r - 忽略 keras 中 R 的缺失目标值的损失函数
问题描述
我正在使用 LSTM 模型拟合多元时间序列keras
R
-package(关于 Python 或 PyTorch 中的 keras 的答案也会有所帮助,因为我可以切换)并且有多个输出(3 个连续的,一个分类的)。一些目标在某些时间步长内丢失(编码为 -1,因为所有观察到的值都是 $\geq 0$,但我显然可以将其更改为其他任何值)。我认为有意义的是,如果缺少目标变量(=-1),模型的任何预测都被认为是正确的(=没有损失)。我对预测值是否缺失没有兴趣,因此即使模型可以可靠地预测缺失值,我也不会对强制模型输出 -1 感兴趣。我更愿意预测缺失值是什么(即使我无法检查这是否正确)。
如何创建“忽略”-1 值/认为它们正确的自定义损失函数?
如果更多的上下文很重要,下图是说明我的模型的图表,下面是R
用于生成一些示例数据并在没有丢失数据的情况下拟合模型的代码。在下面的代码中删除该# %>% mutate_at(vars(x1:x4, y1:y4), randomly_set_to_minus_one)
行的注释后,您会得到一些编码为 -1 的输入和输出。我没有强烈的意见应该如何将这些编码为特征,我也可以将这些值设置为中值输入值,并为缺失或其他内容添加一个标志。(对我而言)真正重要的是我的损失函数正确处理 -1 目标值。在帖子的最后,我尝试编写这样的损失函数失败了。
library(tidyverse)
library(keras)
# A function I use to set some values randomly to -1
randomly_set_to_minus_one = function(x){
ifelse(rnorm(length(x))>1, -1, x)
}
# randomly_set_to_minus_one(rnorm(100))
set.seed(1234)
subjects = 250
records_per_subject = 25
# Simulate some time series for multiple subject with multiple records per subject.
example = tibble(subject = rep(1:subjects, each=records_per_subject),
rand1 = rep(rnorm(subjects), each=records_per_subject),
rand2 = rep(rnorm(subjects), each=records_per_subject),
rand3 = rnorm(subjects*records_per_subject),
rand4 = rnorm(subjects*records_per_subject)) %>%
mutate(x1 = 0.8*rand1 + 0.2*rand2 + 0.8*rand3 + 0.2*rand4 + rnorm(n=n(),sd=0.1),
x2 = 0.1*rand1 + 0.9*rand2 + 2*rand3 + rnorm(n=n(),sd=0.1),
x3 = 0.5*rand1 + 0.5*rand2 + 0.2*rand4 + rnorm(n=n(),sd=0.25),
x4 = 0.2*rand1 + 0.2*rand2 + 0.5*rand3 + 0.5*rand4 + rnorm(n=n(),sd=0.1),
x5 = rep(1:records_per_subject, subjects),
y1 = 1+tanh(rand1 + rand2 + 0.05*rand3 + 0.05*rand4 + 2*x5/records_per_subject + rnorm(n=n(),sd=0.05)),
y2 = 10*plogis(0.2*rand1 + 0.2*rand2 + 0.2*rand3 + 0.2*rand4),
y3 = 3*plogis(0.8*rand1 + 0.8*rand4 + 2*(x5-records_per_subject/2)/records_per_subject),
prob1 = exp(rand1/4*3+rand3/4),
prob2 = exp(rand2/4*3+rand4/4),
prob3 = exp(-rand1-rand2-rand3-rand4),
total = prob1+prob2+prob3,
prob1 = prob1/total,
prob2 = prob2/total,
prob3 = prob3/total,
y4 = pmap(list(prob1, prob2, prob3), function(x,y,z) sample(1:3, 1, replace=T, prob=c(x,y,z)))) %>%
unnest(y4) %>%
mutate(x1 = x1 + min(x1),
x2 = x2 + min(x2),
x3 = x3 + min(x3),
x4 = x4 + min(x4)) %>%
dplyr::select(subject, x1:x5, y1:y4)
# %>% mutate_at(vars(x1:x4, y1:y4), randomly_set_to_minus_one)
# Create arrays the way keras wants them as inputs/outputs:
# 250, 25, 5 array of predictors
x_array = map(sort(unique(example$subject)), function(x) {
example %>%
filter(subject==x) %>%
dplyr::select(x1:x5) %>%
as.matrix()
}) %>%
abind::abind(along=3 ) %>%
aperm(perm=c(3,1,2))
# 250, 25, 3 array of continuous target variables
y13_array = map(sort(unique(example$subject)), function(x) {
example %>%
filter(subject==x) %>%
dplyr::select(y1:y3) %>%
as.matrix()
}) %>%
abind::abind(along=3 ) %>%
aperm(perm=c(3,1,2))
# 250, 25, 1 array of categorical target variables (one-hot-encoded)
y4_array = map(sort(unique(example$subject)), function(x) {
example %>%
filter(subject==x) %>%
