Recent advancements in field of Artificial Intelligence, especially in the field of Deep Learning (DL), have paved way for new and improved solutions to complex problems occurring in almost all domains. Often we have some prior knowledge and beliefs of the underlying system of the problem at-hand which we want to capture in the corresponding deep learning architectures. Sometimes, it is not clear on how to include our prior beliefs into the traditionally recommended deep architectures like Recurrent neural networks, Convolutional neural networks, Variational Autoencoders and others. Often the post-hoc techniques of modifying these architectures are not straightforward and provide little performance gain. There have been efforts on developing domain specific architectures but those techniques are generally not transferable to other domains. We ask the question that can we come up with generic and intuitive techniques to design deep learning architectures that takes our prior knowledge of the system as an inductive bias? In this dissertation, we develop two novel approaches towards this end. The first one called `Cooperative Neural Networks' can incorporate the inductive bias from the underlying probabilistic graphical model representation of the domain. The second one called problem dependent `Unrolled Algorithms' parameterizes the recurrent structure of unrolling the iterations of an optimization algorithm for the objective function defining the problem. We found that the neural network architectures obtained from our approaches typically end up with very fewer learnable parameters and provide considerable improvement in run-time compared to other deep learning methods. We have successfully applied our techniques to solve Natural Language processing related tasks, doing sparse graph recovery and computational biology problems like doing gene regulatory network inference. Firstly, we introduce the Cooperative Neural Networks approach which is a new theoretical approach for implementing learning systems that can exploit both prior insights about the independence structure of the problem domain and the universal approximation capability of the deep neural networks. Specifically, we develop CoNN-sLDA model for the document classification task. We use the popular Latent Dirichlet Allocation graphical model as the inductive bias for the CoNN-sLDA model. We demonstrate a 23% reduction in error on the challenging MultiSent data set compared to state-of-the-art and also derived ways to make the learned representations more interpretable. Secondly, we elucidate the idea of using problem dependent `Unrolled Algorithms' for the sparse graph recovery task. We propose a deep learning architecture, GLAD, which uses an Alternating Minimization algorithm as our model inductive bias and learns the model parameters via supervised learning. We show that GLAD learns a very compact and effective model for recovering sparse graphs from data. We do an extensive theoretical analysis that strengthen our claims for using similar approaches for other problems as well. Finally, we further build up on the proposed `Unrolled Algorithm' technique for a challenging real world computational biology problem. To this end, we design GRNUlar, a novel deep learning framework for supervised learning of gene regulatory networks (GRNs) from single cell RNA-Sequencing data. Our framework incorporates two intertwined models. We first leverage the expressive ability of neural networks to capture complex dependencies between transcription factors and the corresponding genes they regulate, by developing a multi-task learning framework. Then, in order to capture sparsity of GRNs observed in the real world, we design an unrolled algorithm technique for our framework. Our deep architecture requires supervision for training, for which we repurpose existing synthetic data simulators that generate scRNA-Seq data guided by an underlying GRN. Experimental results demonstrate GRNUlar outperforms state-of-the-art methods on both synthetic and real datasets. Our work also demonstrates the novel and successful use of expression data simulators for supervised learning of GRN inference.
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