We introduce Variational State-Space Filters (VSSF), a new method for unsupervised learning, identification, and filtering of latent Markov state space models from raw pixels. We present a theoretically sound framework for latent state space inference under heterogeneous sensor configurations. The resulting model can integrate an arbitrary subset of the sensor measurements used during training, enabling the learning of semi-supervised state representations, thus enforcing that certain components of the learned latent state space to agree with interpretable measurements. From this framework we derive L-VSSF, an explicit instantiation of this model with linear latent dynamics and Gaussian distribution parameterizations. We experimentally demonstrate L-VSSF's ability to filter in latent space beyond the sequence length of the training dataset across several different test environments.
We present a variational inference (VI) framework that unifies and leverages sequential Monte-Carlo (particle filtering) with \emph{approximate} rejection sampling to construct a flexible family of variational distributions. Furthermore, we augment this approach with a resampling step via Bernoulli race, a generalization of a Bernoulli factory, to obtain a low-variance estimator of the marginal likelihood. Our framework, Variational Rejection Particle Filtering (VRPF), leads to novel variational bounds on the marginal likelihood, which can be optimized efficiently with respect to the variation…
We present a variational method for online state estimation and parameter learning in state-space models (SSMs), a ubiquitous class of latent variable models for sequential data. As per standard batch variational techniques, we use stochastic gradients to simultaneously optimize a lower bound on the log evidence with respect to both model parameters and a variational approximation of the states' posterior distribution. However, unlike existing approaches, our method is able to operate in an entirely online manner, such that historic observations do not require revisitation after being incorpor…
Variational inference (VI) combined with Bayesian nonlinear filtering produces state-of-the-art results for latent time-series modeling. A body of recent work has focused on sequential Monte Carlo (SMC) and its variants, e.g., forward filtering backward simulation (FFBSi). Although these studies have succeeded, serious problems remain in particle degeneracy and biased gradient estimators. In this paper, we propose Ensemble Kalman Variational Objective (EnKO), a hybrid method of VI and the ensemble Kalman filter (EnKF), to infer state space models (SSMs). Our proposed method can efficiently ide…
Outlier-robust Kalman Filtering through Generalised Bayes
School of Mathematical Sciences, Queen Mary University（伦敦玛丽大学数学科学学院）；Oxford-Man Institute of Quantitative Finance, University of Oxford（牛津大学牛津-曼量化金融研究所）；Department of Statistical Science, University College London（伦敦大学学院统计科学系）；Department of Mathematics and Statistics, Memorial University of Newfoundland（纽芬兰纪念大学数学与统计系）；Mathematical Institute, University of Oxford（牛津大学数学研究所）；Institute for Cognitive Science, University of Colorado Boulder（科罗拉多大学博尔德分校认知科学研究所）；Google DeepMind（谷歌DeepMind）
Manning College of Information and Computer Sciences, University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校曼宁信息与计算机科学学院）
Variational inference for state space models (SSMs) is known to be hard in general. Recent works focus on deriving variational objectives for SSMs from unbiased sequential Monte Carlo estimators. We reveal that the marginal particle filter is obtained from sequential Monte Carlo by applying Rao-Blackwellization operations, which sacrifices the trajectory information for reduced variance and differentiability. We propose the variational marginal particle filter (VMPF), which is a differentiable and reparameterizable variational filtering objective for SSMs based on an unbiased estimator. We fin…
Collaborative Filtering using Variational Quantum Hopfield Associative Memory
Pasargad Institue of Advanced Innovative Solutions（帕萨格德先进创新解决方案研究所）；Department of Mathematics and Computer Science（数学与计算机科学系）；Iran University of Science and Technology（伊朗科学技术大学）；Qatar Center for Quantum Computing（卡塔尔量子计算中心）；College of Science and Engineering（科学与工程学院）；Hamad Bin Khalifa University（哈马德·本·卡伊夫大学）
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 e…
Partial differential equation (PDE) models and their associated variational energy formulations are often rotationally invariant by design. This ensures that a rotation of the input results in a corresponding rotation of the output, which is desirable in applications such as image analysis. Convolutional neural networks (CNNs) do not share this property, and existing remedies are often complex. The goal of our paper is to investigate how diffusion and variational models achieve rotation invariance and transfer these ideas to neural networks. As a core novelty we propose activation functions wh…
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.
