Recurrent neural networks (RNNs) have achieved state-of-the-art performances in many natural language processing tasks, such as language modeling and machine translation. However, when the vocabulary is large, the RNN model will become very big (e.g., possibly beyond the memory capacity of a GPU device) and its training will become very inefficient. In this work, we propose a novel technique to tackle this challenge. The key idea is to use 2-Component (2C) shared embedding for word representations. We allocate every word in the vocabulary into a table, each row of which is associated with a vector, and each column associated with another vector. Depending on its position in the table, a word is jointly represented by two components: a row vector and a column vector. Since the words in the same row share the row vector and the words in the same column share the column vector, we only need $2 \sqrt{|V|}$ vectors to represent a vocabulary of $|V|$ unique words, which are far less than the $|V|$ vectors required by existing approaches. Based on the 2-Component shared embedding, we design a new RNN algorithm and evaluate it using the language modeling task on several benchmark datasets. The results show that our algorithm significantly reduces the model size and speeds up the training process, without sacrifice of accuracy (it achieves similar, if not better, perplexity as compared to state-of-the-art language models). Remarkably, on the One-Billion-Word benchmark Dataset, our algorithm achieves comparable perplexity to previous language models, whilst reducing the model size by a factor of 40-100, and speeding up the training process by a factor of 2. We name our proposed algorithm \emph{LightRNN} to reflect its very small model size and very high training speed.

Person Re-Identification is the task of matching images of a person across multiple camera views. Almost all prior approaches address this challenge by attempting to learn the possible transformations that relate the different views of a person from a training corpora. Then, they utilize these transformation patterns for matching a query image to those in a gallery image bank at test time. This necessitates learning good feature representations of the images and having a robust feature matching technique. Deep learning approaches, such as Convolutional Neural Networks (CNN), simultaneously do both and have shown great promise recently. In this work, we propose two CNN-based architectures for Person Re-Identification. In the first, given a pair of images, we extract feature maps from these images via multiple stages of convolution and pooling. A novel inexact matching technique then matches pixels in the first representation with those of the second. Furthermore, we search across a wider region in the second representation for matching. Our novel matching technique allows us to tackle the challenges posed by large viewpoint variations, illumination changes or partial occlusions. Our approach shows a promising performance and requires only about half the parameters as a current state-of-the-art technique. Nonetheless, it also suffers from false matches at times. In order to mitigate this issue, we propose a fused architecture that combines our inexact matching pipeline with a state-of-the-art exact matching technique. We observe substantial gains with the fused model over the current state-of-the-art on multiple challenging datasets of varying sizes, with gains of up to about 21%.

We propose two stochastic gradient MCMC methods for sampling from Bayesian posterior distributions defined on Riemann manifolds with a known geodesic flow, e.g. hyperspheres. Our methods are the first scalable sampling methods on these manifolds, with the aid of stochastic gradients. Novel dynamics are conceived and 2nd-order integrators are developed. By adopting embedding techniques and the geodesic integrator, the methods do not require a global coordinate system of the manifold and do not involve inner iterations. Synthetic experiments show the validity of the method, and its application to the challenging inference for spherical topic models indicate practical usability and efficiency.

An iterative regularization path with structural sparsity is proposed in this paper based on variable splitting and the Linearized Bregman Iteration, hence called \emph{Split LBI}. Despite its simplicity, Split LBI outperforms the popular generalized Lasso in both theory and experiments. A theory of path consistency is presented that equipped with a proper early stopping, Split LBI may achieve model selection consistency under a family of Irrepresentable Conditions which can be weaker than the necessary and sufficient condition for generalized Lasso. Furthermore, some $\ell_2$ error bounds are also given at the minimax optimal rates. The utility and benefit of the algorithm are illustrated by applications on both traditional image denoising and a novel example on partial order ranking.

