Maximum likelihood (ML) and adversarial learning are two popular approaches for training generative models, and from many perspectives these techniques are complementary. ML learning encourages the capture of all data modes, and it is typically characterized by stable training. However, ML learning tends to distribute probability mass diffusely over the data space, $e.g.$, yielding blurry synthetic images. Adversarial learning is well known to synthesize highly realistic natural images, despite practical challenges like mode dropping and delicate training. We propose an $α$-Bridge to unify the advantages of ML and adversarial learning, enabling the smooth transfer from one to the other via the $α$-divergence. We reveal that generalizations of the $α$-Bridge are closely related to approaches developed recently to regularize adversarial learning, providing insights into that prior work, and further understanding of why the $α$-Bridge performs well in practice.
The University of Tokyo（东京大学）；CyberAgent, Inc.（赛博艾金特公司）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）；Preferred Networks, Inc.（优选网络公司）
This paper provides a unified perspective for the Kullback-Leibler (KL)-divergence and the integral probability metrics (IPMs) from the perspective of maximum likelihood density-ratio estimation (DRE). Both the KL-divergence and the IPMs are widely used in various fields in applications such as generative modeling. However, a unified understanding of these concepts has still been unexplored. In this paper, we show that the KL-divergence and the IPMs can be represented as maximal likelihoods differing only by sampling schemes, and use this result to derive a unified form of the IPMs and a relax…
Our goal is to learn a semantic parser that maps natural language utterances into executable programs when only indirect supervision is available: examples are labeled with the correct execution result, but not the program itself. Consequently, we must search the space of programs for those that output the correct result, while not being misled by spurious programs: incorrect programs that coincidentally output the correct result. We connect two common learning paradigms, reinforcement learning (RL) and maximum marginal likelihood (MML), and then present a new learning algorithm that combines …
Department of Medicine, University of Chicago（芝加哥大学医学院）
Recognizing subtle historical patterns is central to modeling and forecasting problems in time series analysis. Here we introduce and develop a new approach to quantify deviations in the underlying hidden generators of observed data streams, resulting in a new efficiently computable universal metric for time series. The proposed metric is in the sense that we can compare and contrast data streams regardless of where and how they are generated and without any feature engineering step. The approach proposed in this paper is conceptually distinct from our previous work on data smashing, and vastl…
Black box variational inference (BBVI) with reparameterization gradients triggered the exploration of divergence measures other than the Kullback-Leibler (KL) divergence, such as alpha divergences. In this paper, we view BBVI with generalized divergences as a form of estimating the marginal likelihood via biased importance sampling. The choice of divergence determines a bias-variance trade-off between the tightness of a bound on the marginal likelihood (low bias) and the variance of its gradient estimators. Drawing on variational perturbation theory of statistical physics, we use these insight…
In this work, we propose a new family of generative flows on an augmented data space, with an aim to improve expressivity without drastically increasing the computational cost of sampling and evaluation of a lower bound on the likelihood. Theoretically, we prove the proposed flow can approximate a Hamiltonian ODE as a universal transport map. Empirically, we demonstrate state-of-the-art performance on standard benchmarks of flow-based generative modeling.
