Online papers: Chris Williams

Chris Williams: Papers available online

2024

A Short History of the Early Years of Artificial Intelligence at Edinburgh pdf: Christopher K.I. Williams, Vassilis Galanos and Xiao Yang. In Proc. of the Workshop on on the History of AI in Europe (WHAI@EU), Santiago de Compostela, Spain, 20 Oct 2024.
Of Mice and Mates: Automated Classification and Modelling of Mouse Behaviour in Groups using a Single Model across Cages full text: Michael P. J. Camilleri, Rasneer S. Bains and Christopher K.I. Williams. Published in Int J Comput Vis 2024, doi.org/10.1007/s11263-024-02118-3 . arxiv version.
Naive Bayes Classifiers and One-hot Encoding of Categorical Variables pdf: Christopher K. I. Williams. Posted on arXiv 28 Apr 2024.

2023

Persistent Animal Identification Leveraging Non-Visual Markers pdf: Michael P. J. Camilleri, Li Zhang, Rasneer S. Bains, Andrew Zisserman, Christopher K. I. Williams. Final m/s version of paper published in Machine Vision and Applications 34, 68 (2023), https://doi.org/10.1007/s00138-023-01414-1. v1 posted on arXiv 13, 17 Dec 2021.
Structured Generative Models for Scene Understanding pdf: Christopher K.I. Williams. Published on arXiv 7 Feb 2023, v2 on 2 Sept 2024.
AI Assistants: A Framework for Semi-Automated Data Wrangling pdf: Tomas Petricek, Gerrit J. J. van den Burg, Alfredo Nazabal, Taha Ceritli, Ernesto Jimenez-Ruiz, Christopher K. I. Williams. IEEE Transactions on Knowledge and Data Engineering 35(9) 9295-9306 (2023), doi:10.1109/TKDE.2022.3222538. Final m/s version published on arXiv 31 Oct 2022.

2022

Multi-Task Dynamical Systems pdf: Alex Bird, Christopher K.I. Williams, Christopher Hawthorne. Journal of Machine Learning Research 23(230) 1-52 (2022).
The Elliptical Quartic Exponential Distribution: An Annular Distribution Obtained via Maximum Entropy pdf: Christopher K.I. Williams. Published on arXiv 9 Oct 2022.
Inference and Learning for Generative Capsule Models pdf: Alfredo Nazabal, Nikolaos Tsagkas, Christopher K.I. Williams. Posted on arXiv 7 Sept 2022, revised 21 Oct. Published in Neural Computation 35(4) 727-761 (2023), doi:10.1162/neco_a_01564. This paper extends our previous work arXiv:2103.06676 by covering the learning of the models as well as inference.
On Suspicious Coincidences and Pointwise Mutual Information pdf: Christopher K. I. Williams. Neural Computation 34(10) 2037-2046 (2022). v1 posted on arXiv 15 Mar 2022, v2 on 13 June 2022.
Inference for Generative Capsule Models pdf: Alfredo Nazabal, Nikolaos Tsagkas, Christopher K.I. Williams. v1 posted on arXiv 11 March 2021, v2 on 14 March 2022.
Automating Data Science pdf: Tijl De Bie, Luc De Raedt, Jose Hernandez-Orallo, Holger H. Hoos, Padhraic Smyth, Christopher K. I. Williams. Communications of the ACM 65(3) 76-87 (2022), doi:10.1145/3495256. Finals m/s version published on arXiv 12 May 2021, pdf.
Align-Deform-Subtract: An Interventional Framework for Explaining Object Differences pdf: Cian Eastwood, Li Nanbo, Christopher K. I. Williams. Accepted as a poster at ICLR 2022 Workshop on the Elements of Reasoning: Objects, Structure, and Causality (OSC). Posted on arXiv 9 Mar 2022, v2 20 July 2022.

2021

Unit-level surprise in neural networks paper: Cian Eastwood, Ian Mason, Christopher K. I. Williams. Presented at the NeurIPS 2021 Workshop: I Can't Believe it's Not Better!, 13 December 2021.
ptype-cat: Inferring the Type and Values of Categorical Variables pdf: Taha Ceritli and Christopher K. I. Williams. Presented at the ECML-PKDD Workshop on Automating Data Science, 17 Sept 2021.
Published on arXiv 23 November 2021, link. code is available.
Identifying the Units of Measurement in Tabular Data pdf: Taha Ceritli and Christopher K. I. Williams. Presented at the ECML-PKDD Workshop on Automating Data Science, 17 Sept 2021.
Published on arXiv 23 November 2021, link.
Source-Free Adaptation to Measurement Shift via Bottom-Up Feature Restoration pdf: Cian Eastwood, Ian Mason, Christopher K. I. Williams, Bernhard Schölkopf. Accepted for publication at ICLR 2022. Published on arXiv 12 July 2021, updated 8 Oct 2021.
On Memorization in Probabilistic Deep Generative Models pdf: Gerrit J. J. van den Burg, Christopher K. I. Williams. NeurIPS 2021. v1 published on arXiv 6 June 2021.

