Probabilistic regression techniques in control and robotics applications have to fulfill different criteria of data-driven adaptability, computational efficiency, scalability to high dimensions, and the capacity to deal with different modalities in the data. Classical regressors usually fulfill only a subset of these properties. In this work, we extend seminal work on Bayesian nonparametric mixtures and derive an efficient variational Bayes inference technique for infinite mixtures of probabilistic local polynomial models with well-calibrated certainty quantification. We highlight the model's power in combining data-driven complexity adaptation, fast prediction and the ability to deal with discontinuous functions and heteroscedastic noise. We benchmark this technique on a range of large real inverse dynamics datasets, showing that the infinite mixture formulation is competitive with classical Local Learning methods and regularizes model complexity by adapting the number of components based on data and without relying on heuristics. Moreover, to showcase the practicality of the approach, we use the learned models for online inverse dynamics control of a Barrett-WAM manipulator, significantly improving the trajectory tracking performance.
Unlike previous studies on mixture distributions, a bagging and boosting based convexly combined mixture probabilistic model has been suggested. This model is a result of iteratively searching for obtaining the optimum probabilistic model that provides the maximum p value.
This letter presents a continuous probabilistic modeling methodology for spatial point cloud data using finite Gaussian Mixture Models (GMMs) where the number of components are adapted based on the scene complexity. Few hierarchical and adaptive methods have been proposed to address the challenge of balancing model fidelity with size. Instead, state-of-the-art mapping approaches require tuning parameters for specific use cases, but do not generalize across diverse environments. To address this gap, we utilize a self-organizing principle from information-theoretic learning to automatically adap…
We present a new algorithm for approximate inference in probabilistic programs, based on a stochastic gradient for variational programs. This method is efficient without restrictions on the probabilistic program; it is particularly practical for distributions which are not analytically tractable, including highly structured distributions that arise in probabilistic programs. We show how to automatically derive mean-field probabilistic programs and optimize them, and demonstrate that our perspective improves inference efficiency over other algorithms.
Deep probabilistic time series forecasting models have become an integral part of machine learning. While several powerful generative models have been proposed, we provide evidence that their associated inference models are oftentimes too limited and cause the generative model to predict mode-averaged dynamics. Modeaveraging is problematic since many real-world sequences are highly multi-modal, and their averaged dynamics are unphysical (e.g., predicted taxi trajectories might run through buildings on the street map). To better capture multi-modality, we develop variational dynamic mixtures (V…
University of Toronto（多伦多大学）；Vector Institute（向量研究院）
Bayesian methods estimate a measure of uncertainty by using the posterior distribution. One source of difficulty in these methods is the computation of the normalizing constant. Calculating exact posterior is generally intractable and we usually approximate it. Variational Inference (VI) methods approximate the posterior with a distribution usually chosen from a simple family using optimization. The main contribution of this work is described is a set of update rules for natural gradient variational inference with mixture of Gaussians, which can be run independently for each of the mixture com…
In many data-driven applications, collecting data from different sources is increasingly desirable for enhancing performance. In this paper, we are interested in the problem of probabilistic forecasting with multi-source time series. We propose a neural mixture structure-based probability model for learning different predictive relations and their adaptive combinations from multi-source time series. We present the prediction and uncertainty quantification methods that apply to different distributions of target variables. Additionally, given the imbalanced and unstable behaviors observed during…
Kogakuin University of Technology and Engineering（工学院大学）
Finite mixture models, typically Gaussian mixtures, are well known and widely used as model-based clustering. In practical situations, there are many non-Gaussian data that are heavy-tailed and/or asymmetric. Normal inverse Gaussian (NIG) distributions are normal-variance mean which mixing densities are inverse Gaussian distributions and can be used for both haavy-tail and asymmetry. For NIG mixture models, both expectation-maximization method and variational Bayesian (VB) algorithms have been proposed. However, the existing VB algorithm for NIG mixture have a disadvantage that the shape of th…
Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所 HIIT）；Aalto University（阿尔托大学）
The expressive power of Gaussian processes depends heavily on the choice of kernel. In this work we propose the novel harmonizable mixture kernel (HMK), a family of expressive, interpretable, non-stationary kernels derived from mixture models on the generalized spectral representation. As a theoretically sound treatment of non-stationary kernels, HMK supports harmonizable covariances, a wide subset of kernels including all stationary and many non-stationary covariances. We also propose variational Fourier features, an inter-domain sparse GP inference framework that offers a representative set …
Aiming at a comprehensive and concise tutorial survey, recap of variational inference and reinforcement learning with Probabilistic Graphical Models are given with detailed derivations. Reviews and comparisons on recent advances in deep reinforcement learning are made from various aspects. We offer detailed derivations to a taxonomy of Probabilistic Graphical Model and Variational Inference methods in deep reinforcement learning, which serves as a complementary material on top of the original contributions.
