OxCSML : People : Chris J. Maddison

Probabilistic inference, Monte Carlo methods, neural networks, point processes

I am a DPhil student of statistics at the University of Oxford supervised by Yee Whye Teh and Arnaud Doucet. I also spend two days a week as a Research Scientist at DeepMind. Previously, I received my MSc. from the University of Toronto supervised by Geoffrey Hinton. I was one of the primary contributors to the AlphaGo project.

Publications

2019

E. Mathieu , C. Le Lan , C. J. Maddison , R. Tomioka , Y. W. Teh , Continuous Hierarchical Representations with Poincaré Variational Auto-Encoders, in Advances in Neural Information Processing Systems 32, 2019, 12565–12576.
The Variational Auto-Encoder (VAE) is a popular method for learning a generative model and embeddings of the data. Many real datasets are hierarchically structured. However, traditional VAEs map data in a Euclidean latent space which cannot efficiently embed tree-like structures. Hyperbolic spaces with negative curvature can. We therefore endow VAEs with a Poincaré ball model of hyperbolic geometry as a latent space and rigorously derive the necessary methods to work with two main Gaussian generalisations on that space. We empirically show better generalisation to unseen data than the Euclidean counterpart, and can qualitatively and quantitatively better recover hierarchical structures.
```
@inproceedings{mathieu2019Continuous,
  title = {Continuous Hierarchical Representations with Poincar\'{e} Variational Auto-Encoders},
  author = {Mathieu, Emile and Le Lan, Charline and Maddison, Chris J. and Tomioka, Ryota and Teh, Yee Whye},
  booktitle = {Advances in Neural Information Processing Systems 32},
  pages = {12565--12576},
  year = {2019},
  publisher = {Curran Associates, Inc.}
}
```

2018

T. Rainforth , A. R. Kosiorek , T. A. Le , C. J. Maddison , M. Igl , F. Wood , Y. W. Teh , Tighter Variational Bounds are Not Necessarily Better, in International Conference on Machine Learning (ICML), 2018.
Project: bigbayes

We provide theoretical and empirical evidence that using tighter evidence lower bounds (ELBOs) can be detrimental to the process of learning an inference network by reducing the signal-to-noise ratio of the gradient estimator. Our results call into question common implicit assumptions that tighter ELBOs are better variational objectives for simultaneous model learning and inference amortization schemes. Based on our insights, we introduce three new algorithms: the partially importance weighted auto-encoder (PIWAE), the multiply importance weighted auto-encoder (MIWAE), and the combination importance weighted auto-encoder (CIWAE), each of which includes the standard importance weighted auto-encoder (IWAE) as a special case. We show that each can deliver improvements over IWAE, even when performance is measured by the IWAE target itself. Moreover, PIWAE can simultaneously deliver improvements in both the quality of the inference network and generative network, relative to IWAE.
```
@inproceedings{rainforth2018tighter,
  title = {Tighter Variational Bounds are Not Necessarily Better},
  author = {Rainforth, Tom and Kosiorek, Adam R. and Le, Tuan Anh and Maddison, Chris J. and Igl, Maximilian and Wood, Frank and Teh, Yee Whye},
  booktitle = {International Conference on Machine Learning (ICML)},
  year = {2018},
  month = jul
}
```

2017

C. J. Maddison , D. Lawson , G. Tucker , N. Heess , M. Norouzi , A. Mnih , A. Doucet , Y. W. Teh , Filtering Variational Objectives, in Advances in Neural Information Processing Systems (NeurIPS), 2017.
Project: deepmind

