r - R中的矢量化滚动/累积马氏距离

Question

我正在尝试计算滚动马哈拉诺比斯距离而不求助于 for 循环并惨遭失败。

这是一个示例数据集:

df <- data.frame(label = c(rep("A", 5), rep("B", 5)),
               date = rep(seq.Date(from = as.Date("2018-01-01"), by = "days", length.out = 5), 2),
               valx = c(rnorm(5, mean = 0, sd = 1), rnorm(5, mean = 1.5, sd = 1)),
               valy = c(rnorm(5, mean = 100, sd = 10), rnorm(5, mean = 115, sd = 10)),
               valz = c(rnorm(5, mean = 0, sd = 10), rnorm(5, mean = 0, sd = 30)))

我正在尝试按组 ( label ) 计算 valx 的马哈拉诺比斯距离, valy , 和 valz , 但仅使用该日期 ( date ) 或之前的行。我目前的解决方案是遍历每个 label , 遍历每个 date ，将数据集过滤为匹配数据，使用 stats::mahalanobis 计算距离, 将该距离添加到列表中，然后是 do.call和 rbind他们在循环之外*。显然这并不理想。

我怀疑有某种写法:

cum.mdist <- function(df, cols) {...}
df %>%
  group_by(label) %>%
  arrange(date) %>%
  mutate(mdist = xapply(., c(valx, valy, valz), cum.mdist)) %>%
  ungroup()

以类似于这样计算滚动一元函数的方式:

cumsd <- function(x) sapply(seq_along(x), function(k, z) sd(z[1:k]), z = x)

如果没有协方差，我可以计算与组成部分的距离(滚动方差方差很容易使用上述函数计算)，但我认为我的变量确实具有协方差，并且我不确定如何构建滚动协方差矩阵...

是否存在 for 循环之外的解决方案？

---

*循环解决方案的代码如下:

library("tidyverse")
df <- data.frame(label = c(rep("A", 5), rep("B", 5)),
                 date = rep(seq.Date(from = as.Date("2018-01-01"), by = "days", length.out = 5), 2),
                 valx = c(rnorm(5, mean = 0, sd = 1), rnorm(5, mean = 1.5, sd = 1)),
                 valy = c(rnorm(5, mean = 100, sd = 10), rnorm(5, mean = 115, sd = 10)),
                 valz = c(rnorm(5, mean = 0, sd = 10), rnorm(5, mean = 0, sd = 30)))
mdist.list <- vector(length = nrow(df), mode = "list")
counter <- 1

for(l in seq_along(unique(df$label))){
  label_data <- df %>%
    filter(label == unique(df$label)[l])

  for(d in seq_along(unique(label_data$date))){
    label_date_data <- label_data %>%
      filter(date <= unique(label_data$date)[d])

    if(nrow(label_date_data) > 3){
      label_date_data$mdist <- mahalanobis(label_date_data %>% select(contains("val")),
                                           colMeans(label_date_data %>% select(contains("val"))),
                                           cov(label_date_data %>% select(contains("val"))))
    } else{
      label_date_data$mdist <- NA
    }

    mdist.list[[counter]] <- filter(label_date_data, 
                                    date == unique(label_data$date)[d])

    counter <- counter + 1
  }
}

mdist.df <- do.call(rbind, mdist.list)

Answer 1

不确定我是否正确理解了您的要求或期望的输出，下面是使用 data.table 帮助您入门的内容:

library(data.table)
setDT(df)
df[, mdist := 
    .SD[, transpose(lapply(1L:.N, function(n) {
        ma <- .SD[1L:n]
        ans <- tryCatch(mahalanobis(ma, colMeans(ma), var(ma)), error=function(e) NA)
        ans[length(ans)]            
    })), by=.(label), .SDcols=valx:valz]$V1]

输出:

    label       date         valx       valy        valz     mdist
 1:     A 2018-01-01  1.262954285   7.635935  -2.2426789        NA
 2:     A 2018-01-02 -0.326233361  -7.990092   3.7739565        NA
 3:     A 2018-01-03  1.329799263 -11.476570   1.3333636        NA
 4:     A 2018-01-04  1.272429321  -2.894616   8.0418951 2.2500000
 5:     A 2018-01-05  0.414641434  -2.992151  -0.5710677 0.7260652
 6:     B 2018-01-01 -1.539950042  -4.115108  15.1082392        NA
 7:     B 2018-01-02 -0.928567035   2.522234  32.5730809        NA
 8:     B 2018-01-03 -0.294720447  -8.919211 -20.7286152        NA
 9:     B 2018-01-04 -0.005767173   4.356833 -38.5379806 2.2500000
10:     B 2018-01-05  2.404653389 -12.375384   1.4017852 3.0800360

数据:

set.seed(0L)
df <- data.frame(label = c(rep("A", 5), rep("B", 5)),
    date = rep(seq.Date(from = as.Date("2018-01-01"), by = "days", length.out = 5), 2),
    valx = c(rnorm(5, mean = 0, sd = 1), rnorm(5, mean = 0, sd = 1)),
    valy = c(rnorm(5, mean = 0, sd = 10), rnorm(5, mean = 0, sd = 10)),
    valz = c(rnorm(5, mean = 0, sd = 10), rnorm(5, mean = 0, sd = 30)))

如果您只是在寻找 tidyverse 解决方案，我将删除这篇文章。