Regional Effects (unknown black-box function)
- Author: givasile
- Runtime: ~55 s
- Description: The realistic follow-up to tutorial 03: a neural network is fitted on the data and explained with regional PDP, RHALE and SHAP-DP, under uncorrelated and correlated features.
- π The whole notebook in one page: PDP report
This tutorial use the same dataset with the previous tutorial, but instead of explaining the known (synthetic) predictive function, we fit a neural network on the data and explain the neural network. This is a more realistic scenario, since in real-world applications we do not know the underlying function and we only have access to the data. We advise the reader to first read the previous tutorial.
import numpy as np
import effector
import keras
import tensorflow as tf
np.random.seed(12345)
tf.random.set_seed(12345)
WARNING: All log messages before absl::InitializeLog() is called are written to STDERR
I0000 00:00:1784066339.959660 16943 cpu_feature_guard.cc:227] 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.
Simulation example
Data Generating Distribution
We will generate \(N=1000\) examples with \(D=3\) features, which are in the uncorrelated setting all uniformly distributed as follows:
| Feature | Description | Distribution |
|---|---|---|
| \(x_1\) | Uniformly distributed between \(-1\) and \(1\) | \(x_1 \sim \mathcal{U}(-1,1)\) |
| \(x_2\) | Uniformly distributed between \(-1\) and \(1\) | \(x_2 \sim \mathcal{U}(-1,1)\) |
| \(x_3\) | Uniformly distributed between \(-1\) and \(1\) | \(x_3 \sim \mathcal{U}(-1,1)\) |
For the correlated setting, we keep the distributional assumptions for \(x_2\) and \(x_3\), but define \(x_1\) such that it is highly correlated with \(x_3\) by:
\(x_1 = x_3 + \delta\) with \(\delta \sim \mathcal{N}(0,0.0625)\).
def generate_dataset_uncorrelated(N):
x1 = np.random.uniform(-1, 1, size=N)
x2 = np.random.uniform(-1, 1, size=N)
x3 = np.random.uniform(-1, 1, size=N)
return np.stack((x1, x2, x3), axis=-1)
def generate_dataset_correlated(N):
x3 = np.random.uniform(-1, 1, size=N)
x2 = np.random.uniform(-1, 1, size=N)
x1 = x3 + np.random.normal(loc = np.zeros_like(x3), scale = 0.25)
return np.stack((x1, x2, x3), axis=-1)
# generate the dataset for the uncorrelated and correlated setting
N = 1000
X_uncor_train = generate_dataset_uncorrelated(N)
X_uncor_test = generate_dataset_uncorrelated(10000)
X_cor_train = generate_dataset_correlated(N)
X_cor_test = generate_dataset_correlated(10000)
Black-box function
We will use the following linear model with a subgroup-specific interaction term: $$ y = 3x_1I_{x_3>0} - 3x_1I_{x_3\leq0} + x_3$$
On a global level, there is a high heterogeneity for the features \(x_1\) and \(x_3\) due to their interaction with each other. However, this heterogeneity vanishes to 0 if the feature space is separated into subregions:
def generate_target(X):
f = np.where(X[:,2] > 0, 3*X[:,0] + X[:,2], -3*X[:,0] + X[:,2])
epsilon = np.random.normal(loc = np.zeros_like(X[:,0]), scale = 0.1)
Y = f + epsilon
return(Y)
# generate target for uncorrelated and correlated setting
Y_uncor_train = generate_target(X_uncor_train)
Y_uncor_test = generate_target(X_uncor_test)
Y_cor_train = generate_target(X_cor_train)
Y_cor_test = generate_target(X_cor_test)
Fit a Neural Network
We create a two-layer feedforward Neural Network, a weight decay of 0.01 for 100 epochs. We train two instances of this NN, one on the uncorrelated and one on the correlated setting. In both cases, the NN achieves a Mean Squared Error of about \(0.17\) units.
