Sinkhorn Distributionally Robust Optimization

We study distributionally robust optimization (DRO) with Sinkhorn distance -- a variant of Wasserstein distance based on entropic regularization. We derive convex programming dual reformulation for a general nominal distribution. Compared with Wasserstein DRO, it is computationally tractable for a larger class of loss functions, and its worst-case distribution is more reasonable for practical applications. To solve the dual reformulation, we develop a stochastic mirror descent algorithm using biased gradient oracles and analyze its convergence rate. Finally, we provide numerical examples using synthetic and real data to demonstrate its superior performance.Comment: 56 pages, 8 figure

Two-sample Test using Projected Wasserstein Distance: Breaking the Curse of Dimensionality

We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to circumvent the curse of dimensionality in Wasserstein distance: when the dimension is high, it has diminishing testing power, which is inherently due to the slow concentration property of Wasserstein metrics in the high dimension space. A key contribution is to couple optimal projection to find the low dimensional linear mapping to maximize the Wasserstein distance between projected probability distributions. We characterize the theoretical property of the finite-sample convergence rate on IPMs and present practical algorithms for computing this metric. Numerical examples validate our theoretical results.Comment: 10 pages, 3 figures. Accepted in ISIT-2

Two-sample Test with Kernel Projected Wasserstein Distance

We develop a kernel projected Wasserstein distance for the two-sample test, an essential building block in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. This method operates by finding the nonlinear mapping in the data space which maximizes the distance between projected distributions. In contrast to existing works about projected Wasserstein distance, the proposed method circumvents the curse of dimensionality more efficiently. We present practical algorithms for computing this distance function together with the non-asymptotic uncertainty quantification of empirical estimates. Numerical examples validate our theoretical results and demonstrate good performance of the proposed method.Comment: 49 pages, 10 figures, 4 table

Cellular-Connected UAV with Adaptive Air-to-Ground Interference Cancellation and Trajectory Optimization

This letter studies a cellular-connected unmanned aerial vehicle (UAV) scenario, in which a UAV user communicates with ground base stations (GBSs) in cellular uplink by sharing the spectrum with ground users (GUs). To deal with the severe air-to-ground (A2G) co-channel interference, we consider an adaptive interference cancellation (IC) approach, in which each GBS can decode the GU's messages by adaptively switching between the modes of IC (i.e., precanceling the UAV's resultant interference) and treating interference as noise (TIN). By designing the GBSs' decoding modes, jointly with the wireless resource allocation and the UAV's trajectory control, we maximize the UAV's data-rate throughput over a finite mission period, while ensuring the minimum data-rate requirements at individual GUs. We propose an efficient algorithm to solve the throughput maximization problem by using the techniques of alternating optimization and successive convex approximation (SCA). Numerical results show that our proposed design significantly improves the UAV's throughput as compared to the benchmark schemes without the adaptive IC and/or trajectory optimization.Comment: Technical Repor

Contextual Stochastic Bilevel Optimization

We introduce contextual stochastic bilevel optimization (CSBO) -- a stochastic bilevel optimization framework with the lower-level problem minimizing an expectation conditioned on some contextual information and the upper-level decision variable. This framework extends classical stochastic bilevel optimization when the lower-level decision maker responds optimally not only to the decision of the upper-level decision maker but also to some side information and when there are multiple or even infinite many followers. It captures important applications such as meta-learning, personalized federated learning, end-to-end learning, and Wasserstein distributionally robust optimization with side information (WDRO-SI). Due to the presence of contextual information, existing single-loop methods for classical stochastic bilevel optimization are unable to converge. To overcome this challenge, we introduce an efficient double-loop gradient method based on the Multilevel Monte-Carlo (MLMC) technique and establish its sample and computational complexities. When specialized to stochastic nonconvex optimization, our method matches existing lower bounds. For meta-learning, the complexity of our method does not depend on the number of tasks. Numerical experiments further validate our theoretical results.Comment: The paper is accepted by NeurIPS 202

