Integration of data from multiple omics techniques is becoming increasingly important in biomedical research. Due to non-uniformity and technical limitations in omics platforms, such integrative analyses on multiple omics, which we refer to as views, involve learning from incomplete observations with various view-missing patterns. This is challenging because i) complex interactions within and across observed views need to be properly addressed for optimal predictive power and ii) observations with various view-missing patterns need to be flexibly integrated. To address such challenges, we propose a deep variational information bottleneck (IB) approach for incomplete multi-view observations. Our method applies the IB framework on marginal and joint representations of the observed views to focus on intra-view and inter-view interactions that are relevant for the target. Most importantly, by modeling the joint representations as a product of marginal representations, we can efficiently learn from observed views with various view-missing patterns. Experiments on real-world datasets show that our method consistently achieves gain from data integration and outperforms state-of-the-art benchmarks.
Data Science Institute, Imperial College London（伦敦帝国理工学院数据科学研究所）
Different aspects of a clinical sample can be revealed by multiple types of omics data. Integrated analysis of multi-omics data provides a comprehensive view of patients, which has the potential to facilitate more accurate clinical decision making. However, omics data are normally high dimensional with large number of molecular features and relatively small number of available samples with clinical labels. The "dimensionality curse" makes it challenging to train a machine learning model using high dimensional omics data like DNA methylation and gene expression profiles. Here we propose an end-…
The Information Bottleneck theory provides a theoretical and computational framework for finding approximate minimum sufficient statistics. Analysis of the Stochastic Gradient Descent (SGD) training of a neural network on a toy problem has shown the existence of two phases, fitting and compression. In this work, we analyze the SGD training process of a Deep Neural Network on MNIST classification and confirm the existence of two phases of SGD training. We also propose a setup for estimating the mutual information for a Deep Neural Network through Variational Inference.
MODIS: Multi-Omics Data Integration for Small and unpaired datasets
Aix Marseille Univ（阿ix马赛大学）；INSERM（国家健康与医学研究中心）；MMG（马赛医学中心）；Aix Marseille Univ & Ecole Centrale de Marseille（阿ix马赛大学及马赛中央理工大学）；CNRS（法国国家科学研究中心）；LIS（丽兹研究所）
Xi'an Jiaotong University（西安交通大学）；UiT - The Arctic University of Norway（挪威北极大学）
By "intelligently" fusing the complementary information across different views, multi-view learning is able to improve the performance of classification tasks. In this work, we extend the information bottleneck principle to a supervised multi-view learning scenario and use the recently proposed matrix-based R{é}nyi's $α$-order entropy functional to optimize the resulting objective directly, without the necessity of variational approximation or adversarial training. Empirical results in both synthetic and real-world datasets suggest that our method enjoys improved robustness to noise and redund…
Massachusetts Institute of Technology, Computational and Systems Biology Program（麻省理工学院计算与系统生物学计划）；Broad Institute of MIT and Harvard（MIT和哈佛大学博德研究所）；Massachusetts Institute of Technology, Department of Biological Engineering（麻省理工学院生物工程系）
An Interpretable Ensemble Framework for Multi-Omics Dementia Biomarker Discovery Under HDLSS Conditions
Department of Mathematics and Physics, Mathematics Major, Gangneung-Wonju National University（数学与物理系，数学专业，江陵-Wonju国立大学）；Department of Data Science, Gangneung-Wonju National University（数据科学系，江陵-Wonju国立大学）
Université Bourgogne-Franche-Comté（勃艮第-弗朗什孔泰大学）；UTBM（贝尔福-蒙贝利亚技术大学）；Université de Lorraine（洛林大学）
Recognizing user location with WiFi fingerprints is a popular approach for accurate indoor positioning problems. In this work, our goal is to interpret WiFi fingerprints into actual user locations. However, WiFi fingerprint data can be very high dimensional in some cases, we need to find a good representation of the input data for the learning task first. Otherwise, using neural networks will suffer from severe overfitting. In this work, we solve this issue by combining the Information Bottleneck method and Variational Inference. Based on these two approaches, we propose a Variational Informat…
In this paper, we provide an information-theoretic interpretation of the Vector Quantized-Variational Autoencoder (VQ-VAE). We show that the loss function of the original VQ-VAE can be derived from the variational deterministic information bottleneck (VDIB) principle. On the other hand, the VQ-VAE trained by the Expectation Maximization (EM) algorithm can be viewed as an approximation to the variational information bottleneck(VIB) principle.