2020

VAEs in the Presence of Missing Data pdf: Mark Collier, Alfredo Nazabal, Christopher K.I. Williams. Published on arXiv 13 July 2020. Presented at the first Workshop on the Art of Learning with Missing Values (Artemiss) hosted by the 37th International Conference on Machine Learning (ICML 2020).
The Effect of Class Imbalance on Precision-Recall Curves pdf: Christopher K. I. Williams. Posted on arXiv 3 July 2020, updated 14 Oct 2020 and 27 Apr 2021. Final manuscript version of paper published in Neural Computation 33(4) 853–857 (2021), https://doi.org/10.1162/neco_a_01362.
Learning Direct Optimization for Scene Understanding pdf: Lukasz Romaszko, Christopher K. I. Williams, John Winn. Final m/s version of paper published in Pattern Recognition vol 105, 107369, https://doi.org/10.1016/j.patcog.2020.107369. Initial verson posted on arXiv 18 Dec 2018.
Data Engineering for Data Analytics: A Classification of the Issues, and Case Studies pdf: Alfredo Nazabal, Christopher K.I. Williams, Giovanni Colavizza, Camila Rangel Smith, Angus Williams. Published on arXiv 27 April 2020.
An Evaluation of Change Point Detection Algorithms pdf: Gerrit J.J. van den Burg, Christopher K.I. Williams. First published on arXiv 13 March 2020, v2 25 May 2020.
Robust Variational Autoencoders for Outlier Detection in Mixed-Type Data pdf: Simão Eduardo, Alfredo Nazábal, Christopher K. I. Williams, Charles Sutton. In 23rd International Conference on Artificial Intelligence and Statistics (AISTATS) 2020. PMLR Vol 108. supplementary material.
Earlier version as arXiv 1907.06671
The Extended Dawid-Skene Model: Fusing Information from Multiple Data Schemas pdf: Michael P. J. Camilleri, Christopher K. I. Williams. Final m/s version of paper to appear in P. Cellier and K. Driessens (Eds.): ECML PKDD 2019 Workshops, CCIS 1167, pp. 121 - 136, 2020. Final version at doi:10.1007/978-3-030-43823-4_11. Code on github.

2019

ptype: Probabilistic Type Inference pdf: Taha Ceritli, Christopher K. I. Williams, James Geddes.
The pdf is a post-peer-review, pre-copyedit version of an article published in Data Mining and Knowledge Discovery 34 870-904 (2020). The final authenticated version is available online at: http://dx.doi.org/10.1007/s10618-020-00680-1. Posted on arXiv 22 Nov 2019, updated 23 Mar 2020. Code on github.
Customizing Sequence Generation with Multi-Task Dynamical Systems pdf: Alex Bird, Christopher K. I. Williams. Posted on arXiv 11 October 2019.
Multi-Task Time Series Analysis applied to Drug Response Modelling pdf: Alex Bird, Christopher K. I. Williams, Christopher Hawthorne. In 22nd International Conference on Artificial Intelligence and Statistics (AISTATS) 2019. PMLR Vol 89. supplementary material
Inverting Supervised Representations with Autoregressive Neural Density Models pdf: Charlie Nash, Nate Kushman, Christopher K. I. Williams. In 22nd International Conference on Artificial Intelligence and Statistics (AISTATS) 2019. PMLR Vol 89. See also arXiv version
Endoscopic sensing of distal lung physiology pdf: Choudhury, D, Tanner, MG, Mcaughtrie, S, Yu, F, Mills, B, Choudhary, TR, Seth, S, Craven, TH, Stone, JM, Mati, IK, Campbell, CJ, Bradley, M, Williams, CKI, Dhaliwal, K, Birks, TA & Thomson, RR. Journal of Physics: Conference Series. 1151 012009 (2019).

2018

A Framework for the Quantitative Evaluation of Disentangled Representations pdf: Cian Eastwood, Christopher K. I. Williams. Sixth International Conference on Learning Representations (ICLR 2018), April 2018.
Autoencoders and Probabilistic Inference with Missing Data: An Exact Solution for The Factor Analysis Case pdf: Christopher K. I. Williams, Charlie Nash, Alfredo Nazabal. Posted on arXiv 11 Jan 2018, updated 3 Sept 2018, 19 Feb 2019.
Estimating Bacterial and Cellular Load in FCFM Imaging pdf: Sohan Seth, Ahsan R. Akram, Kevin Dhaliwal, Christopher K. I. Williams. J. Imaging 2018, 4(1) 11, doi:10.3390/jimaging4010011

2017

Model Criticism in Latent Space pdf: Sohan Seth, Iain Murray, Christopher K. I. Williams. v1 posted on arXiv 13 Nov 2017, updated to v2 on 2 Jul 2018, pdf. Published in Bayesian Analysis 14(3) pp 703-725 (2019),
Vision-as-Inverse-Graphics: Obtaining a Rich 3D Explanation of a Scene from a Single Image pdf: Lukasz Romaszko, Christopher K.I. Williams, Pol Moreno, Pushmeet Kohli. ICCV 2017 Geometry Meets Deep Learning workshop, October 2017 (oral presenatation). supplementary material.
The shape variational autoencoder: A deep generative model of part-segmented 3D objects pdf: Charlie Nash, Christopher K.I. Williams. Accepted version of the paper to appear in Computer Graphics Forum 36(5) (2017) 1-12, presented at the Symposium on Geometry Processing, July 2017.
Estimating Bacterial Load in FCFM Imaging pdf: Sohan Seth, Ahsan R. Akram, Kevin Dhaliwal, Christopher K.I. Williams. Accepted for publication at Medical Image Understanding and Analysis (MIUA) 2017.
Endoscopic sensing of alveolar pH pdf: Choudhury, D, Tanner, MG, Mcaughtrie, S, Yu, F, Mills, B, Choudhary, TR, Seth, S, Craven, TH, Stone, JM, Mati, IK, Campbell, CJ, Bradley, M, Williams, CKI, Dhaliwal, K, Birks, TA & Thomson, RR. Biomedical Optics Express, 8(1) pp. 243-259, DOI 10.1364/BOE.8.000243.

2016

Generative models of part-structured 3D objects pdf: Charlie Nash, Christopher K.I. Williams. Extended abstract for NIPS 2016 Workshop on 3D Deep Learning.
Predicting Patient State-of-Health using Sliding Window and Recurrent Classifiers pdf: Adam McCarthy, Christopher K.I. Williams. NIPS 2016 Workshop on Machine Learning for Health.
Overcoming Occlusion with Inverse Graphics pdf: Pol Moreno, Christopher K.I. Williams, Charlie Nash and Pushmeet Kohli. Presented at: Geometry Meets Deep Learning workshop, ECCV 2016 (oral presentation). Final m/s version of paper appearing in Computer Vision-ECCV 2016 Workshops Proceedings Part III, eds. H. Gang and H. Jegou, Springer LNCS 9915 pp 170-185.
Code is available.
Input-Output Non-Linear Dynamical Systems applied to Physiological Condition Monitoring pdf: Konstantinos Georgatzis, Christopher K.I. Williams and Christopher Hawthorne. Proc Machine Learning in Health Care, JMLR W&C Track Volume 56, 2016.
Assessing the utility of autofluorescence-based pulmonary optical endomicroscopy to predict the malignant potential of solitary pulmonary nodules in humans pdf: Sohan Seth, Ahsan R. Akram, Paul McCool, Jody Westerfeld, David Wilson, Stephen McLaughlin, Kevin Dhaliwal, Christopher K. I. Williams.
Scientific Reports 6:31372 (2016). doi: 10.1038/srep31372
Neural Maps: Their Function and Development pdf: James A. Bednar and Christopher K.I. Williams. Chapter in From Neuron to Cognition via Computational Neuroscience Michael Arbib and James Bonaiuto, Eds., MIT Press, 2016.

