A General Method for Amortizing Variational Filtering

We introduce the variational filtering EM algorithm, a simple, general-purpose method for performing variational inference in dynamical latent variable models using information from only past and present variables, i.e. filtering. The algorithm is derived from the variational objective in the filtering setting and consists of an optimization procedure at each time step. By performing each inference optimization procedure with an iterative amortized inference model, we obtain a computationally efficient implementation of the algorithm, which we call amortized variational filtering. We present experiments demonstrating that this general-purpose method improves inference performance across several recent deep dynamical latent variable models.

[1]  Jonathan G. Fiscus,et al.  DARPA TIMIT:: acoustic-phonetic continuous speech corpus CD-ROM, NIST speech disc 1-1.1 , 1993 .

[2]  Yoshua Bengio,et al.  Z-Forcing: Training Stochastic Recurrent Networks , 2017, NIPS.

[3]  Yu Zhang,et al.  Unsupervised Learning of Disentangled and Interpretable Representations from Sequential Data , 2017, NIPS.

[4]  Chong Wang,et al.  Stochastic variational inference , 2012, J. Mach. Learn. Res..

[5]  Yoshua Bengio,et al.  A Recurrent Latent Variable Model for Sequential Data , 2015, NIPS.

[6]  Ryan P. Adams,et al.  Composing graphical models with neural networks for structured representations and fast inference , 2016, NIPS.

[7]  Scott W. Linderman,et al.  Variational Sequential Monte Carlo , 2017, AISTATS.

[8]  Yann LeCun,et al.  Prediction Under Uncertainty with Error-Encoding Networks , 2017, ArXiv.

[9]  Yoshua Bengio,et al.  Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling , 2014, ArXiv.

[10]  Yisong Yue,et al.  Iterative Amortized Inference , 2018, ICML.

[11]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[12]  Ole Winther,et al.  Sequential Neural Models with Stochastic Layers , 2016, NIPS.

[13]  Karl J. Friston,et al.  A theory of cortical responses , 2005, Philosophical Transactions of the Royal Society B: Biological Sciences.

[14]  Daan Wierstra,et al.  Stochastic Backpropagation and Approximate Inference in Deep Generative Models , 2014, ICML.

[15]  Jiawei He,et al.  Probabilistic Video Generation using Holistic Attribute Control , 2018, ECCV.

[16]  Geoffrey E. Hinton,et al.  A View of the Em Algorithm that Justifies Incremental, Sparse, and other Variants , 1998, Learning in Graphical Models.

[17]  Sergey Levine,et al.  Stochastic Variational Video Prediction , 2017, ICLR.

[18]  Nitish Srivastava,et al.  Unsupervised Learning of Video Representations using LSTMs , 2015, ICML.

[19]  Jiajun Wu,et al.  Visual Dynamics: Probabilistic Future Frame Synthesis via Cross Convolutional Networks , 2016, NIPS.

[20]  Rob Fergus,et al.  Stochastic Video Generation with a Learned Prior , 2018, ICML.

[21]  Michael I. Jordan,et al.  An Introduction to Variational Methods for Graphical Models , 1999, Machine Learning.

[22]  Christian Osendorfer,et al.  Learning Stochastic Recurrent Networks , 2014, NIPS 2014.

[23]  Geoffrey E. Hinton,et al.  The Helmholtz Machine , 1995, Neural Computation.

[24]  Yee Whye Teh,et al.  Filtering Variational Objectives , 2017, NIPS.

[25]  Sergey Levine,et al.  Unsupervised Learning for Physical Interaction through Video Prediction , 2016, NIPS.

[26]  Geoffrey E. Hinton,et al.  Layer Normalization , 2016, ArXiv.

[27]  Ole Winther,et al.  A Disentangled Recognition and Nonlinear Dynamics Model for Unsupervised Learning , 2017, NIPS.

[28]  Sean Gerrish,et al.  Black Box Variational Inference , 2013, AISTATS.

[29]  Martial Hebert,et al.  An Uncertain Future: Forecasting from Static Images Using Variational Autoencoders , 2016, ECCV.

[30]  Noah D. Goodman,et al.  Amortized Inference in Probabilistic Reasoning , 2014, CogSci.

[31]  Barbara Caputo,et al.  Recognizing human actions: a local SVM approach , 2004, Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004..

[32]  Diederik P. Kingma,et al.  Stochastic Gradient VB and the Variational Auto-Encoder , 2013 .

[33]  David Amos,et al.  Generative Temporal Models with Memory , 2017, ArXiv.

[34]  Maximilian Karl,et al.  Deep Variational Bayes Filters: Unsupervised Learning of State Space Models from Raw Data , 2016, ICLR.

[35]  Stephan Mandt,et al.  A Deep Generative Model for Disentangled Representations of Sequential Data , 2018, ICML 2018.

[36]  Daan Wierstra,et al.  Deep AutoRegressive Networks , 2013, ICML.

[37]  Sepp Hochreiter,et al.  Fast and Accurate Deep Network Learning by Exponential Linear Units (ELUs) , 2015, ICLR.

[38]  Yoshua Bengio,et al.  Modeling Temporal Dependencies in High-Dimensional Sequences: Application to Polyphonic Music Generation and Transcription , 2012, ICML.

[39]  Tuan Anh Le,et al.  Auto-Encoding Sequential Monte Carlo , 2017, ICLR.

[40]  Jonathan G. Fiscus,et al.  Darpa Timit Acoustic-Phonetic Continuous Speech Corpus CD-ROM {TIMIT} | NIST , 1993 .

[41]  Marcin Andrychowicz,et al.  Learning to learn by gradient descent by gradient descent , 2016, NIPS.

[42]  Gabriel Kreiman,et al.  Deep Predictive Coding Networks for Video Prediction and Unsupervised Learning , 2016, ICLR.

[43]  Rajesh P. N. Rao,et al.  Predictive coding in the visual cortex: a functional interpretation of some extra-classical receptive-field effects. , 1999 .

[44]  Ole Winther,et al.  Ladder Variational Autoencoders , 2016, NIPS.