Mohamed Bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）
For personalized medicines, very crucial intrinsic information is present in high dimensional omics data which is difficult to capture due to the large number of molecular features and small number of available samples. Different types of omics data show various aspects of samples. Integration and analysis of multi-omics data give us a broad view of tumours, which can improve clinical decision making. Omics data, mainly DNA methylation and gene expression profiles are usually high dimensional data with a lot of molecular features. In recent years, variational autoencoders (VAE) have been exten…
We present a simple case study, demonstrating that Variational Information Bottleneck (VIB) can improve a network's classification calibration as well as its ability to detect out-of-distribution data. Without explicitly being designed to do so, VIB gives two natural metrics for handling and quantifying uncertainty.
Beijing Institute of Technology（北京理工大学）；University of Aberdeen（阿伯丁大学）
Causal inference is to estimate the causal effect in a causal relationship when intervention is applied. Precisely, in a causal model with binary interventions, i.e., control and treatment, the causal effect is simply the difference between the factual and counterfactual. The difficulty is that the counterfactual may never been obtained which has to be estimated and so the causal effect could only be an estimate. The key challenge for estimating the counterfactual is to identify confounders which effect both outcomes and treatments. A typical approach is to formulate causal inference as a supe…
We propose a VAE for Transformers by developing a variational information bottleneck regulariser for Transformer embeddings. We formalise the embedding space of Transformer encoders as mixture probability distributions, and use Bayesian nonparametrics to derive a nonparametric variational information bottleneck (NVIB) for such attention-based embeddings. The variable number of mixture components supported by nonparametric methods captures the variable number of vectors supported by attention, and the exchangeability of our nonparametric distributions captures the permutation invariance of atte…
We present a variational approximation to the information bottleneck of Tishby et al. (1999). This variational approach allows us to parameterize the information bottleneck model using a neural network and leverage the reparameterization trick for efficient training. We call this method "Deep Variational Information Bottleneck", or Deep VIB. We show that models trained with the VIB objective outperform those that are trained with other forms of regularization, in terms of generalization performance and robustness to adversarial attack.
Imperial College London（帝国理工学院）；University College London（伦敦大学学院）；Hong Kong Baptist University（香港浸会大学）
The lack of explainability is one of the most prominent disadvantages of deep learning applications in omics. This "black box" problem can undermine the credibility and limit the practical implementation of biomedical deep learning models. Here we present XOmiVAE, a variational autoencoder (VAE) based interpretable deep learning model for cancer classification using high-dimensional omics data. XOmiVAE is capable of revealing the contribution of each gene and latent dimension for each classification prediction, and the correlation between each gene and each latent dimension. It is also demonst…
Osaka University（大阪大学）；Nara Institute of Science and Technology（奈良先端科学技术大学院大学）；Yunnan University（云南大学）
Defining and separating cancer subtypes is essential for facilitating personalized therapy modality and prognosis of patients. The definition of subtypes has been constantly recalibrated as a result of our deepened understanding. During this recalibration, researchers often rely on clustering of cancer data to provide an intuitive visual reference that could reveal the intrinsic characteristics of subtypes. The data being clustered are often omics data such as transcriptomics that have strong correlations to the underlying biological mechanism. However, while existing studies have shown promis…
In classic papers, Zellner demonstrated that Bayesian inference could be derived as the solution to an information theoretic functional. Below we derive a generalized form of this functional as a variational lower bound of a predictive information bottleneck objective. This generalized functional encompasses most modern inference procedures and suggests novel ones.