We introduce and demonstrate the variational autoencoder (VAE) for probabilistic non-negative matrix factorisation (PAE-NMF). We design a network which can perform non-negative matrix factorisation (NMF) and add in aspects of a VAE to make the coefficients of the latent space probabilistic. By restricting the weights in the final layer of the network to be non-negative and using the non-negative Weibull distribution we produce a probabilistic form of NMF which allows us to generate new data and find a probability distribution that effectively links the latent and input variables. We demonstrat…
Hezhou University（贺州学院）；North China University of Technology（北方工业大学）；DigApis Information Security Technology Co., Ltd.（江苏迪格艾普斯信息安全技术有限公司）；Jiangsu University（江苏大学）；Beijing University of Posts and Telecommunications（北京邮电大学）
The finite invert Beta-Liouville mixture model (IBLMM) has recently gained some attention due to its positive data modeling capability. Under the conventional variational inference (VI) framework, the analytically tractable solution to the optimization of the variational posterior distribution cannot be obtained, since the variational object function involves evaluation of intractable moments. With the recently proposed extended variational inference (EVI) framework, a new function is proposed to replace the original variational object function in order to avoid intractable moment computation,…
Quanzhou Institute of Equipment Manufacturing, Haixi Institutes, Chinese Academy of Sciences（中国科学院海西研究院泉州装备制造研究所）；University of Reading（雷丁大学）
An improved mixture of probabilistic principal component analysis (PPCA) has been introduced for nonlinear data-driven process monitoring in this paper. To realize this purpose, the technique of a mixture of probabilistic principal component analysers is utilized to establish the model of the underlying nonlinear process with local PPCA models, where a novel composite monitoring statistic is proposed based on the integration of two monitoring statistics in modified PPCA-based fault detection approach. Besides, the weighted mean of the monitoring statistics aforementioned is utilised as a metri…
Institute of Mathematical Sciences (ICMAT)（数学科学研究所（ICMAT））；SAMSI, Duke University（杜克大学SAMSI）
A framework to boost the efficiency of Bayesian inference in probabilistic programs is introduced by embedding a sampler inside a variational posterior approximation. We call it the refined variational approximation. Its strength lies both in ease of implementation and automatically tuning of the sampler parameters to speed up mixing time using automatic differentiation. Several strategies to approximate \emph{evidence lower bound} (ELBO) computation are introduced. Experimental evidence of its efficient performance is shown solving an influence diagram in a high-dimensional space using a cond…
In this paper, we introduce Deep Probabilistic Ensembles (DPEs), a scalable technique that uses a regularized ensemble to approximate a deep Bayesian Neural Network (BNN). We do so by incorporating a KL divergence penalty term into the training objective of an ensemble, derived from the evidence lower bound used in variational inference. We evaluate the uncertainty estimates obtained from our models for active learning on visual classification. Our approach steadily improves upon active learning baselines as the annotation budget is increased.
