This paper addresses the issue of detecting hierarchical changes in latent variable models (HCDL) from data streams. There are three different levels of changes for latent variable models: 1) the first level is the change in data distribution for fixed latent variables, 2) the second one is that in the distribution over latent variables, and 3) the third one is that in the number of latent variables. It is important to detect these changes because we can analyze the causes of changes by identifying which level a change comes from (change interpretability). This paper proposes an information-theoretic framework for detecting changes of the three levels in a hierarchical way. The key idea to realize it is to employ the MDL (minimum description length) change statistics for measuring the degree of change, in combination with DNML (decomposed normalized maximum likelihood) code-length calculation. We give a theoretical basis for making reliable alarms for changes. Focusing on stochastic block models, we employ synthetic and benchmark datasets to empirically demonstrate the effectiveness of our framework in terms of change interpretability as well as change detection.
The bits-back argument suggests that latent variable models can be turned into lossless compression schemes. Translating the bits-back argument into efficient and practical lossless compression schemes for general latent variable models, however, is still an open problem. Bits-Back with Asymmetric Numeral Systems (BB-ANS), recently proposed by Townsend et al. (2019), makes bits-back coding practically feasible for latent variable models with one latent layer, but it is inefficient for hierarchical latent variable models. In this paper we propose Bit-Swap, a new compression scheme that generali…
University of Tübingen（图宾根大学）；IMPRS-IS（马克斯·普朗克智能系统研究所国际马克斯·普朗克研究学院）
Variational Autoencoders (VAEs) were originally motivated (Kingma & Welling, 2014) as probabilistic generative models in which one performs approximate Bayesian inference. The proposal of $β$-VAEs (Higgins et al., 2017) breaks this interpretation and generalizes VAEs to application domains beyond generative modeling (e.g., representation learning, clustering, or lossy data compression) by introducing an objective function that allows practitioners to trade off between the information content ("bit rate") of the latent representation and the distortion of reconstructed data (Alemi et al., 2018)…
Columbia University（哥伦比亚大学）；University of Michigan（密歇根大学）
Hierarchical Latent Attribute Models (HLAMs) are a family of discrete latent variable models that are attracting increasing attention in educational, psychological, and behavioral sciences. The key ingredients of an HLAM include a binary structural matrix and a directed acyclic graph specifying hierarchical constraints on the configurations of latent attributes. These components encode practitioners' design information and carry important scientific meanings. Despite the popularity of HLAMs, the fundamental identifiability issue remains unaddressed. The existence of the attribute hierarchy gra…
Identification of Nonlinear Latent Hierarchical Models
Carnegie Mellon University（卡内基梅隆大学）；University of California San Diego（加州大学圣迭戈分校）；Beijing Technology and Business University（北京工商大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Future Network of Intelligence Institute（未来智能网络研究院）；Radboud University（拉德堡德大学）；Institute for Computing and Information Sciences（计算与信息科学研究所）
Multitask Gaussian process (MTGP) is powerful for joint learning of multiple tasks with complicated correlation patterns. However, due to the assembling of additive independent latent functions, all current MTGPs including the salient linear model of coregionalization (LMC) and convolution frameworks cannot effectively represent and learn the hierarchical latent interactions between its latent functions. In this paper, we further investigate the interactions in LMC of MTGP and then propose a novel kernel representation of the hierarchical interactions, which ameliorates both the expressiveness…
Model complexity is an important factor to consider when selecting among graphical models. When all variables are observed, the complexity of a model can be measured by its standard dimension, i.e. the number of independent parameters. When hidden variables are present, however, standard dimension might no longer be appropriate. One should instead use effective dimension (Geiger et al. 1996). This paper is concerned with the computation of effective dimension. First we present an upper bound on the effective dimension of a latent class (LC) model. This bound is tight and its computation is eas…
We learn multiple hypotheses for related tasks under a latent hierarchical relationship between tasks. We exploit the intuition that for domain adaptation, we wish to share classifier structure, but for multitask learning, we wish to share covariance structure. Our hierarchical model is seen to subsume several previously proposed multitask learning models and performs well on three distinct real-world data sets.
