Deep Sufficient Representation Learning via Mutual Information

We propose a mutual information-based sufficient representation learning (MSRL) approach, which uses the variational formulation of the mutual information and leverages the approximation power of deep neural networks. MSRL learns a sufficient representation with the maximum mutual information with the response and a user-selected distribution. It can easily handle multi-dimensional continuous or categorical response variables. MSRL is shown to be consistent in the sense that the conditional probability density function of the response variable given the learned representation converges to the conditional probability density function of the response variable given the predictor. Non-asymptotic error bounds for MSRL are also established under suitable conditions. To establish the error bounds, we derive a generalized Dudley's inequality for an order-two U-process indexed by deep neural networks, which may be of independent interest. We discuss how to determine the intrinsic dimension of the underlying data distribution. Moreover, we evaluate the performance of MSRL via extensive numerical experiments and real data analysis and demonstrate that MSRL outperforms some existing nonlinear sufficient dimension reduction methods.Comment: 43 pages, 6 figures and 5 table

PcP_c states and their open-charm decays with the complex scaling method

A partial width formula is proposed using the analytical extension of the wave function in momentum space. The distinction of the Riemann sheets is explained from the perspective of the Schrodinger equation. The analytical form in coordinate space and the partial width are derived subsequently. Then a coupled-channel analysis is performed to investigate the open-charm branching ratios of the $P_c$ states, involving the contact interactions and one-pion-exchange potential with the three-body effects. The low energy constants are fitted using the experimental masses and widths as input. The $P_c(4312)$ is found to decay mainly to $\Lambda_c\bar{D}^*$, while the branching ratios of the $P_c(4440)$ and $P_c(4457)$ in different channels are comparable. Under the reasonable assumption that the off-diagonal contact interactions are small, the $J^P$ quantum numbers of the $P_c(4440)$ and the $P_c(4457)$ prefer $\frac{1}{2}^-$ and $\frac{3}{2}^-$ respectively. Three additional $P_c$ states at 4380 MeV, 4504 MeV and 4516 MeV, together with their branching ratios, are predicted. A deduction of the revised one-pion-exchange potential involving the on-shell three-body intermediate states is performed.Comment: 16 pages, 5 figure

ZcsZ_{cs}, ZcZ_c and ZbZ_b states under the complex scaling method

We investigate the $Z_b$, $Z_c$ and $Z_{cs}$ states within the chiral effective field theory framework and the $S$-wave single channel molecule picture. With the complex scaling method, we accurately solve the Schr\"odinger equation in momentum space. Our analysis reveals that the $Z_b(10610)$, $Z_b(10650)$, $Z_c(3900)$ and $Z_c(4020)$ states are the resonances composed of the $S-$wave $(B\bar{B}^{*}+B^{*}\bar{B})/\sqrt{2}$, $B^{*}\bar{B}^*$, $(D\bar{D}^{*}+D^{*}\bar{D})/\sqrt{2}$ and $D^{*}\bar{D}^*$, respectively. Furthermore, although the $Z_{cs}(3985)$ and $Z_{cs}(4000)$ states exhibit a significant difference in width, these two resonances may originate from the same channel, the $S-$wave $(D_{s}\bar{D}^{*}+D_{s}^{*}\bar{D})/\sqrt{2}$. Additionally, we find two resonances in the $S-$wave $D_s^*\bar{D}^*$ channel, corresponding to the $Z_{cs}(4123)$ and $Z_{cs}(4220)$ states that await experimental confirmation.Comment: 10 pages, 5 figures, 4 table

Domain Conditioned Adaptation Network

Tremendous research efforts have been made to thrive deep domain adaptation (DA) by seeking domain-invariant features. Most existing deep DA models only focus on aligning feature representations of task-specific layers across domains while integrating a totally shared convolutional architecture for source and target. However, we argue that such strongly-shared convolutional layers might be harmful for domain-specific feature learning when source and target data distribution differs to a large extent. In this paper, we relax a shared-convnets assumption made by previous DA methods and propose a Domain Conditioned Adaptation Network (DCAN), which aims to excite distinct convolutional channels with a domain conditioned channel attention mechanism. As a result, the critical low-level domain-dependent knowledge could be explored appropriately. As far as we know, this is the first work to explore the domain-wise convolutional channel activation for deep DA networks. Moreover, to effectively align high-level feature distributions across two domains, we further deploy domain conditioned feature correction blocks after task-specific layers, which will explicitly correct the domain discrepancy. Extensive experiments on three cross-domain benchmarks demonstrate the proposed approach outperforms existing methods by a large margin, especially on very tough cross-domain learning tasks.Comment: Accepted by AAAI 202

Understanding Daily Travel Patterns of Subway Users – An Example from the Beijing Subway

The daily travel patterns (DTPs) present short-term and timely characteristics of the users’ travel behaviour, and they are helpful for subway planners to better understand the travel choices and regularity of subway users (SUs) in details. While several well-known subway travel patterns have been detected, such as commuting modes and shopping modes, specific features of many patterns are still confused or omitted. Now, based on the automatic fare collection (AFC) system, a data-mining procedure to recognize DTPs of all SUs has become possible and effective. In this study, DTPs are identified by the station sequences (SSs), which are modelled from smart card transaction data of the AFC system. The data-mining procedure is applied to a large weekly sample from the Beijing Subway to understand DTPs. The results show that more than 93% SUs of the Beijing Subway travel in 7 DTPs, which are remarkably stable in share and distribution. Different DTPs have their own unique characteristics in terms of time distribution, activity duration and repeatability, which provide a wealth of information to calibrate different types of users and characterize their travel patterns.</p