Difference between revisions of "GP SSM"

Revision as of 18:06, 16 January 2018

This page gathers references and materials related to the study of

• Gaussian Process (GP) State Space Models (SSM)
• Deep Learning
• Koopman Spectral Methods.

Gaussian Process Approaches

Basic Gaussian Process Info

• Rasmussen and Williams

Web Links

• Bibliography on GP Models in Dynamical Systems

Papers on GP-SSMs

• J.M. Wang, D.J. Fleet, A. Hertzmann, Gaussian Process Dynamical Models
• R. Turner, M.P. Deisenroth, C.E. Rasmussen, State-Space Inference and Learning with Gaussian Process;
• A. McHutchon, Nonlinear Modelling and Control Using Gaussian Processes (Ph.D. thesis, Cambridge University)
• J. Ko, D. Fox, GP-BayesFilters: Bayesian filtering using Gaussian Process Prediction and Observation Models
• F. Perez-Cruz, S.V. Vaerenbergh, J.J. Murrillo-Fuentes, M. Lazarro-Gredilla, and I. Santamaria, Gaussian Processes for Nonlinear Signal Processing;
• A. Svensson, A. Solin, S. Sarkka, T.B. Schon, Computationall Efficient Bayesian Learning of Gaussian Process State Space Models
• A.C. Damianou, M.K. Titsias, N.D. Lawrence, Variational Gaussian Process Dynamical Systems
• M.P. Deisenroth, D. Fox, C.E. Rasmussen, Gaussian Processes for Data-Efficient Learning in Robotics and Control;
• K. Jocikan, Dynamic GP Models: An Overview and Recent Developments;
• A. Solin, S. Sarkka, Hilbert Space Methods for Reduced-Rank Gaussian Process Regression; (ArXiv.1401.5508)
• C.L.C. Mattos, Z. Dai, A. Damianou, J. Forth, G.A. Barreto, N. Lawrence, Recorruent Gaussian Processes
• N.D. Lawrence, A.J. Moore, Hierarchical Gaussian Process Latent Variable Models
• M.K. Titsias, N.D. Lawrence, Bayesian Gaussian Process Latent Variable Model
• R. Calandra, J. Peters, C.E. Rasmussen, M.P. Deisenroth, Manifold Gaussian Processes for Regression
• F. Berkenkamp and A.P. Schoellig, Safe and Robust Learning Control with Gaussian Processes
• E.B. Fox, E.B. Sudderth, M.I. Jordan, A.S. Willsky, Sharing Features Among Dynamical Systems with Beta Processes
• J.M. Wang, D.j. Fleet, A. Hertzmann, Gaussian Process Dynamical Models for Human Motion
• E.D. Klenske, P. Hennig, Dual Control for Approximate Bayesian Reinforcement Learning
• Y. Pan and E.A. Theodorou, Data-Driven Differential Dynamic Programming Using Gaussian Processes
• F. Berkenkamp, R. Moriconi, A.P. Schoellig, A. Krause, Safe Learning of Regions of Attraction for Uncertain, Nonlinear Systems with Gaussian Processes
• M.P. Deisenroth, J. Peters, C.E. Rasmussen, Approximate Dynamic Programming with Gaussian Processes
• R. Frigola, F. Lindsten, T.B. Schon, C.E. Rasmussen, Identification of Gaussian Process State-Space Models with Particle Stochastic Approximation EM

• Z.Y. Wan and T.P. Sapsis, Reduced-Space Gaussian Process Regression for Data-Driven Forecast of Chaotic Dynamical Systems, arXiv:1611.01583
• T. Beckers, J. Umlauft, and S. Hirsche, Stable Model-Based Control with Gaussian Process Regression for Robot Manipulators,
• A. Marco, P. Hennig, S. Schaal, S. Trimpe, On the Design of LQR Kernels for Efficient Controller Learning, arXiv:1709.07089v1
• N. Gorbach, S. Bauer, J. Buhmann, Scalable Variational Inference for Dynamical Systems, NIPS 2017, Long Beach, CA, 2017.
• J. Umlauft, T. Beckers, M. Kimmel, S. Hirsche, Feedback Linearization Using Gaussian Processes
• F. Lindsten, M.I. Jordan, T.B. Schon, Particles Gibbs with Ancestor Sampling, J. Machine Learning Research, vo. 15, pp. 2145-2184.

