This paper studies the reduced rank regression problem,which assumes a low-rank structure of the coefficient matrix,together with heavy-tailed noises.To address the heavy-tailed noise,we adopt the quantile loss functi...This paper studies the reduced rank regression problem,which assumes a low-rank structure of the coefficient matrix,together with heavy-tailed noises.To address the heavy-tailed noise,we adopt the quantile loss function instead of commonly used squared loss.However,the non-smooth quantile loss brings new challenges to both the computation and development of statistical properties,especially when the data are large in size and distributed across different machines.To this end,we first transform the response variable and reformulate the problem into a trace-norm regularized least-square problem,which greatly facilitates the computation.Based on this formulation,we further develop a distributed algorithm.Theoretically,we establish the convergence rate of the obtained estimator and the theoretical guarantee for rank recovery.The simulation analysis is provided to demonstrate the effectiveness of our method.展开更多
We study competitive economy equilibrium computation. We show that, for the first time, the equilibrium sets of the following two markets： 1. A mixed Fisher and Arrow- Debreu market with homogeneous and log-concave u...We study competitive economy equilibrium computation. We show that, for the first time, the equilibrium sets of the following two markets： 1. A mixed Fisher and Arrow- Debreu market with homogeneous and log-concave utility functions; 2. The Fisher and Arrow-Debreu markets with several classes of concave non-homogeneous utility functions; are convex or log-convex. Furthermore, an equilibrium can be computed as convex opti- mization by an interior-point algorithm in polynomial time.展开更多
This paper discusses the fixed-hub single allocation problem(FHSAP).In this problem,a network consists of hub nodes and terminal nodes.Hubs are fixed and fully connected;each terminal node is assigned to a single hub ...This paper discusses the fixed-hub single allocation problem(FHSAP).In this problem,a network consists of hub nodes and terminal nodes.Hubs are fixed and fully connected;each terminal node is assigned to a single hub which routes all its traffic.The goal is to minimize the cost of routing the traffic in the network.In this paper,we propose a new linear programming(LP)relaxation for this problem by incorporating a set of validity constraints into the classical formulations by Ernst and Krishnamoorthy(Locat Sci 4:139–154,Ann Op Res 86:141–159).A geometric rounding algorithm is then used to obtain an integral solution from the fractional solution.We show that by incorporating the validity constraints,the strengthened LP often provides much tighter upper bounds than the previous methods with a little more computational effort and the solution obtained often has a much smaller gap with the optimal solution.We also formulate a robust version of the FHSAP and show that it can guard against data uncertainty with little costs.展开更多
The paper provides a broad discussion of the topic "accruals". Though much of what is said is familiar from the literature on accruals, the paper tries to develop concepts and show how theses forge tight lin...The paper provides a broad discussion of the topic "accruals". Though much of what is said is familiar from the literature on accruals, the paper tries to develop concepts and show how theses forge tight links across a variety of themes. The starting point of the analysis concerns the construct of an accrual.The case is made that it should rest solely on consecutive balance sheets and the splitting of assets/liabilities into(i) cash and approximate cash,assets/liabilities and(ii) all other kinds of assets/liabilities. Given this divide of assets/liabilities one can measure the components in the foundation equation: cash earnings + net accrual = comprehensive earnings. The paper then proceeds to discuss how the net accrual relates to growth in a firm's operating activities and the extent to which it can be informative or misleading.This topic in turn integrates with the issue of a firm's quality of earnings and the role of accounting conservatism. Among the remaining topics, the paper discusses how one conceptualizes diagnostics to assess whether or not a period's accrual is likely to be biased upwards or downwards. It gives rise to a consideration of how one constructs accruals that may be more informative than GAAP accruals and the role of value-relevance studies to assess the information content of accrual constructs. The paper ends with a list of suggestions how future research may be modified in light of the discussions in this paper.展开更多
基金supported by National Basic Research Program of China(973 Program)(Grant No.2018AAA0100704)National Natural Science Foundation of China(Grant Nos.11825104 and 11690013)+3 种基金Youth Talent Support Program and Australian Research Councilsupported by National Natural Science Foundation of China(Grant No.12001109)Shanghai Sailing Program(Grant No.19YF1402800)the Science and Technology Commission of Shanghai Municipality(Grant No.20dz1200600)。
文摘This paper studies the reduced rank regression problem,which assumes a low-rank structure of the coefficient matrix,together with heavy-tailed noises.To address the heavy-tailed noise,we adopt the quantile loss function instead of commonly used squared loss.However,the non-smooth quantile loss brings new challenges to both the computation and development of statistical properties,especially when the data are large in size and distributed across different machines.To this end,we first transform the response variable and reformulate the problem into a trace-norm regularized least-square problem,which greatly facilitates the computation.Based on this formulation,we further develop a distributed algorithm.Theoretically,we establish the convergence rate of the obtained estimator and the theoretical guarantee for rank recovery.The simulation analysis is provided to demonstrate the effectiveness of our method.
文摘We study competitive economy equilibrium computation. We show that, for the first time, the equilibrium sets of the following two markets： 1. A mixed Fisher and Arrow- Debreu market with homogeneous and log-concave utility functions; 2. The Fisher and Arrow-Debreu markets with several classes of concave non-homogeneous utility functions; are convex or log-convex. Furthermore, an equilibrium can be computed as convex opti- mization by an interior-point algorithm in polynomial time.
基金the National Natural Science Foundation of China(No.11471205).
文摘This paper discusses the fixed-hub single allocation problem(FHSAP).In this problem,a network consists of hub nodes and terminal nodes.Hubs are fixed and fully connected;each terminal node is assigned to a single hub which routes all its traffic.The goal is to minimize the cost of routing the traffic in the network.In this paper,we propose a new linear programming(LP)relaxation for this problem by incorporating a set of validity constraints into the classical formulations by Ernst and Krishnamoorthy(Locat Sci 4:139–154,Ann Op Res 86:141–159).A geometric rounding algorithm is then used to obtain an integral solution from the fractional solution.We show that by incorporating the validity constraints,the strengthened LP often provides much tighter upper bounds than the previous methods with a little more computational effort and the solution obtained often has a much smaller gap with the optimal solution.We also formulate a robust version of the FHSAP and show that it can guard against data uncertainty with little costs.
文摘The paper provides a broad discussion of the topic "accruals". Though much of what is said is familiar from the literature on accruals, the paper tries to develop concepts and show how theses forge tight links across a variety of themes. The starting point of the analysis concerns the construct of an accrual.The case is made that it should rest solely on consecutive balance sheets and the splitting of assets/liabilities into(i) cash and approximate cash,assets/liabilities and(ii) all other kinds of assets/liabilities. Given this divide of assets/liabilities one can measure the components in the foundation equation: cash earnings + net accrual = comprehensive earnings. The paper then proceeds to discuss how the net accrual relates to growth in a firm's operating activities and the extent to which it can be informative or misleading.This topic in turn integrates with the issue of a firm's quality of earnings and the role of accounting conservatism. Among the remaining topics, the paper discusses how one conceptualizes diagnostics to assess whether or not a period's accrual is likely to be biased upwards or downwards. It gives rise to a consideration of how one constructs accruals that may be more informative than GAAP accruals and the role of value-relevance studies to assess the information content of accrual constructs. The paper ends with a list of suggestions how future research may be modified in light of the discussions in this paper.
