Arrival rate approximation by nonnegative cubic splines
Arrival rate approximation by nonnegative cubic splines
复制标题
通过非负三次样条逼近到达率
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
Gábor Rudolf
中科院分区：
文献类型：
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作者：
F. Alizadeh;Jonathan Eckstein;Nilay Noyan;Gábor Rudolf
我们描述了一种优化方法，以近似数据的到达率，如电子邮件消息，网站访问，数据库的更改，以及由其他服务器镜像的网站的更改。我们根据观测到的到达数据将这些到达率建模为非齐次泊松过程。我们估计的到达函数的三次样条使用最大似然原理。该模型的一个关键特征是样条被约束为处处非负。我们制定了这个约束使用半正定矩阵的非负多项式的特征。我们还描述了我们的模型，允许定期到达率函数和有限精度的输入数据的版本。我们制定的估计问题作为一个凸规划相关的半定规划，并解决它与一个标准的非线性优化包称为KNITRO。我们提出的数值结果使用的电子邮件到达的实际记录在一段时间的60周，和人工生成的数据集。我们还提出了一个交叉验证程序，用于确定适当数量的样条节点来模拟一组到达观测值
We describe an optimization method to approximate the arrival rate of data such as e-mail messages, Web site visits, changes to databases, and changes to Web sites mirrored by other servers. We model these arrival rates as non-homogeneous Poisson process based on observed arrival data. We estimate the arrival function by cubic splines using the maximum likelihood principle. A critical feature of the model is that the splines are constrained to be everywhere nonnegative. We formulate this constraint using a characterization of nonnegative polynomials by positive semidefinite matrices. We also describe versions of our model that allow for periodic arrival rate functions and input data of limited precision. We formulate the estimation problem as a convex program related to semidefinite programming and solve it with a standard nonlinear optimization package called KNITRO. We present numerical results using both an actual record of e-mail arrivals over a period of sixty weeks, and artificially generated data sets. We also present a cross-validation procedure for determining an appropriate number of spline knots to model a set of arrival observations