United States

We study a variant of stochastic bandits where the feedback model is specified by a graph. In this setting, after playing an arm, one can observe rewards of not only the played arm but also other arms that are adjacent to the played arm in the graph. Most of the existing work assumes the reward distributions are stationary over time, which, however, is often violated in common scenarios such as recommendation systems and online advertising. To address this limitation, we study stochastic bandits with graph feedback in non-stationary environments and propose algorithms with graph-dependent dynamic regret bounds. When the number of reward distribution changes L is known in advance, one of our algorithms achieves an Ã•(âˆš(Î±LT)) dynamic regret bound. We also develop an adaptive algorithm that can adapt to unknown L and attain an Ã•(âˆš(Î¸LT)) dynamic regret. Here, Î± and Î¸ are some graph-dependent quantities and T is the time horizon.

AAAI 2021

Stochastic Bandits with Graph Feedback in Non-Stationary Environments

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

technical paper

We propose a novel and principled method to learn a nonparametric graph model called graphon, which is defined in an infinite-dimensional space and represents arbitrary-size graphs. 
Based on the weak regularity lemma from the theory of graphons, we leverage a step function to approximate a graphon. 
We show that the cut distance of graphons can be relaxed to the Gromov-Wasserstein distance of their step functions. 
Accordingly, given a set of graphs generated by an underlying graphon, we learn the corresponding step function as the Gromov-Wasserstein barycenter of the given graphs.
Furthermore, we develop several enhancements and extensions of the basic algorithm, e.g., the smoothed Gromov-Wasserstein barycenter for guaranteeing the continuity of the learned graphons and the mixed Gromov-Wasserstein barycenters for learning multiple structured graphons. 
The proposed approach overcomes drawbacks of prior state-of-the-art methods, and outperforms them on both synthetic and real-world data. 
The code is available at https://github.com/HongtengXu/SGWB-Graphon.

Learning Graphons via Structured Gromov-Wasserstein Barycenters

We develop an auto-encoder-type nonlinear dimensionality reduction algorithm to enable the construction of reduced order models of systems governed by convection-dominated nonlinear partial differential equations (PDEs), i.e. snapshots of solutions with large Kolmogorov n-width. Although several existing nonlinear manifold learning methods, such as LLE, ISOMAP, MDS, etc., appear as compelling candidates to reduce the dimensionality of such data, most are not applicable to reduced order modeling of PDEs, because: (i) they typically lack a straightforward mapping from the latent space to the high-dimensional physical space, and (ii) the identified latent variables are often difficult to interpret. In our proposed method, these limitations are overcome by training a low-rank diffeomorphic spatio-temporal grid that registers the output sequence of the PDEs on a non-uniform parameter/time-varying grid, such that the Kolmogorov n-width of the mapped data on the learned grid is minimized. We demonstrate the efficacy and interpretability of our proposed approach on several challenging manufactured computer vision-inspired tasks and physical systems.

Low-Rank Registration Based Manifolds for Convection-Dominated PDEs

The first provably efficient algorithm for learning graph neural networks (GNNs) with one hidden layer for node information convolution is provided in this paper. Two types of GNNs are investigated, depending on whether labels are attached to nodes or graphs. A comprehensive framework for designing and analyzing convergence of GNN training algorithms is developed. The algorithm proposed is applicable to a wide range of activation functions including ReLU, Leaky ReLU, Sigmod, Softplus and Swish. It is shown that the proposed algorithm guarantees a linear convergence rate to the underlying true parameters of GNNs. For both types of GNNs, sample complexity in terms of the number of nodes or the number of graphs is characterized. The impact of feature dimension and GNN structure on the convergence rate is also theoretically characterized. Numerical experiments are further provided to validate our theoretical analysis.

Learning Graph Neural Networks with Approximate Gradient Descent

We introduce Probabilistic Dependency Graphs (PDGs), a new class of directed graphical models.   PDGs can capture inconsistent beliefs in a natural way and are more modular than Bayesian Networks (BNs), in that they make it easier to incorporate new information and restructure the representation.    We show by example how PDGs are an especially natural modeling tool. We provide three semantics for PDGs, each of which can be derived from a scoring function (on joint distributions over the variables in the network) that can be viewed as representing a distribution's incompatibility with the PDG. For the PDG corresponding to a BN, this function is uniquely minimized by the distribution the BN represents, showing that PDG semantics extend BN semantics. We show further that factor graphs and their exponential families can also be faithfully represented as PDGs, while there are significant barriers to modeling a PDG with a factor graph.

Probabilistic Dependency Graphs

Abstract reasoning refers to the ability to analyze information, discover rules at an intangible level, and solve problems in innovative ways. Raven's Progressive Matrices (RPM) test is typically used to examine the capability of abstract reasoning. The subject is asked to identify the correct choice from the answer set to fill the missing panel at the bottom right of RPM (e.g., a 3Ã—3 matrix), following the underlying rules inside the matrix. Recent studies, taking advantage of Convolutional Neural Networks (CNNs), have achieved encouraging progress to accomplish the RPM test. However, they partly ignore necessary inductive biases of RPM solver, such as order sensitivity within each row/column and incremental rule induction. To address this problem, in this paper we propose a Stratified Rule-Aware Network (SRAN) to generate the rule embeddings for two input sequences. Our SRAN learns multiple granularity rule embeddings at different levels, and incrementally integrates the stratified embedding flows through a gated fusion module. With the help of embeddings, a rule similarity metric is applied to guarantee that SRAN can not only be trained using a tuplet loss but also infer the best answer efficiently. We further point out the severe defects existing in the popular RAVEN dataset for RPM test, which prevent from the fair evaluation of the abstract reasoning ability. To fix the defects, we propose an answer set generation algorithm called Attribute Bisection Tree (ABT), forming an improved dataset named Impartial-RAVEN (I-RAVEN for short). Extensive experiments are conducted on both PGM and I-RAVEN datasets, showing that our SRAN outperforms the state-of-the-art models by a considerable margin.