We introduce a bottleneck method for learning data representations based on information deficiency, rather than the more traditional information sufficiency. A variational upper bound allows us to implement this method efficiently. The bound itself is bounded above by the variational information bottleneck objective, and the two methods coincide in the regime of single-shot Monte Carlo approximations. The notion of deficiency provides a principled way of approximating complicated channels by relatively simpler ones. We show that the deficiency of one channel with respect to another has an oper…
Aalborg University（奥尔堡大学）；University of Glasgow（格拉斯哥大学）；University of Liverpool（利物浦大学）
We propose a new approach to train a variational information bottleneck (VIB) that improves its robustness to adversarial perturbations. Unlike the traditional methods where the hard labels are usually used for the classification task, we refine the categorical class information in the training phase with soft labels which are obtained from a pre-trained reference neural network and can reflect the likelihood of the original class labels. We also relax the Gaussian posterior assumption in the VIB implementation by using the mutual information neural estimation. Extensive experiments have been …
VICatMix: variational Bayesian clustering and variable selection for discrete biomedical data
MRC Biostatistics Unit University of Cambridge East Forvie Building（医学研究理事会生物统计学单位剑桥大学东部大楼）；MRC Biostatistics Unit and CRUK Cambridge Centre Ovarian Programme and Cambridge Institute of Therapeutic Immunology and Infectious Disease (CITIID) University of Cambridge（医学研究理事会生物统计学单位和癌症研究英国委员会剑桥中心卵巢计划及剑桥治疗免疫学和传染病研究所（CITIID）剑桥大学）
Carnegie Mellon University（卡内基梅隆大学）；Petuum Inc.（Petuum公司）；Arizona State University（亚利桑那州立大学）
Interpretable machine learning has gained much attention recently. Briefness and comprehensiveness are necessary in order to provide a large amount of information concisely when explaining a black-box decision system. However, existing interpretable machine learning methods fail to consider briefness and comprehensiveness simultaneously, leading to redundant explanations. We propose the variational information bottleneck for interpretation, VIBI, a system-agnostic interpretable method that provides a brief but comprehensive explanation. VIBI adopts an information theoretic principle, informati…
CAVACHON: a hierarchical variational autoencoder to integrate multi-modal single-cell data
Centre for Molecular Medicine Norway (NCMM)（挪威分子医学中心（NCMM））；Nordic EMBL Partnership（北欧欧洲分子生物学实验室合作组织）；University of Oslo（奥斯陆大学）；National Taiwan University（国立台湾大学）；Oslo University Hospital（奥斯陆大学医院）；CISPA Helmholtz Center for Information Security（CISPA亥姆霍兹信息安全中心）
Beihang University（北京航空航天大学）；Macquarie University（麦考瑞大学）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）
Graph Neural Networks (GNNs) have shown promising results on a broad spectrum of applications. Most empirical studies of GNNs directly take the observed graph as input, assuming the observed structure perfectly depicts the accurate and complete relations between nodes. However, graphs in the real world are inevitably noisy or incomplete, which could even exacerbate the quality of graph representations. In this work, we propose a novel Variational Information Bottleneck guided Graph Structure Learning framework, namely VIB-GSL, in the perspective of information theory. VIB-GSL advances the Info…
In this paper, we develop an unsupervised generative clustering framework that combines the Variational Information Bottleneck and the Gaussian Mixture Model. Specifically, in our approach, we use the Variational Information Bottleneck method and model the latent space as a mixture of Gaussians. We derive a bound on the cost function of our model that generalizes the Evidence Lower Bound (ELBO) and provide a variational inference type algorithm that allows computing it. In the algorithm, the coders' mappings are parametrized using neural networks, and the bound is approximated by Monte Carlo s…
Université Bourgogne Franche-Comté（勃艮第-弗朗什-孔泰大学）；University of Glasgow（格拉斯哥大学）；Tongji University（同济大学）；Southeast University（东南大学）；RMIT University（皇家墨尔本理工大学）；Université de Lorraine（洛林大学）
Multi-task learning (MTL) is an important subject in machine learning and artificial intelligence. Its applications to computer vision, signal processing, and speech recognition are ubiquitous. Although this subject has attracted considerable attention recently, the performance and robustness of the existing models to different tasks have not been well balanced. This article proposes an MTL model based on the architecture of the variational information bottleneck (VIB), which can provide a more effective latent representation of the input features for the downstream tasks. Extensive observatio…
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Center for Excellence in Brain Science and Intelligence Technology, CAS（中国科学院脑科学与智能技术卓越创新中心）
Subgraph recognition aims at discovering a compressed substructure of a graph that is most informative to the graph property. It can be formulated by optimizing Graph Information Bottleneck (GIB) with a mutual information estimator. However, GIB suffers from training instability and degenerated results due to its intrinsic optimization process. To tackle these issues, we reformulate the subgraph recognition problem into two steps: graph perturbation and subgraph selection, leading to a novel Variational Graph Information Bottleneck (VGIB) framework. VGIB first employs the noise injection to mo…