A Manifold Two-Sample Test Study: Integral Probability Metric with Neural Networks

Two-sample tests are important areas aiming to determine whether two collections of observations follow the same distribution or not. We propose two-sample tests based on integral probability metric (IPM) for high-dimensional samples supported on a low-dimensional manifold. We characterize the properties of proposed tests with respect to the number of samples $n$ and the structure of the manifold with intrinsic dimension $d$. When an atlas is given, we propose two-step test to identify the difference between general distributions, which achieves the type-II risk in the order of $n^{-1/\max\{d,2\}}$. When an atlas is not given, we propose H\"older IPM test that applies for data distributions with $(s,\beta)$-H\"older densities, which achieves the type-II risk in the order of $n^{-(s+\beta)/d}$. To mitigate the heavy computation burden of evaluating the H\"older IPM, we approximate the H\"older function class using neural networks. Based on the approximation theory of neural networks, we show that the neural network IPM test has the type-II risk in the order of $n^{-(s+\beta)/d}$, which is in the same order of the type-II risk as the H\"older IPM test. Our proposed tests are adaptive to low-dimensional geometric structure because their performance crucially depends on the intrinsic dimension instead of the data dimension.Comment: 32 pages, 2 figures, 3 tables. Accepted by Information and Inference: A Journal of the IM

Quantifying the temporal stability of international fertilizer trade networks

The importance of fertilizers to agricultural production is undeniable, and most economies rely on international trade for fertilizer use. The stability of fertilizer trade networks is fundamental to food security. We use three valid methods to measure the temporal stability of the overall network and different functional sub-networks of the three fertilizer nutrients N, P and K from 1990 to 2018. The international N, P and K trade systems all have a trend of increasing stability with the process of globalization. The large-weight sub-network has relatively high stability, but is more likely to be impacted by extreme events. The small-weight sub-network is less stable, but has a strong self-healing ability and is less affected by shocks. Overall, all the three fertilizer trade networks exhibit a stable core with restorable periphery. The overall network stability of the three fertilizers is close, but the K trade has a significantly higher stability in the core part, and the N trade is the most stable in the non-core part.Comment: 13 pages including 6 figure

Evaluation of anti-smoking television advertising on tobacco control among urban community population in Chongqing, China

Background China is the largest producer and consumer of tobacco in the world. Considering the constantly growing urban proportion, persuasive tobacco control measures are important in urban communities. Television, as one of the most pervasive mass media, can be used for this purpose. Methods The anti-smoking advertisement was carried out in five different time slots per day from 15 May to 15 June in 2011 across 12 channels of Chongqing TV. A cross-sectional study was conducted in the main municipal areas of Chongqing. A questionnaire was administered in late June to 1,342 native residents aged 18–45, who were selected via street intercept survey. Results Respondents who recognized the advertisement (32.77 %) were more likely to know or believe that smoking cigarettes caused impotence than those who did not recognize the advertisement (26.11 %). According to 25.5 % of smokers, the anti-smoking TV advertising made them consider quitting smoking. However, females (51.7 %) were less likely to be affected by the advertisement to stop and think about quitting smoking compared to males (65.6 %) (OR = 0.517, 95 % CI [0.281–0.950]). In addition, respondents aged 26–35 years (67.4 %) were more likely to try to persuade others to quit smoking than those aged 18–25 years (36.3 %) (OR = 0.457, 95 % CI [0.215–0.974]). Furthermore, non-smokers (87.4 %) were more likely to find the advertisement relevant than smokers (74.8 %) (OR = 2.34, 95 % CI [1.19–4.61]). Conclusions This study showed that this advertisement did not show significant differences on smoking-related knowledge and attitude between non-smokers who had seen the ad and those who had not. Thus, this form may not be the right tool to facilitate change in non-smokers. The ad should instead be focused on the smoking population. Gender, smoking status, and age influenced the effect of anti-smoking TV advertising on the general population in China