We propose a technique for increasing the efficiency of gradient-based inference and learning in Bayesian networks with multiple layers of continuous latent vari- ables. We show that, in many cases, it is possible to express such models in an auxiliary form, where continuous latent variables are conditionally deterministic given their parents and a set of independent auxiliary variables. Variables of mod- els in this auxiliary form have much larger Markov blankets, leading to significant speedups in gradient-based inference, e.g. rapid mixing Hybrid Monte Carlo and efficient gradient-based optimization. The relative efficiency is confirmed in ex- periments.
Massachusetts Institute of Technology（麻省理工学院）；University of Arizona（亚利桑那大学）
We present an approach to data fusion that combines the interpretability of structured probabilistic graphical models with the flexibility of neural networks. The proposed method, lightweight data fusion (LDF), emphasizes posterior analysis over latent variables using two types of information: primary data, which are well-characterized but with limited availability, and auxiliary data, readily available but lacking a well-characterized statistical relationship to the latent quantity of interest. The lack of a forward model for the auxiliary data precludes the use of standard data fusion approa…
Variational inference for latent variable models is prevalent in various machine learning problems, typically solved by maximizing the Evidence Lower Bound (ELBO) of the true data likelihood with respect to a variational distribution. However, freely enriching the family of variational distribution is challenging since the ELBO requires variational likelihood evaluations of the latent variables. In this paper, we propose a novel framework to enrich the variational family by incorporating auxiliary variables to the variational family. The resulting inference network doesn't require density eval…
MILA, Université de Montréal（蒙特利尔大学 MILA）；Microsoft Maluuba（微软 Maluuba）；MILA, Polytechnique Montréal（蒙特利尔理工学院 MILA）
Many efforts have been devoted to training generative latent variable models with autoregressive decoders, such as recurrent neural networks (RNN). Stochastic recurrent models have been successful in capturing the variability observed in natural sequential data such as speech. We unify successful ideas from recently proposed architectures into a stochastic recurrent model: each step in the sequence is associated with a latent variable that is used to condition the recurrent dynamics for future steps. Training is performed with amortized variational inference where the approximate posterior is …
University of Chicago（芝加哥大学）；Carnegie Mellon University（卡内基梅隆大学）
We prove identifiability of a broad class of deep latent variable models that (a) have universal approximation capabilities and (b) are the decoders of variational autoencoders that are commonly used in practice. Unlike existing work, our analysis does not require weak supervision, auxiliary information, or conditioning in the latent space. Specifically, we show that for a broad class of generative (i.e. unsupervised) models with universal approximation capabilities, the side information $u$ is not necessary: We prove identifiability of the entire generative model where we do not observe $u$ a…
Networks play a central role in modern data analysis, enabling us to reason about systems by studying the relationships between their parts. Most often in network analysis, the edges are given. However, in many systems it is difficult or impossible to measure the network directly. Examples of latent networks include economic interactions linking financial instruments and patterns of reciprocity in gang violence. In these cases, we are limited to noisy observations of events associated with each node. To enable analysis of these implicit networks, we develop a probabilistic model that combines …
Universidad Tecnológica de Pereira（佩雷拉理工大学）；The University of Sheffield（谢菲尔德大学）
A latent force model is a Gaussian process with a covariance function inspired by a differential operator. Such covariance function is obtained by performing convolution integrals between Green's functions associated to the differential operators, and covariance functions associated to latent functions. In the classical formulation of latent force models, the covariance functions are obtained analytically by solving a double integral, leading to expressions that involve numerical solutions of different types of error functions. In consequence, the covariance matrix calculation is considerably …
University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；Mount Holyoke College（曼荷莲学院）
We develop nested automatic differentiation (AD) algorithms for exact inference and learning in integer latent variable models. Recently, Winner, Sujono, and Sheldon showed how to reduce marginalization in a class of integer latent variable models to evaluating a probability generating function which contains many levels of nested high-order derivatives. We contribute faster and more stable AD algorithms for this challenging problem and a novel algorithm to compute exact gradients for learning. These contributions lead to significantly faster and more accurate learning algorithms, and are the …
Although with progress in introducing auxiliary amortized inference models, learning discrete latent variable models is still challenging. In this paper, we show that the annoying difficulty of obtaining reliable stochastic gradients for the inference model and the drawback of indirectly optimizing the target log-likelihood can be gracefully addressed in a new method based on stochastic approximation (SA) theory of the Robbins-Monro type. Specifically, we propose to directly maximize the target log-likelihood and simultaneously minimize the inclusive divergence between the posterior and the in…
