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02 california housing

import numpy as np
import keras
import tensorflow as tf
import effector
from sklearn.datasets import fetch_california_housing

california_housing = fetch_california_housing(as_frame=True)

2025-02-26 11:16:08.667707: I tensorflow/core/platform/cpu_feature_guard.cc:210] This TensorFlow binary is optimized to use available CPU instructions in performance-critical operations.
To enable the following instructions: AVX2 FMA, in other operations, rebuild TensorFlow with the appropriate compiler flags.

np.random.seed(21)

print(california_housing.DESCR)

.. _california_housing_dataset:

California Housing dataset
--------------------------

**Data Set Characteristics:**

:Number of Instances: 20640

:Number of Attributes: 8 numeric, predictive attributes and the target

:Attribute Information:
    - MedInc        median income in block group
    - HouseAge      median house age in block group
    - AveRooms      average number of rooms per household
    - AveBedrms     average number of bedrooms per household
    - Population    block group population
    - AveOccup      average number of household members
    - Latitude      block group latitude
    - Longitude     block group longitude

:Missing Attribute Values: None

This dataset was obtained from the StatLib repository.
https://www.dcc.fc.up.pt/~ltorgo/Regression/cal_housing.html

The target variable is the median house value for California districts,
expressed in hundreds of thousands of dollars ($100,000).

This dataset was derived from the 1990 U.S. census, using one row per census
block group. A block group is the smallest geographical unit for which the U.S.
Census Bureau publishes sample data (a block group typically has a population
of 600 to 3,000 people).

A household is a group of people residing within a home. Since the average
number of rooms and bedrooms in this dataset are provided per household, these
columns may take surprisingly large values for block groups with few households
and many empty houses, such as vacation resorts.

It can be downloaded/loaded using the
:func:`sklearn.datasets.fetch_california_housing` function.

.. rubric:: References

- Pace, R. Kelley and Ronald Barry, Sparse Spatial Autoregressions,
  Statistics and Probability Letters, 33 (1997) 291-297

feature_names = california_housing.feature_names
target_name= california_housing.target_names[0]
df = type(california_housing.frame)

X = california_housing.data
y = california_housing.target

print("Design matrix shape: {}".format(X.shape))
print("---------------------------------")
for col_name in X.columns:
    print("Feature: {:15}, unique: {:4d}, Mean: {:6.2f}, Std: {:6.2f}, Min: {:6.2f}, Max: {:6.2f}".format(col_name, len(X[col_name].unique()), X[col_name].mean(), X[col_name].std(), X[col_name].min(), X[col_name].max()))

print("\nTarget shape: {}".format(y.shape))
print("---------------------------------")
print("Target: {:15}, unique: {:4d}, Mean: {:6.2f}, Std: {:6.2f}, Min: {:6.2f}, Max: {:6.2f}".format(y.name, len(y.unique()), y.mean(), y.std(), y.min(), y.max()))

Design matrix shape: (20640, 8)
---------------------------------
Feature: MedInc         , unique: 12928, Mean:   3.87, Std:   1.90, Min:   0.50, Max:  15.00
Feature: HouseAge       , unique:   52, Mean:  28.64, Std:  12.59, Min:   1.00, Max:  52.00
Feature: AveRooms       , unique: 19392, Mean:   5.43, Std:   2.47, Min:   0.85, Max: 141.91
Feature: AveBedrms      , unique: 14233, Mean:   1.10, Std:   0.47, Min:   0.33, Max:  34.07
Feature: Population     , unique: 3888, Mean: 1425.48, Std: 1132.46, Min:   3.00, Max: 35682.00
Feature: AveOccup       , unique: 18841, Mean:   3.07, Std:  10.39, Min:   0.69, Max: 1243.33
Feature: Latitude       , unique:  862, Mean:  35.63, Std:   2.14, Min:  32.54, Max:  41.95
Feature: Longitude      , unique:  844, Mean: -119.57, Std:   2.00, Min: -124.35, Max: -114.31

Target shape: (20640,)
---------------------------------
Target: MedHouseVal    , unique: 3842, Mean:   2.07, Std:   1.15, Min:   0.15, Max:   5.00

def preprocess(X, y):
    # Compute mean and std for outlier detection
    X_mean = X.mean()
    X_std = X.std()

