【论文】变分推断(Variational inference)的总结

2017 年 11 月 16 日 机器学习研究会
【论文】变分推断(Variational inference)的总结

论文《Advances in Variational Inference》摘要:

Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a high-dimensional Bayesian posterior with a simpler variational distribution by solving an optimization problem. This approach has been successfully used in various models and large-scale applications. In this review, we give an overview of recent trends in variational inference. We first introduce standard mean field variational inference, then review recent advances focusing on the following aspects: (a) scalable VI, which includes stochastic approximations, (b) generic VI, which extends the applicability of VI to a large class of otherwise intractable models, such as non-conjugate models, (c) accurate VI, which includes variational models beyond the mean field approximation or with atypical divergences, and (d) amortized VI, which implements the inference over local latent variables with inference networks. Finally, we provide a summary of promising future research directions.


链接:

https://arxiv.org/pdf/1711.05597.pdf


原文链接:

https://m.weibo.cn/2610348974/4174734046717600

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大多数概率模型中, 计算后验边际或准确计算归一化常数都是很困难的. 变分推断(variational inference)是一个近似计算这两者的框架. 变分推断把推断看作优化问题: 我们尝试根据某种距离度量来寻找一个与真实后验尽可能接近的分布(或者类似分布的表示).

Causal inference is a critical research topic across many domains, such as statistics, computer science, education, public policy and economics, for decades. Nowadays, estimating causal effect from observational data has become an appealing research direction owing to the large amount of available data and low budget requirement, compared with randomized controlled trials. Embraced with the rapidly developed machine learning area, various causal effect estimation methods for observational data have sprung up. In this survey, we provide a comprehensive review of causal inference methods under the potential outcome framework, one of the well known causal inference framework. The methods are divided into two categories depending on whether they require all three assumptions of the potential outcome framework or not. For each category, both the traditional statistical methods and the recent machine learning enhanced methods are discussed and compared. The plausible applications of these methods are also presented, including the applications in advertising, recommendation, medicine and so on. Moreover, the commonly used benchmark datasets as well as the open-source codes are also summarized, which facilitate researchers and practitioners to explore, evaluate and apply the causal inference methods.

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课件题目

Lectures on Variational Inference:Approximate Bayesian Inference in Machine Learning

课件简介 本讲座主要讲述了变分推理中的,机器学习近似贝叶斯推理。变分指的是泛函的变分。打个比方,从A点到B点有无数条路径,每一条路径都是一个函数吧,这无数条路径,每一条函数(路径)的长度都是一个数,那你从这无数个路径当中选一个路径最短或者最长的,这就是求泛函的极值问题。有一种老的叫法,函数空间的自变量我们称为宗量(自变函数),当宗量变化了一点点而导致了泛函值变化了多少,这其实就是变分。变分,就是微分在函数空间的拓展,其精神内涵是一致的。求解泛函变分的方法主要有古典变分法、动态规划和最优控制。作者主张将变分推理应用于贝叶斯推理中,并详细地介绍了实现方法。

课件作者

Pierre Alquier,来自布里斯托尔大学,海尔布朗尼学院。

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We reinterpreting the variational inference in a new perspective. Via this way, we can easily prove that EM algorithm, VAE, GAN, AAE, ALI(BiGAN) are all special cases of variational inference. The proof also reveals the loss of standard GAN is incomplete and it explains why we need to train GAN cautiously. From that, we find out a regularization term to improve stability of GAN training.

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Topic models have been widely explored as probabilistic generative models of documents. Traditional inference methods have sought closed-form derivations for updating the models, however as the expressiveness of these models grows, so does the difficulty of performing fast and accurate inference over their parameters. This paper presents alternative neural approaches to topic modelling by providing parameterisable distributions over topics which permit training by backpropagation in the framework of neural variational inference. In addition, with the help of a stick-breaking construction, we propose a recurrent network that is able to discover a notionally unbounded number of topics, analogous to Bayesian non-parametric topic models. Experimental results on the MXM Song Lyrics, 20NewsGroups and Reuters News datasets demonstrate the effectiveness and efficiency of these neural topic models.

