC Open
We introduce deep involutive generative models, a new architecture for deep generative modeling, and use them to define Involutive Neural MCMC, a new approach to fast neural MCMC. An involutive generative model represents a probability ker…
View article: The Fast Loaded Dice Roller: A Near-Optimal Exact Sampler for Discrete\n Probability Distributions
The Fast Loaded Dice Roller: A Near-Optimal Exact Sampler for Discrete\n Probability Distributions Open
This paper introduces a new algorithm for the fundamental problem of\ngenerating a random integer from a discrete probability distribution using a\nsource of independent and unbiased random coin flips. We prove that this\nalgorithm, which …
View article: The Fast Loaded Dice Roller: A Near-Optimal Exact Sampler for Discrete Probability Distributions
The Fast Loaded Dice Roller: A Near-Optimal Exact Sampler for Discrete Probability Distributions Open
This paper introduces a new algorithm for the fundamental problem of generating a random integer from a discrete probability distribution using a source of independent and unbiased random coin flips. We prove that this algorithm, which we …
View article: On the Computability of Conditional Probability
On the Computability of Conditional Probability Open
As inductive inference and machine-learning methods in computer science see continued success, researchers are aiming to describe ever more complex probabilistic models and inference algorithms. It is natural to ask whether there is a univ…
View article: Feedback computability on Cantor space
Feedback computability on Cantor space Open
We introduce the notion of feedback computable functions from $2^\omega$ to $2^\omega$, extending feedback Turing computation in analogy with the standard notion of computability for functions from $2^\omega$ to $2^\omega$. We then show th…
View article: A Family of Exact Goodness-of-Fit Tests for High-Dimensional Discrete Distributions
A Family of Exact Goodness-of-Fit Tests for High-Dimensional Discrete Distributions Open
The objective of goodness-of-fit testing is to assess whether a dataset of observations is likely to have been drawn from a candidate probability distribution. This paper presents a rank-based family of goodness-of-fit tests that is specia…
View article: On the computability of graphons
On the computability of graphons Open
We investigate the relative computability of exchangeable binary relational data when presented in terms of the distribution of an invariant measure on graphs, or as a graphon in either $L^1$ or the cut distance. We establish basic computa…
View article: The Beta-Bernoulli process and algebraic effects
The Beta-Bernoulli process and algebraic effects Open
In this paper we use the framework of algebraic effects from programming language theory to analyze the Beta-Bernoulli process, a standard building block in Bayesian models. Our analysis reveals the importance of abstract data types, and t…
View article: The Beta-Bernoulli process and algebraic effects
The Beta-Bernoulli process and algebraic effects Open
In this paper we use the framework of algebraic effects from programming language theory to analyze the Beta-Bernoulli process, a standard building block in Bayesian models. Our analysis reveals the importance of abstract data types, and t…
View article: Stable regularity for relational structures
Stable regularity for relational structures Open
We generalize the stable graph regularity lemma of Malliaris and Shelah to the case of finite structures in finite relational languages, e.g., finite hypergraphs. We show that under the model-theoretic assumption of stability, such a struc…
View article: Properly ergodic structures
Properly ergodic structures Open
We consider ergodic $\mathrm{Sym}(\mathbb{N})$-invariant probability measures on the space of $L$-structures with domain $\mathbb{N}$ (for $L$ a countable relational language), and call such a measure a properly ergodic structure when no i…
View article: Countable infinitary theories admitting an invariant measure
Countable infinitary theories admitting an invariant measure Open
Let $L$ be a countable language. We characterize, in terms of definable closure, those countable theories $Σ$ of $\mathcal{L}_{ω_1, ω}(L)$ for which there exists an $S_\infty$-invariant probability measure on the collection of models of $Σ…
View article: Feedback computability on Cantor space
Feedback computability on Cantor space Open
We introduce the notion of feedback computable functions from $2^ω$ to $2^ω$, extending feedback Turing computation in analogy with the standard notion of computability for functions from $2^ω$ to $2^ω$. We then show that the feedback comp…
View article: On the computability of graph Turing machines
On the computability of graph Turing machines Open
We consider graph Turing machines, a model of parallel computation on a graph, in which each vertex is only capable of performing one of a finite number of operations. This model of computation is a natural generalization of several well-s…
View article: On computability and disintegration
On computability and disintegration Open
We show that the disintegration operator on a complete separable metric space along a projection map, restricted to measures for which there is a unique continuous disintegration, is strongly Weihrauch equivalent to the limit operator Lim.…
View article: Priors on exchangeable directed graphs
Priors on exchangeable directed graphs Open
Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which exten…