Coupled norms have emerged as a convex method to solve coupled tensor completion. A limitation with coupled norms is that they only induce low-rankness using the multilinear rank of coupled tensors. In this paper, we introduce a new set of coupled norms known as coupled nuclear norms by constraining the CP rank of coupled tensors. We propose new coupled completion models using the coupled nuclear norms as regularizers, which can be optimized using computationally efficient optimization methods. We derive excess risk bounds for proposed coupled completion models and show that proposed norms lead to better performance. Through simulation and real-data experiments, we demonstrate that proposed norms achieve better performance for coupled completion compared to existing coupled norms.

In this paper, we study the generalization performance of multi-class classification and obtain a shaper data-dependent generalization error bound with fast convergence rate, substantially improving the state-of-art bounds in the existing data-dependent generalization analysis. The theoretical analysis motivates us to devise two effective multi-class kernel learning algorithms with statistical guarantees. Experimental results show that our proposed methods can significantly outperform the existing multi-class classification methods.

We present Memory Augmented Policy Optimization (MAPO), a simple and novel way to leverage a memory buffer of promising trajectories to reduce the variance of policy gradient estimate. MAPO is applicable to deterministic environments with discrete actions, such as structured prediction and combinatorial optimization tasks. We express the expected return objective as a weighted sum of two terms: an expectation over the high-reward trajectories inside the memory buffer, and a separate expectation over trajectories outside the buffer. To make an efficient algorithm of MAPO, we propose: (1) memory weight clipping to accelerate and stabilize training; (2) systematic exploration to discover high-reward trajectories; (3) distributed sampling from inside and outside of the memory buffer to scale up training. MAPO improves the sample efficiency and robustness of policy gradient, especially on tasks with sparse rewards. We evaluate MAPO on weakly supervised program synthesis from natural language (semantic parsing). On the WikiTableQuestions benchmark, we improve the state-of-the-art by 2.6%, achieving an accuracy of 46.3%. On the WikiSQL benchmark, MAPO achieves an accuracy of 74.9% with only weak supervision, outperforming several strong baselines with full supervision. Our source code is available at https://goo.gl/TXBp4e

Recent attempts to achieve fairness in predictive models focus on the balance between fairness and accuracy. In sensitive applications such as healthcare or criminal justice, this trade-off is often undesirable as any increase in prediction error could have devastating consequences. In this work, we argue that the fairness of predictions should be evaluated in context of the data, and that unfairness induced by inadequate samples sizes or unmeasured predictive variables should be addressed through data collection, rather than by constraining the model. We decompose cost-based metrics of discrimination into bias, variance, and noise, and propose actions aimed at estimating and reducing each term. Finally, we perform case-studies on prediction of income, mortality, and review ratings, confirming the value of this analysis. We find that data collection is often a means to reduce discrimination without sacrificing accuracy.

Machine Comprehension (MC) is one of the core problems in natural language processing, requiring both understanding of the natural language and knowledge about the world. Rapid progress has been made since the release of several benchmark datasets, and recently the state-of-the-art models even surpass human performance on the well-known SQuAD evaluation. In this paper, we transfer knowledge learned from machine comprehension to the sequence-to-sequence tasks to deepen the understanding of the text. We propose MacNet: a novel encoder-decoder supplementary architecture to the widely used attention-based sequence-to-sequence models. Experiments on neural machine translation (NMT) and abstractive text summarization show that our proposed framework can significantly improve the performance of the baseline models, and our method for the abstractive text summarization achieves the state-of-the-art results on the Gigaword dataset.

We consider the semi-supervised clustering problem where crowdsourcing provides noisy information about the pairwise comparisons on a small subset of data, i.e., whether a sample pair is in the same cluster. We propose a new approach that includes a deep generative model (DGM) to characterize low-level features of the data, and a statistical relational model for noisy pairwise annotations on its subset. The two parts share the latent variables. To make the model automatically trade-off between its complexity and fitting data, we also develop its fully Bayesian variant. The challenge of inference is addressed by fast (natural-gradient) stochastic variational inference algorithms, where we effectively combine variational message passing for the relational part and amortized learning of the DGM under a unified framework. Empirical results on synthetic and real-world datasets show that our model outperforms previous crowdsourced clustering methods.

Neyshabur and Srebro proposed SIMPLE-LSH, which is the state-of-the-art hashing based algorithm for maximum inner product search (MIPS). We found that the performance of SIMPLE-LSH, in both theory and practice, suffers from long tails in the 2-norm distribution of real datasets. We propose NORM-RANGING LSH, which addresses the excessive normalization problem caused by long tails by partitioning a dataset into sub-datasets and building a hash index for each sub-dataset independently. We prove that NORM-RANGING LSH achieves lower query time complexity than SIMPLE-LSH under mild conditions. We also show that the idea of dataset partitioning can improve another hashing based MIPS algorithm. Experiments show that NORM-RANGING LSH probes much less items than SIMPLE-LSH at the same recall, thus significantly benefiting MIPS based applications.

Learning to classify new categories based on just one or a few examples is a long-standing challenge in modern computer vision. In this work, we propose a simple yet effective method for few-shot (and one-shot) object recognition. Our approach is based on a modified auto-encoder, denoted delta-encoder, that learns to synthesize new samples for an unseen category just by seeing few examples from it. The synthesized samples are then used to train a classifier. The proposed approach learns to both extract transferable intra-class deformations, or "deltas", between same-class pairs of training examples, and to apply those deltas to the few provided examples of a novel class (unseen during training) in order to efficiently synthesize samples from that new class. The proposed method improves the state-of-the-art of one-shot object-recognition and performs comparably in the few-shot case.

Visual attention, derived from cognitive neuroscience, facilitates human perception on the most pertinent subset of the sensory data. Recently, significant efforts have been made to exploit attention schemes to advance computer vision systems. For visual tracking, it is often challenging to track target objects undergoing large appearance changes. Attention maps facilitate visual tracking by selectively paying attention to temporal robust features. Existing tracking-by-detection approaches mainly use additional attention modules to generate feature weights as the classifiers are not equipped with such mechanisms. In this paper, we propose a reciprocative learning algorithm to exploit visual attention for training deep classifiers. The proposed algorithm consists of feed-forward and backward operations to generate attention maps, which serve as regularization terms coupled with the original classification loss function for training. The deep classifier learns to attend to the regions of target objects robust to appearance changes. Extensive experiments on large-scale benchmark datasets show that the proposed attentive tracking method performs favorably against the state-of-the-art approaches.

The state-of-the-art methods for solving optimization problems in big dimensions are variants of randomized coordinate descent (RCD). In this paper we introduce a fundamentally new type of acceleration strategy for RCD based on the augmentation of the set of coordinate directions by a few spectral or conjugate directions. As we increase the number of extra directions to be sampled from, the rate of the method improves, and interpolates between the linear rate of RCD and a linear rate independent of the condition number. We develop and analyze also inexact variants of these methods where the spectral and conjugate directions are allowed to be approximate only. We motivate the above development by proving several negative results which highlight the limitations of RCD with importance sampling.