Variational autoencoders often assume isotropic Gaussian priors and mean-field posteriors, hence do not exploit structure in scenarios where we may expect similarity or consistency across latent variables. Gaussian process variational autoencoders alleviate this problem through the use of a latent Gaussian process, but lead to a cubic inference time complexity. We propose a more scalable extension of these models by leveraging the independence of the auxiliary features, which is present in many datasets. Our model factorizes the latent kernel across these features in different dimensions, lead…
Uncovering Physical Drivers of Dark Matter Halo Structures with Auxiliary-Variable-Guided Generative Models
Mathematics and Computer Science Division Argonne National Laboratory（阿贡国家实验室数学与计算机科学部）；High Energy Physics Division Argonne National Laboratory（阿贡国家实验室高能物理部）；Computational Science Division Argonne National Laboratory（阿贡国家实验室计算科学部）；Computational Science Center Data, Analysis and Visualization Group National Renewable Energy Laboratory（国家可再生能源实验室计算科学中心数据、分析与可视化组）
Variational autoencoders learn unsupervised data representations, but these models frequently converge to minima that fail to preserve meaningful semantic information. For example, variational autoencoders with autoregressive decoders often collapse into autodecoders, where they learn to ignore the encoder input. In this work, we demonstrate that adding an auxiliary decoder to regularize the latent space can prevent this collapse, but successful auxiliary decoding tasks are domain dependent. Auxiliary decoders can increase the amount of semantic information encoded in the latent space and visi…
Nonresponse is present in almost all surveys and can severely bias estimates. It is usually distinguished between unit and item nonresponse: in the former, we completely fail to have information from a unit selected in the sample, while in the latter, we observe only part of the information on the selected unit. Unit nonresponse is usually dealt with by reweighting: each unit selected in the sample has associated a sampling weight and an unknown response probability; the initial sampling weight is multiplied by the inverse of estimated response probability. Item nonresponse is usually dealt wi…
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, …
Empirical observations suggest that in practice, community membership does not completely explain the dependency between the edges of an observation graph. The residual dependence of the graph edges are modeled in this paper, to first order, by auxiliary node latent variables that affect the statistics of the graph edges but carry no information about the communities of interest. We then study community detection in graphs obeying the stochastic block model and censored block model with auxiliary latent variables. We analyze the conditions for exact recovery when these auxiliary latent variabl…
We define a novel class of additive models, called Extended Latent Gaussian Models, that allow for a wide range of response distributions and flexible relationships between the additive predictor and mean response. The new class covers a broad range of interesting models including multi-resolution spatial processes, partial likelihood-based survival models, and multivariate measurement error models. Because computation of the exact posterior distribution is infeasible, we develop a fast, scalable approximate Bayesian inference methodology for this class based on nested Gaussian, Laplace, and a…
As a general-purpose generative model architecture, VAE has been widely used in the field of image and natural language processing. VAE maps high dimensional sample data into continuous latent variables with unsupervised learning. Sampling in the latent variable space of the feature, VAE can construct new image or text data. As a general-purpose generation model, the vanilla VAE can not fit well with various data sets and neural networks with different structures. Because of the need to balance the accuracy of reconstruction and the convenience of latent variable sampling in the training proce…
The latent block model is used to simultaneously rank the rows and columns of a matrix to reveal a block structure. The algorithms used for estimation are often time consuming. However, recent work shows that the log-likelihood ratios are equivalent under the complete and observed (with unknown labels) models and the groups posterior distribution to converge as the size of the data increases to a Dirac mass located at the actual groups configuration. Based on these observations, the algorithm $Largest$ $Gaps$ is proposed in this paper to perform clustering using only the marginals of the matri…
Stochastic differential equations (SDEs) or diffusions are continuous-valued continuous-time stochastic processes widely used in the applied and mathematical sciences. Simulating paths from these processes is usually an intractable problem, and typically involves time-discretization approximations. We propose an exact Markov chain Monte Carlo sampling algorithm that involves no such time-discretization error. Our sampler is applicable to the problem of prior simulation from an SDE, posterior simulation conditioned on noisy observations, as well as parameter inference given noisy observations. …
Gait-Based Hand Load Estimation via Deep Latent Variable Models with Auxiliary Information
Department of Systems and Information Engineering, University of Virginia（系统与信息工程系，弗吉尼亚大学）；Department of Industrial and Systems Engineering, Virginia Polytechnic Institute and State University（工业与系统工程系，弗吉尼亚理工学院和州立大学）
University of Tsukuba（筑波大学）；NTT Communication Science Laboratories, NTT Corporation（日本电报电话公司NTT通信科学实验室）