2015

Detecting Artifactual Events in Vital Signs Monitoring Data pdf: Partha Lal, Christopher K. I. Williams, Konstantinos Georgatzis, Christopher Hawthorne, Paul McMonagle, Ian Piper, Martin Shaw. Technical report, October 2015. Associated software.
A slightly revised version is published as a chapter in Machine Learning for Healthcare Technologies, ed. David A. Clifton, Institution of Engineering and Technology, 2016.
Tree-Cut for Probabilistic Image Segmentation: Shell X. Hu, Christopher K. I. Williams, Sinisa Todorovic. Posted on arXiv 11 June 2015 (pdf).
Discriminative Switching Linear Dynamical Systems applied to Physiological Condition Monitoring pdf: Konstantinos Georgatzis, Christopher K. I. Williams. In Proc UAI 2015.
An earlier version was posted on arXiv 24 April 2015 (pdf).

2014

Localisation microscopy with quantum dots using non-negative matrix factorisation pdf: Ondrej Mandula, Ivana Sumanovac Sestak, Rainer Heintzmann, Christopher K. I. Williams
Optics Express, Vol. 22, Issue 20, pp. 24594-24605 (2014), http://dx.doi.org/10.1364/OE.22.024594. Software developed for this project is available.
A Hierarchical Switching Linear Dynamical System Applied to the Detection of Sepsis in Neonatal Condition Monitoring pdf: Ioan Stanculescu, Christopher K. I. Williams, Yvonne Freer
In Proceedings of the 30th Conference on Uncertainty in Artificial Intelligence (UAI 2014).
The PASCAL Visual Object Classes Challenge - a Retrospective pdf: Mark Everingham, S. M. Ali Eslami, Luc Van Gool, Christopher K. I. Williams, John Winn, Andrew Zisserman.
Accepted for publication in International Journal of Computer Vision on 20 May 2014. Published: International Journal of Computer Vision 111(1), pp 98-136, 2015.
The final publication is available at http://link.springer.com, DOI 10.1007/s11263-014-0733-5
Visual Boundary Prediction: A Deep Neural Prediction Network and Quality Dissection pdf, supplementary material: Jyri J. Kivinen, Christopher K. I. Williams, Nicolas Heess
In Proceedings of the 17th International Conference on Artificial Intelligence and Statistics (AISTATS) 2014, Reykjavik, Iceland. JMLR: W&CP volume 33.

2013

Dictionary of Computer Vision and Image Processing (second edition) website: Robert B. Fisher, Toby Breckon, Kenneth Dawson-Howe, Andrew Fitzgibbon, Craig Robertson, Emanuele Trucco, Christopher K. I. Williams.
Wiley, 2014, ISBN: 978-1-119-94186-6.
Autoregressive Hidden Markov Models for the Early Detection of Neonatal Sepsis preprint pdf: Ioan Stanculescu, Christopher K.I. Williams, and Yvonne Freer
Accepted for publication in IEEE Journal of Biomedical and Health Informatics on 1 Dec 2013. Published in J-BHI 18(5) 1560-1570, September 2014.
The Shape Boltzmann Machine: a Strong Model of Object Shape preprint pdf: S. M. Ali Eslami, Nicolas Heess, Christopher K. I. Williams, John Winn
Int Journal of Computer Vision, doi 10.1007/s11263-013-0669-1 (Nov 2013).
The final publication is available at http://link.springer.com as Int Journal of Computer Vision, 107(2) 155-176 (2014)
Assessing the Significance of Performance Differences on the PASCAL VOC Challenges via Bootstrapping pdf: Mark Everingham, S. M. Ali Eslami, Luc Van Gool, Christopher K. I. Williams, John Winn, Andrew Zisserman
Technical note, October 2013.

2012

A Generative Model for Parts-based Object Segmentation pdf, supplementary material: S. M. Ali Eslami, Christopher K. I. Williams
In Advances in Neural Information Processing Systems 25, 2012, eds P. Bartlett, F.C.N. Pereira, C.J.C. Burges, L. Bottou and K.Q. Weinberger.
A Framework for Evaluating Approximation Methods for Gaussian Process Regression: Krzysztof Chalupka, Christopher K. I. Williams, Iain Murray
v2 posted on arXiv, 5 Nov 2012.
Accepted for publication in Journal of Machine Learning Research 17 Dec 2012, published in vol 14 pp 333-350 (2013) JMLR pdf. link to code and data.
Multiple Texture Boltzmann Machines pdf, supplementary material: J. J. Kivinen and Christopher K. I. Williams
In Proceedings AISTATS 2012, Volume 22 of JMLR W&CP.

