Hierarchical models represent a challenging setting for inference algorithms. MCMC methods struggle to scale to large models with many local variables and observations, and variational inference (VI) may fail to provide accurate approximations due to the use of simple variational families. Some variational methods (e.g. importance weighted VI) integrate Monte Carlo methods to give better accuracy, but these tend to be unsuitable for hierarchical models, as they do not allow for subsampling and their performance tends to degrade for high dimensional models. We propose a new family of variational bounds for hierarchical models, based on the application of tightening methods (e.g. importance weighting) separately for each group of local random variables. We show that our approach naturally allows the use of subsampling to get unbiased gradients, and that it fully leverages the power of methods that build tighter lower bounds by applying them independently in lower dimensional spaces, leading to better results and more accurate posterior approximations than relevant baselines.
It is difficult to use subsampling with variational inference in hierarchical models since the number of local latent variables scales with the dataset. Thus, inference in hierarchical models remains a challenge at large scale. It is helpful to use a variational family with structure matching the posterior, but optimization is still slow due to the huge number of local distributions. Instead, this paper suggests an amortized approach where shared parameters simultaneously represent all local distributions. This approach is similarly accurate as using a given joint distribution (e.g., a full-ra…
London School of Economics（伦敦政治经济学院）；JP Morgan Chase & Co.（摩根大通公司）
Current variational inference methods for hierarchical Bayesian nonparametric models can neither characterize the correlation structure among latent variables due to the mean-field setting, nor infer the true posterior dimension because of the universal truncation. To overcome these limitations, we propose the conditional and adaptively truncated variational inference method (CATVI) by maximizing the nonparametric evidence lower bound and integrating Monte Carlo into the variational inference framework. CATVI enjoys several advantages over traditional methods, including a smaller divergence be…
The recently developed variational autoencoders (VAEs) have proved to be an effective confluence of the rich representational power of neural networks with Bayesian methods. However, most work on VAEs use a rather simple prior over the latent variables such as standard normal distribution, thereby restricting its applications to relatively simple phenomena. In this work, we propose hierarchical nonparametric variational autoencoders, which combines tree-structured Bayesian nonparametric priors with VAEs, to enable infinite flexibility of the latent representation space. Both the neural paramet…
Variational Inference makes a trade-off between the capacity of the variational family and the tractability of finding an approximate posterior distribution. Instead, Boosting Variational Inference allows practitioners to obtain increasingly good posterior approximations by spending more compute. The main obstacle to widespread adoption of Boosting Variational Inference is the amount of resources necessary to improve over a strong Variational Inference baseline. In our work, we trace this limitation back to the global curvature of the KL-divergence. We characterize how the global curvature imp…
Amsterdam Machine Learning Lab, University of Amsterdam（阿姆斯特丹大学阿姆斯特丹机器学习实验室）
Neural processes (NPs) constitute a family of variational approximate models for stochastic processes with promising properties in computational efficiency and uncertainty quantification. These processes use neural networks with latent variable inputs to induce predictive distributions. However, the expressiveness of vanilla NPs is limited as they only use a global latent variable, while target specific local variation may be crucial sometimes. To address this challenge, we investigate NPs systematically and present a new variant of NP model that we call Doubly Stochastic Variational Neural Pr…
Texas A&M University（得克萨斯农工大学）；The University of Texas at Austin（得克萨斯大学奥斯汀分校）
Semi-implicit graph variational auto-encoder (SIG-VAE) is proposed to expand the flexibility of variational graph auto-encoders (VGAE) to model graph data. SIG-VAE employs a hierarchical variational framework to enable neighboring node sharing for better generative modeling of graph dependency structure, together with a Bernoulli-Poisson link decoder. Not only does this hierarchical construction provide a more flexible generative graph model to better capture real-world graph properties, but also does SIG-VAE naturally lead to semi-implicit hierarchical variational inference that allows faithf…
Columbia University（哥伦比亚大学）；Princeton University（普林斯顿大学）
Implicit probabilistic models are a flexible class of models defined by a simulation process for data. They form the basis for theories which encompass our understanding of the physical world. Despite this fundamental nature, the use of implicit models remains limited due to challenges in specifying complex latent structure in them, and in performing inferences in such models with large data sets. In this paper, we first introduce hierarchical implicit models (HIMs). HIMs combine the idea of implicit densities with hierarchical Bayesian modeling, thereby defining models via simulators of data …
Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
There are many forms of feature information present in video data. Principle among them are object identity information which is largely static across multiple video frames, and object pose and style information which continuously transforms from frame to frame. Most existing models confound these two types of representation by mapping them to a shared feature space. In this paper we propose a probabilistic approach for learning separable representations of object identity and pose information using unsupervised video data. Our approach leverages a deep generative model with a factored prior d…
