获取尾随求解器结果
我有一个数据集，用于计算（近似）非线性函数的参数。
原始数据点按时间分布，目前我的求解器能够计算出在给定时间段内对数据项的函数进行建模的最佳参数集。当我合并更大的数据集时，函数逼近的准确性会提高。但与此同时，我不希望太旧的数据项在很大程度上影响函数逼近。我现在计划使用位于预定义时间窗口内的数据项。这个预定义的窗口将随着时间的推移而移动，合并新的数据项并丢弃旧的数据项。然而，要包含或排除数据元素，我总是必须从修改后的数据集开始该过程，这是一个耗时且不适合实时操作的过程。
我试图解决的问题是如何将从附加数据项中学习的内容合并到近似函数中，而不必遍历整个原始数据集。最初的想法是通过子集中的总数据项与所有子集中的总数据项的比率来对从每个数据子集学习到的函数参数进行加权。有人能想到更好的方法吗？对于任何可能的解决方案的提示将不胜感激。
I have a dataset that is being used to compute(approximate) the parameters of a non-linear function.
The raw data points are spread out in time and currently my solver is able to compute the best set of parameters that model the function for data items in a given period of time. The accuracy of the function approximation improves as I incorporate a larger data set. At the same time however, I don't want data items that are too old to largely effect the function approximation. I am now planning to use data items that fall within a pre-defined window in time. This predefined window will move as time progresses, incorporating new data items and discarding old ones. However to include or exclude data elements I always have to start the process from the beginning with the modified data set, a process which is time consuming and not suited for real time-time operation.
The problem I am trying to tackle is how to incorporate learning from additional data items into the approximated function without having to go through the entire original data set. An initial idea is to weight the function parameters learned from each subset of data by the ratio of the total data items in the subset to the total data items in all the subsets. Can anybody think of a better approach? A hint toward any possible solution would be greatly appreciated.
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借鉴一些时间序列技术，一种简单（启发式）方法是对模型使用指数平滑参数，您计算新学习的参数（基于最近的数据）和旧参数的加权平均值（必须使用某种交叉验证/回测来调整权重值）。如果新数据中的信噪比不随时间发生显着变化，则这种方法通常效果很好。
另一种方法是根据早期数据对模型参数施加“先验” - 最简单的方法之一（不需要完整的贝叶斯学习）是在损失函数中添加二次惩罚，以惩罚偏离旧的参数值（使用交叉验证/回测调整惩罚系数）应注意确保在构造惩罚时考虑旧模型参数的方差-协方差矩阵。这大致相当于基于旧模型参数施加高斯先验。
Borrowing from some time series techniques, one simple (heuristic) approach is to use exponential smoothing of your model parameters where you calculate weighted average of the newly learned parameters (based on recent data) and the older parameters (value of the weight would have to be tuned using some sort of cross-validation / backtesting). This usually works quite well if the signal-to-noise ratio does not change dramatically in the new data as a function of time.
Another approach is to impose a "prior" for your model parameters based on earlier data - one of the simplest ways to do that (which does not require full bayesian learning) is to add a quadratic penalty to your loss function that penalizes for deviating from the older parameter values (with the penalty coefficient tuned using cross-validation/backtesting) Some care should be taken to make sure that the variance-covariance matrix of the older model parameters is taken into account when constructing the penalty. This is roughly equivalent to imposing Gaussian prior based on older model parameters.