It is reasonable to consider, in many cases, that individuals' latent traits have a hierarchical structure such that more general traits are a suitable composition of more specific ones. Existing item response models that account for such hierarchical structure feature have considerable limitations in terms of modelling and/or inference. Motivated by those limitations and the importance of the theme, this paper aims at proposing an improved methodology in terms of both modelling and inference to deal with hierarchically structured latent traits in an item response theory context. From a modell…
We make the following striking observation: fully convolutional VAE models trained on 32x32 ImageNet can generalize well, not just to 64x64 but also to far larger photographs, with no changes to the model. We use this property, applying fully convolutional models to lossless compression, demonstrating a method to scale the VAE-based 'Bits-Back with ANS' algorithm for lossless compression to large color photographs, and achieving state of the art for compression of full size ImageNet images. We release Craystack, an open source library for convenient prototyping of lossless compression using pr…
Deep neural networks have been shown to be very successful at learning feature hierarchies in supervised learning tasks. Generative models, on the other hand, have benefited less from hierarchical models with multiple layers of latent variables. In this paper, we prove that hierarchical latent variable models do not take advantage of the hierarchical structure when trained with existing variational methods, and provide some limitations on the kind of features existing models can learn. Finally we propose an alternative architecture that do not suffer from these limitations. Our model is able t…
Samsung AI Center（三星人工智能中心）；Rutgers University（罗格斯大学）
We propose a family of novel hierarchical Bayesian deep auto-encoder models capable of identifying disentangled factors of variability in data. While many recent attempts at factor disentanglement have focused on sophisticated learning objectives within the VAE framework, their choice of a standard normal as the latent factor prior is both suboptimal and detrimental to performance. Our key observation is that the disentangled latent variables responsible for major sources of variability, the relevant factors, can be more appropriately modeled using long-tail distributions. The typical Gaussian…
University of California Berkeley（加州大学伯克利分校）；Duke University School of Medicine（杜克大学医学院）；Beth Israel Deaconess Medical Center（贝斯以色列女执事医疗中心）；Harvard Medical School（哈佛医学院）；Intel Labs（英特尔实验室）
We introduce a novel, probabilistic binary latent variable model to detect noisy or approximate repeats of patterns in sparse binary data. The model is based on the "Noisy-OR model" (Heckerman, 1990), used previously for disease and topic modelling. The model's capability is demonstrated by extracting structure in recordings from retinal neurons, but it can be widely applied to discover and model latent structure in noisy binary data. In the context of spiking neural data, the task is to "explain" spikes of individual neurons in terms of groups of neurons, "Cell Assemblies" (CAs), that often f…
Hierarchical Bayesian models can be especially useful in precision medicine settings, where clinicians are interested in estimating the patient-level latent variables associated with an individual's current health state and its trajectory. Such models are often fit using batch Markov Chain Monte Carlo (MCMC). However, the slow speed of batch MCMC computation makes it difficult to implement in clinical settings, where immediate latent variable estimates are often desired in response to new patient data. In this report, we discuss how importance sampling (IS) can instead be used to obtain fast, …
This paper proposes a hierarchical, fine-grained and interpretable latent variable model for prosody based on the Tacotron 2 text-to-speech model. It achieves multi-resolution modeling of prosody by conditioning finer level representations on coarser level ones. Additionally, it imposes hierarchical conditioning across all latent dimensions using a conditional variational auto-encoder (VAE) with an auto-regressive structure. Evaluation of reconstruction performance illustrates that the new structure does not degrade the model while allowing better interpretability. Interpretations of prosody a…
We consider posterior sampling in the very common Bayesian hierarchical model in which observed data depends on high-dimensional latent variables that, in turn, depend on relatively few hyperparameters. When the full conditional over the latent variables has a known form, the marginal posterior distribution over hyperparameters is accessible and can be sampled using a Markov chain Monte Carlo (MCMC) method on a low-dimensional parameter space. This may improve computational efficiency over standard Gibbs sampling since computation is not over the high-dimensional space of latent variables and …