Mila, University of Montreal（蒙特利尔大学Mila）；Element AI；CIFAR（加拿大高等研究院）
Importance weighted variational inference (Burda et al., 2015) uses multiple i.i.d. samples to have a tighter variational lower bound. We believe a joint proposal has the potential of reducing the number of redundant samples, and introduce a hierarchical structure to induce correlation. The hope is that the proposals would coordinate to make up for the error made by one another to reduce the variance of the importance estimator. Theoretically, we analyze the condition under which convergence of the estimator variance can be connected to convergence of the lower bound. Empirically, we confirm t…
Efficient modeling of relational data arising in physical, social, and information sciences is challenging due to complicated dependencies within the data. In this work, we build off of semi-implicit graph variational auto-encoders to capture higher-order statistics in a low-dimensional graph latent representation. We incorporate hyperbolic geometry in the latent space through a Poincare embedding to efficiently represent graphs exhibiting hierarchical structure. To address the naive posterior latent distribution assumptions in classical variational inference, we use semi-implicit hierarchical…
University of Montreal（蒙特利尔大学）；MILA（蒙特利尔学习算法研究所）；Element AI
Despite the advances in the representational capacity of approximate distributions for variational inference, the optimization process can still limit the density that is ultimately learned. We demonstrate the drawbacks of biasing the true posterior to be unimodal, and introduce Annealed Variational Objectives (AVO) into the training of hierarchical variational methods. Inspired by Annealed Importance Sampling, the proposed method facilitates learning by incorporating energy tempering into the optimization objective. In our experiments, we demonstrate our method's robustness to deterministic w…
Hierarchical Semi-Implicit Variational Inference with Application to Diffusion Model Acceleration
Peking University（北京大学）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；Beijing Academy of Artificial Intelligence（北京人工智能研究院）；Megvii Technology Inc.（旷视科技有限公司）
Bayesian hierarchical models are increasing popular in economics. When using hierarchical models, it is useful not only to calculate posterior expectations, but also to measure the robustness of these expectations to reasonable alternative prior choices. We use variational Bayes and linear response methods to provide fast, accurate posterior means and robustness measures with an application to measuring the effectiveness of microcredit in the developing world.
Non-linear hierarchical models are commonly used in many disciplines. However, inference in the presence of non-nested effects and on large datasets is challenging and computationally burdensome. This paper provides two contributions to scalable and accurate inference. First, I derive a new mean-field variational algorithm for estimating binomial logistic hierarchical models with an arbitrary number of non-nested random effects. Second, I propose "marginally augmented variational Bayes" (MAVB) that further improves the initial approximation through a step of Bayesian post-processing. I prove t…
Hierarchical models with gamma hyperpriors provide a flexible, sparse-promoting framework to bridge $L^1$ and $L^2$ regularizations in Bayesian formulations to inverse problems. Despite the Bayesian motivation for these models, existing methodologies are limited to \textit{maximum a posteriori} estimation. The potential to perform uncertainty quantification has not yet been realized. This paper introduces a variational iterative alternating scheme for hierarchical inverse problems with gamma hyperpriors. The proposed variational inference approach yields accurate reconstruction, provides meani…
Model comparison is the cornerstone of theoretical progress in psychological research. Common practice overwhelmingly relies on tools that evaluate competing models by balancing in-sample descriptive adequacy against model flexibility, with modern approaches advocating the use of marginal likelihood for hierarchical cognitive models. Cross-validation is another popular approach but its implementation has remained out of reach for cognitive models evaluated in a Bayesian hierarchical framework, with the major hurdle being prohibitive computational cost. To address this issue, we develop novel a…
Stochastic variational inference for collapsed models has recently been successfully applied to large scale topic modelling. In this paper, we propose a stochastic collapsed variational inference algorithm in the sequential data setting. Our algorithm is applicable to both finite hidden Markov models and hierarchical Dirichlet process hidden Markov models, and to any datasets generated by emission distributions in the exponential family. Our experiment results on two discrete datasets show that our inference is both more efficient and more accurate than its uncollapsed version, stochastic vari…
Samsung AI Center Moscow（三星莫斯科人工智能中心）；National Research University Higher School of Economics（国立研究型高等经济学院）；NRU HSE（国立研究型高等经济学院）
Variational Inference is a powerful tool in the Bayesian modeling toolkit, however, its effectiveness is determined by the expressivity of the utilized variational distributions in terms of their ability to match the true posterior distribution. In turn, the expressivity of the variational family is largely limited by the requirement of having a tractable density function. To overcome this roadblock, we introduce a new family of variational upper bounds on a marginal log density in the case of hierarchical models (also known as latent variable models). We then give an upper bound on the Kullba…
University of Victoria（维多利亚大学）；Pacific Forestry Centre, National Resources Canada（加拿大自然资源部太平洋林业中心）
A clustering termination procedure which is locally adaptive (with respect to the hierarchical tree of sets representative of the agglomerative merging) is proposed, for agglomerative hierarchical clustering on a set equipped with a distance function. It represents a multi-scale alternative to conventional scale dependent threshold based termination criteria.