This paper proposes an alternative algorithm for multichannel variational autoencoder (MVAE), a recently proposed multichannel source separation approach. While MVAE is notable in its impressive source separation performance, the convergence-guaranteed optimization algorithm and that it allows us to estimate source-class labels simultaneously with source separation, there are still two major drawbacks, i.e., the high computational complexity and unsatisfactory source classification accuracy. To overcome these drawbacks, the proposed method employs an auxiliary classifier VAE, an information-th…
Discovering the underlying physical behavior of complex systems is a crucial, but less well-understood topic in many engineering disciplines. This study proposes a finite-difference inspired convolutional neural network framework to learn hidden partial differential equations from given data and iteratively estimate future dynamical behavior. The methodology designs the filter sizes such that they mimic the finite difference between the neighboring points. By learning the governing equation, the network predicts the future evolution of the solution by using only a few trainable parameters. In …
Bocconi University（博科尼大学）；Bocconi Institute for Data Science and Analytics（博科尼数据科学与分析研究所）；University of Verona（威尼斯大学）；HUMATICS - SYS-DAT Group（HUMATICS-SYS-DAT组）；University of Milano-Bicocca（米兰-比科卡大学）
South China University of Technology（华南理工大学）；Guangdong General Hospital（广东省人民医院）
The tongue image provides important physical information of humans. It is of great importance for diagnoses and treatments in clinical medicine. Herbal prescriptions are simple, noninvasive and have low side effects. Thus, they are widely applied in China. Studies on the automatic construction technology of herbal prescriptions based on tongue images have great significance for deep learning to explore the relevance of tongue images for herbal prescriptions, it can be applied to healthcare services in mobile medical systems. In order to adapt to the tongue image in a variety of photographic en…
Idiap Research Institute（伊迪亚普研究所）；Yahoo! Labs（雅虎实验室）
In this work we consider the learning setting where, in addition to the training set, the learner receives a collection of auxiliary hypotheses originating from other tasks. We focus on a broad class of ERM-based linear algorithms that can be instantiated with any non-negative smooth loss function and any strongly convex regularizer. We establish generalization and excess risk bounds, showing that, if the algorithm is fed with a good combination of source hypotheses, generalization happens at the fast rate $\mathcal{O}(1/m)$ instead of the usual $\mathcal{O}(1/\sqrt{m})$. On the other hand, if…
Mila - Quebec AI Institute（米拉-魁北克人工智能研究所）；Université de Montréal（蒙特利尔大学）
The theory of representation learning aims to build methods that provably invert the data generating process with minimal domain knowledge or any source of supervision. Most prior approaches require strong distributional assumptions on the latent variables and weak supervision (auxiliary information such as timestamps) to provide provable identification guarantees. In this work, we show that if one has weak supervision from observations generated by sparse perturbations of the latent variables--e.g. images in a reinforcement learning environment where actions move individual sprites--identific…
Deep directed generative models have attracted much attention recently due to their generative modeling nature and powerful data representation ability. In this paper, we review different structures of deep directed generative models and the learning and inference algorithms associated with the structures. We focus on a specific structure that consists of layers of Bayesian Networks due to the property of capturing inherent and rich dependencies among latent variables. The major difficulty of learning and inference with deep directed models with many latent variables is the intractable inferen…
We address the problem of latent truth discovery, LTD for short, where the goal is to discover the underlying true values of entity attributes in the presence of noisy, conflicting or incomplete information. Despite a multitude of algorithms to address the LTD problem that can be found in literature, only little is known about their overall performance with respect to effectiveness (in terms of truth discovery capabilities), efficiency and robustness. A practical LTD approach should satisfy all these characteristics so that it can be applied to heterogeneous datasets of varying quality and deg…
Google Brain（谷歌大脑）；Johns Hopkins University（约翰斯·霍普金斯大学）
Many reinforcement learning (RL) tasks provide the agent with high-dimensional observations that can be simplified into low-dimensional continuous states. To formalize this process, we introduce the concept of a DeepMDP, a parameterized latent space model that is trained via the minimization of two tractable losses: prediction of rewards and prediction of the distribution over next latent states. We show that the optimization of these objectives guarantees (1) the quality of the latent space as a representation of the state space and (2) the quality of the DeepMDP as a model of the environment…
Deep learning models have significantly improved the visual quality and accuracy on compressive sensing recovery. In this paper, we propose an algorithm for signal reconstruction from compressed measurements with image priors captured by a generative model. We search and constrain on latent variable space to make the method stable when the number of compressed measurements is extremely limited. We show that, by exploiting certain structures of the latent variables, the proposed method produces improved reconstruction accuracy and preserves realistic and non-smooth features in the image. Our al…
