Neural processes are a family of probabilistic models that inherit the flexibility of neural networks to parameterize stochastic processes. Despite providing well-calibrated predictions, especially in regression problems, and quick adaptation to new tasks, the Gaussian assumption that is commonly used to represent the predictive likelihood fails to capture more complicated distributions such as multimodal ones. To overcome this limitation, we propose Conditional Quantile Neural Processes (CQNPs), a new member of the neural processes family, which exploits the attractive properties of quantile regression in modeling the distributions irrespective of their form. By introducing an extension of quantile regression where the model learns to focus on estimating informative quantiles, we show that the sampling efficiency and prediction accuracy can be further enhanced. Our experiments with real and synthetic datasets demonstrate substantial improvements in predictive performance compared to the baselines, and better modeling of heterogeneous distributions’ characteristics such as multimodality.

Stochastic recurrent neural networks with latent random variables of complex dependency structures have shown to be more successful in modeling sequential data than deterministic deep models. However, the majority of existing methods have limited expressive power due to the Gaussian assumption of latent variables. In this paper, we advocate learning implicit latent representations using semi-implicit variational inference to further increase model flexibility. Semi-implicit stochastic recurrent neural network (SIS-RNN) is developed to enrich inferred model posteriors that may have no analytic density functions, as long as independent random samples can be generated via reparameterization. Extensive experiments in different tasks on real-world datasets show that SIS-RNN outperforms the existing methods.

We propose a unified framework for adaptive connection sampling in graph neural networks (GNNs) that generalizes existing stochastic regularization methods for training GNNs. The proposed framework not only alleviates over-smoothing and over-fitting tendencies of deep GNNs, but also enables learning with uncertainty in graph analytic tasks with GNNs. Instead of using fixed sampling rates or hand-tuning themas model hyperparameters in existing stochastic regularization methods, our adaptive connection sampling can be trained jointly with GNN model parameters in both global and local fashions. GNN training with adaptive connection sampling is shown to be mathematically equivalent to an efficient approximation of training BayesianGNNs. Experimental results with ablation studies on benchmark datasets validate that adaptively learning the sampling rate given graph training data is the key to boost the performance of GNNs in semi-supervised node classification, less prone to over-smoothing and over-fitting with more robust prediction.

High-throughput molecular profiling technologies have produced high-dimensional multi-omics data, enabling systematic understanding of living systems at the genome scale. Studying molecular interactions across different data types helps reveal signal transduction mechanisms across different classes of molecules. In this paper, we develop a novel Bayesian representation learning method that infers the relational interactions across multi-omics data types. Our method, Bayesian Relational Learning (BayReL) for multi-omics data integration, takes advantage of a priori known relationships among the same class of molecules, modeled as a graph at each corresponding view, to learn view-specific latent variables as well as a multi-partite graph that encodes the interactions across views. Our experiments on several real-world datasets demonstrate enhanced performance of BayReL in inferring meaningful interactions compared to existing baselines.

MOTIVATION: Combination therapy has shown to improve therapeutic efficacy while reducing side effects. Importantly, it has become an indispensable strategy to overcome resistance in antibiotics, antimicrobials and anticancer drugs. Facing enormous chemical space and unclear design principles for small-molecule combinations, computational drug-combination design has not seen generative models to meet its potential to accelerate resistance-overcoming drug combination discovery. RESULTS: We have developed the first deep generative model for drug combination design, by jointly embedding graph-structured domain knowledge and iteratively training a reinforcement learning-based chemical graph-set designer. First, we have developed hierarchical variational graph auto-encoders trained end-to-end to jointly embed gene-gene, gene-disease and disease-disease networks. Novel attentional pooling is introduced here for learning disease representations from associated genes' representations. Second, targeting diseases in learned representations, we have recast the drug-combination design problem as graph-set generation and developed a deep learning-based model with novel rewards. Specifically, besides chemical validity rewards, we have introduced novel generative adversarial award, being generalized sliced Wasserstein, for chemically diverse molecules with distributions similar to known drugs. We have also designed a network principle-based reward for disease-specific drug combinations. Numerical results indicate that, compared to state-of-the-art graph embedding methods, hierarchical variational graph auto-encoder learns more informative and generalizable disease representations. Results also show that the deep generative models generate drug combinations following the principle across diseases. Case studies on four diseases show that network-principled drug combinations tend to have low toxicity. The generated drug combinations collectively cover the disease module similar to FDA-approved drug combinations and could potentially suggest novel systems pharmacology strategies. Our method allows for examining and following network-based principle or hypothesis to efficiently generate disease-specific drug combinations in a vast chemical combinatorial space. AVAILABILITY AND IMPLEMENTATION: https://github.com/Shen-Lab/Drug-Combo-Generator. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Stationarity is a key assumption in many statistical models for random processes. With recent developments in the field of graph signal processing, the conventional notion of wide-sense stationarity has been extended to random processes defined on the vertices of graphs. It has been shown that well-known spectral graph kernel methods assume that the underlying random process over a graph is stationary. While many approaches have been proposed, both in machine learning and signal processing literature, to model stationary random processes over graphs, they are too restrictive to characterize real-world datasets as most of them are non-stationary processes. In this paper, to well-characterize a non-stationary process over graph, we propose a novel model and a computationally efficient algorithm that partitions a large graph into disjoint clusters such that the process is stationary on each of the clusters but independent across clusters. We evaluate our model for traffic prediction on a large-scale dataset of fine-grained highway travel times in the Dallas-Fort Worth area. The accuracy of our method is very close to the state-of-the-art graph based deep learning methods while the computational complexity of our model is substantially smaller.

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.

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. SIG-VAE integrates a carefully designed generative model, well suited to model real-world sparse graphs, and a sophisticated variational inference network, which propagates the graph structural information and distribution uncertainty to capture complex posteriors. SIG-VAE clearly outperforms a simple combination of VGAE with variational inference, including semi-implicit variational inference~(SIVI) or normalizing flow (NF), which does not propagate uncertainty in its inference network, and provides more interpretable latent representations than VGAE does. 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.