University of California Santa Barbara（加州大学圣巴巴拉分校）；Harbin Institute of Technology（哈尔滨工业大学）；Microsoft Research Asia（微软亚洲研究院）；University of Science Technology of China（中国科学技术大学）；Beijing University of Aeronautics Astronautics（北京航空航天大学）
In order to alleviate data sparsity and overfitting problems in maximum likelihood estimation (MLE) for sequence prediction tasks, we propose the Generative Bridging Network (GBN), in which a novel bridge module is introduced to assist the training of the sequence prediction model (the generator network). Unlike MLE directly maximizing the conditional likelihood, the bridge extends the point-wise ground truth to a bridge distribution conditioned on it, and the generator is optimized to minimize their KL-divergence. Three different GBNs, namely uniform GBN, language-model GBN and coaching GBN, …
Information divergence that measures the difference between two nonnegative matrices or tensors has found its use in a variety of machine learning problems. Examples are Nonnegative Matrix/Tensor Factorization, Stochastic Neighbor Embedding, topic models, and Bayesian network optimization. The success of such a learning task depends heavily on a suitable divergence. A large variety of divergences have been suggested and analyzed, but very few results are available for an objective choice of the optimal divergence for a given task. Here we present a framework that facilitates automatic selectio…
StAD: Stein Amortized Divergence for Fast Likelihoods with Diffusion and Flow
Institute of Astronomy（天文研究所）；Kavli Institute for Cosmology, University of Cambridge, Cambridge, UK（剑桥大学卡文迪许实验室，剑桥，英国）；Research Computing Services, University of Cambridge, Cambridge, UK（剑桥大学研究计算服务）；The Oskar Klein Centre, Department of Physics, Stockholm University, Stockholm, SE（斯德哥尔摩大学物理系奥斯卡·克莱因中心）；Cavendish Laboratory, Department of Physics, University of Cambridge, Cambridge, UK（剑桥大学物理系卡文迪许实验室）
Helsinki Institute of Information Technology (HIIT)（赫尔辛基信息技术研究所）；University of Helsinki（赫尔辛基大学）；University of Oslo（奥斯陆大学）；Wellcome Sanger Institute（惠康桑格研究所）；KTH Royal Institute of Technology（瑞典皇家理工学院）
Likelihood-free inference for simulator-based statistical models has recently attracted a surge of interest, both in the machine learning and statistics communities. The primary focus of these research fields has been to approximate the posterior distribution of model parameters, either by various types of Monte Carlo sampling algorithms or deep neural network -based surrogate models. Frequentist inference for simulator-based models has been given much less attention to date, despite that it would be particularly amenable to applications with big data where implicit asymptotic approximation of…
Energy-based models (EBMs) offer flexible distribution parametrization. However, due to the intractable partition function, they are typically trained via contrastive divergence for maximum likelihood estimation. In this paper, we propose pseudo-spherical contrastive divergence (PS-CD) to generalize maximum likelihood learning of EBMs. PS-CD is derived from the maximization of a family of strictly proper homogeneous scoring rules, which avoids the computation of the intractable partition function and provides a generalized family of learning objectives that include contrastive divergence as a …
University of Helsinki（赫尔辛基大学）；University of Oslo（奥斯陆大学）；Wellcome Sanger Institute（威康桑格研究所）；KTH Royal Institute of Technology（KTH皇家理工学院）
Choice of appropriate structure and parametric dimension of a model in the light of data has a rich history in statistical research, where the first seminal approaches were developed in 1970s, such as the Akaike's and Schwarz's model scoring criteria that were inspired by information theory and embodied the rationale called Occam's razor. After those pioneering works, model choice was quickly established as its own field of research, gaining considerable attention in both computer science and statistics. However, to date, there have been limited attempts to derive scoring criteria for simulato…
The Energy-Based Model (EBM) framework is a very general approach to generative modeling that tries to learn and exploit probability distributions only defined though unnormalized scores. It has risen in popularity recently thanks to the impressive results obtained in image generation by parameterizing the distribution with Convolutional Neural Networks (CNN). However, the motivation and theoretical foundations behind modern EBMs are often absent from recent papers and this sometimes results in some confusion. In particular, the theoretical justifications behind the popular MCMC-based learning…
Max Planck Institute for Informatics（马克斯·普朗克信息学研究所）
Generative Adversarial Networks (GANs) can achieve state-of-the-art sample quality in generative modelling tasks but suffer from the mode collapse problem. Variational Autoencoders (VAE) on the other hand explicitly maximize a reconstruction-based data log-likelihood forcing it to cover all modes, but suffer from poorer sample quality. Recent works have proposed hybrid VAE-GAN frameworks which integrate a GAN-based synthetic likelihood to the VAE objective to address both the mode collapse and sample quality issues, with limited success. This is because the VAE objective forces a trade-off bet…
Restricted Boltzmann Machines (RBMs) are general unsupervised learning devices to ascertain generative models of data distributions. RBMs are often trained using the Contrastive Divergence learning algorithm (CD), an approximation to the gradient of the data log-likelihood. A simple reconstruction error is often used to decide whether the approximation provided by the CD algorithm is good enough, though several authors (Schulz et al., 2010; Fischer & Igel, 2010) have raised doubts concerning the feasibility of this procedure. However, not many alternatives to the reconstruction error have been…