    # Exclude instances with any feature 2 std away from the mean
    mask = (X - X_mean).abs() <= 2 * X_std
    mask = mask.all(axis=1)

    X_filtered = X[mask]
    y_filtered = y[mask]

    # Standardize X
    X_mean = X_filtered.mean()
    X_std = X_filtered.std()
    X_standardized = (X_filtered - X_mean) / X_std

    # Standardize y
    y_mean = y_filtered.mean()
    y_std = y_filtered.std()
    y_standardized = (y_filtered - y_mean) / y_std

    return X_standardized, y_standardized, X_mean, X_std, y_mean, y_std



# shuffle and standarize all features
X_df, Y_df, x_mean, x_std, y_mean, y_std = preprocess(X, y)

def split(X_df, Y_df):
    # shuffle indices
    indices = np.arange(len(X_df))
    np.random.shuffle(indices)

    # data split
    train_size = int(0.8 * len(X_df))

    X_train = X_df.iloc[indices[:train_size]]
    Y_train = Y_df.iloc[indices[:train_size]]
    X_test = X_df.iloc[indices[train_size:]]
    Y_test = Y_df.iloc[indices[train_size:]]

    return X_train, Y_train, X_test, Y_test

# train/test split
X_train, Y_train, X_test, Y_test = split(X_df, Y_df)

# Train - Evaluate - Explain a neural network
model = keras.Sequential([
    keras.layers.Dense(1024, activation="relu"),
    keras.layers.Dense(512, activation="relu"),
    keras.layers.Dense(256, activation="relu"),
    keras.layers.Dense(1)
])

optimizer = keras.optimizers.Adam(learning_rate=0.001)
model.compile(optimizer=optimizer, loss="mse", metrics=["mae", keras.metrics.RootMeanSquaredError()])
model.fit(X_train, Y_train, batch_size=1024, epochs=20, verbose=1)
model.evaluate(X_train, Y_train, verbose=1)
model.evaluate(X_test, Y_test, verbose=1)

Epoch 1/20
15/15 ━━━━━━━━━━━━━━━━━━━━ 2s 19ms/step - loss: 0.5963 - mae: 0.5775 - root_mean_squared_error: 0.7677
Epoch 2/20
15/15 ━━━━━━━━━━━━━━━━━━━━ 0s 20ms/step - loss: 0.3338 - mae: 0.4156 - root_mean_squared_error: 0.5777
Epoch 3/20
15/15 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.2985 - mae: 0.3941 - root_mean_squared_error: 0.5463
Epoch 4/20
15/15 ━━━━━━━━━━━━━━━━━━━━ 0s 20ms/step - loss: 0.2891 - mae: 0.3813 - root_mean_squared_error: 0.5377
Epoch 5/20
15/15 ━━━━━━━━━━━━━━━━━━━━ 0s 20ms/step - loss: 0.2772 - mae: 0.3718 - root_mean_squared_error: 0.5265
Epoch 6/20
15/15 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.2798 - mae: 0.3762 - root_mean_squared_error: 0.5289
Epoch 7/20
15/15 ━━━━━━━━━━━━━━━━━━━━ 0s 20ms/step - loss: 0.2643 - mae: 0.3626 - root_mean_squared_error: 0.5140
Epoch 8/20
15/15 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.2650 - mae: 0.3613 - root_mean_squared_error: 0.5148
Epoch 9/20
15/15 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.2559 - mae: 0.3569 - root_mean_squared_error: 0.5058
Epoch 10/20
15/15 ━━━━━━━━━━━━━━━━━━━━ 0s 20ms/step - loss: 0.2578 - mae: 0.3547 - root_mean_squared_error: 0.5077
Epoch 11/20
15/15 ━━━━━━━━━━━━━━━━━━━━ 0s 20ms/step - loss: 0.2499 - mae: 0.3488 - root_mean_squared_error: 0.4998
Epoch 12/20
15/15 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.2500 - mae: 0.3488 - root_mean_squared_error: 0.4999
Epoch 13/20
15/15 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.2405 - mae: 0.3424 - root_mean_squared_error: 0.4903
Epoch 14/20
15/15 ━━━━━━━━━━━━━━━━━━━━ 0s 19ms/step - loss: 0.2378 - mae: 0.3383 - root_mean_squared_error: 0.4876
Epoch 15/20
15/15 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.2382 - mae: 0.3391 - root_mean_squared_error: 0.4879
Epoch 16/20
15/15 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.2360 - mae: 0.3422 - root_mean_squared_error: 0.4858
Epoch 17/20
15/15 ━━━━━━━━━━━━━━━━━━━━ 0s 17ms/step - loss: 0.2246 - mae: 0.3293 - root_mean_squared_error: 0.4739
Epoch 18/20
15/15 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.2233 - mae: 0.3259 - root_mean_squared_error: 0.4725
Epoch 19/20
15/15 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.2144 - mae: 0.3216 - root_mean_squared_error: 0.4631
Epoch 20/20
15/15 ━━━━━━━━━━━━━━━━━━━━ 0s 18ms/step - loss: 0.2099 - mae: 0.3204 - root_mean_squared_error: 0.4581
456/456 ━━━━━━━━━━━━━━━━━━━━ 1s 1ms/step - loss: 0.2090 - mae: 0.3247 - root_mean_squared_error: 0.4572
114/114 ━━━━━━━━━━━━━━━━━━━━ 0s 1ms/step - loss: 0.3026 - mae: 0.3725 - root_mean_squared_error: 0.5495