Stratified Rule-Aware Network for Abstract Visual Reasoning

The behaviors of deep neural networks (DNNs) are notoriously resistant to human interpretations. In this paper, we propose Hypergradient Data Relevance Analysis, or HyDRA, which interprets the predictions made by DNNs as effects of their training data. Existing approaches generally estimate data contributions around the final model parameters and ignore how the training data shape the optimization trajectory. By unrolling the hypergradient of test loss w.r.t. the weights of training data, HyDRA assesses the contribution of training data toward test data points throughout the training trajectory. In order to accelerate computation, we remove the Hessian from the calculation and prove that, under moderate conditions, the approximation error is bounded. Corroborating this theoretical claim, empirical results indicate the error is indeed small. In addition, we quantitatively demonstrate that HyDRA outperforms influence functions in accurately estimating data contribution and detecting noisy data labels. The source code is available at https://github.com/cyyever/aaai_hydra.

HyDRA: Hypergradient Data Relevance Analysis for Interpreting Deep Neural Networks

A considerable amount of mobility data has been accumulated due to the proliferation of location-based service. Nevertheless, compared with mobility data from transportation systems like the GPS module in taxis, this kind of data is commonly sparse in terms of individual trajectories in the sense that users do not access mobile services and contribute their data all the time. Consequently, the sparsity inevitably weakens the practical value of the data even it has a high user penetration rate. To solve this problem, we propose a novel attentional neural network-based model, named AttnMove, to densify individual trajectories by recovering unobserved locations at a fine-grained spatial-temporal resolution. To tackle the challenges posed by sparsity, we design various intra- and inter- trajectory attention mechanisms to better model the mobility regularity of users and fully exploit the periodical pattern from long-term history. We evaluate our model on two real-world datasets, and extensive results demonstrate the performance gain compared with the state-of-the-art methods. This also shows that, by providing high-quality mobility data, our model can benefit a variety of mobility-oriented down-stream applications.

AttnMove: History Enhanced Trajectory Recovery via Attentional Network

Capsule Networks, as alternatives to Convolutional Neural Networks, have been proposed to recognize objects from images. The current literature demonstrates many advantages of CapsNets over CNNs. However, how to create explanations for individual classifications of CapsNets has not been well explored. The widely used saliency methods are mainly proposed for explaining CNN-based classifications; they create saliency map explanations by combining activation values and the corresponding gradients, e.g., Grad-CAM. These saliency methods require a specific architecture of the underlying classifiers and cannot be trivially applied to CapsNets due to the iterative routing mechanism therein. To overcome the lack of interpretability, we can either propose new post-hoc interpretation methods for CapsNets or modifying the model to have build-in explanations. In this work, we explore the latter. Specifically, we propose interpretable Graph Capsule Networks (GraCapsNets), where we replace the routing part with a multi-head attention-based Graph Pooling approach. In the proposed model, individual classification explanations can be created effectively and efficiently. Our model also demonstrates some unexpected benefits, even though it replaces the fundamental part of CapsNets. Our GraCapsNets achieve better classification performance with fewer parameters and better adversarial robustness, when compared to CapsNets. Besides, GraCapsNets also keep other advantages of CapsNets, namely, disentangled representations and affine transformation robustness.

Interpretable Graph Capsule Networks for Object Recognition

With the capability of trading accuracy for latency on-the-fly, the technique of adaptive early-exit inference has emerged as a promising line of research to accelerate the deep learning inference. However, studies in this line of research commonly use a group of thresholds to control the accuracy-latency trade-off, where a thorough and general methodology on how to determine these thresholds has not been conducted yet, especially with regard to the common requirements of average inference latency. To address this issue and enable latency-aware adaptive early-exit inference, in the present paper, we approximately formulate the threshold determination problem of finding the accuracy-maximum threshold setting that meets a given average latency requirement, and then propose a threshold determination method to tackle our formulated non-convex problem. Theoretically, we prove that, for certain parameter settings, our method finds an approximate stationary point of the formulated problem. Empirically, on top of various models across multiple datasets (CIFAR-10, CIFAR-100, ImageNet and two time-series datasets), we show that our method can well handle the average latency requirements, and consistently finds good threshold settings in negligible time.

Empowering Adaptive Early-Exit Inference with Latency Awareness

With the rapid evolution of social media, fake news has become a significant social problem, which cannot be addressed in a timely manner using manual investigation. This has motivated numerous studies on automating fake news detection. Most studies explore supervised training models with different modalities (e.g., text, images, and propagation networks) of news records to identify fake news. However, the performance of such techniques generally drops if news records are coming from different domains (e.g., politics, entertainment), especially for domains that are unseen or rarely-seen during training. As motivation, we empirically show that news records from different domains have significantly different word usage and propagation patterns. Furthermore, due to the sheer volume of unlabelled news records, it is challenging to select news records for manual labelling so that the domain-coverage of the labelled dataset is maximised. Hence, this work: (1) proposes a novel framework that jointly preserves domain-specific and cross-domain knowledge in news records to detect fake news from different domains; and (2) introduces an unsupervised technique to select a set of unlabelled informative news records for manual labelling, which can be ultimately used to train a fake news detection model that performs well for many domains while minimizing the labelling cost. Our experiments show that the integration of the proposed fake news model and the selective annotation approach achieves state-of-the-art performance for cross-domain news datasets, while yielding notable improvements for rarely-appearing domains in news datasets.

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