2011

Factored Shapes and Appearances for Parts-based Object Understanding pdf, supplementary material, abstract: S. M. Ali Eslami and Christopher K. I. Williams
In Proceedings BMVC 2011
Transformation Equivariant Boltzmann Machines pdf: Jyri J. Kivinen and Christopher K. I. Williams
In Proceedings ICANN 2011, eds. T. Honkela et al, LNCS 6791, Springer-Verlag (2011).
Automating the Calibration of a Neonatal Condition Monitoring System pdf: Christopher K. I. Williams and Ioan Stansculescu
In Proc AIME 2011, eds M. Peleg, N. Lavrač, and C. Combi, LNAI 6747, pp. 240--249. Springer (2011)
Milepost GCC: Machine Learning Enabled Self-tuning Compiler pdf: Grigori Fursin, Yuriy Kashnikov, Abdul Wahid Memon, Zbigniew Chamski, Olivier Temam, Mircea Namolaru, Elad Yom-Tov, Bilha Mendelson, Ayal Zaks, Eric Courtois, Francois Bodin, Phil Barnard, Elton Ashton, Edwin Bonilla, John Thomson, Christopher K. I. Williams, Michael O'Boyle.
International Journal of Parallel Programming 39(3) pp 296-327 (2011)
DOI:10.1007/s10766-010-0161-2

2010

Advances in Neural Information Processing Systems 23: editors J. Lafferty, C. K. I. Williams, J. Shawe-Taylor, R. S. Zemel, and A. Culotta, (2010).
Kick-starting GPLVM Optimization via a Connection to Metric MDS pdf: S. Bitzer and C. K. I.Williams
In Proceedings of the NIPS 2010 workshop on Challenges of Data Visualization, December 2010.
Physiological Monitoring with Factorial Switching Linear Dynamical Systems pdf: J.A. Quinn and C.K.I. Williams.
Chapter appearing in Bayesian Time Series Models, eds. D. Barber, A. T. Cemgil, S. Chiappa, Cambridge University Press, 2011.
Greedy Learning of Binary Latent Trees pdf: S. Harmeling and C. K. I. Williams
Final manuscript version of the paper accepted to appear in IEEE PAMI.
Published in IEEE Transactions on Pattern Analysis and Machine Intelligence 33(6) 1087-1097 (2011).
Matlab code is available.
The PASCAL Visual Object Classes (VOC) Challenge pdf: M. Everingham, L. Van Gool, C. K. I. Williams, J. Winn, A. Zisserman
Final manuscript version of the paper in International Journal of Computer Vision 88(2), 303-338 (2010)

2009

Advances in Neural Information Processing Systems 22: editors Y. Bengio, D. Schuurmans, J. Lafferty, C. K. I. Williams and A. Culotta, (2009).
Learning generative texture models with extended Fields-of-Experts pdf, supplementary material: N. Heess, C. K. I. Williams, G. E. Hinton
Proceedings BMVC 2009
Object localisation using the Generative Template of Features pdf: M. Allan, C. K. I. Williams
Final manuscript version of the paper in Computer Vision and Image Understanding 113 824-838 (2009)
Multi-task Gaussian Process Learning of Robot Inverse Dynamics pdf: K. M. A. Chai, C. K. I. Williams, S. Klanke, S. Vijayakumar
In Advances in Neural Information Processing Systems 21, eds D. Koller, Y. Bengio, D. Schuurmans, L. Bottou (2009)
A new method of spike modelling and interval analysis: D.J. MacGregor, C.K.I. Williams, G. Leng.
Journal of Neuroscience Methods, 176(1) 2009, Pages 45-56, doi:10.1016/j.jneumeth.2008.08.011

2008

Factorial Switching Linear Dynamical Systems applied to Physiological Condition Monitoring pdf: John A. Quinn, Christopher K.I. Williams, Neil McIntosh.
Accepted to IEEE Trans. on Pattern Analysis and Machine Intelligence (July 2008), published T-PAMI 31(9) pp 1537-1551 (2009). Matlab code is available.
MILEPOST GCC: machine learning based research compiler pdf: G. Fursin, C. Miranda. O. Teman et al [including C. K. I. Williams], Proceedings of the GCC Developers' Summit, 2008
Signal Masking in Gaussian Channels pdf: John A. Quinn, Christopher K. I. Williams.
Proc ICASSP 2008.
Multi-task Gaussian Process Prediction pdf: Edwin V. Bonilla, Kian Ming A. Chai, Christopher K. I. Williams.
In Advances in Neural Information Processing Systems 20, eds. J. C. Platt, D. Koller, Y. Singer, S. Roweis, MIT Press (2008)
NB See this correction note concerning the results reported in section 6 (Jan 2009)

2007

EDI-INF-RR-1228 A Note on Noise-free Gaussian Process Prediction with Separable Covariance Functions and Grid Designs pdf: Christopher K. I. Williams, Kian Ming A. Chai, Edwin V. Bonilla
Informatics Research Report, December 2007.
Approximation Methods for Gaussian Process Regression pdf: Joaquin Quinonero-Candela, Carl Edward Rasmussen, Christopher K. I. Williams.
Final draft of a chapter in Large Scale Kernel Machines eds. L. Bottou, O. Chapelle, D. DeCoste, J. Weston, pages 203-223 MIT Press, 2007
Known Unknowns: Novelty Detection in Condition Monitoring pdf: John A. Quinn, Christopher K. I. Williams.
Invited paper in Proc 3rd Iberian Conference on Pattern Recognition and Image Analysis (IbPRIA 2007),
eds J. Marti, J. M. Benedi, A. M. Mendonca, J. Serrat, LNCS 4477 pp 1-6, Springer-Verlag
Kernel Multi-task Learning using Task-specific Features pdf: Edwin V. Bonilla, Felix V. Agakov, Christopher K. I. Williams. Proc AISTATS 2007.

