Measuring the Discrepancy between Conditional Distributions: Methods, Properties and Applications

We propose a simple yet powerful test statistic to quantify the discrepancy between two conditional distributions. The new statistic avoids the explicit estimation of the underlying distributions in highdimensional space and it operates on the cone of symmetric positive semidefinite (SPS) matrix using the Bregman matrix divergence. Moreover, it inherits the merits of the correntropy function to explicitly incorporate high-order statistics in the data. We present the properties of our new statistic and illustrate its connections to prior art. We finally show the applications of our new statistic on three different machine learning problems, namely the multi-task learning over graphs, the concept drift detection, and the information-theoretic feature selection, to demonstrate its utility and advantage. Code of our statistic is available at https://bit.ly/BregmanCorrentropy.

Information Plane Analysis of Deep Neural Networks via Matrix-Based Renyi's Entropy and Tensor Kernels

Analyzing deep neural networks (DNNs) via information plane (IP) theory has gained tremendous attention recently as a tool to gain insight into, among others, their generalization ability. However, it is by no means obvious how to estimate mutual information (MI) between each hidden layer and the input/desired output, to construct the IP. For instance, hidden layers with many neurons require MI estimators with robustness towards the high dimensionality associated with such layers. MI estimators should also be able to naturally handle convolutional layers, while at the same time being computationally tractable to scale to large networks. None of the existing IP methods to date have been able to study truly deep Convolutional Neural Networks (CNNs), such as the e.g.\ VGG-16. In this paper, we propose an IP analysis using the new matrix--based R\'enyi's entropy coupled with tensor kernels over convolutional layers, leveraging the power of kernel methods to represent properties of the probability distribution independently of the dimensionality of the data. The obtained results shed new light on the previous literature concerning small-scale DNNs, however using a completely new approach. Importantly, the new framework enables us to provide the first comprehensive IP analysis of contemporary large-scale DNNs and CNNs, investigating the different training phases and providing new insights into the training dynamics of large-scale neural networks.

Multiscale Principle of Relevant Information for Hyperspectral Image Classification

This paper proposes a novel architecture, termed multiscale principle of relevant information (MPRI), to learn discriminative spectral-spatial features for hyperspectral image (HSI) classification. MPRI inherits the merits of the principle of relevant information (PRI) to effectively extract multiscale information embedded in the given data, and also takes advantage of the multilayer structure to learn representations in a coarse-to-fine manner. Specifically, MPRI performs spectral-spatial pixel characterization (using PRI) and feature dimensionality reduction (using regularized linear discriminant analysis) iteratively and successively. Extensive experiments on four benchmark data sets demonstrate that MPRI outperforms existing state-of-the-art HSI classification methods (including deep learning based ones) qualitatively and quantitatively, especially in the scenario of limited training samples.

Closed-Loop Adaptation for Weakly-Supervised Semantic Segmentation

Weakly-supervised semantic segmentation aims to assign each pixel a semantic category under weak supervisions, such as image-level tags. Most of existing weakly-supervised semantic segmentation methods do not use any feedback from segmentation output and can be considered as open-loop systems. They are prone to accumulated errors because of the static seeds and the sensitive structure information. In this paper, we propose a generic self-adaptation mechanism for existing weakly-supervised semantic segmentation methods by introducing two feedback chains, thus constituting a closed-loop system. Specifically, the first chain iteratively produces dynamic seeds by incorporating cross-image structure information, whereas the second chain further expands seed regions by a customized random walk process to reconcile inner-image structure information characterized by superpixels. Experiments on PASCAL VOC 2012 suggest that our network outperforms state-of-the-art methods with significantly less computational and memory burden.

Simple stopping criteria for information theoretic feature selection

Information theoretic feature selection aims to select a smallest feature subset such that the mutual information between the selected features and the class labels is maximized. Despite the simplicity of this objective, there still remains several open problems to optimize it. These include, for example, the automatic determination of the optimal subset size (i.e., the number of features) or a stopping criterion if the greedy searching strategy is adopted. In this letter, we suggest two stopping criteria by just monitoring the conditional mutual information (CMI) among groups of variables. Using the recently developed multivariate matrix-based Renyi's \alpha-entropy functional, we show that the CMI among groups of variables can be easily estimated without any decomposition or approximation, hence making our criteria easily implemented and seamlessly integrated into any existing information theoretic feature selection methods with greedy search strategy.