University of Toulouse, IRIT/INP-ENSEEIHT（图卢兹大学 IRIT/INP-ENSEEIHT）
Within a supervised classification framework, labeled data are used to learn classifier parameters. Prior to that, it is generally required to perform dimensionality reduction via feature extraction. These preprocessing steps have motivated numerous research works aiming at recovering latent variables in an unsupervised context. This paper proposes a unified framework to perform classification and low-level modeling jointly. The main objective is to use the estimated latent variables as features for classification and to incorporate simultaneously supervised information to help latent variable…
Due to the rapid development of high-throughput experimental techniques and fast-dropping prices, many transcriptomic datasets have been generated and accumulated in the public domain. Meta-analysis combining multiple transcriptomic studies can increase the statistical power to detect disease-related biomarkers. In this paper, we introduce a Bayesian latent hierarchical model to perform transcriptomic meta-analysis. This method is capable of detecting genes that are differentially expressed (DE) in only a subset of the combined studies, and the latent variables help quantify homogeneous and he…
This article considers the estimation of the number of severely disabled people using data from the Italian survey on Health Conditions and Appeal to Medicare. Disability is indirectly measured using a set of categorical items, which survey a set of functions concerning the ability of a person to accomplish everyday tasks. Latent Class Models can be employed to classify the population according to different levels of a latent variable connected with disability. The survey, however, is designed to provide reliable estimates at the level of Administrative Regions (NUTS2 level), while local autho…
Bayesian nonparametric hierarchical priors are highly effective in providing flexible models for latent data structures exhibiting sharing of information between and across groups. Most prominent is the Hierarchical Dirichlet Process (HDP), and its subsequent variants, which model latent clustering between and across groups. The HDP, may be viewed as a more flexible extension of Latent Dirichlet Allocation models (LDA), and has been applied to, for example, topic modelling, natural language processing, and datasets arising in health-care. We focus on analogous latent feature allocation models,…
We propose a comprehensive Bayesian hierarchical model for monthly maxima of instantaneous flow in river catchments. The Gumbel distribution is used as the probabilistic model for the observations, which are assumed to come from several catchments. Our suggested latent model is Gaussian and designed for monthly maxima, making better use of the data than the standard approach using annual maxima. At the latent level, linear mixed models are used for both the location and scale parameters of the Gumbel distribution, accounting for seasonal dependence and covariates from the catchments. The speci…
In this article, we present a Bayesian hierarchical model for predicting a latent health state from longitudinal clinical measurements. Model development is motivated by the need to integrate multiple sources of data to improve clinical decisions about whether to remove or irradiate a patient's prostate cancer. Existing modeling approaches are extended to accommodate measurement error in cancer state determinations based on biopsied tissue, clinical measurements possibly not missing at random, and informative partial observation of the true state. The proposed model enables estimation of wheth…
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…
University of Oxford（牛津大学）；Alan Turing Institute（艾伦·图灵研究所）；Oxford-Man Institute（牛津-曼彻斯特研究所）
Successfully training Variational Autoencoders (VAEs) with a hierarchy of discrete latent variables remains an area of active research. Vector-Quantised VAEs are a powerful approach to discrete VAEs, but naive hierarchical extensions can be unstable when training. Leveraging insights from classical methods of inference we introduce \textit{Relaxed-Responsibility Vector-Quantisation}, a novel way to parameterise discrete latent variables, a refinement of relaxed Vector-Quantisation that gives better performance and more stable training. This enables a novel approach to hierarchical discrete var…
Volkswagen Group（大众汽车集团）；Technical University of Munich（慕尼黑工业大学）
We propose to learn a hierarchical prior in the context of variational autoencoders to avoid the over-regularisation resulting from a standard normal prior distribution. To incentivise an informative latent representation of the data, we formulate the learning problem as a constrained optimisation problem by extending the Taming VAEs framework to two-level hierarchical models. We introduce a graph-based interpolation method, which shows that the topology of the learned latent representation corresponds to the topology of the data manifold---and present several examples, where desired propertie…
