We elucidate a practical method in Deep Learning called the minibatch which is very useful to avoid local minima. The mathematical structure of this method is, however, a bit obscure. We emphasize that a certain condi...We elucidate a practical method in Deep Learning called the minibatch which is very useful to avoid local minima. The mathematical structure of this method is, however, a bit obscure. We emphasize that a certain condition, which is not explicitly stated in ordinary expositions, is essential for the minibatch method. We present a comprehensive description Deep Learning for non-experts with the mathematical reinforcement.展开更多
This paper presents a selective review of statistical computation methods for massive data analysis.A huge amount of statistical methods for massive data computation have been rapidly developed in the past decades.In ...This paper presents a selective review of statistical computation methods for massive data analysis.A huge amount of statistical methods for massive data computation have been rapidly developed in the past decades.In this work,we focus on three categories of statistical computation methods:(1)distributed computing,(2)subsampling methods,and(3)minibatch gradient techniques.The first class of literature is about distributed computing and focuses on the situation,where the dataset size is too huge to be comfortably handled by one single computer.In this case,a distributed computation system with multiple computers has to be utilized.The second class of literature is about subsampling methods and concerns about the situation,where the blacksample size of dataset is small enough to be placed on one single computer but too large to be easily processed by its memory as a whole.The last class of literature studies those minibatch gradient related optimization techniques,which have been extensively used for optimizing various deep learning models.展开更多
Affected by the limited interchange spacing,the operational risk of vehicles in expressway small-spacing interchanges(SSIs)is more complex compared to other interchanges.In this study,unmanned aerial vehicle(UAV)measu...Affected by the limited interchange spacing,the operational risk of vehicles in expressway small-spacing interchanges(SSIs)is more complex compared to other interchanges.In this study,unmanned aerial vehicle(UAV)measurements were integrated with joint simulation data to explore the risk characteristics of SSIs with the help of traffic conflict theory.Seven traffic flow parameters,including mainline traffic volume,were selected to evaluate their impact on traffic conflicts.The distribution of four traffic conflict indicators,such as time to collision(TTC),was analyzed,and their severity was categorized using cumulative frequency analysis and minibatch K-means clustering.By varying the spacing,the study scrutinized trends in traffic conflicts,emphasizing the influence of various traffic flow parameters,distinctions in conflict indicators,and the ratio of severe conflicts to total conflicts.Additionally,an analysis of the spatial distribution of severe conflicts was conducted.The results suggested that traffic conflicts in SSIs are influenced by multiple factors,with mainline and entry traffic volumes being the most significant.Heavy vehicle proportions and entry ramp speeds had notable effects under certain spacing conditions.Considerable variations were observed in conflict indicators across different spacings,with the maximum conflict speed being the most affected by spacing,while TTC was the least.As spacing increased,the proportion of severe conflicts decreased,with severe TTC dropping from 18%to 10%.High-density conflict zones were identified near merging points in the second and third lanes.With larger spacing,the conflict zone range narrowed while the density of conflict points intensified.展开更多
文摘We elucidate a practical method in Deep Learning called the minibatch which is very useful to avoid local minima. The mathematical structure of this method is, however, a bit obscure. We emphasize that a certain condition, which is not explicitly stated in ordinary expositions, is essential for the minibatch method. We present a comprehensive description Deep Learning for non-experts with the mathematical reinforcement.
基金supported by the National Natural Science Foundation of China[grant numbers 72301070,72171226,12271012,12171020,12071477,72371241,72222009,71991472 and 12331009]the National Statistical Science Research Project[grant number 2023LD008]+3 种基金the Fundamental Research Funds for the Central Universities in UIBE[grant number CXTD13-04]the MOE Project of Key Research Institute of Humanities and Social Sciences[grant number 22JJD110001]the Program for Innovation Research,the disciplinary funding and the Emerging Interdisciplinary Project of Central University of Finance and Economicsthe Postdoctoral Fellowship Program of CPSF[grant numbers GZC20231522,GZC20230111 and GZB20230070].
文摘This paper presents a selective review of statistical computation methods for massive data analysis.A huge amount of statistical methods for massive data computation have been rapidly developed in the past decades.In this work,we focus on three categories of statistical computation methods:(1)distributed computing,(2)subsampling methods,and(3)minibatch gradient techniques.The first class of literature is about distributed computing and focuses on the situation,where the dataset size is too huge to be comfortably handled by one single computer.In this case,a distributed computation system with multiple computers has to be utilized.The second class of literature is about subsampling methods and concerns about the situation,where the blacksample size of dataset is small enough to be placed on one single computer but too large to be easily processed by its memory as a whole.The last class of literature studies those minibatch gradient related optimization techniques,which have been extensively used for optimizing various deep learning models.
基金supported in part by the National Natural Science Foundation of China(No.52172340).
文摘Affected by the limited interchange spacing,the operational risk of vehicles in expressway small-spacing interchanges(SSIs)is more complex compared to other interchanges.In this study,unmanned aerial vehicle(UAV)measurements were integrated with joint simulation data to explore the risk characteristics of SSIs with the help of traffic conflict theory.Seven traffic flow parameters,including mainline traffic volume,were selected to evaluate their impact on traffic conflicts.The distribution of four traffic conflict indicators,such as time to collision(TTC),was analyzed,and their severity was categorized using cumulative frequency analysis and minibatch K-means clustering.By varying the spacing,the study scrutinized trends in traffic conflicts,emphasizing the influence of various traffic flow parameters,distinctions in conflict indicators,and the ratio of severe conflicts to total conflicts.Additionally,an analysis of the spatial distribution of severe conflicts was conducted.The results suggested that traffic conflicts in SSIs are influenced by multiple factors,with mainline and entry traffic volumes being the most significant.Heavy vehicle proportions and entry ramp speeds had notable effects under certain spacing conditions.Considerable variations were observed in conflict indicators across different spacings,with the maximum conflict speed being the most affected by spacing,while TTC was the least.As spacing increased,the proportion of severe conflicts decreased,with severe TTC dropping from 18%to 10%.High-density conflict zones were identified near merging points in the second and third lanes.With larger spacing,the conflict zone range narrowed while the density of conflict points intensified.