Robust Visual Tracking using Multi-Frame Multi-Feature Joint Modeling

It remains a huge challenge to design effective and efficient trackers under complex scenarios, including occlusions, illumination changes and pose variations. To cope with this problem, a promising solution is to integrate the temporal consistency across consecutive frames and multiple feature cues in a unified model. Motivated by this idea, we propose a novel correlation filter-based tracker in this work, in which the temporal relatedness is reconciled under a multi-task learning framework and the multiple feature cues are modeled using a multi-view learning approach. We demonstrate the resulting regression model can be efficiently learned by exploiting the structure of blockwise diagonal matrix. A fast blockwise diagonal matrix inversion algorithm is developed thereafter for efficient online tracking. Meanwhile, we incorporate an adaptive scale estimation mechanism to strengthen the stability of scale variation tracking. We implement our tracker using two types of features and test it on two benchmark datasets. Experimental results demonstrate the superiority of our proposed approach when compared with other state-of-the-art trackers. project homepage http://bmal.hust.edu.cn/project/KMF2JMTtracking.html

Understanding Convolutional Neural Network Training with Information Theory

Using information theoretic concepts to understand and explore the inner organization of deep neural networks (DNNs) remains a big challenge. Recently, the concept of an information plane (coupled with the famed information bottleneck principle) began to shed light on the analysis of multilayer perceptrons (MLPs). We provided an in-depth insight into stacked autoencoders (SAEs) using a novel matrix-based Renyi's {\alpha}-entropy functional, enabling for the first time the analysis of the dynamics of learning using information flow in the real-world scenario involving complex network architecture and large data. Despite the great potential of these past works, there are several open questions when it comes to applying information theoretic concepts to understand convolutional neural networks (CNNs). These include for instance the accurate estimation of information quantities among multiple variables, and the many different training methodologies. By extending the novel matrix-based Renyi's {\alpha}-entropy functional to a multivariate scenario and introducing the partial information decomposition (PID) framework, this paper presents a systematic method to analyze CNNs training using information theory. Our results validate two fundamental data processing inequalities in CNNs, and also reveals some fundamental issues embedded in the training phase of CNNs.

Coarse-to-Fine Salient Object Detection with Low-Rank Matrix Recovery

Low-Rank Matrix Recovery (LRMR) has recently been applied to saliency detection by decomposing image features into a low-rank component associated with background and a sparse component associated with visual salient regions. Despite its great potential, existing LRMR-based saliency detection methods seldom consider the inter-relationship among elements within these two components, thus are prone to generating scattered or incomplete saliency maps. In this paper, we introduce a novel and efficient LRMR-based saliency detection model under a coarse-to-fine framework to circumvent this limitation. First, we roughly measure the saliency of image regions with a baseline LRMR model that integrates a $\ell_1$-norm sparsity constraint and a Laplacian regularization smooth term. Given samples from the coarse saliency map, we then learn a projection that maps image features to refined saliency values, to significantly sharpen the object boundaries and to preserve the object entirety. We evaluate our framework against existing LRMR based methods on three benchmark datasets. Experimental results validate the superiority of our method as well as the effectiveness of our suggested coarse-to-fine framework, especially for images containing multiple objects.

Concept Drift Detection and Adaptation with Hierarchical Hypothesis Testing

A fundamental issue for statistical classification models in a streaming environment is that the joint distribution between predictor and response variables changes over time (a phenomenon also known as concept drifts), such that their classification performance deteriorates dramatically. In this paper, we first present a hierarchical hypothesis testing (HHT) framework that can detect and also adapt to various concept drift types (e.g., recurrent or irregular, gradual or abrupt), even in the presence of imbalanced data labels. A novel concept drift detector, namely Hierarchical Linear Four Rates (HLFR), is implemented under the HHT framework thereafter. By substituting a widely-acknowledged retraining scheme with an adaptive training strategy, we further demonstrate that the concept drift adaptation capability of HLFR can be significantly boosted. The theoretical analysis on the Type-I and Type-II errors of HLFR is also performed. Experiments on both simulated and real-world datasets illustrate that our methods outperform state-of-the-art methods in terms of detection precision, detection delay as well as the adaptability across different concept drift types.

Understanding Autoencoders with Information Theoretic Concepts

Despite their great success in practical applications, there is still a lack of theoretical and systematic methods to analyze deep neural networks. In this paper, we illustrate an advanced information theoretic methodology to understand the dynamics of learning and the design of autoencoders, a special type of deep learning architectures that resembles a communication channel. By generalizing the information plane to any cost function, and inspecting the roles and dynamics of different layers using layer-wise information quantities, we emphasize the role that mutual information plays in quantifying learning from data. We further suggest and also experimentally validate, for mean square error training, three fundamental properties regarding the layer-wise flow of information and intrinsic dimensionality of the bottleneck layer, using respectively the data processing inequality and the identification of a bifurcation point in the information plane that is controlled by the given data. Our observations have direct impact on the optimal design of autoencoders, the design of alternative feedforward training methods, and even in the problem of generalization.