Deep learning provides accurate collaborative filtering models to improve recommender system results. Deep matrix factorization and their related collaborative neural networks are the state-of-art in the field; nevertheless, both models lack the necessary stochasticity to create the robust, continuous, and structured latent spaces that variational autoencoders exhibit. On the other hand, data augmentation through variational autoencoder does not provide accurate results in the collaborative filtering field due to the high sparsity of recommender systems. Our proposed models apply the variation…
In today's day and age when almost every industry has an online presence with users interacting in online marketplaces, personalized recommendations have become quite important. Traditionally, the problem of collaborative filtering has been tackled using Matrix Factorization which is linear in nature. We extend the work of [11] on using variational autoencoders (VAEs) for collaborative filtering with implicit feedback by proposing a hybrid, multi-modal approach. Our approach combines movie embeddings (learned from a sibling VAE network) with user ratings from the Movielens 20M dataset and appl…
Recommender Systems have become an integral part of online e-Commerce platforms, driving customer engagement and revenue. Most popular recommender systems attempt to learn from users' past engagement data to understand behavioral traits of users and use that to predict future behavior. In this work, we present an approach to use causal inference to learn user-attribute affinities through temporal contexts. We formulate this objective as a Probabilistic Machine Learning problem and apply a variational inference based method to estimate the model parameters. We demonstrate the performance of the…
Texas A&M University（德州农工大学）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；IBM Research（IBM研究院）
We focus on the problem of streaming recommender system and explore novel collaborative filtering algorithms to handle the data dynamicity and complexity in a streaming manner. Although deep neural networks have demonstrated the effectiveness of recommendation tasks, it is lack of explorations on integrating probabilistic models and deep architectures under streaming recommendation settings. Conjoining the complementary advantages of probabilistic models and deep neural networks could enhance both model effectiveness and the understanding of inference uncertainties. To bridge the gap, in this …
University of Electronic Science and Technology of China（电子科技大学）；University of Science and Technology of China（中国科学技术大学）；Huawei Cloud Computing Technologies Co., Ltd.（华为云计算技术有限公司）
Variational AutoEncoder (VAE) has been extended as a representative nonlinear method for collaborative filtering. However, the bottleneck of VAE lies in the softmax computation over all items, such that it takes linear costs in the number of items to compute the loss and gradient for optimization. This hinders the practical use due to millions of items in real-world scenarios. Importance sampling is an effective approximation method, based on which the sampled softmax has been derived. However, existing methods usually exploit the uniform or popularity sampler as proposal distributions, leadin…
DeepMind；University of Oxford（牛津大学）；Google Brain（谷歌大脑）
When used as a surrogate objective for maximum likelihood estimation in latent variable models, the evidence lower bound (ELBO) produces state-of-the-art results. Inspired by this, we consider the extension of the ELBO to a family of lower bounds defined by a particle filter's estimator of the marginal likelihood, the filtering variational objectives (FIVOs). FIVOs take the same arguments as the ELBO, but can exploit a model's sequential structure to form tighter bounds. We present results that relate the tightness of FIVO's bound to the variance of the particle filter's estimator by consideri…
Volkswagen Group（大众汽车集团）；Technische Universität Darmstadt（达姆施塔特工业大学）
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 constraint…
Royal Institute of Technology（皇家理工学院）；Volvo Car Corporation（沃尔沃汽车公司）；Chalmers University of Technology（查尔姆斯理工大学）
Learning generative models and inferring latent trajectories have shown to be challenging for time series due to the intractable marginal likelihoods of flexible generative models. It can be addressed by surrogate objectives for optimization. We propose Monte Carlo filtering objectives (MCFOs), a family of variational objectives for jointly learning parametric generative models and amortized adaptive importance proposals of time series. MCFOs extend the choices of likelihood estimators beyond Sequential Monte Carlo in state-of-the-art objectives, possess important properties revealing the fact…
