Assistant Professor

Department of Statistical Sciences

Department of Computer Science (cross-appointment)

University of Toronto

Department of Computer and Mathematical Sciences

University of Toronto Scarborough

**Founding Faculty**, Vector Institute

Jump to: Teaching | Research Articles | News | Probabilistic Programming | Curriculum Vitæ | Contact

I am seeking students at all levels with strong quantitative backgrounds interested in foundational problems at the intersection of machine learning, statistics, and computer science. I am also seeking qualified postdoctoral researchers for two- and three- year positions. Click to read instructions before contacting me, or your email is likely to be deleted. I value people who are attentive to details.

NOV 2017

Joint work with J. Huggins (Harvard) accepted to Bernoulli. This work introduces a new notion of effective sample size in order to control the quality of the *samples* produced by Sequential Monte Carlo.

JUL 2017

Pleased to hear that my article characterizing product-form exchangeable feature allocations with Battison, Favaro, and Teh has been accepted to the Annals of Applied Probability.

JUN 2017

Happy to announce my paper with Gintare Dziugaite on neural network generalization bounds has been accepted for a plenary talk at UAI in Australia this August.

MAR 2017

I'm excited to be part of the **Vector Institute**. We're looking to hire the best and brightest, from all corners. Come join us!

FEB 2017

I'm happy to announce that I've received a 2017 Google Research Award.

- Alexander Edmonds, MsC candidate, CS
- Zacharie Naulet, Postdoctoral fellow
- Jeffrey Negrea, Ph.D. candidate, Stats
- Ekansh Sharma, Ph.D. candidate, CS
- Jun Yang, Ph.D. candidate, Stats
- Yuxing Zhang, M.Sc. candidate, CS

- Haosui (Kevin) Duanmu, Ph.D., Statistics → Postdoc at Berkeley
- Victor Veitch, Ph.D., Statistics (Departmental Thesis Award) → Postdoc at Columbia
- Siddharth Ancha

M.Sc., CS → Ph.D. at CMU - Pablo García Moreno

Postdoc → Permanent researcher at Amazon

My research blends computer science, statistics and probability theory; I study "probabilistic programming" and develop computational perspectives on fundamental ideas in probability theory and statistics. I am particularly interested in: representation theorems that connect computability, complexity, and probabilistic structures; stochastic processes, the use of recursion to define stochastic processes, and applications to nonparametric Bayesian statistics; and the complexity of probabilistic and statistical inference, especially in the context of probabilistic programming. Ultimately, I am motivated by the long term goal of making lasting contributions to our understanding of complex adaptive systems and especially Artificial Intelligence.

**STA3000** (Fall 2017)

**Advanced Theory of Statistics, Part I**

**STA4516** (Fall 2017)

**Nonstandard Analysis and Applications to Statistics and Probability**

**STAD68** (Fall 2017)

**Advanced Machine Learning and Data Mining**

**STAD68** (Fall 2016)

**Advanced Machine Learning and Data Mining**

**STA4516** (Fall 2015)

**Topics in Probabilistic Programming**

**STAC63** (Fall 2015)

**Probability Models**

**STAD68** (Winter 2015)

**Advanced Machine Learning and Data Mining**

**STA4513** (Fall 2014)

**Statistical models of networks, graphs, and other relational structures**

Programs can be used to give compact representations of distributions: in order to represent a distribution, one simply gives a program that would generate an exact sample were the random number generator to produce realizations of independent and identically distributed random variables. This approach to representing distributions by *probabilistic programs* works not only for simple distributions on numbers like Poissons, Gaussians, etc., and combinations thereof, but also for more exotic distributions on, e.g., phrases in natural language, rendered 2D images of 3D scenes, and climate sensor measurements.

*Probabilistic programming systems* support statistical inference on models defined by probabilistic programs.
By constraining some variables of a program (e.g., simulated sensor readings in some climate model) and studying the *conditional* distribution of other variables (e.g., the parameters of the climate model), we can identify plausible variable settings that agree with the constraints. Conditional inferences like this would allow us to, e.g., build predictive text systems for mobile phones, guess the 3D shape of an object from only a photograph, or study the underlying mechanisms driving observed climate measurements.