Domain adaptation aims to leverage the supervision signal of source domain to obtain an accurate model for target domain, where the labels are not available. To leverage and adapt the label information from source domain, most existing methods employ a feature extracting function and match the marginal distributions of source and target domains in a shared feature space. In this paper, from the perspective of information theory, we show that representation matching is actually an insufficient constraint on the feature space for obtaining a model with good generalization performance in target d…
Mila, University of Montreal（蒙特利尔大学Mila研究所）；Deepmind（深度思维公司）；University of California, Berkeley（加州大学伯克利分校）
In many applications, it is desirable to extract only the relevant information from complex input data, which involves making a decision about which input features are relevant. The information bottleneck method formalizes this as an information-theoretic optimization problem by maintaining an optimal tradeoff between compression (throwing away irrelevant input information), and predicting the target. In many problem settings, including the reinforcement learning problems we consider in this work, we might prefer to compress only part of the input. This is typically the case when we have a sta…
Deep Variational Multivariate Information Bottleneck -- A Framework for Variational Losses
Department of Physics Emory University（埃默里大学物理系）；Departments of Physics and Biology Initiative in Theory and Modeling of Living Systems Emory University（埃默里大学物理与生物学理论与活体系统建模研究所）；Georgia Institute of Technology（佐治亚理工学院）
Adversarial learning methods have been proposed for a wide range of applications, but the training of adversarial models can be notoriously unstable. Effectively balancing the performance of the generator and discriminator is critical, since a discriminator that achieves very high accuracy will produce relatively uninformative gradients. In this work, we propose a simple and general technique to constrain information flow in the discriminator by means of an information bottleneck. By enforcing a constraint on the mutual information between the observations and the discriminator's internal repr…
University at Buffalo（布法罗大学）；Criteo（Criteo公司）；Duke University（杜克大学）
Variational autoencoders (VAEs) are essential tools in end-to-end representation learning. However, the sequential text generation common pitfall with VAEs is that the model tends to ignore latent variables with a strong auto-regressive decoder. In this paper, we propose a principled approach to alleviate this issue by applying a discretized bottleneck to enforce an implicit latent feature matching in a more compact latent space. We impose a shared discrete latent space where each input is learned to choose a combination of latent atoms as a regularized latent representation. Our model endows …
University of California, San Francisco（加利福尼亚大学旧金山分校）
Multiview data contain information from multiple modalities and have potentials to provide more comprehensive features for diverse machine learning tasks. A fundamental question in multiview analysis is what is the additional information brought by additional views and can quantitatively identify this additional information. In this work, we try to tackle this challenge by decomposing the entangled multiview features into shared latent representations that are common across all views and private representations that are specific to each single view. We formulate this feature disentanglement in…
We present a preliminary study on an end-to-end variational autoencoder (VAE) for sound morphing. Two VAE variants are compared: VAE with dilation layers (DC-VAE) and VAE only with regular convolutional layers (CC-VAE). We combine the following loss functions: 1) the time-domain mean-squared error for reconstructing the input signal, 2) the Kullback-Leibler divergence to the standard normal distribution in the bottleneck layer, and 3) the classification loss calculated from the bottleneck representation. On a database of spoken digits, we use 1-nearest neighbor classification to show that the …
Recent advances in sophisticated synthetic speech generated from text-to-speech (TTS) or voice conversion (VC) systems cause threats to the existing automatic speaker verification (ASV) systems. Since such synthetic speech is generated from diverse algorithms, generalization ability with using limited training data is indispensable for a robust anti-spoofing system. In this work, we propose a transfer learning scheme based on the wav2vec 2.0 pretrained model with variational information bottleneck (VIB) for speech anti-spoofing task. Evaluation on the ASVspoof 2019 logical access (LA) database…
Zellner (1988) modeled statistical inference in terms of information processing and postulated the Information Conservation Principle (ICP) between the input and output of the information processing block, showing that this yielded Bayesian inference as the optimum information processing rule. Recently, Alemi (2019) reviewed Zellner's work in the context of machine learning and showed that the ICP could be seen as a special case of a more general optimum information processing criterion, namely the Predictive Information Bottleneck Objective. However, Alemi modeled the model training step in m…
