mxnet LinearRegressionOutput性能差

Question

我一直无法获得合理的性能使用mxnet LinearRegressionOutput层。

下面的自给示例尝试执行简单多项式函数(y = x1 + x2^2 + x3^3)的回归，并加入少量随机噪声。

使用给定这里的mxnet回归示例，以及包含一个隐藏层的稍微复杂的网络。

下面的示例还使用neuralnet和nnet包对回归网络进行了培训，从图中可以看出这两个包的性能要好得多。

我意识到对性能不佳的网络的答案是做一些超参数调优，但是我已经尝试了一系列的值，但性能没有任何改善。因此，我有以下问题：

1. 我的mxnet回归实现中有错误吗？
2. 有没有人有经验可以帮助我从mxnet获得一个简单的回归问题的合理性能，就像这里考虑的问题？
3. 还有其他人有一个性能良好的mxnet回归示例吗？

我的安排如下：

MXNet version: 0.7
R `sessionInfo()`: R version 3.3.2 (2016-10-31)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 7 x64 (build 7601) Service Pack 1

mxnet的不良回归结果

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从这个可复制的例子来看：

## SIMPLE REGRESSION PROBLEM
# Check mxnet out-of-the-box performance VS neuralnet, and caret/nnet

library(mxnet)
library(neuralnet)
library(nnet)
library(caret)
library(tictoc)
library(reshape)

# Data definitions
nObservations <- 1000
noiseLvl <- 0.1

# Network config
nHidden <- 3
learnRate <- 2e-6
momentum <- 0.9
batchSize <- 20
nRound <- 1000
verbose <- FALSE
array.layout = "rowmajor"

# GENERATE DATA:
df <- data.frame(x1=runif(nObservations),
                 x2=runif(nObservations),
                 x3=runif(nObservations))

df$y <- df$x1 + df$x2^2 + df$x3^3 + noiseLvl*runif(nObservations)
# normalize data columns
# df <- scale(df)

# Seperate data into train/test
test.ind = seq(1, nObservations, 10)    # 1 in 10 samples for testing
train.x = data.matrix(df[-test.ind, -which(colnames(df) %in% c("y"))])
train.y = df[-test.ind, "y"]
test.x = data.matrix(df[test.ind, -which(colnames(df) %in% c("y"))])
test.y = df[test.ind, "y"]

# Define mxnet network, following 5-minute regression example from here:
# http://mxnet-tqchen.readthedocs.io/en/latest//packages/r/fiveMinutesNeuralNetwork.html#regression
data <- mx.symbol.Variable("data")
label <- mx.symbol.Variable("label")
fc1 <- mx.symbol.FullyConnected(data, num_hidden=1, name="fc1")
lro1 <- mx.symbol.LinearRegressionOutput(data=fc1, label=label, name="lro")

# Train MXNET model
mx.set.seed(0)
tic("mxnet training 1")
mxModel1 <- mx.model.FeedForward.create(lro1, X=train.x, y=train.y,
                                        eval.data=list(data=test.x, label=test.y),
                                        ctx=mx.cpu(), num.round=nRound,
                                        array.batch.size=batchSize,
                                        learning.rate=learnRate, momentum=momentum,
                                        eval.metric=mx.metric.rmse,
                                        verbose=FALSE, array.layout=array.layout)
toc()

# Train network with a hidden layer
fc1 <- mx.symbol.FullyConnected(data, num_hidden=nHidden, name="fc1")
tanh1 <- mx.symbol.Activation(fc1, act_type="tanh", name="tanh1")
fc2 <- mx.symbol.FullyConnected(tanh1, num_hidden=1, name="fc2")
lro2 <- mx.symbol.LinearRegressionOutput(data=fc2, label=label, name="lro")
tic("mxnet training 2")
mxModel2 <- mx.model.FeedForward.create(lro2, X=train.x, y=train.y,
                                        eval.data=list(data=test.x, label=test.y),
                                        ctx=mx.cpu(), num.round=nRound,
                                        array.batch.size=batchSize,
                                        learning.rate=learnRate, momentum=momentum,
                                        eval.metric=mx.metric.rmse,
                                        verbose=FALSE, array.layout=array.layout)
toc()

# Train neuralnet model
mx.set.seed(0)
tic("neuralnet training")
nnModel <- neuralnet(y~x1+x2+x3, data=df[-test.ind, ], hidden=c(nHidden),
                     linear.output=TRUE, stepmax=1e6)
toc()

# Train caret model
mx.set.seed(0)
tic("nnet training")
nnetModel <- nnet(y~x1+x2+x3, data=df[-test.ind, ], size=nHidden, trace=F,
                   linout=TRUE)
toc()

# Check response VS targets on training data:
par(mfrow=c(2,2))
plot(train.y, compute(nnModel, train.x)$net.result, 
     main="neuralnet Train Fitting Fake Data", xlab="Target", ylab="Response")
abline(0,1, col="red")

plot(train.y, predict(nnetModel, train.x), 
     main="nnet Train Fitting Fake Data", xlab="Target", ylab="Response")
abline(0,1, col="red")

plot(train.y, predict(mxModel1, train.x, array.layout=array.layout), 
     main="MXNET (no hidden) Train Fitting Fake Data", xlab="Target",
     ylab="Response")
abline(0,1, col="red")

plot(train.y, predict(mxModel2, train.x, array.layout=array.layout),
     main="MXNET (with hidden) Train Fitting Fake Data", xlab="Target",
     ylab="Response")
abline(0,1, col="red")

Answer 1

我在mxnet github (链接)中也问了同样的问题，乌照建议使用一种不同的优化方法，所以这都归功于他们。

使用"rmsprop“优化器，以及增加批处理大小，使mxnet能够在这个简单的回归任务上提供与neuralnet和nnet工具相当的性能。我还包括了线性lm回归的性能。

