The paper proposes Metropolis adjusted Langevin and Hamiltonian Monte Carlo sampling methods defined on the Riemann manifold to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for Metropolis-Hastings or indeed Hamiltonian Monte Carlo and Metropolis adjusted Langevin algorithms. This allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the Markov chain. The methodology proposed exploits the Riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold, providing highly efficient convergence and exploration of the target density. The performance of these Riemann manifold Monte Carlo methods is rigorously assessed by performing inference on logistic regression models, log-Gaussian Cox point processes, stochastic volatility models and Bayesian estimation of dynamic systems described by non-linear differential equations. Substantial improvements in the time-normalized effective sample size are reported when compared with alternative sampling approaches. MATLAB code that is available from http://www.ucl.ac.uk/statistics/research/rmhmc allows replication of all the results reported.

Riemann manifold Langevin and Hamiltonian Monte Carlo methods

L E Reichl 1980 Austin: University of Texas Press xii + 709 pp price $29.95 I can thoroughly recommend this book and congratulate the author for having brought together so many aspects of statistical physics in a comprehensible manner. The subject matter is modern; all the recent developments such as stochastic theory, theories of quantum fluids and critical phenomena, nonlinear chemical physics and hydrodynamics are included and yet each topic is built up from its foundations.

A Modern Course in Statistical Physics

Information geometry is a new mathematical discipline which applies the methodology of differential geometry to statistics. Therefore, families of exponential distributions are considered as embedded manifolds, called statistical manifolds. This includes so important families like the multivariate normal or the gamma distributions. Fisher information — well known in information theory — becomes a metric on statistical manifolds. The Fisher information metric enables a hyperbolic structure on the multivariate normal distributions. Information geometry offers new methods for hypothesis testings, estimation theory or stochastic filtering. These can be used in engineering areas like signal processing or video processing or finance.

http://ieeexplore.ieee.org/iel5/6423297/6450609/06450636.pdf

Information geometry and its applications

This article addresses a timely problem, especially within the context of the Internet, which is accessible by anyone in any discipline from virtually anywhere in the world. The problem of cross-language retrieval is not new. Then at now, cross-language information retrieval was seen to be a function that would facilitate the effective search for, exchange of, and retrieval information. This chapter reviews research and practice in CLIR that allows users to state queries in their native language and retrieve documents in any other language supported by the system. CLIR can simplify searching by multilingual users and, if translation resources are limited, can allow monolingual users to allocate those resources to the more promising documents. This review begins with an examination of the literature on user needs for CLIR. The chapter largely follows the retrieval system model (document preprocessing, query formulation, matching, selection, and delivery). Each section highlights the unique requirements imposed on one more stages of the model in cross-language retrieval applications. The authors describe evaluation techniques and conclude with observations regarding future directions for CLIR research.

Cross-Language Information Retrieval.

The Variational Auto-Encoder (VAE) is one of the most used unsupervised machine learning models. But although the default choice of a Gaussian distribution for both the prior and posterior represents a mathematically convenient distribution often leading to competitive results, we show that this parameterization fails to model data with a latent hyperspherical structure. To address this issue we propose using a von Mises-Fisher (vMF) distribution instead, leading to a hyperspherical latent space. Through a series of experiments, we show how such a hyperspherical VAE, or S-VAE, is more suitable for capturing data with a hyperspherical latent structure, while outperforming a normal, N-VAE, in low dimensions on other data types.

/pdf/hyperspherical-variational-auto-encoders-2dd1k2qqwe.pdf

Hyperspherical variational auto-encoders

/pdf/generalizing-to-unseen-domains-a-survey-on-domain-1gs2ai5gjo.pdf

Generalizing to Unseen Domains: A Survey on Domain Generalization.