mutate(y41 = case_when(y4==1~1, y4==-1~-1, TRUE~0),
y42 = case_when(y4==2~1, y4==-1~-1, TRUE~0),
y43 = case_when(y4==3~1, y4==-1~-1, TRUE~0)) %>%
dplyr::select(y41:y43) %>%
as.matrix()
}) %>%
abind::abind(along=3 ) %>%
aperm(perm=c(3,1,2))
# Define LSTM neural network
nn_inputs <- layer_input(shape = c(dim(x_array)[2], dim(x_array)[3]))
nn_lstm_layers <- nn_inputs %>%
layer_lstm(units = 32, return_sequences = TRUE,
dropout = 0.3, # That's dropout applied to the inputs, the below is recurrent drop-out applied to LSTM memory cells
recurrent_dropout = 0.3) %>%
layer_lstm(units = 16,
return_sequences = TRUE,
dropout = 0.3,
recurrent_dropout = 0.3)
# First continuous output (3 variables)
cont_target <- nn_lstm_layers %>%
layer_dense(units = dim(y13_array)[3], name = "cont_target")
# Categorical outcome (3 categories one-hot-encoded)
cat_target <- nn_lstm_layers %>%
layer_dense(units = dim(y4_array)[3], activation = "sigmoid", name = "cat_target")
model <- keras_model(nn_inputs,
list(cont_target, cat_target))
summary(model)
val_samples = sample(x=c( rep(FALSE, floor(dim(x_array)[1]*0.8)),
rep(TRUE, ceiling(dim(x_array)[1]*0.2))),
size = dim(x_array)[1],
replace = F)
model %>% compile(
optimizer = "rmsprop",
loss = list( cont_target = "mse",
cat_target = "categorical_crossentropy"),
loss_weights = list(cont_target = 1.0, cat_target = 1.0))
history <- model %>%
fit(
x_array[!val_samples,,],
list(cont_target = y13_array[!val_samples,,],
cat_target = y4_array[!val_samples,,]),
epochs = 100,
batch_size = 32,
validation_data = list(x_array[val_samples,,],
list(cont_target = y13_array[val_samples,,],
cat_target = y4_array[val_samples,,])),
callbacks = list(callback_reduce_lr_on_plateau(
monitor = "val_loss", factor = 0.5, patience = 10, verbose = 0,
mode = "min", min_delta = 1e-04, cooldown = 0, min_lr = 0),
callback_early_stopping(monitor = "val_loss",
min_delta = 0,
patience = 20,
restore_best_weights = TRUE,
verbose = 0, mode = c("auto")))
)
plot(history) + scale_y_log10()
这是我尝试编写一个忽略 -1 值的修改后的 MSE 损失函数:
# Custom loss functions to deal with missing values (coded as -1)
mse_na_loss <- function(y_true, y_pred){
K <- backend()
#K$mean( K$switch(K$equal(y_true, -1), K$zeros(shape=K$constant(y_true)$shape), K$pow(y_true-y_pred, 2)), axis=-1)
#K$mean( K$pow(y_true-y_pred, 2))
#K$zeros(shape=K$constant(y_true)$shape)
#K$equal(y_true, -1)
K$mean(
K$switch( K$equal(y_true, -1),
K$zeros(shape=K$constant(y_true)$shape, dtype = "float64"),
K$pow(y_true-y_pred, 2)),
axis=-1L)
}
解决方案
我认为有意义的是,如果缺少目标变量(=-1),模型的任何预测都被认为是正确的(=没有损失)。
您可以=no loss incurred
通过检查 y_true 是否与 -1 ( k_not_equal
) 不同,然后将二进制转换为数字 ( ) 来实现这一点 ( k_cast
)。这将为您提供诸如 (1,0,1,1,0) 之类的值,该值可以与 MSE 相乘。
mse_na_loss <- function(y_true, y_pred){
k_pow(y_true-y_pred, 2) * k_cast(k_not_equal(y_true, -1), 'float32')
}
这基本上会为您提供您在问题结束时尝试制作的损失函数。并回答您问题的引用部分。
但是,我认为这不是一个好方法。如您所说,此损失函数不会“忽略”这些观察结果。它只是知道任何值都适合这里。这可能会给您的学习带来不必要的噪音。
基于域,其他 NA 处理方法,例如“最后一次观察结转”( na.locf
) 可能比 -1 更好。
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