2006

On the Extension of Eigenvectors to New Datapoints pdf: C. K. I. Williams. Technical note, November 2006.
Sequential Learning of Layered Models from Video pdf: M. K. Titsias, C. K. I. Williams. In Toward Category-Level Object Recognition, eds. J. Ponce, M. Hebert, C. Schmid, and A. Zisserman, LNCS 4170, Springer-Verlag, pp 577-595, 2006.
Dataset Issues in Object Recognition pdf: J. Ponce, T.L. Berg, M.R. Everingham, D.A. Forsyth, M. Hebert, S. Lazebnik, M. Marszalek, C. Schmid, B.C. Russell, A. Torralba, C.K.I. Williams, J. Zhang, and A. Zisserman. In Toward Category-Level Object Recognition, eds. J. Ponce, M. Hebert, C. Schmid, and A. Zisserman, LNCS 4170, Springer-Verlag, pp 29-48 2006.
The PASCAL Visual Object Classes Challenge 2006 (VOC 2006) Results pdf: Mark Everingham, Andrew Zisserman, Chris Williams, Luc Van Gool
Technical Report, September 2006.
Predictive Search Distributions pdf: Edwin V. Bonilla, Christopher K. I. Williams, Felix V. Agakov, John Cavazos, John Thomson, Michael F.P. O'Boyle
In Proc. ICML 2006
Using Machine Learning to Focus Iterative Optimization pdf: F. Agakov, E. Bonilla, J. Cavazos, B. Franke, G. Fusin, M. F. P. O'Boyle, J. Thomson, M. Toussaint, C. K. I. Williams.
The 4th Annual International Symposium on Code Generation and Optimization (CGO), March 2006.
A regularized discriminative model for the prediction of protein-peptide interactions: Wolfgang P. Lehrach, Dirk Husmeier, Christopher K. I. Williams
Bioinformatics 22(5):532-540 (2006)
EDI-INF-RR-0719 On a Connection between Object Localization with a Generative Template of Features and Pose-space Prediction Methods pdf: Christopher K. I. Williams and Moray Allan
Informatics Research Report, January 2006.
Gaussian Processes for Machine Learning: Carl Edward Rasmussen and Christopher K. I. Williams, MIT Press (2006).
Book website, MIT Press site
Factorial Switching Kalman Filters for Condition Monitoring in Neonatal Intensive Care pdf: Christopher K. I. Williams, John Quinn, Neil McIntosh
To appear in Advances in Neural Information Processing Systems 18, eds. Y. Weiss, B. Schoelkopf, J. C. Platt, MIT Press (2006)

2005

Unsupervised Learning of Multiple Aspects of Moving Objects from Video pdf: Michalis K. Titsias, Christopher K. I. Williams
In: Advances in Informatics, 10th Panhellenic Conference on Informatics, PCI 2005, Volos, Greece, November 11-13, 2005, LNCS 3746 Springer (2005), pp 746-756, © Springer-Verlag.
The 2005 PASCAL Visual Object Classes Challenge pdf: M. Everingham, A. Zisserman, C. K. I. Williams, L. Van Gool, et al.
In Machine Learning Challenges, eds. J. Quinonero-Candela, I. Dagan, B. Magnini, F. d'Alche-Buc, LNAI 3944, Springer-Verlag, 2006.
EDI-INF-RR-0318 An Expectation Maximisation Algorithm for One-to-Many Record Linkage, Illustrated on the Problem of Matching Far Infra-Red Astronomical Sources to Optical Counterparts: A. J. Storkey, C. K. I. Williams, E. Taylor, R. G. Mann
Informatics Research Report, August 2005.
Understanding Gaussian Process Regression Using the Equivalent Kernel pdf: Peter Sollich, Christopher K. I. Williams
In: Deterministic and Statistical Methods in Machine Learning, eds. J. Winkler, N. D. Lawrence and M. Niranjan, LNAI 3635, © Springer-Verlag.
Fast Learning of Sprites using Invariant Fetaures pdf: Moray Allan, Michalis K. Titsias, Christopher K. I. Williams
In Proc. British Machine Vision Conference 2005 (BMVC 2005)
Video sequences.
The Impact of Using Related Individuals for Haplotype Reconstruction in Population Studies pdf: Michael T. Schouten, Christopher K. I. Williams, Chris S. Haley
Genetics 171(3) 1321-1330 (2005)
On the Eigenspectrum of the Gram Matrix and the Generalization Error of Kernel PCA pdf: John Shawe-Taylor, Christopher K. I. Williams, Nello Cristianini, Jaz Kandola
IEEE Tranactions on Information Theory 51(7) 2510-2522 (2005)
Using the Equivalent Kernel to Understand Gaussian Process Regression pdf: Peter Sollich, Christopher K. I. Williams
Advances in Neural Information Processing Systems 17 MIT Press (2005)
Harmonising Chorales by Probabilistic Inference pdf: Moray Allan, Christopher K. I. Williams
Advances in Neural Information Processing Systems 17 MIT Press (2005)
How to pretend that correlated variables are independent by using difference observations pdf: Christopher K. I. Williams
Neural Computation 17(1) 1-6 (2005)

2004

Fast Unsupervised Greedy Learning of Multiple Objects and Parts from Video pdf: Michalis K. Titsias, Christopher K. I. Williams
Persented at Generative-Model Based Vision Workshop held in conjunction with CVPR, 2004, published in 2004 CVPR Workshop vol 12
Greedy Learning of Multiple Objects in Images using Robust Statistics and Factorial Learning pdf: Christopher K. I. Williams, Michalis K. Titsias
Neural Computation 16(5) 1039-1062 (2004).
Extreme Components Analysis pdf: Max Welling, Felix V. Agakov, Christopher K. I. Williams
Advances in Neural Information Processing Systems 16 eds. S. Thrun, L. Saul, B. Schoelkopf, MIT Press (2004).

2003

EDI-INF-RR-0185 An isotropic Gaussian mixture can have more modes than components pdf: Miguel A. Carreira-Perpinan, Christopher K. I. Williams
Informatics Research Report, December 2003.

