For node level graph encoding, a recent important state-of-art method is the graph convolutional networks (GCN), which nicely integrate local vertex features and graph topology in the spectral domain. However, current studies suffer from several drawbacks: (1) graph CNNs relies on Chebyshev polynomial approximation which results in oscillatory approximation at jump discontinuities; (2) Increasing the order of Chebyshev polynomial can reduce the oscillations issue, but also incurs unaffordable computational cost; (3) Chebyshev polynomials require degree $\Omega$(poly(1/$\epsilon$)) to approximate a jump signal such as $|x|$, while rational function only needs $\mathcal{O}$(poly log(1/$\epsilon$))\cite{liang2016deep,telgarsky2017neural}. However, it's non-trivial to apply rational approximation without increasing computational complexity due to the denominator. In this paper, the superiority of rational approximation is exploited for graph signal recovering. RatioanlNet is proposed to integrate rational function and neural networks. We show that rational function of eigenvalues can be rewritten as a function of graph Laplacian, which can avoid multiplication by the eigenvector matrix. Focusing on the analysis of approximation on graph convolution operation, a graph signal regression task is formulated. Under graph signal regression task, its time complexity can be significantly reduced by graph Fourier transform. To overcome the local minimum problem of neural networks model, a relaxed Remez algorithm is utilized to initialize the weight parameters. Convergence rate of RatioanlNet and polynomial based methods on jump signal is analyzed for a theoretical guarantee. The extensive experimental results demonstrated that our approach could effectively characterize the jump discontinuities, outperforming competing methods by a substantial margin on both synthetic and real-world graphs.

As the issue of freshwater shortage is increasing daily, it is critical to take effective measures for water conservation. According to previous studies, device level consumption could lead to significant freshwater conservation. Existing water disaggregation methods focus on learning the signatures for appliances; however, they are lack of the mechanism to accurately discriminate parallel appliances' consumption. In this paper, we propose a Bayesian Discriminative Sparse Coding model using Laplace Prior (BDSC-LP) to extensively enhance the disaggregation performance. To derive discriminative basis functions, shape features are presented to describe the low-sampling-rate water consumption patterns. A Gibbs sampling based inference method is designed to extend the discriminative capability of the disaggregation dictionaries. Extensive experiments were performed to validate the effectiveness of the proposed model using both real-world and synthetic datasets.

Deep convolutional neural networks (CNNs) have demonstrated impressive performance on visual object classification tasks. In addition, it is a useful model for predication of neuronal responses recorded in visual system. However, there is still no clear understanding of what CNNs learn in terms of visual neuronal circuits. Visualizing CNN's features to obtain possible connections to neuronscience underpinnings is not easy due to highly complex circuits from the retina to higher visual cortex. Here we address this issue by focusing on single retinal ganglion cells with a simple model and electrophysiological recordings from salamanders. By training CNNs with white noise images to predicate neural responses, we found that convolutional filters learned in the end are resembling to biological components of the retinal circuit. Features represented by these filters tile the space of conventional receptive field of retinal ganglion cells. These results suggest that CNN could be used to reveal structure components of neuronal circuits.

The analysis of interactions between social media and traditional news streams is becoming increasingly relevant for a variety of applications, including: understanding the underlying factors that drive the evolution of data sources, tracking the triggers behind events, and discovering emerging trends.Researchers have explored such interactions by examining volume changes or information diffusions,however, most of them ignore the semantical and topical relationships between news and social media data.Our work is the first attempt to study how news influences social media, or inversely, based on topical knowledge.We propose a hierarchical Bayesian model that jointly models the news and social media topics and their interactions.We show that our proposed model can capture distinct topics for individual datasets as well as discover the topic influences among multiple datasets.By applying our model to large sets of news and tweets, we demonstrate its significant improvement over baseline methods and explore its power in the discovery of interesting patterns for real world cases.

Non-parametric graph scan (NPGS) statistics are used to detect anomalous connected subgraphs on graphs, and have a wide variety of applications, such as disease outbreak detection, road traffic congestion detection, and event detection in social media. In contrast to traditional parametric scan statistics (e.g., the Kulldorff statistic), NPGS statistics are free of distributional assumptions and can be applied to heterogeneous graph data. In this paper, we make a number of contributions to the computational study of NPGS statistics. First, we present a novel reformulation of the problem as a sequence of Budget Price-Collecting Steiner Tree (B-PCST) sub-problems. Second, we show that this reformulated problem is NP-hard for a large class of nonparametric statistic functions. Third, we further develop efficient exact and approximate algorithms for a special category of graphs in which the anomalous subgraphs can be reformulated in a fixed tree topology. Finally, using extensive experiments we demonstrate the performance of our proposed algorithms in two real-world application domains (water pollution detection in water sensor networks and spatial event detection in social media networks) and contrast against state-of-the-art connected subgraph detection methods.

Markov Decision Processes (MDPs) are extremely useful for modeling and solving sequential decision making problems. Graph-based MDPs provide a compact representation for MDPs with large numbers of random variables. However, the complexity of exactly solving a graph-based MDP usually grows exponentially in the number of variables, which limits their application. We present a new variational framework to describe and solve the planning problem of MDPs, and derive both exact and approximate planning algorithms. In particular, by exploiting the graph structure of graph-based MDPs, we propose a factored variational value iteration algorithm in which the value function is first approximated by the multiplication of local-scope value functions, then solved by minimizing a Kullback-Leibler (KL) divergence. The KL divergence is optimized using the belief propagation algorithm, with complexity exponential in only the cluster size of the graph. Experimental comparison on different models shows that our algorithm outperforms existing approximation algorithms at finding good policies.

Anomaly detection for mixed-type data is an important problem that has not been well addressed in the machine learning field. There are two challenging issues for mixed-type datasets, namely modeling mutual correlations between mixed-type attributes and capturing large variations due to anomalies. This paper presents BuffDetect, a robust error buffering approach for anomaly detection in mixed-type datasets. A new variant of the generalized linear model is proposed to model the dependency between mixed-type attributes. The model incorporates an error buffering component based on Student-t distribution to absorb the variations caused by anomalies. However, because of the non- Gaussian design, the problem becomes analytically intractable. We propose a novel Bayesian inference approach, which integrates Laplace approximation and several computational optimizations, and is able to efficiently approximate the posterior of high dimensional latent variables by iteratively updating the latent variables in groups. Extensive experimental evaluations based on 13 benchmark datasets demonstrate the effectiveness and efficiency of BuffDetect.

We study the marginal-MAP problem on graphical models, and present a novel approximation method based on direct approximation of the sum operation. A primary difficulty of marginal-MAP problems lies in the non-commutativity of the sum and max operations, so that even in highly structured models, marginalization may produce a densely connected graph over the variables to be maximized, resulting in an intractable potential function with exponential size. We propose a chain decomposition approach for summing over the marginalized variables, in which we produce a structured approximation to the MAP component of the problem consisting of only pairwise potentials. We show that this approach is equivalent to the maximization of a specific variational free energy, and it provides an upper bound of the optimal probability. Finally, experimental results demonstrate that our method performs favorably compared to previous methods.