Counterfactuals guided by prototypes on California housing dataset

This notebook goes through an example of prototypical counterfactuals using k-d trees to build the prototypes. Please check out this notebook for a more in-depth application of the method on MNIST using (auto-)encoders and trust scores.

In this example, we will train a simple neural net to predict whether house prices in California districts are above the median value or not. We can then find a counterfactual to see which variables need to be changed to increase or decrease a house price above or below the median value.

Note

To enable support for CounterfactualProto, you may need to run

pip install alibi[tensorflow]

%matplotlib inline
import matplotlib.pyplot as plt

import tensorflow as tf
tf.get_logger().setLevel(40) # suppress deprecation messages
tf.compat.v1.disable_v2_behavior() # disable TF2 behaviour as alibi code still relies on TF1 constructs 
from tensorflow.keras.layers import Dense, Input
from tensorflow.keras.models import Model, load_model
from tensorflow.keras.utils import to_categorical

import os
import numpy as np
import pandas as pd
from sklearn.datasets import fetch_california_housing
from sklearn.model_selection import train_test_split
from alibi.explainers import CounterfactualProto

print('TF version: ', tf.__version__)
print('Eager execution enabled: ', tf.executing_eagerly()) # False

TF version:  2.7.4
Eager execution enabled:  False

Load and prepare California housing dataset

california = fetch_california_housing(as_frame=True)
X = california.data.to_numpy()
target = california.target.to_numpy()
feature_names = california.feature_names

california.data.head()

	MedInc	HouseAge	AveRooms	AveBedrms	Population	AveOccup	Latitude	Longitude
0	8.3252	41.0	6.984127	1.023810	322.0	2.555556	37.88	-122.23
1	8.3014	21.0	6.238137	0.971880	2401.0	2.109842	37.86	-122.22
2	7.2574	52.0	8.288136	1.073446	496.0	2.802260	37.85	-122.24
3	5.6431	52.0	5.817352	1.073059	558.0	2.547945	37.85	-122.25
4	3.8462	52.0	6.281853	1.081081	565.0	2.181467	37.85	-122.25

Each row represents a whole census group. Explanation of features:

• 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

For more details on the dataset, refer to the scikit-learn documentation.

Transform into classification task: target becomes whether house price is above the overall median or not

y = np.zeros((target.shape[0],))
y[np.where(target > np.median(target))[0]] = 1

Standardize data

mu = X.mean(axis=0)
sigma = X.std(axis=0)
X = (X - mu) / sigma

Define train and test set

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)
y_train = to_categorical(y_train)
y_test = to_categorical(y_test)

Train model

np.random.seed(42)
tf.random.set_seed(42)

def nn_model():
    x_in = Input(shape=(8,))
    x = Dense(40, activation='relu')(x_in)
    x = Dense(40, activation='relu')(x)
    x_out = Dense(2, activation='softmax')(x)
    nn = Model(inputs=x_in, outputs=x_out)
    nn.compile(loss='categorical_crossentropy', optimizer='sgd', metrics=['accuracy'])
    return nn

nn = nn_model()
nn.summary()
nn.fit(X_train, y_train, batch_size=64, epochs=500, verbose=0)
nn.save('nn_california.h5', save_format='h5')

nn = load_model('nn_california.h5')
score = nn.evaluate(X_test, y_test, verbose=0)
print('Test accuracy: ', score[1])

Test accuracy:  0.87863374

Generate counterfactual guided by the nearest class prototype

Original instance:

X = X_test[1].reshape((1,) + X_test[1].shape)
shape = X.shape

Run counterfactual:

# define model
nn = load_model('nn_california.h5')

# initialize and fit the explainer
cf = CounterfactualProto(nn, shape, use_kdtree=True, theta=10., max_iterations=1000,
                         feature_range=(X_train.min(axis=0), X_train.max(axis=0)), 
                         c_init=1., c_steps=10)

cf.fit(X_train)

# generate a counterfactual
explanation = cf.explain(X)

The prediction flipped from 0 (value below the median) to 1 (above the median):

print(f'Original prediction: {explanation.orig_class}')
print(f'Counterfactual prediction: {explanation.cf["class"]}')

Original prediction: 0
Counterfactual prediction: 1

Let's take a look at the counterfactual. To make the results more interpretable, we will first undo the pre-processing step and then check where the counterfactual differs from the original instance:

orig = X * sigma + mu
counterfactual = explanation.cf['X'] * sigma + mu
delta = counterfactual - orig
for i, f in enumerate(feature_names):
    if np.abs(delta[0][i]) > 1e-4:
        print(f'{f}: {delta[0][i]}')

AveOccup: -0.9049749915631999
Latitude: -0.31885583625280134

So in order for the model to consider the census group as having above median house prices, the average occupancy would have to be lower by almost a whole household member, and the location of the census group would need to shift slightly South.

Comparing the original instance and the counterfactual side-by-side:

pd.DataFrame(orig, columns=feature_names)

	MedInc	HouseAge	AveRooms	AveBedrms	Population	AveOccup	Latitude	Longitude
0	2.5313	30.0	5.039384	1.193493	1565.0	2.679795	35.14	-119.46

pd.DataFrame(counterfactual, columns=feature_names)

	MedInc	HouseAge	AveRooms	AveBedrms	Population	AveOccup	Latitude	Longitude
0	2.5313	30.0	5.039384	1.193493	1565.000004	1.77482	34.821144	-119.46

Clean up:

os.remove('nn_california.h5')