While recommendation plays an increasingly critical role in our living, study, work, and entertainment, the recommendations we receive are often for irrelevant, duplicate, or uninteresting products and ser- vices. A c...While recommendation plays an increasingly critical role in our living, study, work, and entertainment, the recommendations we receive are often for irrelevant, duplicate, or uninteresting products and ser- vices. A critical reason for such bad recommendations lies in the intrinsic assumption that recommend- ed users and items are independent and identically distributed （liD） in existing theories and systems. Another phenomenon is that, while tremendous efforts have been made to model specific aspects of users or items, the overall user and item characteristics and their non-IIDness have been overlooked. In this paper, the non-liD nature and characteristics of recommendation are discussed, followed by the non-liD theoretical framework in order to build a deep and comprehensive understanding of the in- trinsic nature of recommendation problems, from the perspective of both couplings and heterogeneity. This non-liD recommendation research triggers the paradigm shift from lid to non-liD recommendation research and can hopefully deliver informed, relevant, personalized, and actionable recommendations. It creates exciting new directions and fundamental solutions to address various complexities including cold-start, sparse data-based, cross-domain, group-based, and shilling attack-related issues.展开更多
For a sampled-data control system with nonuniform sampling, the sampling interval sequence, which is continuously distributed in a given interval, is described as a multiple independent and identically distributed (i....For a sampled-data control system with nonuniform sampling, the sampling interval sequence, which is continuously distributed in a given interval, is described as a multiple independent and identically distributed (i.i.d.) process. With this process, the closed-loop system is transformed into an asynchronous dynamical impulsive model with input delays. Sufficient conditions for the closed-loop mean-square exponential stability are presented in terms of linear matrix inequalities (LMIs), in which the relation between the nonuniform sampling and the mean-square exponential stability of the closed-loop system is explicitly established. Based on the stability conditions, the controller design method is given, which is further formulated as a convex optimization problem with LMI constraints. Numerical examples and experiment results are given to show the effectiveness and the advantages of the theoretical results.展开更多
We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed(IID) random variables for sub-linear expectations initiated by Peng.It turns out...We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed(IID) random variables for sub-linear expectations initiated by Peng.It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.展开更多
In radar target detection, an optimum processor needs to automatically adapt its weights to the environment change. Conventionally, the optimum weights are obtained by substantial independently and identically distrib...In radar target detection, an optimum processor needs to automatically adapt its weights to the environment change. Conventionally, the optimum weights are obtained by substantial independently and identically distributed (i.i.d.) interference samplings, which is not always realistic in an inhomogeneous clutter background of airborne radar. The lack of i.i.d. samplings will inevitably lead to performance deterioration for optimum processing. In this paper, a novel parametric adaptive processing method is proposed for airborne radar target detection based on the modified Doppler distributed clutter (DDC) model with contribution of clutter's internal motion. It is different from the conventional methods in that the adaptive weights are determined by two parameters of DDC model, i.e., angular center and spread. A low-complexity nonlinear operators approach is also proposed to estimate these parameters. Simulation and performance analysis are also provided to show that the proposed method can remarkably reduce the dependence of i.i.d. samplings and it is computationally efficient for practical use.展开更多
文摘While recommendation plays an increasingly critical role in our living, study, work, and entertainment, the recommendations we receive are often for irrelevant, duplicate, or uninteresting products and ser- vices. A critical reason for such bad recommendations lies in the intrinsic assumption that recommend- ed users and items are independent and identically distributed （liD） in existing theories and systems. Another phenomenon is that, while tremendous efforts have been made to model specific aspects of users or items, the overall user and item characteristics and their non-IIDness have been overlooked. In this paper, the non-liD nature and characteristics of recommendation are discussed, followed by the non-liD theoretical framework in order to build a deep and comprehensive understanding of the in- trinsic nature of recommendation problems, from the perspective of both couplings and heterogeneity. This non-liD recommendation research triggers the paradigm shift from lid to non-liD recommendation research and can hopefully deliver informed, relevant, personalized, and actionable recommendations. It creates exciting new directions and fundamental solutions to address various complexities including cold-start, sparse data-based, cross-domain, group-based, and shilling attack-related issues.
基金supported by National Natural Science Foundation of China (Nos.61104105,U0735003 and 60974047)Natural Science Foundation of Guangdong Province of China (No.9451009001002702)
文摘For a sampled-data control system with nonuniform sampling, the sampling interval sequence, which is continuously distributed in a given interval, is described as a multiple independent and identically distributed (i.i.d.) process. With this process, the closed-loop system is transformed into an asynchronous dynamical impulsive model with input delays. Sufficient conditions for the closed-loop mean-square exponential stability are presented in terms of linear matrix inequalities (LMIs), in which the relation between the nonuniform sampling and the mean-square exponential stability of the closed-loop system is explicitly established. Based on the stability conditions, the controller design method is given, which is further formulated as a convex optimization problem with LMI constraints. Numerical examples and experiment results are given to show the effectiveness and the advantages of the theoretical results.
基金supported by National Natural Science Foundation of China(Grant No.11231005)
文摘We investigate three kinds of strong laws of large numbers for capacities with a new notion of independently and identically distributed(IID) random variables for sub-linear expectations initiated by Peng.It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov's strong law of large numbers to the case where probability measures are no longer additive. An important feature of these strong laws of large numbers is to provide a frequentist perspective on capacities.
文摘In radar target detection, an optimum processor needs to automatically adapt its weights to the environment change. Conventionally, the optimum weights are obtained by substantial independently and identically distributed (i.i.d.) interference samplings, which is not always realistic in an inhomogeneous clutter background of airborne radar. The lack of i.i.d. samplings will inevitably lead to performance deterioration for optimum processing. In this paper, a novel parametric adaptive processing method is proposed for airborne radar target detection based on the modified Doppler distributed clutter (DDC) model with contribution of clutter's internal motion. It is different from the conventional methods in that the adaptive weights are determined by two parameters of DDC model, i.e., angular center and spread. A low-complexity nonlinear operators approach is also proposed to estimate these parameters. Simulation and performance analysis are also provided to show that the proposed method can remarkably reduce the dependence of i.i.d. samplings and it is computationally efficient for practical use.
