Cameron Freer


My research involves connections between computability, model theory, probability, and physics, including the computability and complexity theory of Bayesian inference, the model theory of probabilistic structures, and the statistics of large graphs.
I am Chief Scientist at Borelian. At MIT I was an Instructor in Pure Mathematics 2008–2010, a Postdoctoral Fellow in the Computer Science and Artificial Intelligence Laboratory 2011–2013, and a Postdoctoral Associate in the Department of Brain and Cognitive Sciences 2013–2015. I was a Junior Researcher in the Mathematics Department of the University of Hawaii at Manoa 2010–2011, a Lyric Labs Visiting Fellow at Analog Devices 2013–2014, a Research Scientist at Gamalon Labs 2013–2016, and Chief Scientist at Remine 2017–2018.
Publications
The BetaBernoulli process and algebraic effects, with Sam Staton, Dario Stein, Hongseok Yang, Nate Ackerman, and Daniel Roy, in Proceedings of the 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018), 141:1141:15, 2018. arXiv:1802.09598. On computability and disintegration, with Nate Ackerman and Daniel Roy, Mathematical Structures in Computer Science 27, no. 8, 1287–1314, 2017. arXiv:1509.02992. Graph Turing machines, with Nate Ackerman, in Logic, Language, Information, and Computation, Proceedings of WoLLIC 2017, LNCS Vol. 10388, 1–13, 2017. A classification of orbits admitting a unique invariant measure, with Nate Ackerman, Aleksandra Kwiatkowska, and Rehana Patel, Annals of Pure and Applied Logic, 168, no. 1, 19–36, 2017. arXiv:1412.2735. Priors on exchangeable directed graphs, with Diana Cai and Nate Ackerman, Electronic Journal of Statistics, 10, no. 2, 3490–3515, 2016. arXiv:1510.08440. Invariant measures concentrated on countable structures, with Nate Ackerman and Rehana Patel, Forum of Mathematics Sigma 4, e17, 59 pp., 2016. arXiv:1206.4011. Invariant measures via inverse limits of finite structures, with Nate Ackerman, Jaroslav Nešetřil, and Rehana Patel, European Journal of Combinatorics 52, 248–289, 2016. arXiv:1310.8147. Feedback Turing computability, and Turing computability as feedback, with Nate Ackerman and Robert Lubarsky, in Proceedings of the 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2015), 523–534, 2015. Algorithmic aspects of Lipschitz functions, with Bjørn KjosHanssen, André Nies, and Frank Stephan, Computability 3, 45–61, 2014. arXiv:1402.2429. Towards commonsense reasoning via conditional simulation: legacies of Turing in Artificial Intelligence, with Daniel Roy and Joshua Tenenbaum, in Turing's Legacy: Developments from Turing's Ideas in Logic, ed. Rod Downey, ASL Lecture Notes in Logic 42, Cambridge University Press, 2014. arXiv:1212.4799. Randomness extraction and asymptotic Hamming distance, with Bjørn KjosHanssen, Selected Papers of the Ninth International Conference on Computability and Complexity in Analysis (CCA 2012), Logical Methods in Computer Science, 2013. arXiv:1008.0821.
Causal entropic forces, with Alexander WissnerGross, Physical Review Letters 110, 168702, 2013. Supplemental Material.
A notion of a computational step for Partial Combinatory Algebras, with Nate Ackerman, in Proceedings of the 10th Annual Conference on Theory and Applications of Models of Computation (TAMC 2013), LNCS Vol. 7876, 133–143, 2013. Computable de Finetti measures, with Daniel Roy, Annals of Pure and Applied Logic 163, no. 5, 530–546, 2012. arXiv:0912.1072. Noncomputable conditional distributions, with Nate Ackerman and Daniel Roy, in Proceedings of the 26th Annual IEEE Symposium on Logic in Computer Science (LICS 2011), 107–116, 2011. Relativistic statistical arbitrage, with Alexander WissnerGross, Physical Review E 82, 056104, 2010. Posterior distributions are computable from predictive distributions, with Daniel Roy, in Proceedings of the 13th International Conference on Artificial Intelligence and Statistics (AISTATS 2010), Journal of Machine Learning Research (JMLR) Workshop and Conference Proceedings 9, 2010. Computable exchangeable sequences have computable de Finetti measures, with Daniel Roy, in Mathematical Theory and Computational Practice, Proceedings of Computability in Europe (CiE 2009), LNCS Vol. 5635, 218–231, 2009.
Preprints
The entropy function of an invariant measure, with Nate Ackerman and Rehana Patel. arXiv:1809.02290. On the computability of graphons, with Nate Ackerman, with Jeremy Avigad, Daniel Roy, and Jason Rute. arXiv:1801.10387. Stable regularity for relational structures, with Nate Ackerman and Rehana Patel. arXiv:1712.09305. Properly ergodic structures, with Nate Ackerman, Alex Kruckman, and Rehana Patel. arXiv:1710.09336. Countable infinitary theories admitting an invariant measure, with Nate Ackerman and Rehana Patel. arXiv:1710.06128. Feedback computability on Cantor space, with Nate Ackerman and Robert Lubarsky. arXiv:1708.01139. On the computability of graph Turing machines, with Nate Ackerman. arXiv:1703.09406. An iterative stepfunction estimator for graphons, with Diana Cai and Nate Ackerman. arXiv:1412.2129. On the computability of conditional probability, with Nate Ackerman and Daniel Roy. arXiv:1005.3014.
PhD Thesis Models with High Scott Rank, PhD thesis, Harvard University, 2008.
Patents System and method for relativistic statistical securities trading, with Alexander WissnerGross, U.S. Patent 8,635,133 (2014).