[0.2769879102706909, 0.36055105924606323, 0.5262964367866516]

def model_jac(x):
    x_tensor = tf.convert_to_tensor(x, dtype=tf.float32)
    with tf.GradientTape() as t:
        t.watch(x_tensor)
        pred = model(x_tensor)
        grads = t.gradient(pred, x_tensor)
    return grads.numpy()

def model_forward(x):
    return model(x).numpy().squeeze()

scale_y = {"mean": y_mean, "std": y_std}
scale_x_list =[{"mean": x_mean.iloc[i], "std": x_std.iloc[i]} for i in range(len(x_mean))]

y_limits = [0, 4]
dy_limits = [-3, 3]

Global effects

rhale = effector.RHALE(data=X_train.to_numpy(), model=model_forward, model_jac=model_jac, feature_names=feature_names, target_name=target_name, nof_instances="all")
for i in range(len(feature_names)):
    rhale.plot(feature=i, centering=True, scale_x=scale_x_list[i], scale_y=scale_y, y_limits=y_limits, dy_limits=dy_limits)

png

png

png

png

png

png

png

png

Regional Effects

reg_rhale = effector.RegionalRHALE(data=X_train.to_numpy(), model=model_forward, model_jac=model_jac, feature_names=feature_names, target_name=target_name, nof_instances="all")
reg_rhale.fit("all", space_partitioner=effector.space_partitioning.Best(min_heterogeneity_decrease_pcg=0.25))
reg_rhale.summary(features="all", scale_x_list=scale_x_list)

100%|██████████| 8/8 [00:34<00:00,  4.30s/it]



Feature 0 - Full partition tree:
🌳 Full Tree Structure:
───────────────────────
MedInc 🔹 [id: 0 | heter: 0.05 | inst: 14576 | w: 1.00]
--------------------------------------------------
Feature 0 - Statistics per tree level:
🌳 Tree Summary:
─────────────────
Level 0🔹heter: 0.05




Feature 1 - Full partition tree:
🌳 Full Tree Structure:
───────────────────────
HouseAge 🔹 [id: 0 | heter: 0.05 | inst: 14576 | w: 1.00]
--------------------------------------------------
Feature 1 - Statistics per tree level:
🌳 Tree Summary:
─────────────────
Level 0🔹heter: 0.05




Feature 2 - Full partition tree:
🌳 Full Tree Structure:
───────────────────────
AveRooms 🔹 [id: 0 | heter: 0.04 | inst: 14576 | w: 1.00]
--------------------------------------------------
Feature 2 - Statistics per tree level:
🌳 Tree Summary:
─────────────────
Level 0🔹heter: 0.04