See Miguel's webpage for some animations relating to these results.
Cleaning Sky Survey Databases using Hough Transform and Renewal String Approaches electronic versions available: Storkey A.J., N.C. Hambly, C.K.I. Williams, R.G. Mann
Monthly Notices of the Royal Astronomical Society 347, 36-51(2003).
Renewal Strings for Cleaning Astronomical Databases electronic versions available: Storkey A.J., N.C. Hambly, C.K.I. Williams, R.G. Mann
In Uncertainty in Artificial Intelligence: Proceedings of the Nineteenth Conference (UAI-2003), 559-566.
Dynamic Trees for Image Modelling pdf: Nicholas J. Adams, Christopher K. I. Williams
Final draft of paper appearing in Image and Vision Computing 20(10) 865-877 (2003)
EDI-INF-RR-0159 On the Number of Modes of a Gaussian Mixture pdf: Miguel A. Carreira-Perpinan, Christopher K. I. Williams
Informatics Research Report, February 2003.
A slightly shortened version appears in Scale Space '03 (Proceedings of the 4th International Conference on Scale Space Theories in Computer Vision, June 2003). preprint pdf
Note (Dec 03): The conjecture given in this paper that if the components of the mixture have the same covariance matrix then the number of modes cannot exceed the number of components is false. See EDI-INF-RR-0185 for details.
Learning About Multiple Objects in Images: Factorial Learning without Factorial Search gzipped postscript: Christopher K. I. Williams, Michalis K. Titsias
Advances in Neural Information Processing Systems 15 eds. S. Becker, S. Thrun, K. Obermayer MIT Press (2003)
The Stability of Kernel Principal Components Analysis and its Relation to the Process Eigenspectrum gzipped postscript: John Shawe-Taylor, Christopher K. I. Williams
Advances in Neural Information Processing Systems 15 eds. S. Becker, S. Thrun, K. Obermayer MIT Press (2003)
A longer version of this paper (with author list John Shawe-Taylor, Chris Williams, Nello Cristianini, and Jaz Kandola) also appeared in the Proceedings of the 5th International Conference on Discovery Science, eds Steffen Lange, Ken Satoh, and Carl H. Smith, Lecture Notes in Computer Science vol 2534, Springer-Verlag (2002).

2002

UKeS-2002-06 Scientific Data Mining, Integration and Visualisation: Bob Mann, Roy Williams, Malcolm Atkinson, Ken Brodlie, Amos Storkey, Chris Williams.
Final Report of the meeting on Scientific Data Mining, Integration and Visualisation held at the eScience Institute, Edinburgh, 24-25 October 2002.
Image modelling with position-encoding dynamic trees pdf: Amos J. Storkey, Christopher K. I. Williams.
Final draft of paper appearing in IEEE Pattern Analysis and Machine Intelligence 25(7) 859-871 (2003).
IEEE legal stuff This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without explicit permission of the copyright holder.
Fast Forward Selection to Speed Up Sparse Gaussian Process Regression gzipped postscript: Matthias Seeger, Christopher K.I. Williams and Neil Lawrence.
AI-STATS 2003
Observations on the Nystroem Method for Gaussian Process Prediction gzipped postscript: Christopher K. I. Williams, Carl Edward Rasmussen, Anton Schwaighofer, Volker Tresp.
An Analysis of Contrastive Divergence Learning in Gaussian Boltzmann Machines pdf: Christopher K. I. Williams and Felix V. Agakov
Informatics Research Report EDI-INF-RR-0120, May 2002.
Gaussian Processes gzipped postscript: Christopher K. I. Williams
The Handbook of Brain Theory and Neural Networks, Second edition (M.A. Arbib, Ed.), Cambridge, MA: © The MIT Press, 2002.
Dynamic Trees: Learning to Model Outdoor Scenes gzipped postscript: Nicholas J. Adams, Christopher K. I. Williams
Proceedings of the European Conference on Computer Vision 2002. Lecture Notes in Computer Science. © Springer-Verlag (2002)
Products of Gaussians gzipped postscript: Christopher K. I. Williams, Felix V. Agakov, Stephen N. Felderof
Advances in Neural Information Processing Systems 14 eds. T. G. Diettrich, S. Becker, Z. Ghahramani MIT Press (2002)

2001

Products of Gaussians and Probabilistic Minor Component Analysis gzipped postscript: C. K. I. Williams and F. V. Agakov
Informatics Research Report EDI-INF-RR-0043, July 2001. A shortened version of this report has been published in Neural Computation, 14(5), 1169-1182 (2002).
Comparing Mean Field and Exact EM in Tree Structured Belief Networks gzipped postscript: Nicholas J. Adams, Christopher K. I. Williams and Amos J. Storkey
In Proceedings of Fourth International ICSC Symposium on Soft Computing and Intelligent Systems for Industry, June 2001.
Products and Sums of Tree-Structured Gaussian Processes gzipped postscript: Christopher K. I. Williams and Stephen N. Felderhof
In Proceedings of Fourth International ICSC Symposium on Soft Computing and Intelligent Systems for Industry, June 2001.
Comparing Bayesian Neural Network Algorithms for Classifying Segmented Outdoor Images gzipped postscript: Francesco Vivarelli and Christopher K. I. Williams
Technical report, July 2001. This TR is a close-to-final draft of a paper which was published in Neural Networks 14(4-5) May 2001, 427-437.
Combining belief networks and neural networks for scene segmentation gzipped postscript: Xiaojuan Feng, C. K. I. Williams and S. N. Felderhof
Submitted to IEEE Trans PAMI, April 1999. Revised version March 2001, accepted for publication July 2001. Published in IEEE Trans PAMI 24(4) 467-483 (2002)
IEEE legal stuff This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without explicit permission of the copyright holder.
Software developed for this project is available.
Using the Nystrom Method to Speed Up Kernel Machines gzipped postscript: Christopher K. I. Williams and Matthias Seeger
Advances in Neural Information Processing Systems 13 eds. T. K. Leen, T. G. Diettrich, V. Tresp. MIT Press (2001)
The version above is final, replaces version as submitted to NIPS which was posted on this page 18 June 2000
NB See the later paper "Observations on the Nystroem Method for Gaussian Process Prediction" by Christopher K. I. Williams, Carl Edward Rasmussen, Anton Schwaighofer, Volker Tresp (2002) [available above] for important additional comments on the Nystroem method.
On a Connection between Kernel PCA and Metric Multidimensional Scaling gzipped postscript: Christopher K. I. Williams
Advances in Neural Information Processing Systems 13 eds. T. K. Leen, T. G. Diettrich, V. Tresp. MIT Press (2001)
Dynamic Positional Trees for Structural Image Analysis gzipped postscript: Amos J. Storkey and Christopher K. I. Williams
In: Proceedings of the Eighth International Workshop on Artificial Intelligence and Statistics (2001)