The empirical studies of Graph Neural Networks (GNNs) broadly take the original node feature and adjacency relationship as singleview input, ignoring the rich information of multiple graph views. To circumvent this issue, the multiview graph analysis framework has been developed to fuse graph information across views. How to model and integrate shared (i.e. consistency) and view-specific (i.e. complementarity) information is a key issue in multiview graph analysis. In this paper, we propose a novel Multiview Variational Graph Information Bottleneck (MVGIB) principle to maximize the agreement f…
Scientific Computing and Imaging Institute（科学计算与成像研究所）；University of Utah（犹他大学）
Statistical shape modeling (SSM) directly from 3D medical images is an underutilized tool for detecting pathology, diagnosing disease, and conducting population-level morphology analysis. Deep learning frameworks have increased the feasibility of adopting SSM in medical practice by reducing the expert-driven manual and computational overhead in traditional SSM workflows. However, translating such frameworks to clinical practice requires calibrated uncertainty measures as neural networks can produce over-confident predictions that cannot be trusted in sensitive clinical decision-making. Existin…
University of Florida（佛罗里达大学）；NEC Laboratories Europe（NEC欧洲实验室）
We introduce the matrix-based Renyi's $α$-order entropy functional to parameterize Tishby et al. information bottleneck (IB) principle with a neural network. We term our methodology Deep Deterministic Information Bottleneck (DIB), as it avoids variational inference and distribution assumption. We show that deep neural networks trained with DIB outperform the variational objective counterpart and those that are trained with other forms of regularization, in terms of generalization performance and robustness to adversarial attack.Code available at https://github.com/yuxi120407/DIB
Indian Institute of Technology Delhi（德里印度理工学院）；Samsung R&D Institute India - Delhi（三星印度德里研发中心）
In the last few years, compression of deep neural networks has become an important strand of machine learning and computer vision research. Deep models require sizeable computational complexity and storage, when used for instance for Human Action Recognition (HAR) from videos, making them unsuitable to be deployed on edge devices. In this paper, we address this issue and propose a method to effectively compress Recurrent Neural Networks (RNNs) such as Gated Recurrent Units (GRUs) and Long-Short-Term-Memory Units (LSTMs) that are used for HAR. We use a Variational Information Bottleneck (VIB) t…
Racah Institute of Physics（拉卡物理研究所）；The Hebrew University of Jerusalem（耶路撒冷希伯来大学）；School of Computer Science（计算机科学学院）
The Information Bottleneck (IB) framework is a general characterization of optimal representations obtained using a principled approach for balancing accuracy and complexity. Here we present a new framework, the Dual Information Bottleneck (dualIB), which resolves some of the known drawbacks of the IB. We provide a theoretical analysis of the dualIB framework; (i) solving for the structure of its solutions (ii) unraveling its superiority in optimizing the mean prediction error exponent and (iii) demonstrating its ability to preserve exponential forms of the original distribution. To approach l…
Bayesian Inference and Information Bottleneck are the two most popular objectives for neural networks, but they can be optimised only via a variational lower bound: the Variational Information Bottleneck (VIB). In this manuscript we show that the two objectives are actually equivalent to the InfoMax: maximise the information between the data and the labels. The InfoMax representation of the two objectives is not relevant only per se, since it helps to understand the role of the network capacity, but also because it allows us to derive a variational objective, the Variational InfoMax (VIM), tha…
Beijing University of Posts and Telecommunications（北京邮电大学）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）
The information bottleneck principle is an elegant and useful approach to representation learning. In this paper, we investigate the problem of representation learning in the context of reinforcement learning using the information bottleneck framework, aiming at improving the sample efficiency of the learning algorithms. %by accelerating the process of discarding irrelevant information when the %input states are extremely high-dimensional. We analytically derive the optimal conditional distribution of the representation, and provide a variational lower bound. Then, we maximize this lower bound…
Representation Learning in Deep RL via Discrete Information Bottleneck
Mila（米拉人工智能研究所）；McGill University（麦吉尔大学）；Microsoft Research Montreal（微软研究院蒙特利尔分院）；Beijing Institute of Technology（北京理工大学）；AMII（阿尔伯塔机器智能研究所）；University of Alberta（阿尔伯塔大学）；University of Montreal（蒙特利尔大学）；University of Virginia（弗吉尼亚大学）；Google DeepMind（谷歌DeepMind）；Microsoft Research NYC（微软研究院纽约分院）
The Hong Kong University of Science and Technology（香港科技大学）；Hong Kong Polytechnic University（香港理工大学）
This paper investigates task-oriented communication for edge inference, where a low-end edge device transmits the extracted feature vector of a local data sample to a powerful edge server for processing. It is critical to encode the data into an informative and compact representation for low-latency inference given the limited bandwidth. We propose a learning-based communication scheme that jointly optimizes feature extraction, source coding, and channel coding in a task-oriented manner, i.e., targeting the downstream inference task rather than data reconstruction. Specifically, we leverage an…
