Cauchy-Schwarz Divergence Information Bottleneck for Regression

The information bottleneck (IB) approach is popular to improve the generalization, robustness and explainability of deep neural networks. Essentially, it aims to find a minimum sufficient representation $\mathbf{t}$ by striking a trade-off between a compression term $I(\mathbf{x};\mathbf{t})$ and a prediction term $I(y;\mathbf{t})$, where $I(\cdot;\cdot)$ refers to the mutual information (MI). MI is for the IB for the most part expressed in terms of the Kullback-Leibler (KL) divergence, which in the regression case corresponds to prediction based on mean squared error (MSE) loss with Gaussian assumption and compression approximated by variational inference. In this paper, we study the IB principle for the regression problem and develop a new way to parameterize the IB with deep neural networks by exploiting favorable properties of the Cauchy-Schwarz (CS) divergence. By doing so, we move away from MSE-based regression and ease estimation by avoiding variational approximations or distributional assumptions. We investigate the improved generalization ability of our proposed CS-IB and demonstrate strong adversarial robustness guarantees. We demonstrate its superior performance on six real-world regression tasks over other popular deep IB approaches. We additionally observe that the solutions discovered by CS-IB always achieve the best trade-off between prediction accuracy and compression ratio in the information plane. The code is available at \url{https://github.com/SJYuCNEL/Cauchy-Schwarz-Information-Bottleneck}.

Adversarial Reweighting with $α$-Power Maximization for Domain Adaptation

The practical Domain Adaptation (DA) tasks, e.g., Partial DA (PDA), open-set DA, universal DA, and test-time adaptation, have gained increasing attention in the machine learning community. In this paper, we propose a novel approach, dubbed Adversarial Reweighting with $\alpha$-Power Maximization (ARPM), for PDA where the source domain contains private classes absent in target domain. In ARPM, we propose a novel adversarial reweighting model that adversarially learns to reweight source domain data to identify source-private class samples by assigning smaller weights to them, for mitigating potential negative transfer. Based on the adversarial reweighting, we train the transferable recognition model on the reweighted source distribution to be able to classify common class data. To reduce the prediction uncertainty of the recognition model on the target domain for PDA, we present an $\alpha$-power maximization mechanism in ARPM, which enriches the family of losses for reducing the prediction uncertainty for PDA. Extensive experimental results on five PDA benchmarks, i.e., Office-31, Office-Home, VisDA-2017, ImageNet-Caltech, and DomainNet, show that our method is superior to recent PDA methods. Ablation studies also confirm the effectiveness of components in our approach. To theoretically analyze our method, we deduce an upper bound of target domain expected error for PDA, which is approximately minimized in our approach. We further extend ARPM to open-set DA, universal DA, and test time adaptation, and verify the usefulness through experiments.

INSURE: An Information Theory Inspired Disentanglement and Purification Model for Domain Generalization

Domain Generalization (DG) aims to learn a generalizable model on the unseen target domain by only training on the multiple observed source domains. Although a variety of DG methods have focused on extracting domain-invariant features, the domain-specific class-relevant features have attracted attention and been argued to benefit generalization to the unseen target domain. To take into account the class-relevant domain-specific information, in this paper we propose an Information theory iNspired diSentanglement and pURification modEl (INSURE) to explicitly disentangle the latent features to obtain sufficient and compact (necessary) class-relevant feature for generalization to the unseen domain. Specifically, we first propose an information theory inspired loss function to ensure the disentangled class-relevant features contain sufficient class label information and the other disentangled auxiliary feature has sufficient domain information. We further propose a paired purification loss function to let the auxiliary feature discard all the class-relevant information and thus the class-relevant feature will contain sufficient and compact (necessary) class-relevant information. Moreover, instead of using multiple encoders, we propose to use a learnable binary mask as our disentangler to make the disentanglement more efficient and make the disentangled features complementary to each other. We conduct extensive experiments on four widely used DG benchmark datasets including PACS, OfficeHome, TerraIncognita, and DomainNet. The proposed INSURE outperforms the state-of-art methods. We also empirically show that domain-specific class-relevant features are beneficial for domain generalization.

Receding Horizon Control on the Broadcast of Information in Stochastic Networks

This paper focuses on the broadcast of information on robot networks with stochastic network interconnection topologies. Problematic communication networks are almost unavoidable in areas where we wish to deploy multi-robotic systems, usually due to a lack of environmental consistency, accessibility, and structure. We tackle this problem by modeling the broadcast of information in a multi-robot communication network as a stochastic process with random arrival times, which can be produced by irregular robot movements, wireless attenuation, and other environmental factors. Using this model, we provide and analyze a receding horizon control strategy to control the statistics of the information broadcast. The resulting strategy compels the robots to re-direct their communication resources to different neighbors according to the current propagation process to fulfill global broadcast requirements. Based on this method, we provide an approach to compute the expected time to broadcast the message to all nodes. Numerical examples are provided to illustrate the results.

