Semi-implicit graph variational auto-encoder (SIG-VAE) is proposed to expand the flexibility of variational graph auto-encoders (VGAE) to model graph data. SIG-VAE employs a hierarchical variational framework to enable neighboring node sharing for better generative modeling of graph dependency structure, together with a Bernoulli-Poisson link decoder. Not only does this hierarchical construction provide a more flexible generative graph model to better capture real-world graph properties, but also does SIG-VAE naturally lead to semi-implicit hierarchical variational inference that allows faithful modeling of implicit posteriors of given graph data, which may exhibit heavy tails, multiple modes, skewness, and rich dependency structures. Compared to VGAE, the derived graph latent representations by SIG-VAE are more interpretable, due to more expressive generative model and more faithful inference enabled by the flexible semi-implicit construction. Extensive experiments with a variety of graph data show that SIG-VAE significantly outperforms state-of-the-art methods on several different graph analytic tasks.
Representation learning over graph structured data has been mostly studied in static graph settings while efforts for modeling dynamic graphs are still scant. In this paper, we develop a novel hierarchical variational model that introduces additional latent random variables to jointly model the hidden states of a graph recurrent neural network (GRNN) to capture both topology and node attribute changes in dynamic graphs. We argue that the use of high-level latent random variables in this variational GRNN (VGRNN) can better capture potential variability observed in dynamic graphs as well as the uncertainty of node latent representation. With semi-implicit variational inference developed for this new VGRNN architecture (SI-VGRNN), we show that flexible non-Gaussian latent representations can further help dynamic graph analytic tasks. Our experiments with multiple real-world dynamic graph datasets demonstrate that SI-VGRNN and VGRNN consistently outperform the existing baseline and state-of-the-art methods by a significant margin in dynamic link prediction.
Segmentation of ultra-high resolution images is increasingly demanded, yet poses significant challenges for algorithm efficiency, in particular considering the (GPU) memory limits. Current approaches either downsample an ultra-high resolution image or crop it into small patches for separate processing. In either way, the loss of local fine details or global contextual information results in limited segmentation accuracy. We propose collaborative Global-Local Networks (GLNet) to effectively preserve both global and local information in a highly memory-efficient manner. GLNet is composed of a global branch and a local branch, taking the downsampled entire image and its cropped local patches as respective inputs. For segmentation, GLNet deeply fuses feature maps from two branches, capturing both the high-resolution fine structures from zoomed-in local patches and the contextual dependency from the downsampled input. To further resolve the potential class imbalance problem between background and foreground regions, we present a coarse-to-fine variant of GLNet, also being memory-efficient. Extensive experiments and analyses have been performed on three real-world ultra-high aerial and medical image datasets (resolution up to 30 million pixels). With only one single 1080Ti GPU and less than 2GB memory used, our GLNet yields high-quality segmentation results and achieves much more competitive accuracy-memory usage trade-offs compared to state-of-the-arts.
Missing values frequently arise in modern biomedical studies due to various reasons, including missing tests or complex profiling technologies for different omics measurements. Missing values can complicate the application of clustering algorithms, whose goals are to group points based on some similarity criterion. A common practice for dealing with missing values in the context of clustering is to first impute the missing values, and then apply the clustering algorithm on the completed data. We consider missing values in the context of optimal clustering, which finds an optimal clustering operator with reference to an underlying random labeled point process (RLPP). We show how the missing-value problem fits neatly into the overall framework of optimal clustering by incorporating the missing value mechanism into the random labeled point process and then marginalizing out the missing-value process. In particular, we demonstrate the proposed framework for the Gaussian model with arbitrary covariance structures. Comprehensive experimental studies on both synthetic and real-world RNA-seq data show the superior performance of the proposed optimal clustering with missing values when compared to various clustering approaches. Optimal clustering with missing values obviates the need for imputation-based pre-processing of the data, while at the same time possessing smaller clustering errors.