By exploiting the property that the RBM log-likelihood function is the difference of convex functions, we formulate a stochastic variant of the difference of convex functions (DC) programming to minimize the negative log-likelihood. Interestingly, the traditional contrastive divergence algorithm is a special case of the above formulation and the hyperparameters of the two algorithms can be chosen such that the amount of computation per mini-batch is identical. We show that for a given computational budget the proposed algorithm almost always reaches a higher log-likelihood more rapidly, compar…
Deep energy-based models (EBMs) are very flexible in distribution parametrization but computationally challenging because of the intractable partition function. They are typically trained via maximum likelihood, using contrastive divergence to approximate the gradient of the KL divergence between data and model distribution. While KL divergence has many desirable properties, other f-divergences have shown advantages in training implicit density generative models such as generative adversarial networks. In this paper, we propose a general variational framework termed f-EBM to train EBMs using a…
Generative Adversarial Networks (GANs) have achieved great success in data generation. However, its statistical properties are not fully understood. In this paper, we consider the statistical behavior of the general $f$-divergence formulation of GAN, which includes the Kullback--Leibler divergence that is closely related to the maximum likelihood principle. We show that for parametric generative models that are correctly specified, all $f$-divergence GANs with the same discriminator classes are asymptotically equivalent under suitable regularity conditions. Moreover, with an appropriately chos…
Restricted Boltzmann Machines (RBMs) are general unsupervised learning devices to ascertain generative models of data distributions. RBMs are often trained using the Contrastive Divergence learning algorithm (CD), an approximation to the gradient of the data log-likelihood. A simple reconstruction error is often used as a stopping criterion for CD, although several authors \cite{schulz-et-al-Convergence-Contrastive-Divergence-2010-NIPSw, fischer-igel-Divergence-Contrastive-Divergence-2010-ICANN} have raised doubts concerning the feasibility of this procedure. In many cases the evolution curve …
To ensure robust and reliable classification results, OoD (out-of-distribution) indicators based on deep generative models are proposed recently and are shown to work well on small datasets. In this paper, we conduct the first large collection of benchmarks (containing 92 dataset pairs, which is 1 order of magnitude larger than previous ones) for existing OoD indicators and observe that none perform well. We thus advocate that a large collection of benchmarks is mandatory for evaluating OoD indicators. We propose a novel theoretical framework, DOI, for divergence-based Out-of-Distribution indi…
Epson Research and Development（爱普生研发部）；University of Illinois（伊利诺伊大学）
We propose a new method for estimating the intrinsic dimension of a dataset by applying the principle of regularized maximum likelihood to the distances between close neighbors. We propose a regularization scheme which is motivated by divergence minimization principles. We derive the estimator by a Poisson process approximation, argue about its convergence properties and apply it to a number of simulated and real datasets. We also show it has the best overall performance compared with two other intrinsic dimension estimators.
The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；University of Texas at Austin（德克萨斯大学奥斯汀分校）；Shanghai Jiao Tong University（上海交通大学）
There are two types of deep generative models: explicit and implicit. The former defines an explicit density form that allows likelihood inference; while the latter targets a flexible transformation from random noise to generated samples. While the two classes of generative models have shown great power in many applications, both of them, when used alone, suffer from respective limitations and drawbacks. To take full advantages of both models and enable mutual compensation, we propose a novel joint training framework that bridges an explicit (unnormalized) density estimator and an implicit sam…
MITA: Bridging the Gap between Model and Data for Test-time Adaptation
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Pennsylvania State University（宾夕法尼亚州立大学）；Kuaishou Technology（快手科技）
University of Copenhagen（哥本哈根大学）；Montreal Institute for Learning Algorithms（蒙特利尔学习算法研究所）；Université de Montréal（蒙特利尔大学）
Estimating the log-likelihood gradient with respect to the parameters of a Restricted Boltzmann Machine (RBM) typically requires sampling using Markov Chain Monte Carlo (MCMC) techniques. To save computation time, the Markov chains are only run for a small number of steps, which leads to a biased estimate. This bias can cause RBM training algorithms such as Contrastive Divergence (CD) learning to deteriorate. We adopt the idea behind Population Monte Carlo (PMC) methods to devise a new RBM training algorithm termed Population-Contrastive-Divergence (pop-CD). Compared to CD, it leads to a consi…
Generative neural samplers are probabilistic models that implement sampling using feedforward neural networks: they take a random input vector and produce a sample from a probability distribution defined by the network weights. These models are expressive and allow efficient computation of samples and derivatives, but cannot be used for computing likelihoods or for marginalization. The generative-adversarial training method allows to train such models through the use of an auxiliary discriminative neural network. We show that the generative-adversarial approach is a special case of an existing…