This paper shows how the variational Bayes method provides a computational efficient technique in the context of hierarchical modelling using Dirichlet process priors, in particular without requiring conjugate prior assumption. It shows, using the so called parameter separation parameterization, a simple criterion under which the variational method works well. Based on this framework, its provides a full variational solution for the Dirichlet process. The numerical results show that the method is very computationally efficient when compared to MCMC. Finally, we propose an empirical method to e…
University of Oxford（牛津大学）；DeepMind（深度思维）；Microsoft Research（微软研究院）
The variational auto-encoder (VAE) is a popular method for learning a generative model and embeddings of the data. Many real datasets are hierarchically structured. However, traditional VAEs map data in a Euclidean latent space which cannot efficiently embed tree-like structures. Hyperbolic spaces with negative curvature can. We therefore endow VAEs with a Poincaré ball model of hyperbolic geometry as a latent space and rigorously derive the necessary methods to work with two main Gaussian generalisations on that space. We empirically show better generalisation to unseen data than the Euclidea…
University of California, Irvine（加州大学欧文分校）；University of California, Berkeley（加州大学伯克利分校）
Autonomous agents can learn by imitating teacher demonstrations of the intended behavior. Hierarchical control policies are ubiquitously useful for such learning, having the potential to break down structured tasks into simpler sub-tasks, thereby improving data efficiency and generalization. In this paper, we propose a variational inference method for imitation learning of a control policy represented by parametrized hierarchical procedures (PHP), a program-like structure in which procedures can invoke sub-procedures to perform sub-tasks. Our method discovers the hierarchical structure in a da…
Decision making is a process that is extremely prone to different biases. In this paper we consider learning fair representations that aim at removing nuisance (sensitive) information from the decision process. For this purpose, we propose to use deep generative modeling and adapt a hierarchical Variational Auto-Encoder to learn these fair representations. Moreover, we utilize the mutual information as a useful regularizer for enforcing fairness of a representation. In experiments on two benchmark datasets and two scenarios where the sensitive variables are fully and partially observable, we s…
COSY, Institute of Neuroscience, Université Catholique de Louvain（比利时布鲁塞尔天主教鲁汶大学神经科学研究所COSY（需注意：COSY为缩写，此处保留原文））
A common problem in Machine Learning and statistics consists in detecting whether the current sample in a stream of data belongs to the same distribution as previous ones, is an isolated outlier or inaugurates a new distribution of data. We present a hierarchical Bayesian algorithm that aims at learning a time-specific approximate posterior distribution of the parameters describing the distribution of the data observed. We derive the update equations of the variational parameters of the approximate posterior at each time step for models from the exponential family, and show that these updates …
Wuhan University（武汉大学）；The University of Adelaide（阿德莱德大学）；Inception Institute of Artificial Intelligence（人工智能初创研究院）
Variational dropout (VD) is a generalization of Gaussian dropout, which aims at inferring the posterior of network weights based on a log-uniform prior on them to learn these weights as well as dropout rate simultaneously. The log-uniform prior not only interprets the regularization capacity of Gaussian dropout in network training, but also underpins the inference of such posterior. However, the log-uniform prior is an improper prior (i.e., its integral is infinite) which causes the inference of posterior to be ill-posed, thus restricting the regularization performance of VD. To address this p…
Black box variational inference allows researchers to easily prototype and evaluate an array of models. Recent advances allow such algorithms to scale to high dimensions. However, a central question remains: How to specify an expressive variational distribution that maintains efficient computation? To address this, we develop hierarchical variational models (HVMs). HVMs augment a variational approximation with a prior on its parameters, which allows it to capture complex structure for both discrete and continuous latent variables. The algorithm we develop is black box, can be used for any HVM,…
Conditional Variational Auto Encoders (VAE) are gathering significant attention as an Explainable Artificial Intelligence (XAI) tool. The codes in the latent space provide a theoretically sound way to produce counterfactuals, i.e. alterations resulting from an intervention on a targeted semantic feature. To be applied on real images more complex models are needed, such as Hierarchical CVAE. This comes with a challenge as the naive conditioning is no longer effective. In this paper we show how relaxing the effect of the posterior leads to successful counterfactuals and we introduce VAEX an Hier…