The Teacher Forcing algorithm trains recurrent networks by supplying observed sequence values as inputs during training and using the network’s own one-step-ahead predictions to do multi-step sampling. We introduce the Professor Forcing algorithm, which uses adversarial domain adaptation to encourage the dynamics of the recurrent network to be the same when training the network and when sampling from the network over multiple time steps. We apply Professor Forcing to language modeling, vocal synthesis on raw waveforms, handwriting generation, and image generation. Empirically we find that Professor Forcing acts as a regularizer, improving test likelihood on character level Penn Treebank and sequential MNIST. We also find that the model qualitatively improves samples, especially when sampling for a large number of time steps. This is supported by human evaluation of sample quality. Trade-offs between Professor Forcing and Scheduled Sampling are discussed. We produce T-SNEs showing that Professor Forcing successfully makes the dynamics of the network during training and sampling more similar.

We consider the assortment optimization problem when customer preferences follow a mixture of Mallows distributions. The assortment optimization problem focuses on determining the revenue/profit maximizing subset of products from a large universe of products; it is an important decision that is commonly faced by retailers in determining what to offer their customers. There are two key challenges: (a) the Mallows distribution lacks a closed-form expression (and requires summing an exponential number of terms) to compute the choice probability and, hence, the expected revenue/profit per customer; and (b) finding the best subset may require an exhaustive search. Our key contributions are an efficiently computable closed-form expression for the choice probability under the Mallows model and a compact mixed integer linear program (MIP) formulation for the assortment problem.

We give a novel formal theoretical framework for unsupervised learning with two distinctive characteristics. First, it does not assume any generative model and based on a worst-case performance metric. Second, it is comparative, namely performance is measured with respect to a given hypothesis class. This allows to avoid known computational hardness results and improper algorithms based on convex relaxations. We show how several families of unsupervised learning models, which were previously only analyzed under probabilistic assumptions and are otherwise provably intractable, can be efficiently learned in our framework by convex optimization.

Deep convolutional neural networks (CNN) have achieved great success. On the other hand, modeling structural information has been proved critical in many vision problems. It is of great interest to integrate them effectively. In a classical neural network, there is no message passing between neurons in the same layer. In this paper, we propose a CRF-CNN framework which can simultaneously model structural information in both output and hidden feature layers in a probabilistic way, and it is applied to human pose estimation. A message passing scheme is proposed, so that in various layers each body joint receives messages from all the others in an efficient way. Such message passing can be implemented with convolution between features maps in the same layer, and it is also integrated with feedforward propagation in neural networks. Finally, a neural network implementation of end-to-end learning CRF-CNN is provided. Its effectiveness is demonstrated through experiments on two benchmark datasets.

In this paper we present a practical solution with performance guarantees to the problem of dimensionality reduction for very large scale sparse matrices. We show applications of our approach to computing the Principle Component Analysis (PCA) of any $n\times d$ matrix, using one pass over the stream of its rows. Our solution uses coresets: a scaled subset of the $n$ rows that approximates their sum of squared distances to \emph{every} $k$-dimensional \emph{affine} subspace. An open theoretical problem has been to compute such a coreset that is independent of both $n$ and $d$. An open practical problem has been to compute a non-trivial approximation to the PCA of very large but sparse databases such as the Wikipedia document-term matrix in a reasonable time. We answer both of these questions affirmatively. Our main technical result is a new framework for deterministic coreset constructions based on a reduction to the problem of counting items in a stream.

For testing two vector random variables for independence, we propose testing whether the distance of one vector from an arbitrary center point is independent from the distance of the other vector from another arbitrary center point by a univariate test. We prove that under minimal assumptions, it is enough to have a consistent univariate independence test on the distances, to guarantee that the power to detect dependence between the random vectors increases to one with sample size. If the univariate test is distribution-free, the multivariate test will also be distribution-free. If we consider multiple center points and aggregate the center-specific univariate tests, the power may be further improved, and the resulting multivariate test may have a distribution-free critical value for specific aggregation methods (if the univariate test is distribution free). We show that certain multivariate tests recently proposed in the literature can be viewed as instances of this general approach. Moreover, we show in experiments that novel tests constructed using our approach can have better power and computational time than competing approaches.