The evidence lower bound (ELBO) appears in many algorithms for maximum likelihood estimation (MLE) with latent variables because it is a sharp lower bound of the marginal log-likelihood. For neural latent variable models, optimizing the ELBO jointly in the variational posterior and model parameters produces state-of-the-art results. Inspired by the success of the ELBO as a surrogate MLE objective, we consider the extension of the ELBO to a family of lower bounds defined by a Monte Carlo estimator of the marginal likelihood. We show that the tightness of such bounds is asymptotically related to the variance of the underlying estimator. We introduce a special case, the filtering variational objectives (FIVOs), which takes the same arguments as the ELBO and passes them through a particle filter to form a tighter bound. FIVOs can be optimized tractably with stochastic gradients, and are particularly suited to MLE in sequential latent variable models. In standard sequential generative modeling tasks we present uniform improvements over models trained with ELBO, including some whole nat-per-timestep improvements.
```
@inproceedings{MadLawTuc2017b,
  author = {Maddison, C. J. and Lawson, D. and Tucker, G. and Heess, N. and Norouzi, M. and Mnih, A. and Doucet, A. and Teh, Y. W.},
  booktitle = {Advances in Neural Information Processing Systems (NeurIPS)},
  title = {Filtering Variational Objectives},
  year = {2017},
  month = dec,
  bdsk-url-1 = {https://arxiv.org/pdf/1705.09279v1.pdf}
}
```
C. J. Maddison , A. Mnih , Y. W. Teh , The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables, in International Conference on Learning Representations (ICLR), 2017.
Project: deepmind

The reparameterization trick enables optimizing large scale stochastic computation graphs via gradient descent. The essence of the trick is to refactor each stochastic node into a differentiable function of its parameters and a random variable with fixed distribution. After refactoring, the gradients of the loss propagated by the chain rule through the graph are low variance unbiased estimators of the gradients of the expected loss. While many continuous random variables have such reparameterizations, discrete random variables lack continuous reparameterizations due to the discontinuous nature of discrete states. In this work we introduce concrete random variables – continuous relaxations of discrete random variables. The concrete distribution is a new family of distributions with closed form densities and a simple reparameterization. Whenever a discrete stochastic node of a computation graph can be refactored into a one-hot bit representation that is treated continuously, concrete stochastic nodes can be used with automatic differentiation to produce low-variance biased gradients of objectives (including objectives that depend on the log-probability of latent stochastic nodes) on the corresponding discrete graph. We demonstrate effectiveness of concrete relaxations on density estimation and structured prediction tasks using neural networks.
```
@inproceedings{maddison2016concrete,
  author = {Maddison, Chris J. and Mnih, Andriy and Teh, Yee Whye},
  booktitle = {International Conference on Learning Representations (ICLR)},
  note = {ArXiv e-prints:1611.00712},
  title = {{The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables}},
  year = {2017},
  bdsk-url-1 = {https://arxiv.org/pdf/1611.00712.pdf}
}
```
C. J. Maddison , D. Lawson , G. Tucker , N. Heess , M. Norouzi , A. Mnih , A. Doucet , Y. W. Teh , Particle Value Functions, in ICLR 2017 Workshop Proceedings, 2017.
Project: deepmind

The policy gradients of the expected return objective can react slowly to rare rewards. Yet, in some cases agents may wish to emphasize the low or high returns regardless of their probability. Borrowing from the economics and control literature, we review the risk-sensitive value function that arises from an exponential utility and illustrate its effects on an example. This risk-sensitive value function is not always applicable to reinforcement learning problems, so we introduce the particle value function defined by a particle filter over the distributions of an agent’s experience, which bounds the risk-sensitive one. We illustrate the benefit of the policy gradients of this objective in Cliffworld.
```
@inproceedings{MadLawTuc2017a,
  author = {Maddison, C. J. and Lawson, D. and Tucker, G. and Heess, N. and Norouzi, M. and Mnih, A. and Doucet, A. and Teh, Y. W.},
  booktitle = {ICLR 2017 Workshop Proceedings},
  note = {ArXiv e-prints: 1703.05820},
  title = {Particle Value Functions},
  year = {2017},
  bdsk-url-1 = {https://arxiv.org/pdf/1705.09279v1.pdf}
}
```