In this paper, we propose a deep probabilistic multi-view model that is composed of a linear multi-view layer based on probabilistic canonical correlation analysis (CCA) description in the latent space together with deep generative networks as observation models. The network is designed to decompose the variations of all views into a shared latent representation and a set of view-specific components where the shared latent representation is intended to describe the common underlying sources of variation among the views. An efficient variational inference procedure is developed that approximate…
We introduce a novel way to incorporate prior information into (semi-) supervised non-negative matrix factorization, which we call differentiable dictionary search. It enables general, highly flexible and principled modelling of mixtures where non-linear sources are linearly mixed. We study its behavior on an audio decomposition task, and conduct an extensive, highly controlled study of its modelling capabilities.
In this paper, we develop an unsupervised generative clustering framework that combines the Variational Information Bottleneck and the Gaussian Mixture Model. Specifically, in our approach, we use the Variational Information Bottleneck method and model the latent space as a mixture of Gaussians. We derive a bound on the cost function of our model that generalizes the Evidence Lower Bound (ELBO) and provide a variational inference type algorithm that allows computing it. In the algorithm, the coders' mappings are parametrized using neural networks, and the bound is approximated by Monte Carlo s…
We present VAEL, a neuro-symbolic generative model integrating variational autoencoders (VAE) with the reasoning capabilities of probabilistic logic (L) programming. Besides standard latent subsymbolic variables, our model exploits a probabilistic logic program to define a further structured representation, which is used for logical reasoning. The entire process is end-to-end differentiable. Once trained, VAEL can solve new unseen generation tasks by (i) leveraging the previously acquired knowledge encoded in the neural component and (ii) exploiting new logical programs on the structured laten…
Lehigh University（理海大学）；University of Virginia（弗吉尼亚大学）
Dimensionality reduction on Riemannian manifolds is challenging due to the complex nonlinear data structures. While probabilistic principal geodesic analysis~(PPGA) has been proposed to generalize conventional principal component analysis (PCA) onto manifolds, its effectiveness is limited to data with a single modality. In this paper, we present a novel Gaussian latent variable model that provides a unique way to integrate multiple PGA models into a maximum-likelihood framework. This leads to a well-defined mixture model of probabilistic principal geodesic analysis (MPPGA) on sub-populations, …
Natural image statistics exhibit hierarchical dependencies across multiple scales. Representing such prior knowledge in non-factorial latent tree models can boost performance of image denoising, inpainting, deconvolution or reconstruction substantially, beyond standard factorial "sparse" methodology. We derive a large scale approximate Bayesian inference algorithm for linear models with non-factorial (latent tree-structured) scale mixture priors. Experimental results on a range of denoising and inpainting problems demonstrate substantially improved performance compared to MAP estimation or to …
This is a tutorial and survey paper on factor analysis, probabilistic Principal Component Analysis (PCA), variational inference, and Variational Autoencoder (VAE). These methods, which are tightly related, are dimensionality reduction and generative models. They assume that every data point is generated from or caused by a low-dimensional latent factor. By learning the parameters of distribution of latent space, the corresponding low-dimensional factors are found for the sake of dimensionality reduction. For their stochastic and generative behaviour, these models can also be used for generatio…
Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所（HIIT））；University of Helsinki（赫尔辛基大学）
Variational approximations are increasingly based on gradient-based optimization of expectations estimated by sampling. Handling discrete latent variables is then challenging because the sampling process is not differentiable. Continuous relaxations, such as the Gumbel-Softmax for categorical distribution, enable gradient-based optimization, but do not define a valid probability mass for discrete observations. In practice, selecting the amount of relaxation is difficult and one needs to optimize an objective that does not align with the desired one, causing problems especially with models havi…
Instituto Superior Técnico, Universidade de Lisboa（里斯本大学高等技术学院）；Instituto de Telecomunicações（电信研究所）