Feature 3 - Full partition tree:
🌳 Full Tree Structure:
───────────────────────
AveBedrms 🔹 [id: 0 | heter: 0.01 | inst: 14576 | w: 1.00]
--------------------------------------------------
Feature 3 - Statistics per tree level:
🌳 Tree Summary:
─────────────────
Level 0🔹heter: 0.01




Feature 4 - Full partition tree:
🌳 Full Tree Structure:
───────────────────────
Population 🔹 [id: 0 | heter: 0.02 | inst: 14576 | w: 1.00]
--------------------------------------------------
Feature 4 - Statistics per tree level:
🌳 Tree Summary:
─────────────────
Level 0🔹heter: 0.02




Feature 5 - Full partition tree:
🌳 Full Tree Structure:
───────────────────────
AveOccup 🔹 [id: 0 | heter: 0.05 | inst: 14576 | w: 1.00]
    HouseAge ≤ 25.60 🔹 [id: 1 | heter: 0.02 | inst: 5587 | w: 0.38]
    HouseAge > 25.60 🔹 [id: 2 | heter: 0.04 | inst: 8989 | w: 0.62]
--------------------------------------------------
Feature 5 - Statistics per tree level:
🌳 Tree Summary:
─────────────────
Level 0🔹heter: 0.05
    Level 1🔹heter: 0.03 | 🔻0.01 (30.28%)




Feature 6 - Full partition tree:
🌳 Full Tree Structure:
───────────────────────
Latitude 🔹 [id: 0 | heter: 0.67 | inst: 14576 | w: 1.00]
    Longitude ≤ -121.55 🔹 [id: 1 | heter: 0.44 | inst: 3810 | w: 0.26]
    Longitude > -121.55 🔹 [id: 2 | heter: 0.30 | inst: 10766 | w: 0.74]
--------------------------------------------------
Feature 6 - Statistics per tree level:
🌳 Tree Summary:
─────────────────
Level 0🔹heter: 0.67
    Level 1🔹heter: 0.34 | 🔻0.33 (49.37%)




Feature 7 - Full partition tree:
🌳 Full Tree Structure:
───────────────────────
Longitude 🔹 [id: 0 | heter: 0.50 | inst: 14576 | w: 1.00]
    Latitude ≤ 36.22 🔹 [id: 1 | heter: 0.23 | inst: 8566 | w: 0.59]
    Latitude > 36.22 🔹 [id: 2 | heter: 0.30 | inst: 6010 | w: 0.41]
--------------------------------------------------
Feature 7 - Statistics per tree level:
🌳 Tree Summary:
─────────────────
Level 0🔹heter: 0.50
    Level 1🔹heter: 0.26 | 🔻0.24 (47.85%)

AveOccup: average number of people residing in a house

reg_rhale.plot(feature=5, node_idx=0, centering=True, scale_x_list=scale_x_list, scale_y=scale_y, y_limits=y_limits)

png

for node_idx in [1, 2]:
    reg_rhale.plot(feature=5, node_idx=node_idx, centering=True, scale_x_list=scale_x_list, scale_y=scale_y, y_limits=y_limits)

png

png

Latitude (south to north)

reg_rhale.plot(feature=6, node_idx=0, centering=True, scale_x_list=scale_x_list, scale_y=scale_y, y_limits=y_limits)

png

Global Trend: House prices decrease as we move north. 

for node_idx in [1, 2]:
    reg_rhale.plot(feature=6, node_idx=node_idx, centering=True, scale_x_list=scale_x_list, scale_y=scale_y, y_limits=y_limits)

png

png

Global Trend: House prices decrease as we move north.

Regional Trends: Moreorless the same, with minor different curves.

Longitude (west to east)

reg_rhale.plot(feature=7, node_idx=0, centering=True, scale_x_list=scale_x_list, scale_y=scale_y)

png

Global Trend: House prices decrease as we move east. 

for node_idx in [1, 2]:
    reg_rhale.plot(feature=7, node_idx=node_idx, centering=True, scale_x_list=scale_x_list, scale_y=scale_y, y_limits=y_limits)

png

png

Global Trend: House prices decrease as we move east.

Regional Trends:
- North (latitude > 35.85): Prices drop more sharply in the first half from east to west.
- South (latitude < 35.85): Prices drop more sharply in the second half from east to west.