2016

C. J. Maddison , A Poisson process model for Monte Carlo, in Perturbation, Optimization, and Statistics, T. Hazan, G. Papandreou, and D. Tarlow, Eds. MIT Press, 2016.
Simulating samples from arbitrary probability distributions is a major research program of statistical computing. Recent work has shown promise in an old idea, that sampling from a discrete distribution can be accomplished by perturbing and maximizing its mass function. Yet, it has not been clearly explained how this research project relates to more traditional ideas in the Monte Carlo literature. This chapter addresses that need by identifying a Poisson process model that unifies the perturbation and accept-reject views of Monte Carlo simulation. Many existing methods can be analyzed in this framework. The chapter reviews Poisson processes and defines a Poisson process model for Monte Carlo methods. This model is used to generalize the perturbation trick to infinite spaces by constructing Gumbel processes, random functions whose maxima are located at samples over infinite spaces. The model is also used to analyze A* sampling and OS*, two methods from distinct Monte Carlo families.
```
@incollection{maddison2016ppmontecarlo,
  author = {Maddison, Chris J.},
  booktitle = {Perturbation, Optimization, and Statistics},
  editor = {Hazan, Tamir and Papandreou, George and Tarlow, Daniel},
  publisher = {MIT Press},
  title = {{A Poisson process model for Monte Carlo}},
  year = {2016},
  bdsk-url-1 = {https://arxiv.org/pdf/1602.05986.pdf}
}
```

D. Silver , A. Huang , C. J. Maddison , A. Guez , L. Sifre , G. Driessche , J. Schrittwieser , I. Antonoglou , V. Panneershelvam , M. Lanctot , S. Dieleman , D. Grewe , J. Nham , N. Kalchbrenner , I. Sutskever , T. Lillicrap , M. Leach , K. Kavukcuoglu , T. Graepel , D. Hassabis , Mastering the game of Go with deep neural networks and tree search, Nature, vol. 529, no. 7587, 484–489, 2016.

@article{silver2016alphago,
  author = {Silver, David and Huang, Aja and Maddison, Chris J. and Guez, Arthur and Sifre, Laurent and van den Driessche, George and Schrittwieser, Julian and Antonoglou, Ioannis and Panneershelvam, Veda and Lanctot, Marc and Dieleman, Sander and Grewe, Dominik and Nham, John and Kalchbrenner, Nal and Sutskever, Ilya and Lillicrap, Timothy and Leach, Madeleine and Kavukcuoglu, Koray and Graepel, Thore and Hassabis, Demis},
  journal = {Nature},
  number = {7587},
  pages = {484 - 489},
  title = {{Mastering the game of Go with deep neural networks and tree search}},
  volume = {529},
  year = {2016},
  bdsk-url-1 = {http://www.nature.com/nature/journal/v529/n7587/full/nature16961.html}
}

2015

C. J. Maddison , A. Huang , I. Sutskever , D. Silver , Move Evaluation in Go Using Deep Convolutional Neural Networks, in International Conference on Learning Representations, 2015.

@inproceedings{maddison2015go,
  author = {Maddison, Chris J. and Huang, Aja and Sutskever, Ilya and Silver, David},
  booktitle = {International Conference on Learning Representations},
  title = {{Move Evaluation in Go Using Deep Convolutional Neural Networks}},
  year = {2015},
  bdsk-url-1 = {https://arxiv.org/pdf/1412.6564.pdf}
}

2014

C. J. Maddison , D. Tarlow , Structured Generative Models of Natural Source Code, in Proceedings of the 31st International Conference on Machine Learning, 2014.

@inproceedings{maddison2014nsc,
  author = {Maddison, Chris J. and Tarlow, Daniel},
  booktitle = {Proceedings of the 31st International Conference on Machine Learning},
  title = {{Structured Generative Models of Natural Source Code}},
  year = {2014},
  bdsk-url-1 = {https://arxiv.org/pdf/1401.0514.pdf}
}