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 obj…
In this paper, we address the problem of convergence of sequential variational inference filter (VIF) through the application of a robust variational objective and Hinf-norm based correction for a linear Gaussian system. As the dimension of state or parameter space grows, performing the full Kalman update with the dense covariance matrix for a large scale system requires increased storage and computational complexity, making it impractical. The VIF approach, based on mean-field Gaussian variational inference, reduces this burden through the variational approximation to the covariance usually i…
Variational autoencoders were proven successful in domains such as computer vision and speech processing. Their adoption for modeling user preferences is still unexplored, although recently it is starting to gain attention in the current literature. In this work, we propose a model which extends variational autoencoders by exploiting the rich information present in the past preference history. We introduce a recurrent version of the VAE, where instead of passing a subset of the whole history regardless of temporal dependencies, we rather pass the consumption sequence subset through a recurrent…
Learning Optimal Filters Using Variational Inference
California Institute of Technology（加州理工学院）；University of Reading（雷丁大学）；National Centre for Earth Observation（国家地球观测中心）；Office of Naval Research（海军研究办公室）
Neural network based models for collaborative filtering have started to gain attention recently. One branch of research is based on using deep generative models to model user preferences where variational autoencoders were shown to produce state-of-the-art results. However, there are some potentially problematic characteristics of the current variational autoencoder for CF. The first is the too simplistic prior that VAEs incorporate for learning the latent representations of user preference. The other is the model's inability to learn deeper representations with more than one hidden layer for …
Matrix factorization (MF) has been widely applied to collaborative filtering in recommendation systems. Its Bayesian variants can derive posterior distributions of user and item embeddings, and are more robust to sparse ratings. However, the Bayesian methods are restricted by their update rules for the posterior parameters due to the conjugacy of the priors and the likelihood. Variational autoencoders (VAE) can address this issue by capturing complex mappings between the posterior parameters and the data. However, current research on VAEs for collaborative filtering only considers the mappings…
In recent years, Variational Autoencoders (VAEs) have been shown to be highly effective in both standard collaborative filtering applications and extensions such as incorporation of implicit feedback. We extend VAEs to collaborative filtering with side information, for instance when ratings are combined with explicit text feedback from the user. Instead of using a user-agnostic standard Gaussian prior, we incorporate user-dependent priors in the latent VAE space to encode users' preferences as functions of the review text. Taking into account both the rating and the text information to represe…
TU Eindhoven（埃因霍温理工大学）；Sioux Technologies（苏克斯科技公司）
We address object tracking by radar and the robustness of the current state-of-the-art methods to process outliers. The standard tracking algorithms extract detections from radar image space to use it in the filtering stage. Filtering is performed by a Kalman filter, which assumes Gaussian distributed noise. However, this assumption does not account for large modeling errors and results in poor tracking performance during abrupt motions. We take the Gaussian Sum Filter (single-object variant of the Multi Hypothesis Tracker) as our baseline and propose a modification by modelling process noise …
The Alan Turing Institute（艾伦·图灵研究所）；Aalto University（阿尔托大学）；NVIDIA（英伟达）；University of Warwick（华威大学）
We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with respect to time. Our natural gradient approach enables application of parallel filtering and smoothing, further reducing the temporal span complexity to be logarithmic in the number of time steps. We derive a sparse approximation that constructs a state-space model over a reduced set of spatial inducing points, and show that for separable Markov kernels the full …
Ensemble Kalman Filtering Meets Gaussian Process SSM for Non-Mean-Field and Online Inference