# Train - Evaluate - Explain a neural network
model_uncor = keras.Sequential([
keras.layers.Dense(10, activation="relu", input_shape=(3,)),
keras.layers.Dense(10, activation="relu", input_shape=(3,)),
keras.layers.Dense(1)
])
optimizer = keras.optimizers.Adam(learning_rate=0.01)
model_uncor.compile(optimizer=optimizer, loss="mse")
model_uncor.fit(X_uncor_train, Y_uncor_train, epochs=100)
model_uncor.evaluate(X_uncor_test, Y_uncor_test)
Epoch 1/100
/home/givasile/github/packages/effector/.venv/lib/python3.10/site-packages/keras/src/layers/core/dense.py:95: UserWarning: Do not pass an `input_shape`/`input_dim` argument to a layer. When using Sequential models, prefer using an `Input(shape)` object as the first layer in the model instead.
super().__init__(activity_regularizer=activity_regularizer, **kwargs)
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m17s[0m 553ms/step - loss: 3.5923
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m1s[0m 2ms/step - loss: 2.4581
Epoch 2/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 1.4139
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.9727
Epoch 3/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.6694
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.4579
Epoch 4/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.3966
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.2979
Epoch 5/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.2973
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.2391
Epoch 6/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 18ms/step - loss: 0.2410
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.2042
Epoch 7/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.2032
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.1818
Epoch 8/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.1761
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.1649
Epoch 9/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 15ms/step - loss: 0.1517
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.1493
Epoch 10/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.1284
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.1368
Epoch 11/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 19ms/step - loss: 0.1124
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.1255
Epoch 12/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0953
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.1174
Epoch 13/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0830
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.1100
Epoch 14/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 15ms/step - loss: 0.0735
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.1049
Epoch 15/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0656
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0998
Epoch 16/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0597
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0954
Epoch 17/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 15ms/step - loss: 0.0552
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0910
Epoch 18/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0525
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 1ms/step - loss: 0.0866
Epoch 19/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0492
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0829
Epoch 20/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0457
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0797
Epoch 21/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0436
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0771
Epoch 22/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0400
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0746
Epoch 23/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0401
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0728
Epoch 24/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0399
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0712
Epoch 25/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0413
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0700
Epoch 26/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0419
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0697
Epoch 27/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0406
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0699
Epoch 28/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 18ms/step - loss: 0.0392
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0698
Epoch 29/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 21ms/step - loss: 0.0403
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0701
Epoch 30/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0388
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0686
Epoch 31/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0395
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0679
Epoch 32/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0399
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0670
Epoch 33/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 18ms/step - loss: 0.0393
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0664
Epoch 34/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0398
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0662
Epoch 35/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0396
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0654
Epoch 36/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0393
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0646
Epoch 37/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 18ms/step - loss: 0.0395
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0643
Epoch 38/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0388
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0635
Epoch 39/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0390
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 1ms/step - loss: 0.0647
Epoch 40/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0372
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0639
Epoch 41/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0366
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0638
Epoch 42/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0369
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0632
Epoch 43/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 19ms/step - loss: 0.0354
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0621
Epoch 44/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0370
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0612
Epoch 45/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0338
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0610
Epoch 46/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0367
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0614
Epoch 47/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0340
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0603
Epoch 48/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 19ms/step - loss: 0.0343
[1m25/32[0m [32mβββββββββββββββ[0m[37mβββββ[0m [1m0s[0m 2ms/step - loss: 0.0492
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0602
Epoch 49/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0350
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0606
Epoch 50/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0335
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0595
Epoch 51/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 15ms/step - loss: 0.0321
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0592
Epoch 52/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0355
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0590
Epoch 53/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 18ms/step - loss: 0.0321
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0579
Epoch 54/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0319
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 1ms/step - loss: 0.0582
Epoch 55/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0315
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0581
Epoch 56/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0305
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0572
Epoch 57/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0316
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0563
Epoch 58/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0302
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0561
Epoch 59/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0287
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0554
Epoch 60/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 15ms/step - loss: 0.0309
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0550
Epoch 61/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0295
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0548
Epoch 62/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0290
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0549
Epoch 63/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0284
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0542
Epoch 64/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0273
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0564
Epoch 65/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0268
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0560
Epoch 66/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0274
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0564
Epoch 67/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0276
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0571
Epoch 68/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 15ms/step - loss: 0.0266
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0569
Epoch 69/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0261
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0547
Epoch 70/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0245
