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. IntroductionDeep auto-regressive models, such as recurrent neural networks (RNNs), are widely used for modeling sequential data due to their effective representation of long-term dependencies [1, 2, 3, 4, ?, 5, 6]. It has been shown that inducing uncertainty in hidden states of deep auto-regressive models could drastically improve their performance in many applications such as speech modeling, text generation, sequential image modeling and dynamic graph representation learning [7,8,9,10,11,12,13,14,15]. These methods integrate the variational auto-encoder (VAE) framework with deep auto-regressive models to infer stochastic latent variables, which can capture higher-level semantic abstraction (e.g. objects, speakers, or graph modules/communities) from the observed variables in a sequence (e.g. pixels, sound-waves, or partially observed dynamic graphs).Existing stochastic recurrent models, while having different encoder and decoder structures, have restricted expressive power due to the commonly adopted Gaussian assumption on prior and posterior distributions of latent variables. The Gaussian assumption has a well-known issue in underestimating the variance of the posterior [16], which can be further amplified by mean field variational inference (MFVI). This issue is often attributed to two key factors: 1) the mismatch between the restricted representation power of the variational family Q and the complexity of the posterior to be approximated by Q; 2) the use of KL divergence, which is an asymmetric measure for the distance between Q and the posterior [17,18].In this paper, we break the Gaussian assumption and propose a semi-implicit stochastic recurrent neural network (SIS-RNN) that is capable of inferring implicit posteriors for sequential data while maintaining simple optimization. Inspired by semi-implicit variational inference (SIVI) [17], we impose a semi-implicit hierarchical construction on a backbone RNN to represent the posterior distribution of stochastic recurrent layers. SIVI enables a flexible (implicit) mixing distribution for variational inference of our proposed SIS-RNN. As a result, even if the marginal of the hierarchy is not tractable, its density can be evaluated by Monte Carlo estimation. Our p...

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.

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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, anti-microbials, and anti-cancer 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 (HVGAE) 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 drug combinations. Numerical results indicate that, compared to state-of-the-art graph embedding methods, HVGAE 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.

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