# Dr Ben Graham

I was an ~~Associate Professor in Statistics and Complexity; I have now left Warwick. I have moved to the Facebook AI Research Lab.~~

## Teaching

ST340: Programming for Data Science Resources

Term 3 office hours:

Monday 10:30-11:30, Friday 14:30-15:30

PhD Research opportunities at Warwick: MathSys DTC Statistics PhDs OxWaSP DTC MASDOC DTC

PhD students: Jeremy Reizenstein Matthew Smith

## Software

### IISignature - Iterated Integral Signature library

Quickly calculate rough-path theoretic iterated integral log-signatures in Python, R, C++ using Lie-algebra technology. With Jeremy Reizenstein. Coming soon (in the process of uploading super-optimized version to Github/PyPI).

### SparseConvNet - Spatially Sparse Convolutional Networks

- In Task 3 of the ICDAR 2013 Chinese Handwriting Recognition Competition 2013, a sparse CNN won with test error of 2.61%. Human performance on the test set was 4.81%.

- Training a sparse CNN, with affine and color-space distortions produced a Kaggle CIFAR-10 (2014) test error of 4.47%. Using fraction max-pooling, the error rate is reduced to 3.47%. Human performance on the CIFAR-10 test set is approximately 6%.

- First place in the Kaggle Diabetic Retinopathy Detection competition (2015) using fractional max-pooling.
- Podiumed in the Kaggle plankton recognition competition (2015) in collaboration with Ryan Munion. The competition solution is being adapted for research purposes.

### Batchwise Dropout

Run fully connected artificial neural networks with dropout applied *(mini)batchwise*, rather than *samplewise*. Given two hidden layers each subject to 50% dropout, the corresponding matrix multiplications for forward- and back-propagation is 75% less work as the dropped out units are not calculated. (GPLv3. Requirements: a Nvidia GPU, CUDA sm_20, and Boost).

## Research

Efficient batchwise dropout training using submatrices

with Jeremy Reizenstein and Leigh Robinson

*Preprint*

Confusing Deep Convolution Networks by Relabelling

with Leigh Robinson

*Preprint*

Fractional Max-Pooling (CIFAR-10 Exteme cases 347 mistakes)

*Preprint*

Spatially sparse convolutional neural networks

*Preprint*

Index learning for unsupervised low dimensional embeddings

*Preprint*

Sparse 3D convolutional neural networks

*BMVC 2015
*Poster

A binary deletion channel with a fixed number of deletions

*Combinatorics, Probability and Computing, volume 24, issue 03, pp. 486-489
*

The diffusive evaporation-deposition model and the voter model

*Preprint*

Metastability in the dilute Ising model

with Thierry Bodineau and Marc Wouts

*Probability Theory and Related Fields, 0178-8051, 2013 (55 pages)*

Helffer-Sjöstrand representation for conservative dynamics

with Thierry Bodineau

*Proceedings of IRS 2010, Markov Processes and Related Fields*

Sublinear variance for directed last passage percolation

*Journal of Theoretical Probability, 25:3:687-702, 2012 *

Sharp thresholds for the random-cluster and Ising models

with Geoffrey Grimmett

*Annals of Applied Probability, 21(1):240-265, 2011*

Borel type bounds for the self-avoiding walk connective constant

Figure: The oscillating coefficients of the spherical model series expansion

*Journal of Physics A: Mathematical and Theoretical 43:235001, 2010 *

Rate of relaxation for a mean-field zero-range process

Animation: The empirical distribution: one million boxes, and twenty balls per box

*Annals of Applied Probability, 19(2):497-520, 2009 *

Interacting Stochastic Systems

*PhD Thesis, University of Cambridge, 2007*

Influence and sharp-threshold theorems for monotonic measures

with Geoffrey Grimmett

*Annals of Probability, 34(5):1726-1745, 2006 *

(In Beffara & Duminil-Copin, Theorem 2.10 is used to show: "The self-dual point of the two-dimensional random-cluster model is critical for q≥1")

Random-current representation of the Blume-Capel model

with Geoffrey Grimmett

*Journal of Statistical Physics, 125(2):283-316, 2006*

SpeedwEyes: an eye-screening management system in diabetic care

with Stephen Corcoran

*British Journal of Healthcare Computing and Information Management; 19(3):23-25, 2002*

Sparse arrays of signatures for online character recognition

*Unpublished (redrafted as Spatially sparse convolutional neural networks)
CUDA Sparse CNN implementation*

CASIA-OLHWDB1.1: DeepCNet(6,100) 3.58% test error