In this paper, we focus on escaping from saddle points in smooth nonconvex optimization problems subject to a convex set $\mathcal{C}$. We propose a generic framework that yields convergence to a second-order stationary point of the problem, if the convex set $\mathcal{C}$ is simple for a quadratic objective function. To be more precise, our results hold if one can find a $\rho$-approximate solution of a quadratic program subject to $\mathcal{C}$ in polynomial time, where $\rho<1$ is a positive constant that depends on the structure of the set $\mathcal{C}$. Under this condition, we show that the sequence of iterates generated by the proposed framework reaches an $(\epsilon,\gamma)$-second order stationary point (SOSP) in at most $\mathcal{O}(\max\{\epsilon^{-2},\rho^{-3}\gamma^{-3}\})$ iterations. We further characterize the overall arithmetic operations to reach an SOSP when the convex set $\mathcal{C}$ can be written as a set of quadratic constraints. Finally, we extend our results to the stochastic setting and characterize the number of stochastic gradient and Hessian evaluations to reach an $(\epsilon,\gamma)$-SOSP.

Stochastic configuration networks (SCNs) as a class of randomized learner model have been successfully employed in data analytics due to its universal approximation capability and fast modelling property. The technical essence lies in stochastically configuring hidden nodes (or basis functions) based on a supervisory mechanism rather than data-independent randomization as usually adopted for building randomized neural networks. Given image data modelling tasks, the use of one-dimensional SCNs potentially demolishes the spatial information of images, and may result in undesirable performance. This paper extends the original SCNs to two-dimensional version, termed 2DSCNs, for fast building randomized learners with matrix-inputs. Some theoretical analyses on the goodness of 2DSCNs against SCNs, including the complexity of the random parameter space, and the superiority of generalization, are presented. Empirical results over one regression, four benchmark handwritten digits classification, and two human face recognition datasets demonstrate that the proposed 2DSCNs perform favourably and show good potential for image data analytics.

Recent work in imitation learning articulate their formulation around the GAIL architecture, relying on the adversarial training procedure introduced in GANs. Albeit successful at generating behaviours similar to those demonstrated to the agent, GAIL suffers from a high sample complexity in the number of interactions it has to carry out in the environment in order to achieve satisfactory performance. In this work, we dramatically shrink the amount of interactions with the environment by leveraging an off-policy actor-critic architecture. Additionally, employing deterministic policy gradients allows us to treat the learned reward as a differentiable node in the computational graph, while preserving the model-free nature of our approach. Our experiments span a variety of continuous control tasks.

We propose Progressive Structure-conditional Generative Adversarial Networks (PSGAN), a new framework that can generate full-body and high-resolution character images based on structural information. Recent progress in generative adversarial networks with progressive training has made it possible to generate high-resolution images. However, existing approaches have limitations in achieving both high image quality and structural consistency at the same time. Our method tackles the limitations by progressively increasing the resolution of both generated images and structural conditions during training. In this paper, we empirically demonstrate the effectiveness of this method by showing the comparison with existing approaches and video generation results of diverse anime characters at 1024x1024 based on target pose sequences. We also create a novel dataset containing full-body 1024x1024 high-resolution images and exact 2D pose keypoints using Unity 3D Avatar models.

Measuring entity relatedness is a fundamental task for many natural language processing and information retrieval applications. Prior work often studies entity relatedness in static settings and an unsupervised manner. However, entities in real-world are often involved in many different relationships, consequently entity-relations are very dynamic over time. In this work, we propose a neural networkbased approach for dynamic entity relatedness, leveraging the collective attention as supervision. Our model is capable of learning rich and different entity representations in a joint framework. Through extensive experiments on large-scale datasets, we demonstrate that our method achieves better results than competitive baselines.

