In compressed sensing, a small number of linear measurements can be used to reconstruct an unknown signal. Existing approaches leverage assumptions on the structure of these signals, such as sparsity or the availability of a generative model. A domain-specific generative model can provide a stronger prior and thus allow for recovery with far fewer measurements. However, unlike sparsity-based approaches, existing methods based on generative models guarantee exact recovery only over their support, which is typically only a small subset of the space on which the signals are defined. We propose Sparse-Gen, a framework that allows for sparse deviations from the support set, thereby achieving the best of both worlds by using a domain specific prior and allowing reconstruction over the full space of signals. Theoretically, our framework provides a new class of signals that can be acquired using compressed sensing, reducing classic sparse vector recovery to a special case and avoiding the restrictive support due to a generative model prior. Empirically, we observe consistent improvements in reconstruction accuracy over competing approaches, especially in the more practical setting of transfer compressed sensing where a generative model for a data-rich, source domain aids sensing on a data-scarce, target domain.

Deep generative models have recently yielded encouraging results in producing subjectively realistic samples of complex data. Far less attention has been paid to making these generative models interpretable. In many scenarios, ranging from scientific applications to finance, the observed variables have a natural grouping. It is often of interest to understand systems of interaction amongst these groups, and latent factor models (LFMs) are an attractive approach. However, traditional LFMs are limited by assuming a linear correlation structure. We present an output interpretable VAE (oi-VAE) for grouped data that models complex, nonlinear latent-to-observed relationships. We combine a structured VAE comprised of group-specific generators with a sparsity-inducing prior. We demonstrate that oi-VAE yields meaningful notions of interpretability in the analysis of motion capture and MEG data. We further show that in these situations, the regularization inherent to oi-VAE can actually lead to improved generalization and learned generative processes.

Recurrent neural networks (RNNs) are powerful models of sequential data. They have been successfully used in domains such as text and speech. However, RNNs are susceptible to overfitting; regularization is important. In this paper we develop Noisin, a new method for regularizing RNNs. Noisin injects random noise into the hidden states of the RNN and then maximizes the corresponding marginal likelihood of the data. We show how Noisin applies to any RNN and we study many different types of noise. Noisin is unbiased--it preserves the underlying RNN on average. We characterize how Noisin regularizes its RNN both theoretically and empirically. On language modeling benchmarks, Noisin improves over dropout by as much as 12.2% on the Penn Treebank and 9.4% on the Wikitext-2 dataset. We also compared the state-of-the-art language model of Yang et al. 2017, both with and without Noisin. On the Penn Treebank, the method with Noisin more quickly reaches state-of-the-art performance.

Multi-Rate Multivariate Time Series (MR-MTS) are the multivariate time series observations which come with various sampling rates and encode multiple temporal dependencies. State-space models such as Kalman filters and deep learning models such as deep Markov models are mainly designed for time series data with the same sampling rate and cannot capture all the dependencies present in the MR-MTS data. To address this challenge, we propose the Multi-Rate Hierarchical Deep Markov Model (MR-HDMM), a novel deep generative model which uses the latent hierarchical structure with a learnable switch mechanism to capture the temporal dependencies of MR-MTS. Experimental results on two real-world datasets demonstrate that our MR-HDMM model outperforms the existing state-of-the-art deep learning and state-space models on forecasting and interpolation tasks. In addition, the latent hierarchies in our model provide a way to show and interpret the multiple temporal dependencies.

One important task of topic modeling for text analysis is interpretability. By discovering structured topics one is able to yield improved interpretability as well as modeling accuracy. In this paper, we propose a novel topic model with a deep structure that explores both inter-topic and intra-topic structures informed by word embeddings. Specifically, our model discovers inter topic structures in the form of topic hierarchies and discovers intra topic structures in the form of sub-topics, each of which is informed by word embeddings and captures a fine-grained thematic aspect of a normal topic. Extensive experiments demonstrate that our model achieves the state-of-the-art performance in terms of perplexity, document classification, and topic quality. Moreover, with topic hierarchies and sub-topics, the topics discovered in our model are more interpretable, providing an illuminating means to understand text data.