C. J. Maddison , D. Tarlow , T. Minka , A* Sampling, in Advances in Neural Information Processing Systems 27, 2014.
The problem of drawing samples from a discrete distribution can be converted into a discrete optimization problem. In this work, we show how sampling from a continuous distribution can be converted into an optimization problem over continuous space. Central to the method is a stochastic process recently described in mathematical statistics that we call the Gumbel process. We present a new construction of the Gumbel process and A* sampling, a practical generic sampling algorithm that searches for the maximum of a Gumbel process using A* search. We analyze the correctness and convergence time of A* sampling and demonstrate empirically that it makes more efficient use of bound and likelihood evaluations than the most closely related adaptive rejection sampling-based algorithms.
```
@inproceedings{maddison2014astar,
  author = {Maddison, Chris J. and Tarlow, Daniel and Minka, Tom},
  booktitle = {Advances in Neural Information Processing Systems 27},
  title = {{A* Sampling}},
  year = {2014},
  bdsk-url-1 = {https://arxiv.org/pdf/1411.0030.pdf}
}
```

2013

R. Grosse , C. J. Maddison , R. Salakhutdinov , Annealing Between Distributions by Averaging Moments, in Advances in Neural Information Processing Systems 26, 2013.
Many powerful Monte Carlo techniques for estimating partition functions, such as annealed importance sampling (AIS), are based on sampling from a sequence of intermediate distributions which interpolate between a tractable initial distribution and an intractable target distribution. The near-universal practice is to use geometric averages of the initial and target distributions, but alternative paths can perform substantially better. We present a novel sequence of intermediate distributions for exponential families: averaging the moments of the initial and target distributions. We derive an asymptotically optimal piecewise linear schedule for the moments path and show that it performs at least as well as geometric averages with a linear schedule. Moment averaging performs well empirically at estimating partition functions of restricted Boltzmann machines (RBMs), which form the building blocks of many deep learning models, including Deep Belief Networks and Deep Boltzmann Machines.
```
@inproceedings{grosse2013momentaverage,
  author = {Grosse, Roger and Maddison, Chris J. and Salakhutdinov, Ruslan},
  booktitle = {Advances in Neural Information Processing Systems 26},
  title = {{Annealing Between Distributions by Averaging Moments}},
  year = {2013},
  bdsk-url-1 = {http://www.stats.ox.ac.uk/\\~{}cmaddis/pubs/aais.pdf},
  bdsk-url-2 = {http://www.stats.ox.ac.uk/\\~{}cmaddis/pubs/aaissup.pdf}
}
```

2012

S. A. Heimovics , N. H. Prior , C. J. Maddison , K. K. Soma , Rapid and Widespread Effects of 17-beta-estradiol on Intracellular Signaling in the Male Songbird Brain: A Seasonal Comparison, Endocrinology, vol. 153, no. 3, 1364–1376, 2012.

@article{Heimovics01032012,
  author = {Heimovics, Sarah A. and Prior, Nora H. and Maddison, Chris J. and Soma, Kiran K.},
  doi = {10.1210/en.2011-1525},
  journal = {Endocrinology},
  number = {3},
  pages = {1364-1376},
  title = {{Rapid and Widespread Effects of 17-beta-estradiol on Intracellular Signaling in the Male Songbird Brain: A Seasonal Comparison}},
  volume = {153},
  year = {2012},
  bdsk-url-1 = {http://endo.endojournals.org/content/153/3/1364.abstract},
  bdsk-url-2 = {http://dx.doi.org/10.1210/en.2011-1525}
}

C. J. Maddison , R. C. Anderson , N. H. Prior , M. D. Taves , K. K. Soma , Soft song during aggressive interactions: Seasonal changes and endocrine correlates in song sparrows, Hormones and Behavior, vol. 62, no. 4, 455–463, 2012.

@article{maddison2012softsong,
  author = {Maddison, Chris J. and Anderson, Rindy C. and Prior, Nora H. and Taves, Matthew D. and Soma, Kiran K.},
  journal = {Hormones and Behavior},
  number = {4},
  pages = {455 - 463},
  title = {{Soft song during aggressive interactions: Seasonal changes and endocrine correlates in song sparrows}},
  volume = {62},
  year = {2012},
  bdsk-url-1 = {https://www.ncbi.nlm.nih.gov/pubmed/22902893}
}