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 performance across several deep dynamical latent variable models.
Amortized variational inference @cite_48 @cite_0 has enabled many recently proposed probabilistic deep dynamical latent variable models, with applications to video @cite_7 @cite_32 @cite_14 @cite_17 @cite_2 @cite_22 @cite_21 @cite_50 @cite_3 @cite_27 , speech @cite_16 @cite_44 @cite_43 @cite_46 @cite_3 , handwriting @cite_16 , music @cite_8 , etc. While these models differ in their functional mappings, most fall within the general form of Eq. . Crucially, simply encoding the observation at each step is insufficient to accurately perform approximate inference, as the prior can vary across steps. Thus, with each model, a hand-crafted amortized inference procedure has been proposed. For instance, many filtering inference methods re-use various components of the generative model @cite_16 @cite_44 @cite_2 @cite_50 , while some methods introduce separate recurrent neural networks into the filtering procedure @cite_13 @cite_50 or encode the previous latent sample @cite_9 . Specifying a filtering method has been an engineering effort, as we have lacked a theoretical framework.
@cite_22 @cite_3 @cite_44 @cite_43 @cite_2 @cite_8 @cite_48 @cite_21 @cite_46 @cite_17 @cite_7 @cite_32 @cite_27 @cite_50 @cite_16 @cite_14 @cite_9 @cite_0 @cite_13
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How can we efficiently propagate uncertainty in a latent state representation with recurrent neural networks? This paper introduces stochastic recurrent neural networks which glue a deterministic recurrent neural network and a state space model together to form a stochastic and sequential neural generative model. The clear separation of deterministic and stochastic layers allows a structured variational inference network to track the factorization of the model's posterior distribution. By retaining both the nonlinear recursive structure of a recurrent neural network and averaging over the uncertainty in a latent path, like a state space model, we improve the state of the art results on the Blizzard and TIMIT speech modeling data sets by a large margin, while achieving comparable performances to competing methods on polyphonic music modeling. In a given scene, humans can often easily predict a set of immediate future events that might happen. However, generalized pixel-level anticipation in computer vision systems is difficult because machine learning struggles with the ambiguity inherent in predicting the future. In this paper, we focus on predicting the dense trajectory of pixels in a scene, specifically what will move in the scene, where it will travel, and how it will deform over the course of one second. We propose a conditional variational autoencoder as a solution to this problem. In this framework, direct inference from the image shapes the distribution of possible trajectories, while latent variables encode any necessary information that is not available in the image. We show that our method is able to successfully predict events in a wide variety of scenes and can produce multiple different predictions when the future is ambiguous. Our algorithm is trained on thousands of diverse, realistic videos and requires absolutely no human labeling. In addition to non-semantic action prediction, we find that our method learns a representation that is applicable to semantic vision tasks. In this paper, we explore the inclusion of latent random variables into the dynamic hidden state of a recurrent neural network (RNN) by combining elements of the variational autoencoder. We argue that through the use of high-level latent random variables, the variational RNN (VRNN)1 can model the kind of variability observed in highly structured sequential data such as natural speech. We empirically evaluate the proposed model against related sequential models on four speech datasets and one handwriting dataset. Our results show the important roles that latent random variables can play in the RNN dynamic hidden state. We introduce Deep Variational Bayes Filters (DVBF), a new method for unsupervised learning of latent Markovian state space models. Leveraging recent advances in Stochastic Gradient Variational Bayes, DVBF can overcome intractable inference distributions by means of variational inference. Thus, it can handle highly nonlinear input data with temporal and spatial dependencies such as image sequences without domain knowledge. Our experiments show that enabling backpropagation through transitions enforces state space assumptions and significantly improves information content of the latent embedding. This also enables realistic long-term prediction. We develop stochastic variational inference, a scalable algorithm for approximating posterior distributions. We develop this technique for a large class of probabilistic models and we demonstrate it with two probabilistic topic models, latent Dirichlet allocation and the hierarchical Dirichlet process topic model. Using stochastic variational inference, we analyze several large collections of documents: 300K articles from Nature, 1.8M articles from The New York Times, and 3.8M articles from Wikipedia. Stochastic inference can easily handle data sets of this size and outperforms traditional variational inference, which can only handle a smaller subset. (We also show that the Bayesian nonparametric topic model outperforms its parametric counterpart.) Stochastic variational inference lets us apply complex Bayesian models to massive data sets.