School of Science & Engineering, The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳）理工学院）；Future Network of Intelligence Institute（未来智能网络研究院）；Shenzhen Research Institute of Big Data（深圳大数据研究院）；National University of Singapore（新加坡国立大学）
Recent years have witnessed rapid developments on collaborative filtering techniques for improving the performance of recommender systems due to the growing need of companies to help users discover new and relevant items. However, the majority of existing literature focuses on delivering items which match the user model learned from users' past preferences. A good recommendation model is expected to recommend items that are known to enjoy and items that are novel to try. In this work, we introduce an exploitation-exploration motivated variational auto-encoder (XploVAE) to collaborative filteri…
Robust volatility updates for Hierarchical Gaussian Filtering
Interacting Minds Centre, Aarhus University（阿arhus大学交互心智中心）；Centre for Humanities Computing, Aarhus University（阿arhus大学人文计算中心）；Translational Neuromodeling Unit, University of Zurich & ETH Zurich（苏黎世大学转化神经建模单元及苏黎世联邦理工学院）；Institute for Cognitive Science, University of Osnabrück（奥斯纳布吕克大学认知科学研究所）
Particle filtering is a standard Monte-Carlo approach for a wide range of sequential inference tasks. The key component of a particle filter is a set of particles with importance weights that serve as a proxy of the true posterior distribution of some stochastic process. In this work, we propose continuous latent particle filters, an approach that extends particle filtering to the continuous-time domain. We demonstrate how continuous latent particle filters can be used as a generic plug-in replacement for inference techniques relying on a learned variational posterior. Our experiments with dif…
University of Kent（肯特大学）；University of Birmingham（伯明翰大学）
Branching Time Active Inference (Champion et al., 2021b,a) is a framework proposing to look at planning as a form of Bayesian model expansion. Its root can be found in Active Inference (Friston et al., 2016; Da Costa et al., 2020; Champion et al., 2021c), a neuroscientific framework widely used for brain modelling, as well as in Monte Carlo Tree Search (Browne et al., 2012), a method broadly applied in the Reinforcement Learning literature. Up to now, the inference of the latent variables was carried out by taking advantage of the flexibility offered by Variational Message Passing (Winn and Bi…
MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）；IBM Research（IBM研究院）
This paper presents a new approach to distributed linear filtering and prediction. The problem under consideration consists of a random dynamical system observed by a multi-agent network of sensors where the network is sparse. Inspired by the consensus+innovations type of distributed estimation approaches, this paper proposes a novel algorithm that fuses the concepts of consensus and innovations. The paper introduces a definition of distributed observability, required by the proposed algorithm, which is a weaker assumption than that of global observability and connected network assumptions com…
Model-based collaborative filtering analyzes user-item interactions to infer latent factors that represent user preferences and item characteristics in order to predict future interactions. Most collaborative filtering algorithms assume that these latent factors are static, although it has been shown that user preferences and item perceptions drift over time. In this paper, we propose a conjugate and numerically stable dynamic matrix factorization (DCPF) based on compound Poisson matrix factorization that models the smoothly drifting latent factors using Gamma-Markov chains. We propose a numer…
The bane of one-class collaborative filtering is interpreting and modelling the latent signal from the missing class. In this paper we present a novel Bayesian generative model for implicit collaborative filtering. It forms a core component of the Xbox Live architecture, and unlike previous approaches, delineates the odds of a user disliking an item from simply not considering it. The latent signal is treated as an unobserved random graph connecting users with items they might have encountered. We demonstrate how large-scale distributed learning can be achieved through a combination of stochas…
Shanghai Jiao Tong University（上海交通大学）；University of Birmingham（伯明翰大学）
We propose an affine-mapping based variational Ensemble Kalman filter for sequential Bayesian filtering problems with generic observation models. Specifically, the proposed method is formulated as to construct an affine mapping from the prior ensemble to the posterior one, and the affine mapping is computed via a variational Bayesian formulation, i.e., by minimizing the Kullback-Leibler divergence between the transformed distribution through the affine mapping and the actual posterior. Some theoretical properties of resulting optimization problem are studied and a gradient descent scheme is pr…
