The problem of adversarial examples has highlighted the need for a theory of regularisation that is general enough to apply to exotic function classes, such as universal approximators. In response, we give a very general equality result regarding the relationship between distributional robustness and regularisation, as defined with a transportation cost uncertainty set. The theory allows us to (tightly) certify the robustness properties of a Lipschitz-regularised model with very mild assumptions. As a theoretical application we show a new result explicating the connection between adversarial learning and distributional robustness. We then give new results for how to achieve Lipschitz regularisation of kernel classifiers, which are demonstrated experimentally.

Despite their success, kernel methods suffer from a massive computational cost in practice. In this paper, in lieu of commonly used kernel expansion with respect to $N$ inputs, we develop a novel optimal design maximizing the entropy among kernel features. This procedure results in a kernel expansion with respect to entropic optimal features (EOF), improving the data representation dramatically due to features dissimilarity. Under mild technical assumptions, our generalization bound shows that with only $O(N^{\frac{1}{4}})$ features (disregarding logarithmic factors), we can achieve the optimal statistical accuracy (i.e., $O(1/\sqrt{N})$). The salient feature of our design is its sparsity that significantly reduces the time and space cost. Our numerical experiments on benchmark datasets verify the superiority of EOF over the state-of-the-art in kernel approximation.

In this work, we develop a principled theoretical framework for understanding the stability of various types of GANs. In particular, we derive conditions that guarantee eventual stationarity of the generator when it is trained with gradient descent, conditions that must be satisfied by the divergence that is minimized by the GAN and the generator's architecture. We find that existing GAN variants satisfy some, but not all, of these conditions. Using tools from convex analysis, optimal transport, and reproducing kernels, we construct a GAN that fulfills these conditions simultaneously. In the process, we explain and clarify the need for various existing GAN stabilization techniques, including Lipschitz constraints, gradient penalties, and smooth activation functions.

Relationships in online social networks often imply social connections in the real world. An accurate understanding of relationship types benefits many applications, e.g. social advertising and recommendation. Some recent attempts have been proposed to classify user relationships into predefined types with the help of pre-labeled relationships or abundant interaction features on relationships. Unfortunately, both relationship feature data and label data are very sparse in real social platforms like WeChat, rendering existing methods inapplicable. In this paper, we present an in-depth analysis of WeChat relationships to identify the major challenges for the relationship classification task. To tackle the challenges, we propose a Local Community-based Edge Classification (LoCEC) framework that classifies user relationships in a social network into real-world social connection types. LoCEC enforces a three-phase processing, namely local community detection, community classification and relationship classification, to address the sparsity issue of relationship features and relationship labels. Moreover, LoCEC is designed to handle large-scale networks by allowing parallel and distributed processing. We conduct extensive experiments on the real-world WeChat network with hundreds of billions of edges to validate the effectiveness and efficiency of LoCEC.

Majority of the modern meta-learning methods for few-shot classification tasks operate in two phases: a meta-training phase where the meta-learner learns a generic representation by solving multiple few-shot tasks sampled from a large dataset and a testing phase, where the meta-learner leverages its learnt internal representation for a specific few-shot task involving classes which were not seen during the meta-training phase. To the best of our knowledge, all such meta-learning methods use a single base dataset for meta-training to sample tasks from and do not adapt the algorithm after meta-training. This strategy may not scale to real-world use-cases where the meta-learner does not potentially have access to the full meta-training dataset from the very beginning and we need to update the meta-learner in an incremental fashion when additional training data becomes available. Through our experimental setup, we develop a notion of incremental learning during the meta-training phase of meta-learning and propose a method which can be used with multiple existing metric-based meta-learning algorithms. Experimental results on benchmark dataset show that our approach performs favorably at test time as compared to training a model with the full meta-training set and incurs negligible amount of catastrophic forgetting

