Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from scientific data thrives as a new attempt to model complex phenomena in nature, but the effectiveness of current practice is typically limited by the scarcity of data and the complexity of phenomena. Especially, the discovery of PDEs with highly nonlinear coefficients from low-quality data remains largely under-addressed. To deal with this challenge, we propose a novel physics-guided learning method, which can not only encode observation knowledge such as initial and boundary conditions but also incorporate the basic physical principles and laws to guide the model optimization. We theoretically show that our proposed method strictly reduces the coefficient estimation error of existing baselines, and is also robust against noise. Extensive experiments show that the proposed method is more robust against data noise, and can reduce the estimation error by a large margin. Moreover, all the PDEs in the experiments are correctly discovered, and for the first time we are able to discover three-dimensional PDEs with highly nonlinear coefficients.

Generative flows are promising tractable models for density modeling that define probabilistic distributions with invertible transformations. However, tractability imposes architectural constraints on generative flows. In this work, we study a previously overlooked constraint that all the intermediate representations must have the same dimensionality with the data due to invertibility, limiting the width of the network. We propose VFlow to tackle this constraint on dimensionality. VFlow augments the data with extra dimensions and defines a maximum evidence lower bound (ELBO) objective for estimating the distribution of augmented data jointly with the variational data augmentation distribution. Under mild assumptions, we show that the maximum ELBO solution of VFlow is always better than the original maximum likelihood solution. For image density modeling on the CIFAR-10 dataset, VFlow achieves a new state-of-the-art 2.98 bits per dimension.

Learning-from-crowds aims to design proper aggregation strategies to infer the unknown true labels from the noisy labels provided by ordinary web workers. This paper presents max-margin majority voting (M$^3$3V) to improve the discriminative ability of majority voting and further presents a Bayesian generalization to incorporate the flexibility of generative methods on modeling noisy observations with worker confusion matrices for different application settings. We first introduce the crowdsourcing margin of majority voting, then we formulate the joint learning as a regularized Bayesian inference (RegBayes) problem, where the posterior regularization is derived by maximizing the margin between the aggregated score of a potential true label and that of any alternative label. Our Bayesian model naturally covers the Dawid-Skene estimator and M$^3$3V as its two special cases. Due to the flexibility of our model, we extend it to handle crowdsourced labels with an ordinal structure with the main ideas about the crowdsourcing margin unchanged. Moreover, we consider an online learning-from-crowds setting where labels coming in a stream. Empirical results demonstrate that our methods are competitive, often achieving better results than state-of-the-art estimators.

To deal with the low qualities of web workers in crowdsourcing, many unsupervised label aggregation methods have been investigated but most of them provide inconsistent performance. In this paper, we explore the learning from crowds with selective verification problem. In addition to the noisy responses from the crowds, it also collects the ground truths for a well-chosen subset of tasks as the reference, then aggregates the redundant responses based on the patterns provided by both the supervised and unsupervised signal. To improve the labeling efficiency, we propose the EBM selecting strategy for choosing the verification subset, which is based on the loss error minimization. Specifically, we first establish the expected loss error given the semi-supervised learning estimate, then find the subset that minimizes this selecting criterion. We do extensive empirical comparisons on both synthetic and real-world datasets to show the benefits of this new learning setting as well as our proposal.

Deep learning on graph structures has shown exciting results in various applications. However, few attentions have been paid to the robustness of such models, in contrast to numerous research work for image or text adversarial attack and defense. In this paper, we focus on the adversarial attacks that fool deep learning models by modifying the combinatorial structure of data. We first propose a reinforcement learning based attack method that learns the generalizable attack policy, while only requiring prediction labels from the target classifier. We further propose attack methods based on genetic algorithms and gradient descent in the scenario where additional prediction confidence or gradients are available. We use both synthetic and real-world data to show that, a family of Graph Neural Network models are vulnerable to these attacks, in both graph-level and node-level classification tasks. We also show such attacks can be used to diagnose the learned classifiers.

We consider the semi-supervised clustering problem where crowdsourcing provides noisy information about the pairwise comparisons on a small subset of data, i.e., whether a sample pair is in the same cluster. We propose a new approach that includes a deep generative model (DGM) to characterize low-level features of the data, and a statistical relational model for noisy pairwise annotations on its subset. The two parts share the latent variables. To make the model automatically trade-off between its complexity and fitting data, we also develop its fully Bayesian variant. The challenge of inference is addressed by fast (natural-gradient) stochastic variational inference algorithms, where we effectively combine variational message passing for the relational part and amortized learning of the DGM under a unified framework. Empirical results on synthetic and real-world datasets show that our model outperforms previous crowdsourced clustering methods.

Finding semantic attributes to describe related concepts is typically a hard problem. The commonly used attributes in most fields are designed by domain experts, which is expensive and time-consuming. In this paper we propose an efficient method to learn human comprehensible attributes with crowdsourcing. We first design an analogical interface to collect relative labels from the crowds. Then we propose a hierarchical Bayesian model, as well as an efficient initialization strategy, to aggregate labels and extract concise attributes. Our experimental results demonstrate promise on discovering diverse and convincing attributes, which significantly improve the performance of the challenging zero-shot learning tasks.

Modeling document structure is of great importance for discourse analysis and related applications. The goal of this research is to capture the document intent structure by modeling documents as a mixture of topic words and rhetorical words. While the topics are relatively unchanged through one document, the rhetorical functions of sentences usually change following certain orders in discourse. We propose GMM-LDA, a topic modeling based Bayesian unsupervised model, to analyze the document intent structure cooperated with order information. Our model is flexible that has the ability to combine the annotations and do supervised learning. Additionally, entropic regularization can be introduced to model the significant divergence between topics and intents. We perform experiments in both unsupervised and supervised settings, results show the superiority of our model over several state-of-the-art baselines.

Learning-from-crowds aims to design proper aggregation strategies to infer the unknown true labels from the noisy labels provided by ordinary web workers. This paper presents max-margin majority voting (M^3V) to improve the discriminative ability of majority voting and further presents a Bayesian generalization to incorporate the flexibility of generative methods on modeling noisy observations with worker confusion matrices. We formulate the joint learning as a regularized Bayesian inference problem, where the posterior regularization is derived by maximizing the margin between the aggregated score of a potential true label and that of any alternative label. Our Bayesian model naturally covers the Dawid-Skene estimator and M^3V. Empirical results demonstrate that our methods are competitive, often achieving better results than state-of-the-art estimators.

The rise of crowdsourcing brings new types of malpractices in Internet advertising. One can easily hire web workers through malicious crowdsourcing platforms to attack other advertisers. Such human generated crowd frauds are hard to detect by conventional fraud detection methods. In this paper, we carefully examine the characteristics of the group behaviors of crowd fraud and identify three persistent patterns, which are moderateness, synchronicity and dispersivity. Then we propose an effective crowd fraud detection method for search engine advertising based on these patterns, which consists of a constructing stage, a clustering stage and a filtering stage. At the constructing stage, we remove irrelevant data and reorganize the click logs into a surfer-advertiser inverted list; At the clustering stage, we define the sync-similarity between surfers' click histories and transform the coalition detection to a clustering problem, solved by a nonparametric algorithm; and finally we build a dispersity filter to remove false alarm clusters. The nonparametric nature of our method ensures that we can find an unbounded number of coalitions with nearly no human interaction. We also provide a parallel solution to make the method scalable to Web data and conduct extensive experiments. The empirical results demonstrate that our method is accurate and scalable.