We consider maximum likelihood estimation of linear dynamical systems with generalized-linear observation models. Maximum likelihood is typically considered to be hard in this setting since latent states and transition parameters must be inferred jointly. Given that expectation-maximization does not scale and is prone to local minima, moment-matching approaches from the subspace identification literature have become standard, despite known statistical efficiency issues. In this paper, we instead reconsider likelihood maximization and develop an optimization based strategy for recovering the latent states and transition parameters. Key to the approach is a two-view reformulation of maximum likelihood estimation for linear dynamical systems that enables the use of global optimization algorithms for matrix factorization. We show that the proposed estimation strategy outperforms widely-used identification algorithms such as subspace identification methods, both in terms of accuracy and runtime.

Optical Character Recognition (OCR) aims to recognize text in natural images. Inspired by a recently proposed model for general image classification, Recurrent Convolution Neural Network (RCNN), we propose a new architecture named Gated RCNN (GRCNN) for solving this problem. Its critical component, Gated Recurrent Convolution Layer (GRCL), is constructed by adding a gate to the Recurrent Convolution Layer (RCL), the critical component of RCNN. The gate controls the context modulation in RCL and balances the feed-forward information and the recurrent information. In addition, an efficient Bidirectional Long Short-Term Memory (BLSTM) is built for sequence modeling. The GRCNN is combined with BLSTM to recognize text in natural images. The entire GRCNN-BLSTM model can be trained end-to-end. Experiments show that the proposed model outperforms existing methods on several benchmark datasets including the IIIT-5K, Street View Text (SVT) and ICDAR.

In this paper, we propose a spatial propagation networks for learning affinity matrix. We show that by constructing a row/column linear propagation model, the spatially variant transformation matrix constitutes an affinity matrix that models dense, global pairwise similarities of an image. Specifically, we develop a three-way connection for the linear propagation model, which (a) formulates a sparse transformation matrix where all elements can be the output from a deep CNN, but (b) results in a dense affinity matrix that is effective to model any task-specific pairwise similarity.

In many machine learning applications, it is important to explain the predictions of a black-box classifier. For example, why does a deep neural network assign an image to a particular class? We cast interpretability of black-box classifiers as a combinatorial maximization problem and propose an efficient streaming algorithm to solve it subject to cardinality constraints. By extending ideas from Badanidiyuru et al. [2014], we provide a constant factor approximation guarantee for our algorithm in the case of random stream order and a weakly submodular objective function. This is the first such theoretical guarantee for this general class of functions, and we also show that no such algorithm exists for a worst case stream order.

In sequential decision making, it is often important and useful for end users to understand the underlying patterns or causes that lead to the corresponding decisions. However, typical deep reinforcement learning algorithms seldom provide such information due to their black-box nature. In this paper, we present a probabilistic model, Q-LDA, to uncover latent patterns in text-based sequential decision processes. The model can be understood as a variant of latent topic models that are tailored to maximize total rewards; we further draw an interesting connection between an approximate maximum-likelihood estimation of Q-LDA and the celebrated Q-learning algorithm. We demonstrate in the text-game domain that our proposed method not only provides a viable mechanism to uncover latent patterns in decision processes, but also obtains state-of-the-art rewards in these games.

We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the Johnson-Lindenstrauss transform and the angular kernel, we show that we can select matrices yielding guaranteed improved performance in accuracy and/or speed compared to earlier methods. We introduce matrices with complex entries which give significant further accuracy improvement. We provide geometric and Markov chain-based perspectives to help understand the benefits, and empirical results which suggest that the approach is helpful in a wider range of applications.

We show that accelerated optimization methods can be seen as particular instances of multi-step integration schemes from numerical analysis, applied to the gradient flow equation. Compared with recent advances in this vein, the differential equation considered here is the basic gradient flow, and we derive a class of multi-step schemes which includes accelerated algorithms, using classical conditions from numerical analysis. Multi-step schemes integrate the differential equation using larger step sizes, which intuitively explains the acceleration phenomenon.

Remarkable recent success of deep neural networks has not been easy to analyze theoretically. It has been particularly hard to disentangle relative significance of architecture and optimization in achieving accurate classification on large datasets. On the flip side, shallow methods (such as kernel methods) have encountered obstacles in scaling to large data, despite excellent performance on smaller datasets, and extensive theoretical analysis. Practical methods, such as variants of gradient descent used so successfully in deep learning, seem to perform below par when applied to kernel methods. This difficulty has sometimes been attributed to the limitations of shallow architecture. In this paper we identify a basic limitation in gradient descent-based optimization methods when used in conjunctions with smooth kernels.

Generative adversarial networks (GANs) have great successes on synthesizing data. However, the existing GANs restrict the discriminator to be a binary classifier, and thus limit their learning capacity for tasks that need to synthesize output with rich structures such as natural language descriptions. In this paper, we propose a novel generative adversarial network, RankGAN, for generating high-quality language descriptions. Rather than training the discriminator to learn and assign absolute binary predicate for individual data sample, the proposed RankGAN is able to analyze and rank a collection of human-written and machine-written sentences by giving a reference group. By viewing a set of data samples collectively and evaluating their quality through relative ranking scores, the discriminator is able to make better assessment which in turn helps to learn a better generator. The proposed RankGAN is optimized through the policy gradient technique. Experimental results on multiple public datasets clearly demonstrate the effectiveness of the proposed approach.

Linear regression models have been successfully used to function estimation and model selection in high-dimensional data analysis. However, most existing methods are built on least squares with the mean square error (MSE) criterion, which are sensitive to outliers and their performance may be degraded for heavy-tailed noise. In this paper, we go beyond this criterion by investigating the regularized modal regression from a statistical learning viewpoint. A new regularized modal regression model is proposed for estimation and variable selection, which is robust to outliers, heavy-tailed noise, and skewed noise. On the theoretical side, we establish the approximation estimate for learning the conditional mode function, the sparsity analysis for variable selection, and the robustness characterization. On the application side, we applied our model to successfully improve the cognitive impairment prediction using the Alzheimer's Disease Neuroimaging Initiative (ADNI) cohort data.