A histogram groups numeric values into bins, making the distribution easier to inspect than a long list of individual observations. In exploratory data analysis, it helps reveal the shape and concentration of a numeric feature and can expose values that merit closer checking. section 2.4.2
Inspecting vehicle features
For Auto MPG data, plot horsepower with 64 bins and acceleration with 24 bins. These views complement boxplots: boxplots flag possible outliers, while histograms show how observations are distributed across the feature’s range. section 2.4.2
Histograms can also accelerate decision-tree training. Rather than test every distinct feature value as a possible split, histogram splitting uses bin boundary values as candidate thresholds. This reduces split-search work when a feature has many unique values, trading exhaustive candidate evaluation for a summarized search. section 5.4.3
Listing 5.14 The histogram split
import numpy as np
def gini_impurity(y):
_, counts = np.unique(y, return_counts=True)
probs = counts / len(y)
return 1 - np.sum(probs**2) #1
def histogram_split(x, y, use_histogram, n_bins=256):
if use_histogram:
hist, thresholds = np.histogram(
x, bins=n_bins, density=False
) #2
else:
thresholds = np.unique(x) #3
best_score = -1
best_threshold = None #4
for threshold in thresholds: #5
left_mask = x <= threshold
right_mask = x > threshold
left_y = y[left_mask]
right_y = y[right_mask] #6
score = (
gini_impurity(left_y) * len(left_y)
+ gini_impurity(right_y) * len(right_y)
) #7
if score > best_score: q #8
best_threshold = threshold
best_score = score
return best_threshold, best_score #9
The implementation compares unique-value threshold search with a configurable histogram-bin search, then scores each candidate using Gini impurity. section 5.4.3
Latitude split search
For a property-price classification task, a 256-bin search over latitude produced the same reported threshold and score as the full unique-value search, while the timed run fell from 46.9 seconds to 563 milliseconds. section 5.4.3
