Minimum entropy production, detailed balance and Wasserstein distance for continuous-time Markov processes

We investigate the problem of minimizing the entropy production for a physical process that can be described in terms of a Markov jump dynamics. We show that, without any further constraints, a given time-evolution may be realized at arbitrarily small entropy production, yet at the expense of diverging activity. For a fixed activity, we find that the dynamics that minimizes the entropy production is given in terms of conservative forces. The value of the minimum entropy production is expressed in terms of the graph-distance based Wasserstein distance between the initial and final configuration. This yields a new kind of speed limit relating dissipation, the average number of transitions and the Wasserstein distance. It also allows us to formulate the optimal transport problem on a graph in term of a continuous-time interpolating dynamics, in complete analogy to the continuous space setting. We demonstrate our findings for simple state networks, a time-dependent pump and for spin flips in the Ising model.

An Evidence Combination Rule Based on New Weight Assignment Scheme

Conflicting evidence and fuzzy evidence have a significant impact on the results of evidence combination in the application of evidence theory. However, the existing weight assignment methods can hardly reflect the significant influence of fuzzy evidence on the combination results. Therefore, a new method for assigning evidence weights and the corresponding combination rule are proposed. The proposed weight assignment method strengthens the consideration of fuzzy evidence and introduces the Wasserstein distance to compute the clarity degree of evidence which is an important reference index for weight assignment in the proposed combination rule and can weaken the effect of ambiguous evidence effectively. In the experiments, it's firstly verified that the impact of fuzzy evidence on the combination results is significant; therefore it should be fully considered in the weight assignment process. Then, the proposed combination rule with new weight assignment method is tested on a set of numerical arithmetic and Iris datasets. Compared with four existing methods, the results show that the proposed method has higher decision accuracy, F1 score, better computational convergence, and more reliable fusion results as well.

Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances

We revisit Markowitz’s mean-variance portfolio selection model by considering a distributionally robust version, in which the region of distributional uncertainty is around the empirical measure and the discrepancy between probability measures is dictated by the Wasserstein distance. We reduce this problem into an empirical variance minimization problem with an additional regularization term. Moreover, we extend the recently developed inference methodology to our setting in order to select the size of the distributional uncertainty as well as the associated robust target return rate in a data-driven way. Finally, we report extensive back-testing results on S&P 500 that compare the performance of our model with those of several well-known models including the Fama–French and Black–Litterman models. This paper was accepted by David Simchi-Levi, finance.

Measuring the Similarity of Metro Stations Based on the Passenger Visit Distribution

The distribution of passengers reflects the characteristics of urban rail stations. The automatic fare collection system of rail transit collects a large amount of passenger trajectory data tracking the entry and exit continuously, which provides a basis for detailed passenger distributions. We first exploit the Automatic Fare Collection (AFC) data to construct the passenger visit pattern distribution for stations. Then we measure the similarity of all stations using Wasserstein distance. Different from other similarity metrics, Wasserstein distance takes the similarity between values of quantitative variables in the one-dimensional distribution into consideration and can reflect the correlation between different dimensions of high-dimensional data. Even though the computational complexity grows, it is applicable in the metro stations since the scale of urban rail transit stations is limited to tens to hundreds and detailed modeling of the stations can be performed offline. Therefore, this paper proposes an integrated method that can cluster multi-dimensional joint distribution considering similarity and correlation. Then this method is applied to cluster the rail transit stations by the passenger visit distribution, which provides some valuable insight into the flow management and the station replanning of urban rail transit in the future.

McKean–Vlasov type stochastic differential equations arising from the random vortex method

We study a class of McKean–Vlasov type stochastic differential equations (SDEs) which arise from the random vortex dynamics and other physics models. By introducing a new approach we resolve the existence and uniqueness of both the weak and strong solutions for the McKean–Vlasov stochastic differential equations whose coefficients are defined in terms of singular integral kernels such as the Biot–Savart kernel. These SDEs which involve the distributions of solutions are in general not Lipschitz continuous with respect to the usual distances on the space of distributions such as the Wasserstein distance. Therefore there is an obstacle in adapting the ordinary SDE method for the study of this class of SDEs, and the conventional methods seem not appropriate for dealing with such distributional SDEs which appear in applications such as fluid mechanics.

An Efficient Online Multiparty Interactive Medical Prediagnosis Scheme with Privacy Protection

Medical prediagnosis systems are now available online to give users quick and preliminary diagnosis information. The need for such a system has become particularly evident in areas with insufficient health professionals. Due to the privacy of patient medical information and the sensitivity of cloud diagnosis models, it is necessary to protect the security of data, models, and communications. These existing diagnosis systems can hardly provide a satisfied diagnosis accuracy while ensuring comprehensive security and high efficiency. In order to solve these problems, we proposed Relief- k minimum Wasserstein distance (Relief- k MW) classification method, which combined data encryption and BLS signature to form a privacy-preserving efficient online multiparty interactive medical prediagnostic scheme (OMPD). Theoretical analysis shows our OMPD effectively provides high-precision prediagnosis services. Extensive experimental results demonstrate that OMPD not only greatly improves the diagnostic accuracy but also reduces the computational and communication overhead.