2000

The Effect of the Input Density Distribution on Kernel-based Classifiers gzipped postscript: Christopher K. I. Williams and Matthias Seeger
In: Proceedings of the Seventeenth International Conference on Machine Learning. Morgan Kaufmann (2000).
MFDTs: Mean Field Dynamic Trees gzipped postscript: Nicholas J. Adams, Amos J. Storkey, Zoubin Ghahramani and Christopher K. I. Williams
In: Proceedings of 15th International Conference on Pattern Recognition, 2000.
A MCMC approach to Hierarchical Mixture Modelling gzipped postscript: C. K. I. Williams
In Advances in Neural Information Processing Systems 12, eds. S. A. Solla, T. K. Leen and K-R. Muller, MIT Press (2000)

1999

Tree-structured Belief Networks as Models of Images gzipped postscript: C. K. I. Williams and Xiaojuan Feng
In ICANN 99: Artificial Neural Networks
SDTs: Sparse Dynamic Trees gzipped postscript: Nicholas J. Adams and C. K. I. Williams
In ICANN 99: Artificial Neural Networks
Finite-dimensional approximation of Gaussian processes gzipped postscript: Giancarlo Ferrari Trecate and C. K. I. Williams and M. Opper
In: Advances in Neural Information Processing Systems 11, eds. M. J. Kearns, S. A. Solla and D. A. Cohn. MIT Press, 1999.
Discovering hidden features with Gaussian processes regression gzipped postscript pdf: Francesco Vivarelli and C. K. I. Williams
In: Advances in Neural Information Processing Systems 11, eds. M. J. Kearns, S. A. Solla and D. A. Cohn. MIT Press, 1999.
DTs: Dynamic Trees gzipped postscript: C. K. I. Williams and Nicholas J. Adams
In: Advances in Neural Information Processing Systems 11, eds. M. J. Kearns, S. A. Solla and D. A. Cohn. MIT Press, 1999.

1998

NCRG/98/002 Regression with Input-dependent Noise: A Gaussian Process Treatment: P. W. Goldberg and C. K. I. Williams and C. M. Bishop
In Advances in Neural Information Processing Systems 10. Editor: M. I. Jordan and M. J. Kearns and S. A. Solla. MIT Press.
NCRG/98/012 Developments of the Generative Topographic Mapping: C. M. Bishop and M. Svensen and C. K. I. Williams
In Neurocomputing 21 203-224 (1998).
NCRG/98/013 Combining neural networks and belief networks for image segmentation: C. K. I. Williams and X. Feng
In Proc. 1998 IEEE Signal Processing Society Workshop on Neural Networks for Signal Processing. Cambridge, UK, 31 August-3 September 1998.
NCRG/98/014 Training Bayesian networks for image segmentation: X. Feng and C. K. I. Williams
In Proceedings of SPIE vol 3457. Presented at SPIE's 43rd Annual Meeting, San Diego, CA, July 19-24 1998.
NCRG/98/015 Upper and lower bounds on the learning curve for Gaussian processes: Revised version of 24 April 1999 available as gzipped postscipt.
Christopher K. I. Williams and Francesco Vivarelli
Final version appears in Machine Learning, 40(1), 77-102 (2000)
NCRG/98/023 Bayesian Inference for Wind Field Retrieval: Dan Cornford and Ian T. Nabney and Christopher K. I. Williams
Neurocomputing , 30(1-4), 3-11, 1999.
NCRG/98/025 Adding Constrained Discontinuities to Gaussian Process Models of Wind Fields: Dan Cornford and Ian T. Nabney and Christopher K. I. Williams
Advances in Neural Information Processing Systems 11, eds. M. J. Kearns, S. A. Solla and D. A. Cohn.
Bayesian Classification with Gaussian Processes gzipped postscript: C. K. I. Williams and David Barber
In: IEEE Trans Pattern Analysis and Machine Intelligence , 20(12) 1342-1351, (1998).
IEEE legal stuff: This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without explicit permission of the copyright holder.
Code is available.

1997

NCRG/97/006 Magnification Factors for the GTM Algorithm: Christopher M. Bishop and Markus Svensen and Christopher K. I. Williams
In Proceedings IEE Fifth International Conference on Artificial Neural Networks.
NCRG/97/007 Using Bayesian neural networks to classify segmented images: Francesco Vivarelli and Christopher K. I. Williams
In Proceedings of the IEE fifth International Conference on Artificial Neural Network s.
NCRG/97/008 Magnification Factors for the SOM and GTM Algorithms: Christopher M. Bishop, Markus Svensen and Christopher K. I. Williams
In Proceedings 1997 Workshop on Self-Organizing Maps, Helsinki, Finland.
NCRG/97/011 Gaussian Regression and Optimal Finite Dimensional Linear Models: Huaiyu Zhu and Christopher K. I. Williams and Richard Rohwer and Michal Morciniec
Aston University. Also appears in C. M. Bishop (editor), Neural Networks and Machine Learning, 1998, Springer-Verlag,
NCRG/97/012 Prediction with Gaussian Processes: From Linear Regression to Linear Prediction and Beyond: C. K. I. Williams
Aston University, UK. In "Learning and Inference in Graphical Models", ed. M. I. Jordan, Kluwer, 1998.
NCRG/97/015 Bayesian Classification with Gaussian Processes: Christopher K. I. Williams and David Barber
Neural Computing Research Group, Aston University. Submitted to IEEE PAMI, 16 November 1997.
NCRG/97/025 Computation with infinite neural networks: Christopher K. I. Williams
Neural Computing Research Group, Aston University. Similar to paper published in Neural Computation 10(5), pp 1203-1216, (1998).