Probabilistic programming systems for machine learning and statistics are still in their infancy, and there are many interesting theoretical and applied problems yet to be tackled. My own work focuses on theoretical questions around representing stochastic processes and the computational complexity of sampling-based approaches to inference. I was involved in the definition of the probabilistic programming language Church, and its first implementation, MIT-Church, a Markov Chain Monte Carlo algorithm operating on the space of execution histories of an interpreter. Some of my key theoretical work includes a study of the computability of conditional probability and de Finetti measures, both central notions in Bayesian statistics. Readers looking for an overview of these results are directed to the introduction of my doctoral dissertation. A less technical description of a probabilistic programming approach to artificial intelligence can be found in a recent book chapter on legacies of Alan Turing, co-authored with Freer and Tenenbaum.

More information on probabilistic programming can be found on probabilistic-programming.org, a wiki that I maintain. In particular, look at the list of research articles and papers on probabilistic programming and the tutorials.

I co-organized the first workshop on probabilistic programming for statistics and machine learning at NIPS*2008 (with Vikash Mansinghka, John Winn, David McAllester and Josh Tenenbaum). Four years later, I co-organized the second workshop on probabilistic programming at NIPS*2012 (with Vikash Mansinghka and Noah Goodman).

Hello, my name is Daniel M. Roy (or simply, Dan) and I am an Assistant Professor of Statistics at the University of Toronto, with a courtesy appointment also in Computer Science.

I received all three of my degrees in (Electrical Engineering and) Computer Science from MIT. As a doctoral student, I was member of the Computer Science and Artificial Intelligence Laboratory (CSAIL), where I was advised by Leslie Kaelbling. I also collaborated with members of Josh Tenenbaum's Computational Cognitive Science group.

After my doctorate, I was a Newton International Fellow of the Royal Society and then Research Fellow of of Emmanuel College at the University of Cambridge. At Cambridge, I was a member of the Machine Learning Group, headed by Zoubin Ghahramani and part of the Computational and Biological Learning Lab in the Department of Engineering.

You may find my abbreviated curriculum vitæ online.

Nate Ackerman, Siddharth Ancha, Matej Balog, Marco Battiston, William Beebee, Keith Bonawitz, Nate Ackerman, Jeremy Avigad, Cristian Cadar, Hal Daumé III, Brian Demsky, Daniel Dumitran, Gintare Karolina Dziugaite, Stefano Favaro, Cameron Freer, Zoubin Ghahramani, Noah Goodman, Creighton Heaukulani, Jonathan Huggins, Eric Jonas, Leslie Kaelbling, Charles Kemp, Balaji Lakshminarayanan, Tudor Leu, James Lloyd, Vikash Mansinghka, Peter Orbanz, Ryan Rifkin, Martin Rinard, Jason Rute, Virginia Savova, Lauren Schmidt, David Sontag, Sam Staton, Yee Whye Teh, Josh Tenenbaum, Victor Veitch, David Wingate, Hongseok Yang

**Family**

Meloney Roy,
Kenny Roy.

Several template .TEX files for producing slides for mathematical talks that more closely mimic the chalk talk aesthetic.

Valid XHTML 1.1 re-validate

Valid CSS
/styles/screen

Data-dependent PAC-Bayes priors via differential privacy

Gintare Karolina Dziugaite and Daniel M. Roy

| arXiv:1802.09583

The Beta-Bernoulli process and algebraic effects

Sam Staton, Dario Stein, Hongseok Yang, Nathanael Ackerman, Cameron Freer, Daniel M. Roy

| arXiv:1802.09598

On the computability of graphons

(with Nathanael L. Ackerman, Jeremy Avigad, Cameron E. Freer, and Jason M. Rute)

| arXiv:1801.10387

Entropy-SGD optimizes the prior of a PAC-Bayes bound: Generalization properties of Entropy-SGD and data-dependent priors

Gintare Karolina Dziugaite and Daniel M. Roy

| arXiv:1712.09376

An estimator for the tail-index of graphex processes

Zacharie Naulet, Ekansh Sharma, Victor Veitch, Daniel M. Roy

| arXiv:1712.01745

Exchangeable modelling of relational data: checking sparsity, train-test splitting, and sparse exchangeable Poisson matrix factorization