Variational Autoencoders (VAEs) have experienced recent success as data-generating models by using simple architectures that do not require significant fine-tuning of hyperparameters. However, VAEs are known to suffer from over-regularization which can lead to failure to escape local maxima. This phenomenon, known as posterior collapse, prevents learning a meaningful latent encoding of the data. Recent methods have mitigated this issue by deterministically moment-matching an aggregated posterior distribution to an aggregate prior. However, abandoning a probabilistic framework (and thus relying…
Learning long-term dependencies is a key long-standing challenge of recurrent neural networks (RNNs). Hierarchical recurrent neural networks (HRNNs) have been considered a promising approach as long-term dependencies are resolved through shortcuts up and down the hierarchy. Yet, the memory requirements of Truncated Backpropagation Through Time (TBPTT) still prevent training them on very long sequences. In this paper, we empirically show that in (deep) HRNNs, propagating gradients back from higher to lower levels can be replaced by locally computable losses, without harming the learning capabil…
University of Amsterdam（阿姆斯特丹大学）；Inception Institute of Artificial Intelligence（Inception人工智能研究院）；National Center for Artificial Intelligence, Saudi Data and Artificial Intelligence Authority（沙特数据与人工智能局国家人工智能中心）
Neural memory enables fast adaptation to new tasks with just a few training samples. Existing memory models store features only from the single last layer, which does not generalize well in presence of a domain shift between training and test distributions. Rather than relying on a flat memory, we propose a hierarchical alternative that stores features at different semantic levels. We introduce a hierarchical prototype model, where each level of the prototype fetches corresponding information from the hierarchical memory. The model is endowed with the ability to flexibly rely on features at di…
Mila, Université de Montréal（米拉，蒙特利尔大学）；Kakao Brain；Rutgers University（罗格斯大学）
We introduce a variational approach to learning and inference of temporally hierarchical structure and representation for sequential data. We propose the Variational Temporal Abstraction (VTA), a hierarchical recurrent state space model that can infer the latent temporal structure and thus perform the stochastic state transition hierarchically. We also propose to apply this model to implement the jumpy-imagination ability in imagination-augmented agent-learning in order to improve the efficiency of the imagination. In experiments, we demonstrate that our proposed method can model 2D and 3D vis…
We address the task of domain generalization, where the goal is to train a predictive model such that it is able to generalize to a new, previously unseen domain. We choose a hierarchical generative approach within the framework of variational autoencoders and propose a domain-unsupervised algorithm that is able to generalize to new domains without domain supervision. We show that our method is able to learn representations that disentangle domain-specific information from class-label specific information even in complex settings where domain structure is not observed during training. Our inte…
I propose a novel approach for nonlinear Logistic regression using a two-layer neural network (NN) model structure with hierarchical priors on the network weights. I present a hybrid of expectation propagation called Variational Expectation Propagation approach (VEP) for approximate integration over the posterior distribution of the weights, the hierarchical scale parameters of the priors and zeta. Using a factorized posterior approximation I derive a computationally efficient algorithm, whose complexity scales similarly to an ensemble of independent sparse logistic models. The approach can be…
University of Electronic Science and Technology of China（电子科技大学）；China Academy of Engineering Physics（中国工程物理研究院）
In this paper, we consider the problem of low-rank phase retrieval whose objective is to estimate a complex low-rank matrix from magnitude-only measurements. We propose a hierarchical prior model for low-rank phase retrieval, in which a Gaussian-Wishart hierarchical prior is placed on the underlying low-rank matrix to promote the low-rankness of the matrix. Based on the proposed hierarchical model, a variational expectation-maximization (EM) algorithm is developed. The proposed method is less sensitive to the choice of the initialization point and works well with random initialization. Simulat…
Deep generative models have achieved great success in unsupervised learning with the ability to capture complex nonlinear relationships between latent generating factors and observations. Among them, a factorized hierarchical variational autoencoder (FHVAE) is a variational inference-based model that formulates a hierarchical generative process for sequential data. Specifically, an FHVAE model can learn disentangled and interpretable representations, which have been proven useful for numerous speech applications, such as speaker verification, robust speech recognition, and voice conversion. Ho…
Normalizing flows, autoregressive models, variational autoencoders (VAEs), and deep energy-based models are among competing likelihood-based frameworks for deep generative learning. Among them, VAEs have the advantage of fast and tractable sampling and easy-to-access encoding networks. However, they are currently outperformed by other models such as normalizing flows and autoregressive models. While the majority of the research in VAEs is focused on the statistical challenges, we explore the orthogonal direction of carefully designing neural architectures for hierarchical VAEs. We propose Nouv…
