Recent research about margin theory has proved that maximizing the minimum margin like support vector machines does not necessarily lead to better performance, and instead, it is crucial to optimize the margin distribution. In the meantime, margin theory has been used to explain the empirical success of deep network in recent studies. In this paper, we present mdNet (the Optimal Margin Distribution Network), a network which embeds a loss function in regard to the optimal margin distribution. We give a theoretical analysis of our method using the PAC-Bayesian framework, which confirms the significance of the margin distribution for classification within the framework of deep networks. In addition, empirical results show that the mdNet model always outperforms the baseline cross-entropy loss model consistently across different regularization situations. And our mdNet model also outperforms the cross-entropy loss (Xent), hinge loss and soft hinge loss model in generalization task through limited training data.

Designing and modifying complex hull forms for optimal vessel performances have been a major challenge for naval architects. In the present study, Principal Component Analysis (PCA) is introduced to compress the geometric representation of a group of existing vessels, and the resulting principal scores are manipulated to generate a large number of derived hull forms, which are evaluated computationally for their calm-water performances. The results are subsequently used to train a Deep Neural Network (DNN) to accurately establish the relation between different hull forms and their associated performances. Then, based on the fast, parallel DNN-based hull-form evaluation, the large-scale search for optimal hull forms is performed.

Dynamic treatment recommendation systems based on large-scale electronic health records (EHRs) become a key to successfully improve practical clinical outcomes. Prior relevant studies recommend treatments either use supervised learning (e.g. matching the indicator signal which denotes doctor prescriptions), or reinforcement learning (e.g. maximizing evaluation signal which indicates cumulative reward from survival rates). However, none of these studies have considered to combine the benefits of supervised learning and reinforcement learning. In this paper, we propose Supervised Reinforcement Learning with Recurrent Neural Network (SRL-RNN), which fuses them into a synergistic learning framework. Specifically, SRL-RNN applies an off-policy actor-critic framework to handle complex relations among multiple medications, diseases and individual characteristics. The "actor" in the framework is adjusted by both the indicator signal and evaluation signal to ensure effective prescription and low mortality. RNN is further utilized to solve the Partially-Observed Markov Decision Process (POMDP) problem due to the lack of fully observed states in real world applications. Experiments on the publicly real-world dataset, i.e., MIMIC-3, illustrate that our model can reduce the estimated mortality, while providing promising accuracy in matching doctors' prescriptions.

Matrix concentration inequalities have attracted much attention in diverse applications such as linear algebra, statistical estimation, combinatorial optimization, etc. In this paper, we present new Bernstein concentration inequalities depending only on the first moments of random matrices, whereas previous Bernstein inequalities are heavily relevant to the first and second moments. Based on those results, we analyze the empirical risk minimization in the presence of label noise. We find that many popular losses used in risk minimization can be decomposed into two parts, where the first part won't be affected and only the second part will be affected by noisy labels. We show that the influence of noisy labels on the second part can be reduced by our proposed LICS (Labeled Instance Centroid Smoothing) approach. The effectiveness of the LICS algorithm is justified both theoretically and empirically.