Air-Aided Communication Between Ground Assets in a Poisson Forest

Ground assets deployed in a cluttered environment with randomized obstacles (e.g., a forest) may experience line of sight (LoS) obstruction due to those obstacles. Air assets can be deployed in the vicinity to aid the communication by establishing two-hop paths between the ground assets. Obstacles that are taller than a position-dependent critical height may still obstruct the LoS between a ground asset and an air asset. In this paper, we provide an analytical framework for computing the probability of obtaining a LoS path in a Poisson forest. Given the locations and heights of a ground asset and an air asset, we establish the critical height, which is a function of distance. To account for this dependence on distance, the blocking is modeled as an inhomogenous Poisson point process, and the LoS probability is its void probability. Examples and closed-form expressions are provided for two obstruction height distributions: uniform and truncated Gaussian. The examples are validated through simulation. Additionally, the end-to-end throughput is determined and shown to be a metric that balances communication distance with the impact of LoS blockage. Throughput is used to determine the range at which it is better to relay communications through the air asset, and, when the air asset is deployed, its optimal height.

Flow-Based Control of Marine Robots in Gyre-Like Environments

We present a flow-based control strategy that enables resource-constrained marine robots to patrol gyre-like flow environments on an orbital trajectory with a periodicity in a given range. The controller does not require a detailed model of the flow field and relies only on the robot's location relative to the center of the gyre. Instead of precisely tracking a pre-defined trajectory, the robots are tasked to stay in between two bounding trajectories with known periodicity. Furthermore, the proposed strategy leverages the surrounding flow field to minimize control effort. We prove that the proposed strategy enables robots to cycle in the flow satisfying the desired periodicity requirements. Our method is tested and validated both in simulation and in experiments using a low-cost, underactuated, surface swimming robot, i.e. the Modboat.

Gated Information Bottleneck for Generalization in Sequential Environments

Deep neural networks suffer from poor generalization to unseen environments when the underlying data distribution is different from that in the training set. By learning minimum sufficient representations from training data, the information bottleneck (IB) approach has demonstrated its effectiveness to improve generalization in different AI applications. In this work, we propose a new neural network-based IB approach, termed gated information bottleneck (GIB), that dynamically drops spurious correlations and progressively selects the most task-relevant features across different environments by a trainable soft mask (on raw features). GIB enjoys a simple and tractable objective, without any variational approximation or distributional assumption. We empirically demonstrate the superiority of GIB over other popular neural network-based IB approaches in adversarial robustness and out-of-distribution (OOD) detection. Meanwhile, we also establish the connection between IB theory and invariant causal representation learning, and observed that GIB demonstrates appealing performance when different environments arrive sequentially, a more practical scenario where invariant risk minimization (IRM) fails. Code of GIB is available at https://github.com/falesiani/GIB

Privacy-Preserving Federated Learning on Partitioned Attributes

Real-world data is usually segmented by attributes and distributed across different parties. Federated learning empowers collaborative training without exposing local data or models. As we demonstrate through designed attacks, even with a small proportion of corrupted data, an adversary can accurately infer the input attributes. We introduce an adversarial learning based procedure which tunes a local model to release privacy-preserving intermediate representations. To alleviate the accuracy decline, we propose a defense method based on the forward-backward splitting algorithm, which respectively deals with the accuracy loss and privacy loss in the forward and backward gradient descent steps, achieving the two objectives simultaneously. Extensive experiments on a variety of datasets have shown that our defense significantly mitigates privacy leakage with negligible impact on the federated learning task.

Deep Deterministic Information Bottleneck with Matrix-based Entropy Functional

We introduce the matrix-based Renyi's $\alpha$-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

Measuring Dependence with Matrix-based Entropy Functional

Measuring the dependence of data plays a central role in statistics and machine learning. In this work, we summarize and generalize the main idea of existing information-theoretic dependence measures into a higher-level perspective by the Shearer's inequality. Based on our generalization, we then propose two measures, namely the matrix-based normalized total correlation ($T_\alpha^*$) and the matrix-based normalized dual total correlation ($D_\alpha^*$), to quantify the dependence of multiple variables in arbitrary dimensional space, without explicit estimation of the underlying data distributions. We show that our measures are differentiable and statistically more powerful than prevalent ones. We also show the impact of our measures in four different machine learning problems, namely the gene regulatory network inference, the robust machine learning under covariate shift and non-Gaussian noises, the subspace outlier detection, and the understanding of the learning dynamics of convolutional neural networks (CNNs), to demonstrate their utilities, advantages, as well as implications to those problems. Code of our dependence measure is available at: https://bit.ly/AAAI-dependence