Emerging wearable sensors have enabled the unprecedented ability to continuously monitor human activities for healthcare purposes. However, with so many ambient sensors collecting different measurements, it becomes important not only to maintain good monitoring accuracy, but also low power consumption to ensure sustainable monitoring. This power-efficient sensing scheme can be achieved by deciding which group of sensors to use at a given time, requiring an accurate characterization of the trade-off between sensor energy usage and the uncertainty in ignoring certain sensor signals while monitoring. To address this challenge in the context of activity monitoring, we have designed an adaptive activity monitoring framework. We first propose a switching Gaussian process to model the observed sensor signals emitting from the underlying activity states. To efficiently compute the Gaussian process model likelihood and quantify the context prediction uncertainty, we propose a block circulant embedding technique and use Fast Fourier Transforms (FFT) for inference. By computing the Bayesian loss function tailored to switching Gaussian processes, an adaptive monitoring procedure is developed to select features from available sensors that optimize the trade-off between sensor power consumption and the prediction performance quantified by state prediction entropy. We demonstrate the effectiveness of our framework on the popular benchmark of UCI Human Activity Recognition using Smartphones.
In multi-objective Bayesian optimization and surrogate-based evolutionary algorithms, Expected HyperVolume Improvement (EHVI) is widely used as the acquisition function to guide the search approaching the Pareto front. This paper focuses on the exact calculation of EHVI given a nondominated set, for which the existing exact algorithms are complex and can be inefficient for problems with more than three objectives. Integrating with different decomposition algorithms, we propose a new method for calculating the integral in each decomposed high-dimensional box in constant time. We develop three new exact EHVI calculation algorithms based on three region decomposition methods. The first grid-based algorithm has a complexity of $O(m\cdot n^m)$ with $n$ denoting the size of the nondominated set and $m$ the number of objectives. The Walking Fish Group (WFG)-based algorithm has a worst-case complexity of $O(m\cdot 2^n)$ but has a better average performance. These two can be applied for problems with any $m$. The third CLM-based algorithm is only for $m=3$ and asymptotically optimal with complexity $\Theta(n\log{n})$. Performance comparison results show that all our three algorithms are at least twice faster than the state-of-the-art algorithms with the same decomposition methods. When $m>3$, our WFG-based algorithm can be over $10^2$ faster than the corresponding existing algorithms. Our algorithm is demonstrated in an example involving efficient multi-objective material design with Bayesian optimization.
Precision medicine aims for personalized prognosis and therapeutics by utilizing recent genome-scale high-throughput profiling techniques, including next-generation sequencing (NGS). However, translating NGS data faces several challenges. First, NGS count data are often overdispersed, requiring appropriate modeling. Second, compared to the number of involved molecules and system complexity, the number of available samples for studying complex disease, such as cancer, is often limited, especially considering disease heterogeneity. The key question is whether we may integrate available data from all different sources or domains to achieve reproducible disease prognosis based on NGS count data. In this paper, we develop a Bayesian Multi-Domain Learning (BMDL) model that derives domain-dependent latent representations of overdispersed count data based on hierarchical negative binomial factorization for accurate cancer subtyping even if the number of samples for a specific cancer type is small. Experimental results from both our simulated and NGS datasets from The Cancer Genome Atlas (TCGA) demonstrate the promising potential of BMDL for effective multi-domain learning without "negative transfer" effects often seen in existing multi-task learning and transfer learning methods.
We present safe active incremental feature selection~(SAIF) to scale up the computation of LASSO solutions. SAIF does not require a solution from a heavier penalty parameter as in sequential screening or updating the full model for each iteration as in dynamic screening. Different from these existing screening methods, SAIF starts from a small number of features and incrementally recruits active features and updates the significantly reduced model. Hence, it is much more computationally efficient and scalable with the number of features. More critically, SAIF has the safe guarantee as it has the convergence guarantee to the optimal solution to the original full LASSO problem. Such an incremental procedure and theoretical convergence guarantee can be extended to fused LASSO problems. Compared with state-of-the-art screening methods as well as working set and homotopy methods, which may not always guarantee the optimal solution, SAIF can achieve superior or comparable efficiency and high scalability with the safe guarantee when facing extremely high dimensional data sets. Experiments with both synthetic and real-world data sets show that SAIF can be up to 50 times faster than dynamic screening, and hundreds of times faster than computing LASSO or fused LASSO solutions without screening.