This paper aims to develop an acoustic signal-based unsupervised anomaly detection method for automatic machine monitoring. Existing approaches such as deep autoencoder (DAE), variational autoencoder (VAE), conditional variational autoencoder (CVAE) etc. have limited representation capabilities in the latent space and, hence, poor anomaly detection performance. Different models have to be trained for each different kind of machines to accurately perform the anomaly detection task. To solve this issue, we propose a new method named as hierarchical conditional variational autoencoder (HCVAE). Th…
Massachusetts Institute of Technology（麻省理工学院）；MIT-IBM Watson AI Lab（麻省理工学院-IBM沃森人工智能实验室）
Hierarchical Bayesian methods can unify many related tasks (e.g. k-shot classification, conditional and unconditional generation) as inference within a single generative model. However, when this generative model is expressed as a powerful neural network such as a PixelCNN, we show that existing learning techniques typically fail to effectively use latent variables. To address this, we develop a modification of the Variational Autoencoder in which encoded observations are decoded to new elements from the same class. This technique, which we call a Variational Homoencoder (VHE), produces a hier…
Variational autoencoders (VAE) combined with hierarchical RNNs have emerged as a powerful framework for conversation modeling. However, they suffer from the notorious degeneration problem, where the decoders learn to ignore latent variables and reduce to vanilla RNNs. We empirically show that this degeneracy occurs mostly due to two reasons. First, the expressive power of hierarchical RNN decoders is often high enough to model the data using only its decoding distributions without relying on the latent variables. Second, the conditional VAE structure whose generation process is conditioned on …
University of Torontoland（托伦托兰大学）；Googol ShallowMind；University of Edenborrow（伊登伯勒大学）
Making inferences from data streams is a pervasive problem in many modern data analysis applications. But it requires to address the problem of continuous model updating and adapt to changes or drifts in the underlying data generating distribution. In this paper, we approach these problems from a Bayesian perspective covering general conjugate exponential models. Our proposal makes use of non-conjugate hierarchical priors to explicitly model temporal changes of the model parameters. We also derive a novel variational inference scheme which overcomes the use of non-conjugate priors while mainta…
Stochastic variance reduced extragradient methods for solving hierarchical variational inequalities
Weierstrass Institute for Applied Analysis and Stochastics（魏尔斯特拉斯应用分析与随机学研究所）；Mannheim University（曼海姆大学）；Technion - Israel Institute of Technology（以色列理工学院）
Variational autoencoders (VAEs) have witnessed great success in performing the compression of image datasets. This success, made possible by the bits-back coding framework, has produced competitive compression performance across many benchmarks. However, despite this, VAE architectures are currently limited by a combination of coding practicalities and compression ratios. That is, not only do state-of-the-art methods, such as normalizing flows, often demonstrate out-performance, but the initial bits required in coding makes single and parallel image compression challenging. To remedy this, we …
Efficient low-variance gradient estimation enabled by the reparameterization trick (RT) has been essential to the success of variational autoencoders. Doubly-reparameterized gradients (DReGs) improve on the RT for multi-sample variational bounds by applying reparameterization a second time for an additional reduction in variance. Here, we develop two generalizations of the DReGs estimator and show that they can be used to train conditional and hierarchical VAEs on image modelling tasks more effectively. First, we extend the estimator to hierarchical models with several stochastic layers by sho…
Interpreting computations in the visual cortex as learning and inference in a generative model of the environment has received wide support both in neuroscience and cognitive science. However, hierarchical computations, a hallmark of visual cortical processing, has remained impervious for generative models because of a lack of adequate tools to address it. Here we capitalize on advances in Variational Autoencoders (VAEs) to investigate the early visual cortex with sparse coding hierarchical VAEs trained on natural images. We design alternative architectures that vary both in terms of the gener…
Shanghai Jiao Tong University（上海交通大学）；University of Technology Sydney（悉尼科技大学）
Learning in the latent variable model is challenging in the presence of the complex data structure or the intractable latent variable. Previous variational autoencoders can be low effective due to the straightforward encoder-decoder structure. In this paper, we propose a variational composite autoencoder to sidestep this issue by amortizing on top of the hierarchical latent variable model. The experimental results confirm the advantages of our model.