Deep Learning

Papers on Deep Learning

• This is the paper that we seek to understand in this reading group.
  • A. Achile and S. Soatto, Emergence of Invariance and Disentanglement in Deep Representations, arXiV:1706.01350v2, Oct. 2017.
• P. Chauderi, A.Oberman, S. Osher, S. Soatto, G. Ccarlier, Deep Relaxation: Partial Differential Equations for Optimizing Deep Neural Networks, arXiV:1704.04932v2
• Here are some background papers
  • N. Tishby and N. Zaslavsky, Deep Learning and the Information Bottleneck Principle, arXiv:1503.02406, March, 2015.

Web Links

• • Deeplearning.net

Koopman Spectral Method

Papers on Koopman Spectral methods

• S. Brunton, J. Proctor, N. Kutz, Discovering Governing Equations from Data: Sparse Identification of Nonlinear Dyanmical Systems, arXiv:1509.03580v1 (also, PNAS Version of the paper).
• S. L. Brunton, B.W.Brunton, J.L. Proctor, J.N. Kutz, Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control, PLOS One, vol. 11, no. 2, 2016.
• M. Budisic, R. Mohr, I. Mezic, Applied Koopmanism, Chaos, vol. 22, 2012.
• M.O. Williams, C.W. Rowley, I. G. Kevrekidis, A Kernel-Based Method for Data-Driven Koopman Spectral Analysis, arXiv:1411.2260v4
• J.L. Proctor, S.L. Brunton, J.N. Kutz, Dynamic Mode Decomposition with Control, SIAM J. Applied Dynamical Systems, vol. 15, no. 1, pp. 142-161, 2016.
• I. Mezic, On the Applications of the Theory of the Koopman Operator in Dynamical Systems and Control Theory, Proc. IEEE Conf. Decision Control, 2015
• M.O. Williams, C. Rowley, I.G. Kevrekidis, A Data-Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition, J. Nonlinear Science, vol. 25, 2015.
• D. Giannakis, Data-Driven Spectral Decomposition and Forecasting of ergodic dynamical systems, arXiv:1507.02338v2
• I. Mezic and A. Surana, Koopman Mode Decomposition for Periodic/Quasi-Periodic Time Dependence, IFAC Papers Online, 48-18, pp. 690697, 2016.
• H. Schaeffer, Learning Partial Differential Equations via Data Discovery and Sparse Optimization, J. Royal Society, Proceedings A, 2017
• J.N. Kutz, X. Fu, S.L. Brunton, Multi-resolution Dynamic Mode Decomposition, arXiv:1506.00564

Papers which are more oriented toward control

• D. Goswami and D.A. Paley, Global Bilinearization and Controllability of Control-Affine Nonlinear Systems: A Koopman Spectral Approach,
• A. Surana, Koopman Based Operator Synthesis for Control-Affine Noninear Systems, Proc. IEEE Conf. Decision and Control, 2016
• A. Surana and A. Banaszuk, Linear Observer Synthesis for Nonlinear Systems Using Koopman Operator Framework, IFAC Papers Online, 49-18, pp. 716-723, 2016.

Papers which are more oriented toward fluids

• I. Mezic, Analysis of Fluid Flows via Spectral Properties of the Koopman Operator, Annual Review of Fluids, vol. 45, 357-378, 2013.
• C.W. Rowley and S.T.M. Dawson, Model Reduction for Flow Analysis and Control, Annual Review Fluids, 49:387-417, 2017.
• M.S Hemati, C.W. Rowley, E.A. Deem, L.N. Cattafesta, De-biasing the Dynamic Mode Decomposition for applied Koopman spectral analysis of noisy data sets, arXiv:1502.03854v2
• J.H. Tu, Dynamic Mode Decomposition, Theory and Applications, Ph.D. Thesis, Princeton, 2013.
• S Bagheri, Analysis and Control of Transitional Shear Flows Using Global Modes, Ph.D. Thesis, Royal Inst. Technology, Sweden, 2010.

Some Early Papers

• Koopman's original paper: Dynamical Systems of Continuous Spectra, PNAS , vol. 18, 1932.
• J. Ding, The Point Spectrum of Frobenius-Perron and Koopman Operators, Proc. AMS, vol. 126, no. 5, 1998.
• I. Mezic and A. Banaszuk, Comparison of Systems with Complex Behavior, Physica D, vol. 197, pp. 101-133, 2004.
• Y. Lan and I. Mezic, Linearization in the Large of Nonlinear Systems and Koopman Operator Spectrum, Physica D, 2013

Other Papers

• E.Berger, M. Sastuba, D. Vogt, B. Jung, H.B. Amor, Estimation of Perturbations in Robotic Behavior using Dynamic Mode Decomposition, Advanced Robotics, vol. 25, no. 5, 2015.
• S. Wang, Z. Qiao, Nuclear Norm Regularized Dynamic Mode Decomposition, IET Signal Processing, 2016.