Victor Veitch, Ekansh Sharma, Zacharie Naulet, Daniel M. Roy

| arXiv:1712.02311

On Extended Admissible Procedures and their Nonstandard Bayes Risk

Haosui Duanmu and Daniel M. Roy

| arXiv:1612.09305

Sampling and Estimation for (Sparse) Exchangeable Graphs

Victor Veitch and Daniel M. Roy

| arXiv:1611.00843

The Class of Random Graphs Arising from Exchangeable Random Measures

Victor Veitch and Daniel M. Roy

| arXiv:1512.03099

Gibbs-type Indian Buffet Processes

(with Creighton Heaukulani)

| arXiv:1512.02543

The continuum-of-urns scheme,

generalized beta and Indian buffet processes,

and hierarchies thereof

| arXiv:1501.00208

On the computability of conditional probability

(with Nate Ackerman and Cameron Freer)

| arXiv:1005.3014

**Note:** *Articles distinguished by "(with ...)" have alphabetical author lists, as is the convention in mathematics and theoretical computer science.*

Computability, inference and modeling in probabilistic programming

Daniel M. Roy

*Ph.D. thesis, Massachusetts Institute of Technology*,
2011.

MIT/EECS George M. Sprowls Doctoral Dissertation Award

Sequential Monte Carlo as Approximate Sampling: bounds, adaptative resampling via \infty-ESS, and an application to Particle Gibbs

(with Jonathan Huggins)

To appear in *Bernoulli*.

| arXiv:1503.00966

A characterization of product-form exchangeable feature probability functions

Marco Battiston, Stefano Favaro, Daniel M. Roy, Yee Whye Teh

To appear in *Annals of Applied Probability*.

| arXiv:1607.02066

Computing Nonvacuous Generalization Bounds for Deep (Stochastic) Neural Networks with Many More Parameters than Training Data

Gintare Karolina Dziugaite and Daniel M. Roy

In *Proc. Uncertainty in Artificial Intelligence* (UAI), 2017.

| arXiv:1703.11008

Measuring the reliability of MCMC inference with bidirectional Monte Carlo

Roger B. Grosse, Siddharth Ancha, and Daniel M. Roy

In *Adv. Neural Information Processing Systems 29* (NIPS), 2016.

| arXiv:1606.02275

| nips

On computability and disintegration

(with Nate Ackerman and Cameron Freer)

In *Mathematical Structures in Computer Science*.

| arXiv:1509.02992 (recommended)

| doi:10.1017/S0960129516000098

The Mondrian Kernel

Matej Balog, Balaji Lakshminarayan, Zoubin Ghahramani, Daniel M. Roy, Yee Whye Teh

In *Proc. Uncertainty in Artificial Intelligence* (UAI), 2016.

| arXiv:1606.05241

Mondrian Forests for Large-Scale Regression when Uncertainty Matters

Balaji Lakshminarayanan,
Daniel M. Roy,
Yee Whye Teh.

In *Proc. Artificial Intelligence and Statistics* (AISTATS), 2016.

| arXiv:1506.03805

Training generative neural networks via Maximum Mean Discrepancy optimization

Gintare Karolina Dziugaite, Daniel M. Roy, and Zoubin Ghahramani

In *Proc. Uncertainty in Artificial Intelligence* (UAI), 2015.

| arXiv:1505.03906

The combinatorial structure of beta negative binomial processes

(with Creighton Heaukulani)

*Bernoulli*, 2016, Vol. 22, No. 4, 2301–2324.

Particle Gibbs for Bayesian Additive Regression Trees

Balaji Lakshminarayanan,
Daniel M. Roy,
Yee Whye Teh

*Proc. Artificial Intelligence and Statistics* (AISTATS), 2015.

| arXiv:1502.04622

Mondrian Forests: Efficient Online Random Forests

Balaji Lakshminarayanan,
Daniel M. Roy,
Yee Whye Teh

*Adv. Neural Information Processing Systems 27* (NIPS), 2014.

| code

Bayesian Models of Graphs, Arrays and Other Exchangeable Random Structures

(with Peter Orbanz)

*IEEE Trans. Pattern Anal. Mach. Intelligence* (PAMI), 2014.

| doi:10.1109/TPAMI.2014.2334607

| arXiv:1312:7857

| slides for talk at CIMAT

Top-down particle filtering for Bayesian decision trees

Balaji Lakshminarayanan,
Daniel M. Roy,
Yee Whye Teh

*Proc. Int. Conf. on Machine Learning* (ICML), 2013.

| code

Towards common-sense reasoning via conditional simulation:

Legacies of Turing in Artificial Intelligence

(with Cameron Freer and Josh Tenenbaum)

*Turing's Legacy (ASL Lecture Notes in Logic)*, 2012.