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 desc…
University of South Carolina（南卡罗来纳大学）；University of North Carolina at Charlotte（北卡罗来纳大学夏洛特分校）
Real-time nonlinear Bayesian filtering algorithms are overwhelmed by data volume, velocity and increasing complexity of computational models. In this paper, we propose a novel ensemble based nonlinear Bayesian filtering approach which only requires a small number of simulations and can be applied to high-dimensional systems in the presence of intractable likelihood functions. The proposed approach uses linear latent projections to estimate the joint probability distribution between states, parameters, and observables using a mixture of Gaussian components generated by the reconstruction error …
We present a Bayesian sequential decision-making formulation of the information filtering problem, in which an algorithm presents items (news articles, scientific papers, tweets) arriving in a stream, and learns relevance from user feedback on presented items. We model user preferences using a Bayesian linear model, similar in spirit to a Bayesian linear bandit. We compute a computational upper bound on the value of the optimal policy, which allows computing an optimality gap for implementable policies. We then use this analysis as motivation in introducing a pair of new Decompose-Then-Decide …
A collaborative filtering system recommends to users products that similar users like. Collaborative filtering systems influence purchase decisions, and hence have become targets of manipulation by unscrupulous vendors. We provide theoretical and empirical results demonstrating that while common nearest neighbor algorithms, which are widely used in commercial systems, can be highly susceptible to manipulation, two classes of collaborative filtering algorithms which we refer to as linear and asymptotically linear are relatively robust. These results provide guidance for the design of future col…
Balyasny Asset Management（巴利亚斯尼资产管理公司）；University College London（伦敦大学学院）；Open Climate Fix（开放气候修复组织）
Short-term forecasting of solar photovoltaic energy (PV) production is important for powerplant management. Ideally these forecasts are equipped with error bars, so that downstream decisions can account for uncertainty. To produce predictions with error bars in this setting, we consider Gaussian processes (GPs) for modelling and predicting solar photovoltaic energy production in the UK. A standard application of GP regression on the PV timeseries data is infeasible due to the large data size and non-Gaussianity of PV readings. However, this is made possible by leveraging recent advances in sca…
University of Washington（华盛顿大学）；Princeton University（普林斯顿大学）；Stanford University（斯坦福大学）
Particle filtering is a popular method for inferring latent states in stochastic dynamical systems, whose theoretical properties have been well studied in machine learning and statistics communities. In many control problems, e.g., partially observed linear dynamical systems (POLDS), oftentimes the inferred latent state is further used for planning at each step. This paper initiates a rigorous study on the efficiency of particle filtering for sequential planning, and gives the first particle complexity bounds. Though errors in past actions may affect the future, we are able to bound the number…
This study addresses the problem of selecting dynamically, at each time instance, the ``optimal'' p-norm to combat outliers in linear adaptive filtering without any knowledge on the potentially time-varying probability distribution function of the outliers. To this end, an online and data-driven framework is designed via kernel-based reinforcement learning (KBRL). Novel Bellman mappings on reproducing kernel Hilbert spaces (RKHSs) are introduced that need no knowledge on transition probabilities of Markov decision processes, and are nonexpansive with respect to the underlying Hilbertian norm. …
Huazhong University of Science and Technology（华中科技大学）；Illinois Institute of Technology（伊利诺伊理工学院）
The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian Lévy noise is present, the conventional Kalman filter may fail to be effective due to the fact that the non-Gaussian Lévy noise may have infinite variance. A modified Kalman filter for linear systems with non-Gaussian Lévy noise is devised. It works effectively with reasonable computational cost. Simulation results are presented to illustrate this non-Gaussian filtering method.