Interpretability and stability are two important features that are desired in many contemporary big data applications arising in economics and finance. While the former is enjoyed to some extent by many existing forecasting approaches, the latter in the sense of controlling the fraction of wrongly discovered features which can enhance greatly the interpretability is still largely underdeveloped in the econometric settings. To this end, in this paper we exploit the general framework of model-X knockoffs introduced recently in Cand\`{e}s, Fan, Janson and Lv (2018), which is nonconventional for reproducible large-scale inference in that the framework is completely free of the use of p-values for significance testing, and suggest a new method of intertwined probabilistic factors decoupling (IPAD) for stable interpretable forecasting with knockoffs inference in high-dimensional models. The recipe of the method is constructing the knockoff variables by assuming a latent factor model that is exploited widely in economics and finance for the association structure of covariates. Our method and work are distinct from the existing literature in that we estimate the covariate distribution from data instead of assuming that it is known when constructing the knockoff variables, our procedure does not require any sample splitting, we provide theoretical justifications on the asymptotic false discovery rate control, and the theory for the power analysis is also established. Several simulation examples and the real data analysis further demonstrate that the newly suggested method has appealing finite-sample performance with desired interpretability and stability compared to some popularly used forecasting methods.

Constrained sequence codes have been widely used in modern communication and data storage systems. Sequences encoded with constrained sequence codes satisfy constraints imposed by the physical channel, hence enabling efficient and reliable transmission of coded symbols. Traditional encoding and decoding of constrained sequence codes rely on table look-up, which is prone to errors that occur during transmission. In this paper, we introduce constrained sequence decoding based on deep learning. With multiple layer perception (MLP) networks and convolutional neural networks (CNNs), we are able to achieve low bit error rates that are close to maximum a posteriori probability (MAP) decoding as well as improve the system throughput. Moreover, implementation of capacity-achieving fixed-length codes, where the complexity is prohibitively high with table look-up decoding, becomes practical with deep learning-based decoding.

Predicting keywords performance, such as number of impressions, click-through rate (CTR), conversion rate (CVR), revenue per click (RPC), and cost per click (CPC), is critical for sponsored search in the online advertising industry. An interesting phenomenon is that, despite the size of the overall data, the data are very sparse at the individual unit level. To overcome the sparsity and leverage hierarchical information across the data structure, we propose a Dynamic Hierarchical Empirical Bayesian (DHEB) model that dynamically determines the hierarchy through a data-driven process and provides shrinkage-based estimations. Our method is also equipped with an efficient empirical approach to derive inferences through the hierarchy. We evaluate the proposed method in both simulated and real-world datasets and compare to several competitive models. The results favor the proposed method among all comparisons in terms of both accuracy and efficiency. In the end, we design a two-phase system to serve prediction in real time.

We propose an adaptive sampling approach for multiple testing which aims to maximize statistical power while ensuring anytime false discovery control. We consider $n$ distributions whose means are partitioned by whether they are below or equal to a baseline (nulls), versus above the baseline (actual positives). In addition, each distribution can be sequentially and repeatedly sampled. Inspired by the multi-armed bandit literature, we provide an algorithm that takes as few samples as possible to exceed a target true positive proportion (i.e. proportion of actual positives discovered) while giving anytime control of the false discovery proportion (nulls predicted as actual positives). Our sample complexity results match known information theoretic lower bounds and through simulations we show a substantial performance improvement over uniform sampling and an adaptive elimination style algorithm. Given the simplicity of the approach, and its sample efficiency, the method has promise for wide adoption in the biological sciences, clinical testing for drug discovery, and online A/B/n testing problems.

This note is a response to [7] in which it is claimed that [13, Proposition 11] is false. We demonstrate here that this assertion in [7] is false, and is based on a misreading of the notion of set membership in [13, Proposition 11]. We maintain that [13, Proposition 11] is true. Based on the empirical risk principle, one should minimize at training time the loss that one wishes to evaluate at test time [10]. In [12, 13], we have studied the construction of surrogates for loss functions that are submodular with respect to the set of mispredictions.