结果和独立的示例代码包括在下面。我希望这对其他人(或将来的我自己)有帮助。

五种模型的均方误差：

$mxModel1
[1] 0.1404579862

$mxModel2
[1] 0.03263213499

$nnet
[1] 0.03222651138

$neuralnet
[1] 0.03054112057

$linearModel
[1] 0.1404421006

显示mxnet回归良好/合理性能的地块(绿色线性回归结果)：

​

最后是这个独立示例的代码：

## SIMPLE REGRESSION PROBLEM
# Check mxnet out-of-the-box performance VS neuralnet, and caret/nnet

library(mxnet)
library(neuralnet)
library(nnet)
library(caret)
library(tictoc)
library(reshape)

# Data definitions
nObservations <- 1000
noiseLvl <- 0.1

# Network config
nHidden <- 3
batchSize <- 100
nRound <- 400
verbose <- FALSE
array.layout = "rowmajor"
optimizer <- "rmsprop"

# GENERATE DATA:
set.seed(0)
df <- data.frame(x1=runif(nObservations),
                 x2=runif(nObservations),
                 x3=runif(nObservations))

df$y <- df$x1 + df$x2^2 + df$x3^3 + noiseLvl*runif(nObservations)
# normalize data columns
# df <- scale(df)

# Seperate data into train/test
test.ind = seq(1, nObservations, 10)    # 1 in 10 samples for testing
train.x = data.matrix(df[-test.ind, -which(colnames(df) %in% c("y"))])
train.y = df[-test.ind, "y"]
test.x = data.matrix(df[test.ind, -which(colnames(df) %in% c("y"))])
test.y = df[test.ind, "y"]

# Define mxnet network, following 5-minute regression example from here:
# http://mxnet-tqchen.readthedocs.io/en/latest//packages/r/fiveMinutesNeuralNetwork.html#regression
data <- mx.symbol.Variable("data")
label <- mx.symbol.Variable("label")
fc1 <- mx.symbol.FullyConnected(data, num_hidden=1, name="fc1")
lro1 <- mx.symbol.LinearRegressionOutput(data=fc1, label=label, name="lro")

# Train MXNET model
mx.set.seed(0)
tic("mxnet training 1")
mxModel1 <- mx.model.FeedForward.create(lro1, X=train.x, y=train.y,
                                        eval.data=list(data=test.x, label=test.y),
                                        ctx=mx.cpu(), num.round=nRound,
                                        array.batch.size=batchSize,
                                        eval.metric=mx.metric.rmse,
                                        verbose=verbose,
                                        array.layout=array.layout,
                                        optimizer=optimizer
                                        )
toc()

# Train network with a hidden layer
fc1 <- mx.symbol.FullyConnected(data, num_hidden=nHidden, name="fc1")
tanh1 <- mx.symbol.Activation(fc1, act_type="tanh", name="tanh1")
fc2 <- mx.symbol.FullyConnected(tanh1, num_hidden=1, name="fc2")
lro2 <- mx.symbol.LinearRegressionOutput(data=fc2, label=label, name="lro2")
tic("mxnet training 2")
mx.set.seed(0)
mxModel2 <- mx.model.FeedForward.create(lro2, X=train.x, y=train.y,
                                        eval.data=list(data=test.x, label=test.y),
                                        ctx=mx.cpu(), num.round=nRound,
                                        array.batch.size=batchSize,
                                        eval.metric=mx.metric.rmse,
                                        verbose=verbose,
                                        array.layout=array.layout,
                                        optimizer=optimizer
                                        )
toc()

# Train neuralnet model
set.seed(0)
tic("neuralnet training")
nnModel <- neuralnet(y~x1+x2+x3, data=df[-test.ind, ], hidden=c(nHidden),
                     linear.output=TRUE, stepmax=1e6)
toc()
# Train caret model
set.seed(0)
tic("nnet training")
nnetModel <- nnet(y~x1+x2+x3, data=df[-test.ind, ], size=nHidden, trace=F,
                   linout=TRUE)
toc()

# Check response VS targets on training data:
par(mfrow=c(2,2))
plot(train.y, compute(nnModel, train.x)$net.result, 
     main="neuralnet Train Fitting Fake Data", xlab="Target", ylab="Response")
abline(0,1, col="red")

# Plot linear model performance for reference
linearModel <- linearModel <- lm(y~., df[-test.ind, ])
points(train.y, predict(linearModel, data.frame(train.x)), col="green")

plot(train.y, predict(nnetModel, train.x), 
     main="nnet Train Fitting Fake Data", xlab="Target", ylab="Response")
abline(0,1, col="red")

plot(train.y, predict(mxModel1, train.x, array.layout=array.layout), 
     main="MXNET (no hidden) Train Fitting Fake Data", xlab="Target",
     ylab="Response")
abline(0,1, col="red")

plot(train.y, predict(mxModel2, train.x, array.layout=array.layout),
     main="MXNET (with hidden) Train Fitting Fake Data", xlab="Target",
     ylab="Response")
abline(0,1, col="red")

# Create and print table of results:
results <- list()
rmse <- function(target, response) {
  return(sqrt(mean((target - response)^2)))
}
results$mxModel1 <- rmse(train.y, predict(mxModel1, train.x,
                                          array.layout=array.layout))
results$mxModel2 <- rmse(train.y, predict(mxModel2, train.x,
                                          array.layout=array.layout))
results$nnet <- rmse(train.y, predict(nnetModel, train.x))
results$neuralnet <- rmse(train.y, compute(nnModel, train.x)$net.result)
results$linearModel <- rmse(train.y, predict(linearModel, data.frame(train.x)))

print(results)