High-resolution digital images are usually downscaled to fit various display screens or save the cost of storage and bandwidth, meanwhile the post-upscaling is adopted to recover the original resolutions or the details in the zoom-in images. However, typical image downscaling is a non-injective mapping due to the loss of high-frequency information, which leads to the ill-posed problem of the inverse upscaling procedure and poses great challenges for recovering details from the downscaled low-resolution images. Simply upscaling with image super-resolution methods results in unsatisfactory recovering performance. In this work, we propose to solve this problem by modeling the downscaling and upscaling processes from a new perspective, i.e. an invertible bijective transformation, which can largely mitigate the ill-posed nature of image upscaling. We develop an Invertible Rescaling Net (IRN) with deliberately designed framework and objectives to produce visually-pleasing low-resolution images and meanwhile capture the distribution of the lost information using a latent variable following a specified distribution in the downscaling process. In this way, upscaling is made tractable by inversely passing a randomly-drawn latent variable with the low-resolution image through the network. Experimental results demonstrate the significant improvement of our model over existing methods in terms of both quantitative and qualitative evaluations of image upscaling reconstruction from downscaled images. Code is available at https://github.com/pkuxmq/Invertible-Image-Rescaling.

Invertible Image Rescaling

High-resolution digital images are usually downscaled to fit various display screens or save the cost of storage and bandwidth, meanwhile the post-upscaling is adpoted to recover the original resolutions or the details in the zoom-in images. However, typical image downscaling is a non-injective mapping due to the loss of high-frequency information, which leads to the ill-posed problem of the inverse upscaling procedure and poses great challenges for recovering details from the downscaled low-resolution images. Simply upscaling with image super-resolution methods results in unsatisfactory recovering performance. In this work, we propose to solve this problem by modeling the downscaling and upscaling processes from a new perspective, i.e. an invertible bijective transformation, which can largely mitigate the ill-posed nature of image upscaling. We develop an Invertible Rescaling Net (IRN) with deliberately designed framework and objectives to produce visually-pleasing low-resolution images and meanwhile capture the distribution of the lost information using a latent variable following a specified distribution in the downscaling process. In this way, upscaling is made tractable by inversely passing a randomly-drawn latent variable with the low-resolution image through the network. Experimental results demonstrate the significant improvement of our model over existing methods in terms of both quantitative and qualitative evaluations of image upscaling reconstruction from downscaled images.

Machine learning systems generally assume that the training and testing distributions are the same. To this end, a key requirement is to develop models that can generalize to unseen distributions. Domain generalization (DG), i.e., out-of-distribution generalization, has attracted increasing interests in recent years. Domain generalization deals with a challenging setting where one or several different but related domain(s) are given, and the goal is to learn a model that can generalize to an unseen test domain. Great progress has been made in the area of domain generalization for years. This paper presents the first review of recent advances in this area. First, we provide a formal definition of domain generalization and discuss several related fields. We then thoroughly review the theories related to domain generalization and carefully analyze the theory behind generalization. We categorize recent algorithms into three classes: data manipulation, representation learning, and learning strategy, and present several popular algorithms in detail for each category. Third, we introduce the commonly used datasets and applications. Finally, we summarize existing literature and present some potential research topics for the future.

Generalizing to Unseen Domains: A Survey on Domain Generalization

Conventional supervised learning methods, especially deep ones, are found to be sensitive to out-of-distribution (OOD) examples, largely because the learned representation mixes the semantic factor with the variation factor due to their domain-specific correlation, while only the semantic factor causes the output. To address the problem, we propose a Causal Semantic Generative model (CSG) based on a causal reasoning so that the two factors are modeled separately, and develop methods for OOD prediction from a single training domain, which is common and challenging. The methods are based on the causal invariance principle, with a novel design for both efficient learning and easy prediction. Theoretically, we prove that under certain conditions, CSG can identify the semantic factor by fitting training data, and this semantic-identification guarantees the boundedness of OOD generalization error and the success of adaptation. Empirical study shows improved OOD performance over prevailing baselines.

Chang Liu

Papers

Generalizing to Unseen Domains: A Survey on Domain Generalization.

Invertible Image Rescaling

Invertible Image Rescaling

Generalizing to Unseen Domains: A Survey on Domain Generalization

Learning Causal Semantic Representation for Out-of-Distribution Prediction