Dataset Information

Learning Linear Dynamical Systems from Multivariate Time Series: A Matrix Factorization Based Framework.

ABSTRACT: The linear dynamical system (LDS) model is arguably the most commonly used time series model for real-world engineering and financial applications due to its relative simplicity, mathematically predictable behavior, and the fact that exact inference and predictions for the model can be done efficiently. In this work, we propose a new generalized LDS framework, gLDS, for learning LDS models from a collection of multivariate time series (MTS) data based on matrix factorization, which is different from traditional EM learning and spectral learning algorithms. In gLDS, each MTS sequence is factorized as a product of a shared emission matrix and a sequence-specific (hidden) state dynamics, where an individual hidden state sequence is represented with the help of a shared transition matrix. One advantage of our generalized formulation is that various types of constraints can be easily incorporated into the learning process. Furthermore, we propose a novel temporal smoothing regularization approach for learning the LDS model, which stabilizes the model, its learning algorithm and predictions it makes. Experiments on several real-world MTS data show that (1) regular LDS models learned from gLDS are able to achieve better time series predictive performance than other LDS learning algorithms; (2) constraints can be directly integrated into the learning process to achieve special properties such as stability, low-rankness; and (3) the proposed temporal smoothing regularization encourages more stable and accurate predictions.

SUBMITTER: Liu Z

PROVIDER: S-EPMC5098501 | biostudies-literature | 2016 May

REPOSITORIES: biostudies-literature

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Publications

Learning Linear Dynamical Systems from Multivariate Time Series: A Matrix Factorization Based Framework.

Liu Zitao Z Hauskrecht Milos M

Proceedings of the ... SIAM International Conference on Data Mining. SIAM International Conference on Data Mining 20160501

The linear dynamical system (LDS) model is arguably the most commonly used time series model for real-world engineering and financial applications due to its relative simplicity, mathematically predictable behavior, and the fact that exact inference and predictions for the model can be done efficiently. In this work, we propose a new generalized LDS framework, gLDS, for learning LDS models from a collection of multivariate time series (MTS) data based on matrix factorization, which is different ...[more]

PMID: 27830108

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Project description:Analysis of dynamical interactions between distributed brain areas is of fundamental importance for understanding cognitive information processing. However, estimating dynamic causal interactions between brain regions using functional magnetic resonance imaging (fMRI) poses several unique challenges. For one, fMRI measures Blood Oxygenation Level Dependent (BOLD) signals, rather than the underlying latent neuronal activity. Second, regional variations in the hemodynamic response function (HRF) can significantly influence estimation of causal interactions between them. Third, causal interactions between brain regions can change with experimental context over time. To overcome these problems, we developed a novel state-space Multivariate Dynamical Systems (MDS) model to estimate intrinsic and experimentally-induced modulatory causal interactions between multiple brain regions. A probabilistic graphical framework is then used to estimate the parameters of MDS as applied to fMRI data. We show that MDS accurately takes into account regional variations in the HRF and estimates dynamic causal interactions at the level of latent signals. We develop and compare two estimation procedures using maximum likelihood estimation (MLE) and variational Bayesian (VB) approaches for inferring model parameters. Using extensive computer simulations, we demonstrate that, compared to Granger causal analysis (GCA), MDS exhibits superior performance for a wide range of signal to noise ratios (SNRs), sample length and network size. Our simulations also suggest that GCA fails to uncover causal interactions when there is a conflict between the direction of intrinsic and modulatory influences. Furthermore, we show that MDS estimation using VB methods is more robust and performs significantly better at low SNRs and shorter time series than MDS with MLE. Our study suggests that VB estimation of MDS provides a robust method for estimating and interpreting causal network interactions in fMRI data.

Project description:BackgroundIn the last few years, the Non-negative Matrix Factorization ( NMF ) technique has gained a great interest among the Bioinformatics community, since it is able to extract interpretable parts from high-dimensional datasets. However, the computing time required to process large data matrices may become impractical, even for a parallel application running on a multiprocessors cluster. In this paper, we present NMF-mGPU, an efficient and easy-to-use implementation of the NMF algorithm that takes advantage of the high computing performance delivered by Graphics-Processing Units ( GPUs ). Driven by the ever-growing demands from the video-games industry, graphics cards usually provided in PCs and laptops have evolved from simple graphics-drawing platforms into high-performance programmable systems that can be used as coprocessors for linear-algebra operations. However, these devices may have a limited amount of on-board memory, which is not considered by other NMF implementations on GPU.ResultsNMF-mGPU is based on CUDA ( Compute Unified Device Architecture ), the NVIDIA's framework for GPU computing. On devices with low memory available, large input matrices are blockwise transferred from the system's main memory to the GPU's memory, and processed accordingly. In addition, NMF-mGPU has been explicitly optimized for the different CUDA architectures. Finally, platforms with multiple GPUs can be synchronized through MPI ( Message Passing Interface ). In a four-GPU system, this implementation is about 120 times faster than a single conventional processor, and more than four times faster than a single GPU device (i.e., a super-linear speedup).ConclusionsApplications of GPUs in Bioinformatics are getting more and more attention due to their outstanding performance when compared to traditional processors. In addition, their relatively low price represents a highly cost-effective alternative to conventional clusters. In life sciences, this results in an excellent opportunity to facilitate the daily work of bioinformaticians that are trying to extract biological meaning out of hundreds of gigabytes of experimental information. NMF-mGPU can be used "out of the box" by researchers with little or no expertise in GPU programming in a variety of platforms, such as PCs, laptops, or high-end GPU clusters. NMF-mGPU is freely available at https://github.com/bioinfo-cnb/bionmf-gpu .

Dataset Information

Learning Linear Dynamical Systems from Multivariate Time Series: A Matrix Factorization Based Framework.

Publications

Learning Linear Dynamical Systems from Multivariate Time Series: A Matrix Factorization Based Framework.

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