Federated learning is gaining significant interests as it enables model training over a large volume of data that is distributedly stored over many users, while protecting the privacy of the individual users. However, a major bottleneck in scaling federated learning to a large number of users is the overhead of secure model aggregation across many users. In fact, the overhead of state-of-the-art protocols for secure model aggregation grows quadratically with the number of users. We propose a new scheme, named Turbo-Aggregate, that in a network with $N$ users achieves a secure aggregation overhead of $O(N\log{N})$, as opposed to $O(N^2)$, while tolerating up to a user dropout rate of $50\%$. Turbo-Aggregate employs a multi-group circular strategy for efficient model aggregation, and leverages additive secret sharing and novel coding techniques for injecting aggregation redundancy in order to handle user dropouts while guaranteeing user privacy. We experimentally demonstrate that Turbo-Aggregate achieves a total running time that grows almost linear in the number of users, and provides up to $14\times$ speedup over the state-of-the-art schemes with upto $N=200$ users. We also experimentally evaluate the impact of several key network parameters (e.g., user dropout rate, bandwidth, and model size) on the performance of Turbo-Aggregate.

Recurrent and convolutional neural networks are the most common architectures used for time series forecasting in deep learning literature. These networks use parameter sharing by repeating a set of fixed architectures with fixed parameters over time or space. The result is that the overall architecture is time-invariant (shift-invariant in the spatial domain) or stationary. We argue that time-invariance can reduce the capacity to perform multi-step-ahead forecasting, where modelling the dynamics at a range of scales and resolutions is required. We propose ForecastNet which uses a deep feed-forward architecture to provide a time-variant model. An additional novelty of ForecastNet is interleaved outputs, which we show assist in mitigating vanishing gradients. ForecastNet is demonstrated to outperform statistical and deep learning benchmark models on several datasets.

We study the information content of nuclear masses from the perspective of global models of nuclear binding energies. To this end, we employ a number of statistical methods and diagnostic tools, including Bayesian calibration, Bayesian model averaging, chi-square correlation analysis, principal component analysis, and empirical coverage probability. Using Bayesian framework, we investigate the structure of the 4-parameter Liquid Drop Model by considering discrepant mass domains for calibration. We then use the chi-square correlation framework to analyze the 14-parameter Skyrme energy density functional calibrated using homogeneous and heterogeneous datasets. We show that a quite dramatic parameter reduction can be achieved in both cases. The advantage of the Bayesian model averaging for improving the uncertainty quantification is demonstrated. The statistical approaches used are pedagogically described; in this context this work can serve as a guide for future applications.

Data corruption, systematic or adversarial, may skew statistical estimation severely. Recent work provides computationally efficient estimators that nearly match the information-theoretic optimal statistic. Yet the corruption model they consider measures sample-level corruption and is not fine-grained enough for many real-world applications. In this paper, we propose a coordinate-level metric of distribution shift over high-dimensional settings with n coordinates. We introduce and analyze robust mean estimation techniques against an adversary who may hide individual coordinates of samples while being bounded by that metric. We show that for structured distribution settings, methods that leverage structure to fill in missing entries before mean estimation can improve the estimation accuracy by a factor of approximately n compared to structure-agnostic methods. We also leverage recent progress in matrix completion to obtain estimators for recovering the true mean of the samples in settings of unknown structure. We demonstrate with real-world data that our methods can capture the dependencies across attributes and provide accurate mean estimation even in high-magnitude corruption settings.

Multi-agent reinforcement learning (MARL) has been applied to many challenging problems including two-team computer games, autonomous drivings, and real-time biddings. Despite the empirical success, there is a conspicuous absence of theoretical study of different MARL algorithms: this is mainly due to the curse of dimensionality caused by the exponential growth of the joint state-action space as the number of agents increases. Mean-field controls (MFC) with infinitely many agents and deterministic flows, meanwhile, provide good approximations to $N$-agent collaborative games in terms of both game values and optimal strategies. In this paper, we study the collaborative MARL under an MFC approximation framework: we develop a model-free kernel-based Q-learning algorithm (CDD-Q) and show that its convergence rate and sample complexity are independent of the number of agents. Our empirical studies on MFC examples demonstrate strong performances of CDD-Q. Moreover, the CDD-Q algorithm can be applied to a general class of Markov decision problems (MDPs) with deterministic dynamics and continuous state-action space.