In the past few years, deep generative models, such as generative adversarial networks \autocite{GAN}, variational autoencoders \autocite{vaepaper}, and their variants, have seen wide adoption for the task of modelling complex data distributions. In spite of the outstanding sample quality achieved by those early methods, they model the target distributions \emph{implicitly}, in the sense that the probability density functions induced by them are not explicitly accessible. This fact renders those methods unfit for tasks that require, for example, scoring new instances of data with the learned d…
University of Oxford（牛津大学）；Alan Turing Institute（艾伦·图灵研究所）；University of Cambridge（剑桥大学）
Learning generative models that span multiple data modalities, such as vision and language, is often motivated by the desire to learn more useful, generalisable representations that faithfully capture common underlying factors between the modalities. In this work, we characterise successful learning of such models as the fulfillment of four criteria: i) implicit latent decomposition into shared and private subspaces, ii) coherent joint generation over all modalities, iii) coherent cross-generation across individual modalities, and iv) improved model learning for individual modalities through m…
Multi-label classification (MLC) is a prediction task where each sample can have more than one label. We propose a novel contrastive learning boosted multi-label prediction model based on a Gaussian mixture variational autoencoder (C-GMVAE), which learns a multimodal prior space and employs a contrastive loss. Many existing methods introduce extra complex neural modules like graph neural networks to capture the label correlations, in addition to the prediction modules. We find that by using contrastive learning in the supervised setting, we can exploit label information effectively in a data-d…
University of British Columbia（不列颠哥伦比亚大学）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）
Natural-gradient methods enable fast and simple algorithms for variational inference, but due to computational difficulties, their use is mostly limited to \emph{minimal} exponential-family (EF) approximations. In this paper, we extend their application to estimate \emph{structured} approximations such as mixtures of EF distributions. Such approximations can fit complex, multimodal posterior distributions and are generally more accurate than unimodal EF approximations. By using a \emph{minimal conditional-EF} representation of such approximations, we derive simple natural-gradient updates. Our…
LTCI, Télécom Paris（巴黎电信学院LTCI实验室）；Institut Polytechnique de Paris（巴黎理工学院）；SAMOVAR, Télécom SudParis（南巴黎电信学院SAMOVAR实验室）
This paper focuses on $α$-divergence minimisation methods for Variational Inference. More precisely, we are interested in algorithms optimising the mixture weights of any given mixture model, without any information on the underlying distribution of its mixture components parameters. The Power Descent, defined for all $α\neq 1$, is one such algorithm and we establish in our work the full proof of its convergence towards the optimal mixture weights when $α<1$. Since the $α$-divergence recovers the widely-used forward Kullback-Leibler when $α\to 1$, we then extend the Power Descent to the case $…
Recently, an audio-visual speech generative model based on variational autoencoder (VAE) has been proposed, which is combined with a nonnegative matrix factorization (NMF) model for noise variance to perform unsupervised speech enhancement. When visual data is clean, speech enhancement with audio-visual VAE shows a better performance than with audio-only VAE, which is trained on audio-only data. However, audio-visual VAE is not robust against noisy visual data, e.g., when for some video frames, speaker face is not frontal or lips region is occluded. In this paper, we propose a robust unsupervi…
In inference, open-set classification is to either classify a sample into a known class from training or reject it as an unknown class. Existing deep open-set classifiers train explicit closed-set classifiers, in some cases disjointly utilizing reconstruction, which we find dilutes the latent representation's ability to distinguish unknown classes. In contrast, we train our model to cooperatively learn reconstruction and perform class-based clustering in the latent space. With this, our Gaussian mixture variational autoencoder (GMVAE) achieves more accurate and robust open-set classification r…
Department of Chemical and Biomolecular Engineering, University of Maryland（马里兰大学化学与生物分子工程系）
Conformational sampling of biomolecules using molecular dynamics simulations often produces large amount of high dimensional data that makes it difficult to interpret using conventional analysis techniques. Dimensionality reduction methods are thus required to extract useful and relevant information. Here we devise a machine learning method, Gaussian mixture variational autoencoder (GMVAE) that can simultaneously perform dimensionality reduction and clustering of biomolecular conformations in an unsupervised way. We show that GMVAE can learn a reduced representation of the free energy landscap…
