leaf_stability.R

# We are going to look at how iterating too much might generate observation instability.
# Obviously, we are in a controlled environment, without issues (real rules).
# Do not do this in a real scenario.

# First, we load our libraries
library(lightgbm)
library(ggplot2)

# Second, we load our data
data(agaricus.train, package = "lightgbm")
train <- agaricus.train
dtrain <- lgb.Dataset(train$data, label = train$label)
data(agaricus.test, package = "lightgbm")
test <- agaricus.test
dtest <- lgb.Dataset.create.valid(dtrain, test$data, label = test$label)

# Third, we setup parameters and we train a model
params <- list(objective = "regression", metric = "l2")
valids <- list(test = dtest)
model <- lgb.train(
    params
    , dtrain
    , 50L
    , valids
    , min_data = 1L
    , learning_rate = 0.1
    , bagging_fraction = 0.1
    , bagging_freq = 1L
    , bagging_seed = 1L
)

# We create a data.frame with the following structure:
# X = average leaf of the observation throughout all trees
# Y = prediction probability (clamped to [1e-15, 1-1e-15])
# Z = logloss
# binned = binned quantile of average leaf
new_data <- data.frame(
    X = rowMeans(predict(
        model
        , agaricus.test$data
        , predleaf = TRUE
    ))
    , Y = pmin(
        pmax(
            predict(model, agaricus.test$data)
            , 1e-15
        )
        , 1.0 - 1e-15
    )
)
new_data$Z <- -1.0 * (agaricus.test$label * log(new_data$Y) + (1L - agaricus.test$label) * log(1L - new_data$Y))
new_data$binned <- .bincode(
    x = new_data$X
    , breaks = quantile(
        x = new_data$X
        , probs = seq_len(9L) / 10.0
    )
    , right = TRUE
    , include.lowest = TRUE
)
new_data$binned[is.na(new_data$binned)] <- 0L
new_data$binned <- as.factor(new_data$binned)

# We can check the binned content
table(new_data$binned)

# We can plot the binned content
# On the second plot, we clearly notice the lower the bin (the lower the leaf value), the higher the loss
# On the third plot, it is smooth!
ggplot(
    data = new_data
    , mapping = aes(x = X, y = Y, color = binned)
) + geom_point() +
  theme_bw() +
  labs(title = "Prediction Depth", x = "Leaf Bin", y = "Prediction Probability")
ggplot(
    data = new_data
    , mapping = aes(x = binned, y = Z, fill = binned, group = binned)
) + geom_boxplot() +
  theme_bw() +
  labs(title = "Prediction Depth Spread", x = "Leaf Bin", y = "Logloss")
ggplot(
    data = new_data
    , mapping = aes(x = Y, y = ..count.., fill = binned)
) + geom_density(position = "fill") +
  theme_bw() +
  labs(title = "Depth Density", x = "Prediction Probability", y = "Bin Density")


# Now, let's show with other parameters
model2 <- lgb.train(
    params
    , dtrain
    , 100L
    , valids
    , min_data = 1L
    , learning_rate = 1.0
)

# We create the data structure, but for model2
new_data2 <- data.frame(
    X = rowMeans(predict(
        model2
        , agaricus.test$data
        , predleaf = TRUE
    ))
    , Y = pmin(
        pmax(
            predict(
                model2
                , agaricus.test$data
            )
            , 1e-15
        )
      , 1.0 - 1e-15
     )
)
new_data2$Z <- -1.0 * (agaricus.test$label * log(new_data2$Y) + (1L - agaricus.test$label) * log(1L - new_data2$Y))
new_data2$binned <- .bincode(
    x = new_data2$X
    , breaks = quantile(
        x = new_data2$X
        , probs = seq_len(9L) / 10.0
    )
    , right = TRUE
    , include.lowest = TRUE
)
new_data2$binned[is.na(new_data2$binned)] <- 0L
new_data2$binned <- as.factor(new_data2$binned)

# We can check the binned content
table(new_data2$binned)

# We can plot the binned content
# On the second plot, we clearly notice the lower the bin (the lower the leaf value), the higher the loss
# On the third plot, it is clearly not smooth! We are severely overfitting the data, but the rules are
# real thus it is not an issue
# However, if the rules were not true, the loss would explode.
ggplot(
    data = new_data2
    , mapping = aes(x = X, y = Y, color = binned)
) + geom_point() +
  theme_bw() +
  labs(title = "Prediction Depth", x = "Leaf Bin", y = "Prediction Probability")
ggplot(
    data = new_data2
    , mapping = aes(x = binned, y = Z, fill = binned, group = binned)
) + geom_boxplot() +
  theme_bw() +
  labs(title = "Prediction Depth Spread", x = "Leaf Bin", y = "Logloss")
ggplot(
    data = new_data2
    , mapping = aes(x = Y, y = ..count.., fill = binned)
) + geom_density(position = "fill") +
  theme_bw() +
  labs(title = "Depth Density", x = "Prediction Probability", y = "Bin Density")


# Now, try with very severe overfitting
model3 <- lgb.train(
    params
    , dtrain
    , 1000L
    , valids
    , min_data = 1L
    , learning_rate = 1.0
)

# We create the data structure, but for model3
new_data3 <- data.frame(
    X = rowMeans(predict(
        model3
        , agaricus.test$data
        , predleaf = TRUE
    ))
    , Y = pmin(
        pmax(
            predict(
                model3
                , agaricus.test$data
            )
            , 1e-15
        )
        , 1.0 - 1e-15
    )
)
new_data3$Z <- -1.0 * (agaricus.test$label * log(new_data3$Y) + (1L - agaricus.test$label) * log(1L - new_data3$Y))
new_data3$binned <- .bincode(
    x = new_data3$X
    , breaks = quantile(
        x = new_data3$X
        , probs = seq_len(9L) / 10.0
    )
    , right = TRUE
    , include.lowest = TRUE
)
new_data3$binned[is.na(new_data3$binned)] <- 0L
new_data3$binned <- as.factor(new_data3$binned)

# We can check the binned content
table(new_data3$binned)

# We can plot the binned content
# On the third plot, it is clearly not smooth! We are severely overfitting the data, but the rules
# are real thus it is not an issue.
# However, if the rules were not true, the loss would explode. See the sudden spikes?
ggplot(
    data = new_data3
    , mapping = aes(x = Y, y = ..count.., fill = binned)
) +
  geom_density(position = "fill") +
  theme_bw() +
  labs(title = "Depth Density", x = "Prediction Probability", y = "Bin Density")

# Compare with our second model, the difference is severe. This is smooth.
ggplot(
    data = new_data2
    , mapping = aes(x = Y, y = ..count.., fill = binned)
) + geom_density(position = "fill") +
  theme_bw() +
  labs(title = "Depth Density", x = "Prediction Probability", y = "Bin Density")