Random function priors for exchangeable arrays with applications to graphs and relational data

James Lloyd, Peter Orbanz, Zoubin Ghahramani, Daniel M. Roy

*Adv. Neural Information Processing Systems 25* (NIPS), 2012.

Computable de Finetti measures

(with
Cameron Freer)

*Annals of Pure and Applied Logic*, 2012.

Complexity of Inference in Latent Dirichlet Allocation

David Sontag and
Daniel Roy

*Adv. Neural Information Processing Systems 24* (NIPS), 2011.

Noncomputable conditional distributions

(with Nate Ackerman and
Cameron Freer)

*Proc. Logic in Computer Science* (LICS), 2011.

Probabilistically Accurate Program Transformations

Sasa Misailovic,
Daniel M. Roy,
and
Martin C. Rinard

*Proc. Int. Static Analysis Symp.*
(SAS), 2011.

Bayesian Policy Search with Policy Priors

David Wingate,
Noah D. Goodman,
Daniel M. Roy,
Leslie P. Kaelbling,
and
Joshua B. Tenenbaum

*Proc. Int. Joint Conf. on Artificial Intelligence*
(IJCAI), 2011.

Posterior distributions are computable from predictive distributions

(with Cameron Freer)

*Proc. Artificial Intelligence and Statistics* (AISTATS), 2010.

The Infinite Latent Events Model

David Wingate,
Noah D. Goodman,
Daniel M. Roy,
and
Joshua B. Tenenbaum

In *Proc. Uncertainty in Artificial Intelligence* (UAI), 2009.

Computable exchangeable sequences have computable de Finetti measures

(with Cameron Freer)

In *Proc. Computability in Europe* (CiE), 2009.

Exact and Approximate Sampling by Systematic Stochastic Search

Vikash Mansinghka,
Daniel M. Roy,
Eric Jonas,
and
Joshua Tenenbaum

In *Proc. Artificial Intelligence and Statistics* (AISTATS), 2009.

The Mondrian Process

(with
Yee Whye Teh)

In *Adv. Neural Information Processing Systems 21* (NIPS), 2009.

Video animation of the Mondrian process as one zooms into the origin (under a beta Levy rate measure at time t=1.0). See also the time evolution of a Mondrian process on the plane as we zoom in with rate proportional to time. In both cases, the colors are chosen at random from a palette. These animations were produced by Yee Whye in Matlab. For now, we reserve copyright, but please email me and we'll be more than likely happy to let you use them.

Chapter 5. Distributions on data structures: a case study

(Mondrian process theory)

Those seeking a more formal presentation of the Mondrian process than the NIPS paper should see Chapter 5 of my dissertation.

Church: a language for generative models

Noah Goodman,
Vikash Mansinghka,
Daniel M. Roy,
Keith Bonawitz,
and
Joshua Tenenbaum

In *Proc. Uncertainty in Artificial Intelligence* (UAI), 2008.

Bayesian Agglomerative Clustering with Coalescents

Yee Whye Teh,
Hal Daumé III,
and
Daniel M. Roy

*Adv. Neural Information Processing Systems 20* (NIPS), 2008.

Discovering Syntactic Hierarchies

Virginia Savova,
Daniel M. Roy,
Lauren Schmidt, and
Joshua B. Tenenbaum

*Proc. Cognitive Science* (COGSCI), 2007.

AClass: An online algorithm for generative classification

Vikash K. Mansinghka,
Daniel M. Roy,
Ryan Rifkin, and
Joshua B. Tenenbaum

*Proc. Artificial Intelligence and Statistics* (AISTATS), 2007.

Efficient Bayesian Task-level Transfer Learning

Daniel M. Roy and
Leslie P. Kaelbling

*Proc. Int. Joint Conf. on Artificial Intelligience*
(IJCAI), 2007.