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Generative models (GMs) such as Generative Adversary Network (GAN) and Variational Auto-Encoder (VAE) have thrived these years and achieved high quality results in generating new samples. Especially in Computer Vision, GMs have been used in image inpainting, denoising and completion, which can be treated as the inference from observed pixels to corrupted pixels. However, images are hierarchically structured which are quite different from many real-world inference scenarios with non-hierarchical features. These inference scenarios contain heterogeneous stochastic variables and irregular mutual dependences. Traditionally they are modeled by Bayesian Network (BN). However, the learning and inference of BN model are NP-hard thus the number of stochastic variables in BN is highly constrained. In this paper, we adapt typical GMs to enable heterogeneous learning and inference in polynomial time.We also propose an extended autoregressive (EAR) model and an EAR with adversary loss (EARA) model and give theoretical results on their effectiveness. Experiments on several BN datasets show that our proposed EAR model achieves the best performance in most cases compared to other GMs. Except for black box analysis, we've also done a serial of experiments on Markov border inference of GMs for white box analysis and give theoretical results.

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The Pachinko Allocation Machine (PAM) is a deep topic model that allows representing rich correlation structures among topics by a directed acyclic graph over topics. Because of the flexibility of the model, however, approximate inference is very difficult. Perhaps for this reason, only a small number of potential PAM architectures have been explored in the literature. In this paper we present an efficient and flexible amortized variational inference method for PAM, using a deep inference network to parameterize the approximate posterior distribution in a manner similar to the variational autoencoder. Our inference method produces more coherent topics than state-of-art inference methods for PAM while being an order of magnitude faster, which allows exploration of a wider range of PAM architectures than have previously been studied.

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Dynamic topic models (DTMs) model the evolution of prevalent themes in literature, online media, and other forms of text over time. DTMs assume that word co-occurrence statistics change continuously and therefore impose continuous stochastic process priors on their model parameters. These dynamical priors make inference much harder than in regular topic models, and also limit scalability. In this paper, we present several new results around DTMs. First, we extend the class of tractable priors from Wiener processes to the generic class of Gaussian processes (GPs). This allows us to explore topics that develop smoothly over time, that have a long-term memory or are temporally concentrated (for event detection). Second, we show how to perform scalable approximate inference in these models based on ideas around stochastic variational inference and sparse Gaussian processes. This way we can train a rich family of DTMs to massive data. Our experiments on several large-scale datasets show that our generalized model allows us to find interesting patterns that were not accessible by previous approaches.

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Owing to the recent advances in "Big Data" modeling and prediction tasks, variational Bayesian estimation has gained popularity due to their ability to provide exact solutions to approximate posteriors. One key technique for approximate inference is stochastic variational inference (SVI). SVI poses variational inference as a stochastic optimization problem and solves it iteratively using noisy gradient estimates. It aims to handle massive data for predictive and classification tasks by applying complex Bayesian models that have observed as well as latent variables. This paper aims to decentralize it allowing parallel computation, secure learning and robustness benefits. We use Alternating Direction Method of Multipliers in a top-down setting to develop a distributed SVI algorithm such that independent learners running inference algorithms only require sharing the estimated model parameters instead of their private datasets. Our work extends the distributed SVI-ADMM algorithm that we first propose, to an ADMM-based networked SVI algorithm in which not only are the learners working distributively but they share information according to rules of a graph by which they form a network. This kind of work lies under the umbrella of `deep learning over networks' and we verify our algorithm for a topic-modeling problem for corpus of Wikipedia articles. We illustrate the results on latent Dirichlet allocation (LDA) topic model in large document classification, compare performance with the centralized algorithm, and use numerical experiments to corroborate the analytical results.

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Topic modeling enables exploration and compact representation of a corpus. The CaringBridge (CB) dataset is a massive collection of journals written by patients and caregivers during a health crisis. Topic modeling on the CB dataset, however, is challenging due to the asynchronous nature of multiple authors writing about their health journeys. To overcome this challenge we introduce the Dynamic Author-Persona topic model (DAP), a probabilistic graphical model designed for temporal corpora with multiple authors. The novelty of the DAP model lies in its representation of authors by a persona --- where personas capture the propensity to write about certain topics over time. Further, we present a regularized variational inference algorithm, which we use to encourage the DAP model's personas to be distinct. Our results show significant improvements over competing topic models --- particularly after regularization, and highlight the DAP model's unique ability to capture common journeys shared by different authors.

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Amortized inference has led to efficient approximate inference for large datasets. The quality of posterior inference is largely determined by two factors: a) the ability of the variational distribution to model the true posterior and b) the capacity of the recognition network to generalize inference over all datapoints. We analyze approximate inference in variational autoencoders in terms of these factors. We find that suboptimal inference is often due to amortizing inference rather than the limited complexity of the approximating distribution. We show that this is due partly to the generator learning to accommodate the choice of approximation. Furthermore, we show that the parameters used to increase the expressiveness of the approximation play a role in generalizing inference rather than simply improving the complexity of the approximation.

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