Latent Force Models.

Journal of Machine Learning Research - Proceedings Track 01/2009; 5:9-16.
Source: DBLP

ABSTRACT Purely data driven approaches for machine learning present diculties when data is scarce relative to the complexity of the model or when the model is forced to extrapolate. On the other hand, purely mechanistic ap- proaches need to identify and specify all the interactions in the problem at hand (which may not be feasible) and still leave the is- sue of how to parameterize the system. In this paper, we present a hybrid approach us- ing Gaussian processes and dierential equa- tions to combine data driven modelling with a physical model of the system. We show how dierent, physically-inspired, kernel func- tions can be developed through sensible, sim- ple, mechanistic assumptions about the un- derlying system. The versatility of our ap- proach is illustrated with three case studies from computational biology, motion capture and geostatistics.

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    ABSTRACT: Current technologies have lead to the availability of multiple genomic data types in sufficient quantity and quality to serve as a basis for automatic global network inference. Accordingly, there are currently a large variety of network inference methods that learn regulatory networks to varying degrees of detail. These methods have different strengths and weaknesses and thus can be complementary. However, combining different methods in a mutually reinforcing manner remains a challenge. We investigate how three scalable methods can be combined into a useful network inference pipeline. The first is a novel t-test-based method that relies on a comprehensive steady-state knock-out dataset to rank regulatory interactions. The remaining two are previously published mutual information and ordinary differential equation based methods (tlCLR and Inferelator 1.0, respectively) that use both time-series and steady-state data to rank regulatory interactions; the latter has the added advantage of also inferring dynamic models of gene regulation which can be used to predict the system's response to new perturbations. Our t-test based method proved powerful at ranking regulatory interactions, tying for first out of methods in the DREAM4 100-gene in-silico network inference challenge. We demonstrate complementarity between this method and the two methods that take advantage of time-series data by combining the three into a pipeline whose ability to rank regulatory interactions is markedly improved compared to either method alone. Moreover, the pipeline is able to accurately predict the response of the system to new conditions (in this case new double knock-out genetic perturbations). Our evaluation of the performance of multiple methods for network inference suggests avenues for future methods development and provides simple considerations for genomic experimental design. Our code is publicly available at
    PLoS ONE 01/2010; 5(10):e13397. · 3.73 Impact Factor
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    ABSTRACT: Interest in multioutput kernel methods is increas- ing, whether under the guise of multitask learn- ing, multisensor networks or structured output data. From the Gaussian process perspective a multioutput Mercer kernel is a covariance func- tion over correlated output functions. One way of constructing such kernels is based on convolution processes (CP). A key problem for this approach is efficient inference. ´ Alvarez and Lawrence re- cently presented a sparse approximation for CPs that enabled efficient inference. In this paper, we extend this work in two directions: we in- troduce the concept of variational inducing func- tions to handle potential non-smooth functions involved in the kernel CP construction and we consider an alternative approach to approximate inference based on variational methods, extend- ing the work by Titsias (2009) to the multiple output case. We demonstrate our approaches on prediction of school marks, compiler perfor- mance and financial time series.
    Journal of Machine Learning Research - Proceedings Track. 01/2010; 9:25-32.
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    ABSTRACT: In this paper we shall discuss an extension to Gaussian process (GP) regression models, where the measurements are modeled as linear functionals of the underlying GP and the estimation objective is a general linear operator of the process. We shall show how this framework can be used for modeling physical processes involved in measurement of the GP and for encoding physical prior information into regression models in form of stochastic partial differential equations (SPDE). We shall also illustrate the practical applicability of the theory in a simulated application.
    Artificial Neural Networks and Machine Learning - ICANN 2011 - 21st International Conference on Artificial Neural Networks, Espoo, Finland, June 14-17, 2011, Proceedings, Part II; 01/2011

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