My research develops clean and conceptually rich mathematical foundations for agents, which are intuitive and well-suited to modern AI systems. The result so far has been an elegant unifying picture that explains a number of standard but seemingly ad-hoc choices made in practice. A key ingredient is a class of models I invented called Probabilistic Dependency Graphs (PDGs), which subsume traditional graphical models, yet can model inconsistent beliefs and most scenarios in machine learning.
For an overview, see my research statement.
Peer-Reviewed Papers and Publications
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workshop
conference
journal
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Mixture LanguagesOliver Richardson and Jialu Bao
POPL 2024 Languages for Inference (LAFI) Workshop
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The Local Inconsistency Resolution AlgorithmOliver Richardson
ICML 2023 Workshop on Structured Probabilistic Inference & Generative Modeling (SPIGM); Workshop on Localized Learning (LLW)
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Inference for Probabilistic Dependency GraphsOliver Richardson, Joseph Halpern, and Christopher De Sa
UAI 2023
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Abstract.
In a world blessed with a great diversity of loss functions, we argue that that choice between them is not a matter of taste or pragmatics, but of model. Probabilistic depencency graphs (PDGs) are probabilistic models that come equipped with a measure of "inconsistency". We prove that many standard loss functions arise as the inconsistency of a natural PDG describing the appropriate scenario, and use the same approach to justify a well-known connection between regularizers and priors. We also show that the PDG inconsistency captures a large class of statistical divergences, and detail benefits of thinking of them in this way, including an intuitive visual language for deriving inequalities between them. In variational inference, we find that the ELBO, a somewhat opaque objective for latent variable models, and variants of it arise for free out of uncontroversial modeling assumptions -- as do simple graphical proofs of their corresponding bounds. Finally, we observe that inconsistency becomes the log partition function (free energy) in the setting where PDGs are factor graphs.
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Probabilistic Dependency GraphsOliver Richardson and Joseph Halpern
AAAI 2021
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Complexity and Scale: Understanding the CreativeOliver Richardson
International Association of Computing and Philosophy (IACAP) 2014
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Capitalization in the St Petersburg Game: Why Statistical Distributions MatterMariam Thalos and Oliver Richardson
Politics, Philosophy & Economics 2014
Academic Talks
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How to Compute with PDGs: Inference, Inconsistency Measurement, and the Close Relationship Between the Two.
Invited Talk @ Cornell CS Theory Seminar, 19 Feb 2024. -
Learning, Inference, and the Pursuit of Consistency.
Invited Talk @ Cornell CS Student Colloquium, 7 Dec 2023. -
Probabilistic (In)consistency as a Basis for Learning and Inference.
Invited Talk @ University of Tenessee CS Dept, 29 Nov 2023. -
A Tutorial on Bialgebra.
@ Cornell Seminar on Programming Languages, 17 Sep 2022. -
Loss as the Inconsistency of a Probabilistic Dependency Graph: Choose Your Model, Not Your Loss Function.
Invited Talk @ Cornell Seminar on Artificial Intelligence, 2 Sep 2022. -
Probabilistic Dependency Graphs and Inconsistency: How to Model, Measure, and Mitigate Internal Conflict.
A Exam @ Cornell CS Department, 17 Sep 2021. -
Probabilistic Dependency Graphs.
@ Cornell CS Theory Tea, 17 Mar 2021. -
Cat Thoughts: An Intro to Categorical Thinking.
@ Cornell Graduate Student Seminar, 20 Feb 2019.