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

Reliable Off-policy Evaluation for Reinforcement Learning

In a sequential decision-making problem, off-policy evaluation estimates the expected cumulative reward of a target policy using logged trajectory data generated from a different behavior policy, without execution of the target policy. Reinforcement learning in high-stake environments, such as healthcare and education, is often limited to off-policy settings due to safety or ethical concerns, or inability of exploration. Hence it is imperative to quantify the uncertainty of the off-policy estimate before deployment of the target policy. In this paper, we propose a novel framework that provides robust and optimistic cumulative reward estimates using one or multiple logged trajectories data. Leveraging methodologies from distributionally robust optimization, we show that with proper selection of the size of the distributional uncertainty set, these estimates serve as confidence bounds with non-asymptotic and asymptotic guarantees under stochastic or adversarial environments. Our results are also generalized to batch reinforcement learning and are supported by empirical analysis.Comment: 39 pages, 4 figure

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

Outpainting by Queries

Image outpainting, which is well studied with Convolution Neural Network (CNN) based framework, has recently drawn more attention in computer vision. However, CNNs rely on inherent inductive biases to achieve effective sample learning, which may degrade the performance ceiling. In this paper, motivated by the flexible self-attention mechanism with minimal inductive biases in transformer architecture, we reframe the generalised image outpainting problem as a patch-wise sequence-to-sequence autoregression problem, enabling query-based image outpainting. Specifically, we propose a novel hybrid vision-transformer-based encoder-decoder framework, named \textbf{Query} \textbf{O}utpainting \textbf{TR}ansformer (\textbf{QueryOTR}), for extrapolating visual context all-side around a given image. Patch-wise mode's global modeling capacity allows us to extrapolate images from the attention mechanism's query standpoint. A novel Query Expansion Module (QEM) is designed to integrate information from the predicted queries based on the encoder's output, hence accelerating the convergence of the pure transformer even with a relatively small dataset. To further enhance connectivity between each patch, the proposed Patch Smoothing Module (PSM) re-allocates and averages the overlapped regions, thus providing seamless predicted images. We experimentally show that QueryOTR could generate visually appealing results smoothly and realistically against the state-of-the-art image outpainting approaches

Evaluation of the differences of myocardial fibers between acute and chronic myocardial infarction: Application of diffusion tensor magnetic resonance imaging in a rhesus monkey model

Objective: To understand microstructural changes after myocardial infarction (MI), we evaluated myocardial fibers of rhesus monkeys during acute or chronic MI, and identified the differences of myocardial fibers between acute and chronic MI. Materials and Methods: Six fixed hearts of rhesus monkeys with left anterior descending coronary artery ligation for 1 hour or 84 days were scanned by diffusion tensor magnetic resonance imaging (MRI) to measure apparent diffusion coefficient (ADC), fractional anisotropy (FA) and helix angle (HA). Results: Comparing with acute MI monkeys (FA: 0.59 +/- 0.02; ADC: 5.0 +/- 0.6 x 10(-4) mm(2)/s; HA: 94.5 +/- 4.4 degrees), chronic MI monkeys showed remarkably decreased FA value (0.26 +/- 0.03), increased ADC value (7.8 +/- 0.8 x 10(-4)mm(2)/s), decreased HA transmural range (49.5 +/- 4.6 degrees) and serious defects on endocardium in infarcted regions. The HA in infarcted regions shifted to more components of negative left-handed helix in chronic MI monkeys (-38.3 +/- 5.0 degrees-11.2 +/- 4.3 degrees) than in acute MI monkeys (-41.4 +/- 5.1 degrees-53.1 +/- 3.7 degrees), but the HA in remote regions shifted to more components of positive right-handed helix in chronic MI monkeys (-43.8 +/- 2.7 degrees-66.5 +/- 4.9 degrees) than in acute MI monkeys (-59.5 +/- 3.4 degrees-64.9 +/- 4.3 degrees). Conclusion: Diffusion tensor MRI method helps to quantify differences of mechanical microstructure and water diffusion of myocardial fibers between acute and chronic MI monkey's models.National Natural Science Foundation of China [81130027, 81301196]SCI(E)[email protected]

Sparse Single Sweep LiDAR Point Cloud Segmentation via Learning Contextual Shape Priors from Scene Completion

LiDAR point cloud analysis is a core task for 3D computer vision, especially for autonomous driving. However, due to the severe sparsity and noise interference in the single sweep LiDAR point cloud, the accurate semantic segmentation is non-trivial to achieve. In this paper, we propose a novel sparse LiDAR point cloud semantic segmentation framework assisted by learned contextual shape priors. In practice, an initial semantic segmentation (SS) of a single sweep point cloud can be achieved by any appealing network and then flows into the semantic scene completion (SSC) module as the input. By merging multiple frames in the LiDAR sequence as supervision, the optimized SSC module has learned the contextual shape priors from sequential LiDAR data, completing the sparse single sweep point cloud to the dense one. Thus, it inherently improves SS optimization through fully end-to-end training. Besides, a Point-Voxel Interaction (PVI) module is proposed to further enhance the knowledge fusion between SS and SSC tasks, i.e., promoting the interaction of incomplete local geometry of point cloud and complete voxel-wise global structure. Furthermore, the auxiliary SSC and PVI modules can be discarded during inference without extra burden for SS. Extensive experiments confirm that our JS3C-Net achieves superior performance on both SemanticKITTI and SemanticPOSS benchmarks, i.e., 4% and 3% improvement correspondingly.Comment: To appear in AAAI 2021. Codes are available at https://github.com/yanx27/JS3C-Ne

Ambient Hydrogenation and Deuteration of Alkenes Using a Nanostructured Ni-Core-Shell Catalyst

A general protocol for the selective hydrogenation and deuteration of a variety of alkenes is presented. Key to success for these reactions is the use of a specific nickel-graphitic shell-based core–shell-structured catalyst, which is conveniently prepared by impregnation and subsequent calcination of nickel nitrate on carbon at 450 °C under argon. Applying this nanostructured catalyst, both terminal and internal alkenes, which are of industrial and commercial importance, were selectively hydrogenated and deuterated at ambient conditions (room temperature, using 1 bar hydrogen or 1 bar deuterium), giving access to the corresponding alkanes and deuterium-labeled alkanes in good to excellent yields. The synthetic utility and practicability of this Ni-based hydrogenation protocol is demonstrated by gram-scale reactions as well as efficient catalyst recycling experiments. © 2021 The Authors. Angewandte Chemie International Edition published by Wiley-VCH Gmb