Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes

  @InProceedings{calderhead-accelerating08, title = {Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes}, author = {Ben Calderhead and Mark Girolami and Neil D. Lawrence}, booktitle = {Advances in Neural Information Processing Systems}, pages = {217}, year = {2009}, editor = {Daphne Koller and Dale Schuurmans and Yoshua Bengio and Leon Bottou}, volume = {21}, address = {Cambridge, MA}, month = {00}, publisher = {MIT Press}, edit = {https://github.com/lawrennd//publications/edit/gh-pages/_posts/2009-01-01-calderhead-accelerating08.md}, url = {http://inverseprobability.com/publications/calderhead-accelerating08.html}, abstract = {Identification and comparison of nonlinear dynamical system models using noisy and sparse experimental data is a vital task in many fields, however current methods are computationally expensive and prone to error due in part to the nonlinear nature of the likelihood surfaces induced. We present an accelerated sampling procedure which enables Bayesian inference of parameters in nonlinear ordinary and delay differential equations via the novel use of Gaussian processes (GP). Our methdo involves GP regression over time-series data, and the resulting derivative and time delay estimates make parameter inference possible *without* solving the dynamical system explicitly, resulting in dramatic savings of computational time. We demonstrate the speed and statistical accuracy of our approach using examples of both ordinary and elay differential equations, and provide a comprehensive comparison with current state of the art methods.}, crossref = {Koller:nips08}, key = {Calderhead:accelerating08}, group = {GP, differential equations, systems biology} }
 %T Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes %A Ben Calderhead and Mark Girolami and Neil D. Lawrence %B %C Advances in Neural Information Processing Systems %D %E Daphne Koller and Dale Schuurmans and Yoshua Bengio and Leon Bottou %F calderhead-accelerating08 %I MIT Press %P 217--224 %R %U http://inverseprobability.com/publications/calderhead-accelerating08.html %V 21 %X Identification and comparison of nonlinear dynamical system models using noisy and sparse experimental data is a vital task in many fields, however current methods are computationally expensive and prone to error due in part to the nonlinear nature of the likelihood surfaces induced. We present an accelerated sampling procedure which enables Bayesian inference of parameters in nonlinear ordinary and delay differential equations via the novel use of Gaussian processes (GP). Our methdo involves GP regression over time-series data, and the resulting derivative and time delay estimates make parameter inference possible *without* solving the dynamical system explicitly, resulting in dramatic savings of computational time. We demonstrate the speed and statistical accuracy of our approach using examples of both ordinary and elay differential equations, and provide a comprehensive comparison with current state of the art methods. 
 TY - CPAPER TI - Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes AU - Ben Calderhead AU - Mark Girolami AU - Neil D. Lawrence BT - Advances in Neural Information Processing Systems PY - 2009/01/01 DA - 2009/01/01 ED - Daphne Koller ED - Dale Schuurmans ED - Yoshua Bengio ED - Leon Bottou ID - calderhead-accelerating08 PB - MIT Press SP - 217 EP - 224 UR - http://inverseprobability.com/publications/calderhead-accelerating08.html AB - Identification and comparison of nonlinear dynamical system models using noisy and sparse experimental data is a vital task in many fields, however current methods are computationally expensive and prone to error due in part to the nonlinear nature of the likelihood surfaces induced. We present an accelerated sampling procedure which enables Bayesian inference of parameters in nonlinear ordinary and delay differential equations via the novel use of Gaussian processes (GP). Our methdo involves GP regression over time-series data, and the resulting derivative and time delay estimates make parameter inference possible *without* solving the dynamical system explicitly, resulting in dramatic savings of computational time. We demonstrate the speed and statistical accuracy of our approach using examples of both ordinary and elay differential equations, and provide a comprehensive comparison with current state of the art methods. ER - 
 Calderhead, B., Girolami, M. & Lawrence, N.D.. (2009). Accelerating Bayesian Inference over Nonlinear Differential Equations with Gaussian Processes. Advances in Neural Information Processing Systems 21:217-224