Probability metrics have become an indispensable part of modern statistics and machine learning, and they play a quintessential role in various applications, including statistical hypothesis testing and generative modeling. However, in a practical setting, the convergence behavior of the algorithms built upon these distances have not been well established, except for a few specific cases. In this paper, we introduce a broad family of probability metrics, coined as Generalized Sliced Probability Metrics (GSPMs), that are deeply rooted in the generalized Radon transform. We first verify that GSPMs are metrics. Then, we identify a subset of GSPMs that are equivalent to maximum mean discrepancy (MMD) with novel positive definite kernels, which come with a unique geometric interpretation. Finally, by exploiting this connection, we consider GSPM-based gradient flows for generative modeling applications and show that under mild assumptions, the gradient flow converges to the global optimum. We illustrate the utility of our approach on both real and synthetic problems.

Multivariate Hawkes Processes (MHPs) are an important class of temporal point processes that have enabled key advances in understanding and predicting social information systems. However, due to their complex modeling of temporal dependencies, MHPs have proven to be notoriously difficult to scale, what has limited their applications to relatively small domains. In this work, we propose a novel model and computational approach to overcome this important limitation. By exploiting a characteristic sparsity pattern in real-world diffusion processes, we show that our approach allows to compute the exact likelihood and gradients of an MHP -- independently of the ambient dimensions of the underlying network. We show on synthetic and real-world datasets that our model does not only achieve state-of-the-art predictive results, but also improves runtime performance by multiple orders of magnitude compared to standard methods on sparse event sequences. In combination with easily interpretable latent variables and influence structures, this allows us to analyze diffusion processes at previously unattainable scale.

We analyze the convergence rate of various momentum-based optimization algorithms from a dynamical systems point of view. Our analysis exploits fundamental topological properties, such as the continuous dependence of iterates on their initial conditions, to provide a simple characterization of convergence rates. In many cases, closed-form expressions are obtained that relate algorithm parameters to the convergence rate. The analysis encompasses discrete time and continuous time, as well as time-invariant and time-variant formulations, and is not limited to a convex or Euclidean setting. In addition, the article rigorously establishes why symplectic discretization schemes are important for momentum-based optimization algorithms, and provides a characterization of algorithms that exhibit accelerated convergence.

This paper presents a novel deep learning based data-driven optimization method. A novel generative adversarial network (GAN) based data-driven distributionally robust chance constrained programming framework is proposed. GAN is applied to fully extract distributional information from historical data in a nonparametric and unsupervised way without a priori approximation or assumption. Since GAN utilizes deep neural networks, complicated data distributions and modes can be learned, and it can model uncertainty efficiently and accurately. Distributionally robust chance constrained programming takes into consideration ambiguous probability distributions of uncertain parameters. To tackle the computational challenges, sample average approximation method is adopted, and the required data samples are generated by GAN in an end-to-end way through the differentiable networks. The proposed framework is then applied to supply chain optimization under demand uncertainty. The applicability of the proposed approach is illustrated through a county-level case study of a spatially explicit biofuel supply chain in Illinois.

Deep learning performs remarkably well on many time series analysis tasks recently. The superior performance of deep neural networks relies heavily on a large number of training data to avoid overfitting. However, the labeled data of many real-world time series applications may be limited such as classification in medical time series and anomaly detection in AIOps. As an effective way to enhance the size and quality of the training data, data augmentation is crucial to the successful application of deep learning models on time series data. In this paper, we systematically review different data augmentation methods for time series. We propose a taxonomy for the reviewed methods, and then provide a structured review for these methods by highlighting their strengths and limitations. We also empirically compare different data augmentation methods for different tasks including time series anomaly detection, classification and forecasting. Finally, we discuss and highlight future research directions, including data augmentation in time-frequency domain, augmentation combination, and data augmentation and weighting for imbalanced class.

