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 performance across several deep dynamical latent variable models.Comment: Advances in Neural Information Processing Systems (NIPS) 201

Music generation with variational recurrent autoencoder supported by history

A new architecture of an artificial neural network that helps to generate longer melodic patterns is introduced alongside with methods for post-generation filtering. The proposed approach called variational autoencoder supported by history is based on a recurrent highway gated network combined with a variational autoencoder. Combination of this architecture with filtering heuristics allows generating pseudo-live acoustically pleasing and melodically diverse music

Gaussian filtering and variational approximations for Bayesian smoothing in continuous-discrete stochastic dynamic systems

The Bayesian smoothing equations are generally intractable for systems described by nonlinear stochastic differential equations and discrete-time measurements. Gaussian approximations are a computationally efficient way to approximate the true smoothing distribution. In this work, we present a comparison between two Gaussian approximation methods. The Gaussian filtering based Gaussian smoother uses a Gaussian approximation for the filtering distribution to form an approximation for the smoothing distribution. The variational Gaussian smoother is based on minimizing the Kullback-Leibler divergence of the approximate smoothing distribution with respect to the true distribution. The results suggest that for highly nonlinear systems, the variational Gaussian smoother can be used to iteratively improve the Gaussian filtering based smoothing solution. We also present linearization and sigma-point methods to approximate the intractable Gaussian expectations in the Variational Gaussian smoothing equations. In addition, we extend the variational Gaussian smoother for certain class of systems with singular diffusion matrix.Comment: 24 pages, 4 figures, submitted to Signal Processin

Variational Autoencoders for Collaborative Filtering

We extend variational autoencoders (VAEs) to collaborative filtering for implicit feedback. This non-linear probabilistic model enables us to go beyond the limited modeling capacity of linear factor models which still largely dominate collaborative filtering research.We introduce a generative model with multinomial likelihood and use Bayesian inference for parameter estimation. Despite widespread use in language modeling and economics, the multinomial likelihood receives less attention in the recommender systems literature. We introduce a different regularization parameter for the learning objective, which proves to be crucial for achieving competitive performance. Remarkably, there is an efficient way to tune the parameter using annealing. The resulting model and learning algorithm has information-theoretic connections to maximum entropy discrimination and the information bottleneck principle. Empirically, we show that the proposed approach significantly outperforms several state-of-the-art baselines, including two recently-proposed neural network approaches, on several real-world datasets. We also provide extended experiments comparing the multinomial likelihood with other commonly used likelihood functions in the latent factor collaborative filtering literature and show favorable results. Finally, we identify the pros and cons of employing a principled Bayesian inference approach and characterize settings where it provides the most significant improvements.Comment: 10 pages, 3 figures. WWW 201

Neural Variational Hybrid Collaborative Filtering

Collaborative Filtering (CF) is one of the most used methods for Recommender System. Because of the Bayesian nature and nonlinearity, deep generative models, e.g. Variational Autoencoder (VAE), have been applied into CF task, and have achieved great performance. However, most VAE-based methods suffer from matrix sparsity and consider the prior of users' latent factors to be the same, which leads to poor latent representations of users and items. Additionally, most existing methods model latent factors of users only and but not items, which makes them not be able to recommend items to a new user. To tackle these problems, we propose a Neural Variational Hybrid Collaborative Filtering, NVHCF. Specifically, we consider both the generative processes of users and items, and the prior of latent factors of users and items to be side informationspecific, which enables our model to alleviate matrix sparsity and learn better latent representations of users and items. For inference purpose, we derived a Stochastic Gradient Variational Bayes (SGVB) algorithm to analytically approximate the intractable distributions of latent factors of users and items. Experiments conducted on two large datasets have showed our methods significantly outperform the state-of-the-art CF methods, including the VAE-based methods.Comment: 7 pages, fix some typos (Eq.7

A Variational Formulation of Optimal Nonlinear Estimation

We propose a variational method to solve all three estimation problems for nonlinear stochastic dynamical systems: prediction, filtering, and smoothing. Our new approach is based upon a proper choice of cost function, termed the {\it effective action}. We show that this functional of time-histories is the unique statistically well-founded cost function to determine most probable histories within empirical ensembles. The ensemble dispersion about the sample mean history can also be obtained from the Hessian of the cost function. We show that the effective action can be calculated by a variational prescription, which generalizes the ``sweep method'' used in optimal linear estimation. An iterative numerical scheme results which converges globally to the variational estimator. This scheme involves integrating forward in time a ``perturbed'' Fokker-Planck equation, very closely related to the Kushner-Stratonovich equation for optimal filtering, and an adjoint equation backward in time, similarly related to the Pardoux-Kushner equation for optimal smoothing. The variational estimator enjoys a somewhat weaker property, which we call ``mean optimality''. However, the variational scheme has the principal advantage---crucial for practical applications---that it admits a wide variety of finite-dimensional moment-closure approximations. The moment approximations are derived reductively from the Euler-Lagrange variational formulation and preserve the good structural properties of the optimal estimator.Comment: 59 pages. Glaring typo on p.2 corrected, refs update

Variational Bayesian Adaptation of Noise Covariances in Non-Linear Kalman Filtering

This paper is considered with joint estimation of state and time-varying noise covariance matrices in non-linear stochastic state space models. We present a variational Bayes and Gaussian filtering based algorithm for efficient computation of the approximate filtering posterior distributions. The Gaussian filtering based formulation of the non-linear state space model computation allows usage of efficient Gaussian integration methods such as unscented transform, cubature integration and Gauss-Hermite integration along with the classical Taylor series approximations. The performance of the algorithm is illustrated in a simulated application

Switching Linear Dynamics for Variational Bayes Filtering

System identification of complex and nonlinear systems is a central problem for model predictive control and model-based reinforcement learning. Despite their complexity, such systems can often be approximated well by a set of linear dynamical systems if broken into appropriate subsequences. This mechanism not only helps us find good approximations of dynamics, but also gives us deeper insight into the underlying system. Leveraging Bayesian inference, Variational Autoencoders and Concrete relaxations, we show how to learn a richer and more meaningful state space, e.g. encoding joint constraints and collisions with walls in a maze, from partial and high-dimensional observations. This representation translates into a gain of accuracy of learned dynamics showcased on various simulated tasks.Comment: Appears in Proceedings of the 36th International Conference on Machine Learning (ICML

Structured Black Box Variational Inference for Latent Time Series Models

Continuous latent time series models are prevalent in Bayesian modeling; examples include the Kalman filter, dynamic collaborative filtering, or dynamic topic models. These models often benefit from structured, non mean field variational approximations that capture correlations between time steps. Black box variational inference with reparameterization gradients (BBVI) allows us to explore a rich new class of Bayesian non-conjugate latent time series models; however, a naive application of BBVI to such structured variational models would scale quadratically in the number of time steps. We describe a BBVI algorithm analogous to the forward-backward algorithm which instead scales linearly in time. It allows us to efficiently sample from the variational distribution and estimate the gradients of the ELBO. Finally, we show results on the recently proposed dynamic word embedding model, which was trained using our method.Comment: 5 pages, 1 figure; presented at the ICML 2017 Time Series Worksho

Adaptive Variational Particle Filtering in Non-stationary Environments

Online convex optimization is a sequential prediction framework with the goal to track and adapt to the environment through evaluating proper convex loss functions. We study efficient particle filtering methods from the perspective of such a framework. We formulate an efficient particle filtering methods for the non-stationary environment by making connections with the online mirror descent algorithm which is known to be a universal online convex optimization algorithm. As a result of this connection, our proposed particle filtering algorithm proves to achieve optimal particle efficiency