Learning Annotated Hierarchies from Relational Data

Daniel M. Roy,
Charles Kemp,
Vikash Mansinghka,
and
Joshua B. Tenenbaum

*Adv. Neural Information Processing Systems 19* (NIPS), 2007.

Clustered Naive Bayes

*MEng thesis*,
Massachusetts Institute of Technology, 2006.

Enhancing Server Availability and Security Through Failure-Oblivious Computing

Martin Rinard, Cristian
Cadar, Daniel Dumitran,
Daniel M. Roy,
Tudor Leu,
and William S. Beebee, Jr.

*Proc. Operating Systems Design and
Implementation* (OSDI), 2004.

A Dynamic Technique for Eliminating Buffer Overflow Vulnerabilities (and Other Memory Errors)

Martin Rinard, Cristian Cadar, Daniel Dumitran,
Daniel M. Roy,
and Tudor Leu

*Proc. Annual Computer Security Applications Conference* (ACSAC), 2004.

On computable representations of exchangeable data

Nathanael L. Ackerman, Jeremy Avigad, Cameron E. Freer, Daniel M. Roy, and Jason M. Rute

Exchangeable Random Processes and Data Abstraction

Sam Staton, Hongseok Yang, Nate Ackerman, Cameron Freer, Dan Roy

A study of the effect of JPG compression on adversarial images

Gintare Karolina Dziugaite, Zoubin Ghahramani, Daniel M. Roy

| arXiv:1608:00853

Neural Network Matrix Factorization

Gintare Karolina Dziugaite and Daniel M. Roy

| arXiv:1511.06443

Exchangeable databases and their functional representation

James Lloyd, Peter Orbanz, Zoubin Ghahramani, Daniel M. Roy

*NIPS Workshop on Frontiers of Network Analysis: Methods, Models, and Applications*, 2013.

On the computability and complexity of Bayesian reasoning

*NIPS Philosophy and Machine Learning Workshop*, 2011.

When are probabilistic programs probably computationally tractable?

(with Cameron Freer and Vikash Mansinghka)

*NIPS Workshop on Monte Carlo Methods for Modern Applications*, 2010.

Complexity of Inference in Topic Models

David Sontag and
Daniel Roy

*NIPS Workshop on Applications for Topic Models: Text and Beyond*, 2009.

A stochastic programming perspective on nonparametric Bayes

Daniel M. Roy,
Vikash Mansinghka,
Noah Goodman,
and
Joshua Tenenbaum

*ICML Workshop on Nonparametric Bayesian*, 2008.

Efficient Specification-Assisted Error Localization

Brian Demsky, Cristian Cadar,
Daniel M. Roy,
and Martin C. Rinard

*Proc. Workshop on Dynamic Analysis* (WODA), 2004.

Efficient Specification-Assisted Error Localization and Correction

Brian Demsky, Cristian Cadar,
Daniel M. Roy,
and Martin C. Rinard

*MIT CSAIL Technical Report 927.*
November, 2003.

Implementation of Constraint Systems for Useless Variable Elimination

(advised by
Mitchell Wand)

*Research Science Institute.*
August, 1998.

I believe that errata, clarifications, missed citations, links to follow-on work, retractions, and other "marginalia" are important, but underappreciated, contributions to the scientific literature. Ultimately, the nature of a scientific document needs to be rethought, but until then I am slowly collecting marginalia in a simple wiki. I encourage everyone to host similar wikis, or contribute to this one.

Marginalia wiki.

*recruiters: no, thank you.*

**(research email)**

droy#utstat.toronto.edu

replace # with @

**(teaching-related email)**

UTSC:
daniel.roy#utsc.utoronto.ca

StG:
daniel.roy#utoronto.ca

**(UTSC office)**

Dept. of Computer and

Mathematical Sciences

Univ. of Toronto Scarborough

IC Building, Room 462

1265 Military Trail

Toronto, ON

M1C 1A4

Canada

t: +1 (416) 287 5653

**(StG office)**

Dept. of Statistical Sciences

Univ. of Toronto

Sidney Smith Hall, 6027F

100 St. George St.

Toronto, ON

M5S 3G3

Canada

t: +1 (416) 978 4220

f: +1 (416) 978 5133

**(mobile phone)**

CA: +1 (647) 993 6380

UK: +44 (0) 7552 784 664

US: +1 (310) 913 6380