Deep neural networks are vulnerable to adversarial examples (Szegedy et al., 2014) - semantical preserving changes such as l p -noise, geometrical perturbations (e.g., rotations and translation) (Engstrom et al., 2017), and Wasserstein perturbations (Wong et al., 2019) which can affect the output of the network in undesirable ways. This is especially problematic when these models are used in safety critical tasks such as medical diagnosis (Amato et al., 2013) or autonomous driving (Bojarski et al., 2016). As a result, recent work (e.g., Gehr et al. (2018); Weng et al. (2018)) started investigating robustness certification methods which guarantee the absence of adversarial examples. However, even with training methods tailored to produce networks amenable to l -certification (Wong & Kolter, 2018; Mirman et al., 2018), current verification techniques still cannot scale to realistic models and datasets. Recently, a promising approach called randomized smoothing was proposed by (Cohen et al., 2019) - it works by constructing a probabilistic classifier with probabilistic certificates and produces state-of-the-art results for l 2 -norm bounded noise on ImageNet.

We introduce a new measure to evaluate the transferability of representations learned by classifiers. Our measure, the Log Expected Empirical Prediction (LEEP), is simple and easy to compute: when given a classifier trained on a source data set, it only requires running the target data set through this classifier once. We analyze the properties of LEEP theoretically and demonstrate its effectiveness empirically. Our analysis shows that LEEP can predict the performance and convergence speed of both transfer and meta-transfer learning methods, even for small or imbalanced data. Moreover, LEEP outperforms recently proposed transferability measures such as negative conditional entropy and H scores. Notably, when transferring from ImageNet to CIFAR100, LEEP can achieve up to 30% improvement compared to the best competing method in terms of the correlations with actual transfer accuracy.

In many high dimensional classification or regression problems set in a biological context, the complete identification of the set of informative features is often as important as predictive accuracy, since this can provide mechanistic insight and conceptual understanding. Lasso and related algorithms have been widely used since their sparse solutions naturally identify a set of informative features. However, Lasso performs erratically when features are correlated. This limits the use of such algorithms in biological problems, where features such as genes often work together in pathways, leading to sets of highly correlated features. In this paper, we examine the performance of a Lasso derivative, the exclusive group Lasso, in this setting. We propose fast algorithms to solve the exclusive group Lasso, and introduce a solution to the case when the underlying group structure is unknown. The solution combines stability selection with random group allocation and introduction of artificial features. Experiments with both synthetic and real-world data highlight the advantages of this proposed methodology over Lasso in comprehensive selection of informative features.

Substantial efforts have been made on improving the generalization abilities of deep neural networks (DNNs) in order to obtain better performances without introducing more parameters. On the other hand, meta-learning approaches exhibit powerful generalization on new tasks in few-shot learning. Intuitively, few-shot learning is more challenging than the standard supervised learning as each target class only has a very few or no training samples. The natural question that arises is whether the meta-learning idea can be used for improving the generalization of DNNs on the standard supervised learning. In this paper, we propose a novel meta-learning based training procedure (MLTP) for DNNs and demonstrate that the meta-learning idea can indeed improve the generalization abilities of DNNs. MLTP simulates the meta-training process by considering a batch of training samples as a task. The key idea is that the gradient descent step for improving the current task performance should also improve a new task performance, which is ignored by the current standard procedure for training neural networks. MLTP also benefits from all the existing training techniques such as dropout, weight decay, and batch normalization. We evaluate MLTP by training a variety of small and large neural networks on three benchmark datasets, i.e., CIFAR-10, CIFAR-100, and Tiny ImageNet. The experimental results show a consistently improved generalization performance on all the DNNs with different sizes, which verifies the promise of MLTP and demonstrates that the meta-learning idea is indeed able to improve the generalization of DNNs on the standard supervised learning.

Imitation learning typically performs training and testing in the same environment. This is by necessity as the Markov Decision Process(MDP) formalism defines a policy on a particular state space. However, real world environments are rarely so cleanly defined and benign changes to the environment can induce a completely new state space. Although deep imitation learning (Ho and Ermon, 2016) still defines a policy on unseen states, it remains extremely difficult to effectively generalize (Duan et al., 2017). Domain adaptation addresses how to generalize a policy defined in a source domain to perform the same task in a target domain (Higgins et al., 2017).