1996

NCRG/96/005 An Upper Bound on the Bayesian Error Bars for Generalized Linear Regression: Cazhaow S. Qazaz and Christopher K. I. Williams and Christopher M. Bishop
. In Mathematics of Neural Networks: Models, Algorithms and Applications. Eds. S. W. Ellacott, J. C. Mason, I. J. Anderson. Kluwer, 1977.
NCRG/96/011 EM Optimization of Latent-Variable Density Models: Christopher M. Bishop and M. Svensen and Christopher K. I. Williams
In Advances in Neural Information Processing Systems. Editor: D. S. Touretzky and M. C. Mozer and M. E. Hasselmo. 8. MIT Press, Cambridge, MA.
NCRG/96/013 Gaussian Processes for Regression: C. K. I. Williams and C. E. Rasmussen
In Advances in Neural Information Processing Systems 8. Editor: D. S. Touretzky and M. C. Mozer and M. E. Hasselmo. MIT Press.
NCRG/96/015 GTM: The Generative Topographic Mapping: Christopher M. Bishop and Markus Svensen and Christopher K. I. Williams
Neural Computation 10(1), 215-234 (1998).
Associated software: GTM toolbox
misc96-007 Using generative models for handwritten digit recognition pdf: Revow, M. and Williams, C. K. I. and Hinton, G. E.
IEEE Transactions on Pattern Analysis and Machine Intelligence . 18(6). pp 592-606.
Code is available from Michael Revow's homepage.
NCRG/96/025 Instantiating deformable models with a neural net pdf: C. K. I. Williams and M. Revow and G. E. Hinton
Computer Vision and Image Understanding 68(1) 120-126 (1997).
NCRG/96/026 Computing with infinite networks: C. K. I. Williams
In Advances in Neural Information Processing Systems 9. Editor: M. C. Mozer and M. I. Jordan and T. Petsche. MIT Press, Cambridge, MA.
NCRG/96/027 Gaussian Processes for Bayesian Classification via Hybrid Monte Carlo: D. Barber and C. K. I. Williams
In Advances in Neural Information Processing Systems 9. Editor: M. C. Mozer and M. I. Jordan and T. Petsche. MIT Press, Cambridge, MA.
NCRG/96/030 GTM: A Principled Alternative to the Self-Organizing Map: Christopher M. Bishop, Markus Svensen and Christopher K. I. Williams
In Advances in Neural Information Processing Systems 9. Eds M. C. Mozer, M. I. Jordan and T. Petsche. MIT Press.
NCRG/96/031 GTM: A Principled Alternative to the Self-Organizing Map: Christopher M. Bishop and M. Svensen and Christopher K. I. Williams
In Proceedings 1996 International Conference on Artificial Neural Networks, ICANN'96. Editor: C. von der Malsburg and W. von Seelen and J. C. Vorbruggen and B. Sendhoff. pp 164--170. Springer-Verlag.

1995

Using a neural net to instantiate a deformable model pdf: Christopher K. I. Williams, Geoffrey E. Hinton, and Michael Revow
In Advances in Neural Information Processing 7, T. Leen, G. Tesauro, and D. Touretzky (eds), MIT Press, 1995
NCRG/95/023 Regression with Gaussian Processes: C. K. I. Williams
Paper presented at the Mathematics of Neural Networks and Applications conference, Oxford, UK, July 1995. In Mathematics of Neural Networks: Models, Algorithms and Applications. Eds. S W Ellacott, J C Mason and I J Anderson, Kluwer, 1997.
NCRG/95/024 On the relationship between Bayesian error bars and the input data density: C. K. I. Williams and C. Qazaz and C. M. Bishop and H. Zhu
In Proc. Fourth International Conference on Artificial Neural Networks.
Lending direction to neural networks gzipped postscript: Richard S. Zemel, C. K. I. Williams, and Michael Mozer. Neural Networks, 8(4), pp. 503-512 (1995).

1994

Combining deformable models and neural networks for handprinted digit recognition compressed postscript: C. K. I. Williams
PhD thesis. Department of Computer Science, University of Toronto.

1993

Unsupervised learning of object models pdf: Christopher K. I. Williams, Richard S. Zemel, Michael C. Mozer
AAAI Fall Symposium on Learning in Computer Vision, AAAI Technical Report FS-93-04, pp 20-24.
Hand-printed digit recognition using deformable models pdf: Christopher K. I. Williams, Michael Revow, Geoffrey E. Hinton
In Spatial Vision in Humans and Robots, eds. L. Harris and M. Jenkin, Cambridge University Press, New York.
Using mixtures of deformable models to capture variations in hand printed digits gzipped postscript, pdf: Michael Revow, Christopher K. I. Williams and Geoffrey E. Hinton
In: Third International workshop on Frontiers in Handwriting Recognition, Buffalo, USA. pp 142-152.

1992

Adaptive elastic models for hand-printed character recognition gzipped postscript, pdf,: Geoffrey E. Hinton, Christopher K. I. Williams and Michael Revow
In Advances in Neural Information Processing 4, J.E. Moody, S.J. Hanson and R.P Lippman (eds), Morgan Kaufmann, 1992
Combining two methods of recognizing hand-printed digits pdf: Geoffrey E. Hinton, Christopher K. I. Williams, Michael Revow
Artificial Neural Networks II: Proceedings of ICANN-92. I. Aleksander and J. Taylor (Eds.), Elsevier North-Holland
Learning to Segment Images Using Dynamic Feature Binding pdf: Michael C. Mozer, Richard S. Zemel, Marlene Behrmann, Christopher K. I. Williams
In Neural Computation 4 650-665 (1992).

1990

Mean field networks that learn to discriminate teporally distorted strings pdf: Christopher K. I. Williams and Geoffrey E. Hinton
In: Proceedings of the 1990 Connmectionist Models Summer School, eds D. S. Touretzky, J. L. Elman, T. J. Sejnowski, G. E. Hinton. Morgan Kaufmann (1990).

1987

Choices in pit latrine emptying pdf: Christopher K. I. Williams
In: Pickford, J. (ed). Rural water and engineering development in Africa: Proceedings of the 13th WEDC International Conference, Lilongwe, Malawi, 6-10 April 1987, pp 28-31.

Chris Williams