In this paper, we propose an end-to-end lifelong learning mixture of experts. Each expert is implemented by a Variational Autoencoder (VAE). The experts in the mixture system are jointly trained by maximizing a mixture of individual component evidence lower bounds (MELBO) on the log-likelihood of the given training samples. The mixing coefficients in the mixture, control the contributions of each expert in the goal representation. These are sampled from a Dirichlet distribution whose parameters are determined through non-parametric estimation during lifelong learning. The model can learn new t…
University of Oxford（牛津大学）；Alan Turing Institute（艾伦·图灵研究所）
In clustering we normally output one cluster variable for each datapoint. However it is not necessarily the case that there is only one way to partition a given dataset into cluster components. For example, one could cluster objects by their colour, or by their type. Different attributes form a hierarchy, and we could wish to cluster in any of them. By disentangling the learnt latent representations of some dataset into different layers for different attributes we can then cluster in those latent spaces. We call this "disentangled clustering". Extending Variational Ladder Autoencoders (Zhao et…
Samsung AI Center（三星人工智能中心）；Rutgers University（罗格斯大学）
Inference networks of traditional Variational Autoencoders (VAEs) are typically amortized, resulting in relatively inaccurate posterior approximation compared to instance-wise variational optimization. Recent semi-amortized approaches were proposed to address this drawback; however, their iterative gradient update procedures can be computationally demanding. To address these issues, in this paper we introduce an accurate amortized inference algorithm. We propose a novel recursive mixture estimation algorithm for VAEs that iteratively augments the current mixture with new components so as to ma…
Recently, Stochastic Variational Inference (SVI) has been increasingly attractive thanks to its ability to find good posterior approximations of probabilistic models. It optimizes the variational objective with stochastic optimization, following noisy estimates of the natural gradient. However, almost all the state-of-the-art SVI algorithms are based on first-order optimization algorithm and often suffer from poor convergence rate. In this paper, we bridge the gap between second-order methods and stochastic variational inference by proposing a second-order based stochastic variational inferenc…
CNR, Institute of Intelligent Industrial Technologies and Systems for Advanced Manufacturing（意大利国家研究委员会 智能工业技术与先进制造系统研究所）；Politecnico di Milano（米兰理工大学）
Probabilistic load forecasting (PLF) is a key component in the extended tool-chain required for efficient management of smart energy grids. Neural networks are widely considered to achieve improved prediction performances, supporting highly flexible mappings of complex relationships between the target and the conditioning variables set. However, obtaining comprehensive predictive uncertainties from such black-box models is still a challenging and unsolved problem. In this work, we propose a novel PLF approach, framed on Bayesian Mixture Density Networks. Both aleatoric and epistemic uncertaint…
ETH Zürich（苏黎世联邦理工学院）；Life Science Graduate School Zurich（苏黎世生命科学研究生院）；Swiss Institute of Bioinformatics（瑞士生物信息学研究所）；University of Tübingen（图宾根大学）
Clustering high-dimensional data, such as images or biological measurements, is a long-standingproblem and has been studied extensively. Recently, Deep Clustering has gained popularity due toits flexibility in fitting the specific peculiarities of complex data. Here we introduce the Mixture-of-Experts Similarity Variational Autoencoder (MoE-Sim-VAE), a novel generative clustering model.The model can learn multi-modal distributions of high-dimensional data and use these to generaterealistic data with high efficacy and efficiency. MoE-Sim-VAE is based on a Variational Autoencoder(VAE), where the…
Variation Autoencoder (VAE) has become a powerful tool in modeling the non-linear generative process of data from a low-dimensional latent space. Recently, several studies have proposed to use VAE for unsupervised clustering by using mixture models to capture the multi-modal structure of latent representations. This strategy, however, is ineffective when there are outlier data samples whose latent representations are meaningless, yet contaminating the estimation of key major clusters in the latent space. This exact problem arises in the context of resting-state fMRI (rs-fMRI) analysis, where c…