The Gatsby Unit UCL（伦敦大学学院盖茨比研究组）；Dept. of CS and HIIT Univ. Helsinki（赫尔辛基大学计算机科学系及赫尔辛基信息技术研究所）；Div. of Info. Sci. NAIST（奈良先端科学技术大学院大学信息科学部）；Univ. Cambridge & Microsoft Research（剑桥大学及微软研究院）
Nonlinear ICA is a fundamental problem for unsupervised representation learning, emphasizing the capacity to recover the underlying latent variables generating the data (i.e., identifiability). Recently, the very first identifiability proofs for nonlinear ICA have been proposed, leveraging the temporal structure of the independent components. Here, we propose a general framework for nonlinear ICA, which, as a special case, can make use of temporal structure. It is based on augmenting the data by an auxiliary variable, such as the time index, the history of the time series, or any other availab…
Optimization problems with an auxiliary latent variable structure in addition to the main model parameters occur frequently in computer vision and machine learning. The additional latent variables make the underlying optimization task expensive, either in terms of memory (by maintaining the latent variables), or in terms of runtime (repeated exact inference of latent variables). We aim to remove the need to maintain the latent variables and propose two formally justified methods, that dynamically adapt the required accuracy of latent variable inference. These methods have applications in large…
While multi-step adversarial training is widely popular as an effective defense method against strong adversarial attacks, its computational cost is notoriously expensive, compared to standard training. Several single-step adversarial training methods have been proposed to mitigate the above-mentioned overhead cost; however, their performance is not sufficiently reliable depending on the optimization setting. To overcome such limitations, we deviate from the existing input-space-based adversarial training regime and propose a single-step latent adversarial training method (SLAT), which leverag…
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；Électricité de France R&D（法国电力研发中心）
We consider the problem of time series forecasting in an adaptive setting. We focus on the inference of state-space models under unknown and potentially time-varying noise variances. We introduce an augmented model in which the variances are represented as auxiliary gaussian latent variables in a tracking mode. As variances are nonnegative, a transformation is chosen and applied to these latent variables. The inference relies on the online variational Bayesian methodology, which consists in minimizing a Kullback-Leibler divergence at each time step. We observe that the minimum of the Kullback-…
Autoregressive sequence models based on deep neural networks, such as RNNs, Wavenet and the Transformer attain state-of-the-art results on many tasks. However, they are difficult to parallelize and are thus slow at processing long sequences. RNNs lack parallelism both during training and decoding, while architectures like WaveNet and Transformer are much more parallelizable during training, yet still operate sequentially during decoding. Inspired by [arxiv:1711.00937], we present a method to extend sequence models using discrete latent variables that makes decoding much more parallelizable. We…
Inducing latent tree structures from sequential data is an emerging trend in the NLP research landscape today, largely popularized by recent methods such as Gumbel LSTM and Ordered Neurons (ON-LSTM). This paper proposes FASTTREES, a new general purpose neural module for fast sequence encoding. Unlike most previous works that consider recurrence to be necessary for tree induction, our work explores the notion of parallel tree induction, i.e., imbuing our model with hierarchical inductive biases in a parallelizable, non-autoregressive fashion. To this end, our proposed FASTTREES achieves competi…
North Carolina State University（北卡罗来纳州立大学）；Chalmers University（查尔姆斯大学）
In this paper, we address the problem of unsupervised Domain Adaptation. The need for such an adaptation arises when the distribution of the target data differs from that which is used to develop the model and the ground truth information of the target data is unknown. We propose an algorithm that uses optimal transport theory with a verifiably efficient and implementable solution to learn the best latent feature representation. This is achieved by minimizing the cost of transporting the samples from the target domain to the distribution of the source domain.
In this project we outline Vedalia, a high performance distributed network for performing inference on latent variable models in the context of Amazon review visualization. We introduce a new model, RLDA, which extends Latent Dirichlet Allocation (LDA) [Blei et al., 2003] for the review space by incorporating auxiliary data available in online reviews to improve modeling while simultaneously remaining compatible with pre-existing fast sampling techniques such as [Yao et al., 2009; Li et al., 2014a] to achieve high performance. The network is designed such that computation is efficiently offloa…
Duke University（杜克大学）；Princeton University（普林斯顿大学）
We develop a generalized method of moments (GMM) approach for fast parameter estimation in a new class of Dirichlet latent variable models with mixed data types. Parameter estimation via GMM has been demonstrated to have computational and statistical advantages over alternative methods, such as expectation maximization, variational inference, and Markov chain Monte Carlo. The key computational advan- tage of our method (MELD) is that parameter estimation does not require instantiation of the latent variables. Moreover, a representational advantage of the GMM approach is that the behavior of th…