University of California, Berkeley（加利福尼亚大学伯克利分校）；Google Brain（谷歌大脑）
In this work, we take a representation learning perspective on hierarchical reinforcement learning, where the problem of learning lower layers in a hierarchy is transformed into the problem of learning trajectory-level generative models. We show that we can learn continuous latent representations of trajectories, which are effective in solving temporally extended and multi-stage problems. Our proposed model, SeCTAR, draws inspiration from variational autoencoders, and learns latent representations of trajectories. A key component of this method is to learn both a latent-conditioned policy and …
The Hong Kong University of Science and Technology（香港科技大学）；The Hong Kong Institute of Education（香港教育学院）
Hierarchical latent tree analysis (HLTA) is recently proposed as a new method for topic detection. It differs fundamentally from the LDA-based methods in terms of topic definition, topic-document relationship, and learning method. It has been shown to discover significantly more coherent topics and better topic hierarchies. However, HLTA relies on the Expectation-Maximization (EM) algorithm for parameter estimation and hence is not efficient enough to deal with large datasets. In this paper, we propose a method to drastically speed up HLTA using a technique inspired by recent advances in the m…
The Hong Kong University of Science and Technology（香港科技大学）；Ant Financial Services Group（蚂蚁金融服务集团）；The Education University of Hong Kong（香港教育大学）
We present a novel method for hierarchical topic detection where topics are obtained by clustering documents in multiple ways. Specifically, we model document collections using a class of graphical models called hierarchical latent tree models (HLTMs). The variables at the bottom level of an HLTM are observed binary variables that represent the presence/absence of words in a document. The variables at other levels are binary latent variables, with those at the lowest latent level representing word co-occurrence patterns and those at higher levels representing co-occurrence of patterns at the l…
The Variational Autoencoder (VAE) has proven to be an effective model for producing semantically meaningful latent representations for natural data. However, it has thus far seen limited application to sequential data, and, as we demonstrate, existing recurrent VAE models have difficulty modeling sequences with long-term structure. To address this issue, we propose the use of a hierarchical decoder, which first outputs embeddings for subsequences of the input and then uses these embeddings to generate each subsequence independently. This structure encourages the model to utilize its latent cod…
Learning Discrete Concepts in Latent Hierarchical Models
Carnegie Mellon University（卡内基梅隆大学）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；University of California San Diego（加州大学圣地亚哥分校）
We address the problem of learning hierarchical deep neural network policies for reinforcement learning. In contrast to methods that explicitly restrict or cripple lower layers of a hierarchy to force them to use higher-level modulating signals, each layer in our framework is trained to directly solve the task, but acquires a range of diverse strategies via a maximum entropy reinforcement learning objective. Each layer is also augmented with latent random variables, which are sampled from a prior distribution during the training of that layer. The maximum entropy objective causes these latent …
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…
NVIDIA（英伟达）；University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Denoising diffusion models (DDMs) have shown promising results in 3D point cloud synthesis. To advance 3D DDMs and make them useful for digital artists, we require (i) high generation quality, (ii) flexibility for manipulation and applications such as conditional synthesis and shape interpolation, and (iii) the ability to output smooth surfaces or meshes. To this end, we introduce the hierarchical Latent Point Diffusion Model (LION) for 3D shape generation. LION is set up as a variational autoencoder (VAE) with a hierarchical latent space that combines a global shape latent representation with…
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…
How to obtain hierarchical representations with an increasing level of abstraction becomes one of the key issues of learning with deep neural networks. A variety of RNN models have recently been proposed to incorporate both explicit and implicit hierarchical information in modeling languages in the literature. In this paper, we propose a novel approach called the latent indicator layer to identify and learn implicit hierarchical information (e.g., phrases), and further develop an EM algorithm to handle the latent indicator layer in training. The latent indicator layer further simplifies a text…