Southwest University（西南大学）；University of Technology Sydney（悉尼科技大学）；Zhejiang Wanli University（浙江万里学院）
High-Dimensional and Incomplete (HDI) data are frequently found in various industrial applications with complex interactions among numerous nodes, which are commonly non-negative for representing the inherent non-negativity of node interactions. A Non-negative Latent Factor (NLF) model is able to extract intrinsic features from such data efficiently. However, existing NLF models all adopt a static divergence metric like Euclidean distance or α-\b{eta} divergence to build its learning objective, which greatly restricts its scalability of accurately representing HDI data from different domains. …
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；The Hong Kong Polytechnic University（香港理工大学）；Imperial College Business School（帝国理工学院商学院）
A fundamental problem arising in many areas of machine learning is the evaluation of the likelihood of a given observation under different nominal distributions. Frequently, these nominal distributions are themselves estimated from data, which makes them susceptible to estimation errors. We thus propose to replace each nominal distribution with an ambiguity set containing all distributions in its vicinity and to evaluate an \emph{optimistic likelihood}, that is, the maximum of the likelihood over all distributions in the ambiguity set. When the proximity of distributions is quantified by the F…
We introduce and motivate generative modeling as a central task for machine learning and provide a critical view of the algorithms which have been proposed for solving this task. We overview how generative modeling can be defined mathematically as trying to make an estimating distribution the same as an unknown ground truth distribution. This can then be quantified in terms of the value of a statistical divergence between the two distributions. We outline the maximum likelihood approach and how it can be interpreted as minimizing KL-divergence. We explore a number of approaches in the maximum …
Federated learning is promising for its capability to collaboratively train models with multiple clients without accessing their data, but vulnerable when clients' data distributions diverge from each other. This divergence further leads to a dilemma: "Should we prioritize the learned model's generic performance (for future use at the server) or its personalized performance (for each client)?" These two, seemingly competing goals have divided the community to focus on one or the other, yet in this paper we show that it is possible to approach both at the same time. Concretely, we propose a nov…
The University of Tokyo（东京大学）；RIKEN AIP（理化学研究所先进智能项目中心）
Approximate Bayesian computation (ABC) is a likelihood-free inference method that has been employed in various applications. However, ABC can be sensitive to outliers if a data discrepancy measure is chosen inappropriately. In this paper, we propose to use a nearest-neighbor-based $γ$-divergence estimator as a data discrepancy measure. We show that our estimator possesses a suitable theoretical robustness property called the redescending property. In addition, our estimator enjoys various desirable properties such as high flexibility, asymptotic unbiasedness, almost sure convergence, and linea…
KTH Royal Institute of Technology（瑞典皇家理工学院）；University of Liège（列日大学）
Likelihood-free inference is concerned with the estimation of the parameters of a non-differentiable stochastic simulator that best reproduce real observations. In the absence of a likelihood function, most of the existing inference methods optimize the simulator parameters through a handcrafted iterative procedure that tries to make the simulated data more similar to the observations. In this work, we explore whether meta-learning can be used in the likelihood-free context, for learning automatically from data an iterative optimization procedure that would solve likelihood-free inference prob…
Scalable Inference-Time Annealing with Surrogate Likelihood Estimators
CMU-Pitt PhD Program in Computational Biology Dept. of Computational & Systems Biology, University of Pittsburgh, Pittsburgh, PA 15260, USA（卡内基梅隆大学-匹兹堡联合博士项目 计算生物学部门 计算与系统生物学系，匹兹堡大学，匹兹堡，PA 15260，USA）
Stanford University（斯坦福大学）；University of Cyprus（塞浦路斯大学）
We consider the parameter estimation problem of a probabilistic generative model prescribed using a natural exponential family of distributions. For this problem, the typical maximum likelihood estimator usually overfits under limited training sample size, is sensitive to noise and may perform poorly on downstream predictive tasks. To mitigate these issues, we propose a distributionally robust maximum likelihood estimator that minimizes the worst-case expected log-loss uniformly over a parametric Kullback-Leibler ball around a parametric nominal distribution. Leveraging the analytical expressi…
We analyze the Dawid-Rissanen prequential maximum likelihood codes relative to one-parameter exponential family models M. If data are i.i.d. according to an (essentially) arbitrary P, then the redundancy grows at rate c/2 ln n. We show that c=v1/v2, where v1 is the variance of P, and v2 is the variance of the distribution m* in M that is closest to P in KL divergence. This shows that prequential codes behave quite differently from other important universal codes such as the 2-part MDL, Shtarkov and Bayes codes, for which c=1. This behavior is undesirable in an MDL model selection setting.