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 1ms/step - loss: 0.0534
Epoch 71/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0238
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0537
Epoch 72/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 18ms/step - loss: 0.0236
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0537
Epoch 73/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 15ms/step - loss: 0.0263
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0529
Epoch 74/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0275
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0518
Epoch 75/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0268
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0528
Epoch 76/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0251
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0523
Epoch 77/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0247
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0519
Epoch 78/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 18ms/step - loss: 0.0242
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0530
Epoch 79/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0258
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0519
Epoch 80/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0247
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0514
Epoch 81/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 15ms/step - loss: 0.0239
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0513
Epoch 82/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0234
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0507
Epoch 83/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 15ms/step - loss: 0.0244
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0514
Epoch 84/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0243
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0506
Epoch 85/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0233
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 1ms/step - loss: 0.0501
Epoch 86/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0234
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0501
Epoch 87/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 18ms/step - loss: 0.0236
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 1ms/step - loss: 0.0498
Epoch 88/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0232
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0509
Epoch 89/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 15ms/step - loss: 0.0239
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0509
Epoch 90/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0239
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0500
Epoch 91/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0240
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0508
Epoch 92/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0234
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0490
Epoch 93/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0234
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0480
Epoch 94/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0227
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 1ms/step - loss: 0.0472
Epoch 95/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0231
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 1ms/step - loss: 0.0477
Epoch 96/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0231
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0476
Epoch 97/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 18ms/step - loss: 0.0236
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0479
Epoch 98/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0235
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0482
Epoch 99/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 15ms/step - loss: 0.0241
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0483
Epoch 100/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0236
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0476
[1m 1/313[0m [37mββββββββββββββββββββ[0m [1m19s[0m 63ms/step - loss: 0.0280
[1m 53/313[0m [32mβββ[0m[37mβββββββββββββββββ[0m [1m0s[0m 972us/step - loss: 0.0534
[1m111/313[0m [32mβββββββ[0m[37mβββββββββββββ[0m [1m0s[0m 920us/step - loss: 0.0633
[1m169/313[0m [32mββββββββββ[0m[37mββββββββββ[0m [1m0s[0m 904us/step - loss: 0.0672
[1m227/313[0m [32mββββββββββββββ[0m[37mββββββ[0m [1m0s[0m 894us/step - loss: 0.0693
[1m285/313[0m [32mββββββββββββββββββ[0m[37mββ[0m [1m0s[0m 889us/step - loss: 0.0697
[1m313/313[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 919us/step - loss: 0.0690
0.06895451992750168
model_cor = keras.Sequential([
keras.layers.Dense(10, activation="relu", input_shape=(3,)),
keras.layers.Dense(10, activation="relu", input_shape=(3,)),
keras.layers.Dense(1)
])
optimizer = keras.optimizers.Adam(learning_rate=0.01)
model_cor.compile(optimizer=optimizer, loss="mse")
model_cor.fit(X_cor_train, Y_cor_train, epochs=100)
model_cor.evaluate(X_cor_test, Y_cor_test)
Epoch 1/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m15s[0m 505ms/step - loss: 3.8755
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m1s[0m 2ms/step - loss: 1.9269
Epoch 2/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.8581
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.4580
Epoch 3/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.3018
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.1648
Epoch 4/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.1879
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.1121
Epoch 5/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.1917
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0988
Epoch 6/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.1987
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0901
Epoch 7/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.1949
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0842
Epoch 8/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.1894
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0793
Epoch 9/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.1834
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0754
Epoch 10/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.1780
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0720
Epoch 11/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.1725
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0688
Epoch 12/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 18ms/step - loss: 0.1668
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 1ms/step - loss: 0.0659
Epoch 13/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.1619
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0634
Epoch 14/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.1578
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0609
Epoch 15/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.1534
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0584
Epoch 16/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.1497
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0562
Epoch 17/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.1462
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0541
Epoch 18/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.1420
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 1ms/step - loss: 0.0524
Epoch 19/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.1390
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0506
Epoch 20/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.1365
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0492
Epoch 21/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.1332
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0479
Epoch 22/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.1312
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0467
Epoch 23/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.1290
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0457
Epoch 24/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.1267
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0449
Epoch 25/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.1239
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0442
Epoch 26/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.1214
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0436
Epoch 27/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.1200
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0429
Epoch 28/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.1176
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0421
Epoch 29/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.1166
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0413
Epoch 30/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.1125
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0409
Epoch 31/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0998
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0398
Epoch 32/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0929
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0391
Epoch 33/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0877
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0381
Epoch 34/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0844
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0372
Epoch 35/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0812
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0362
Epoch 36/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0797
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0352
Epoch 37/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0760
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0344
Epoch 38/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0725
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0342
Epoch 39/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 18ms/step - loss: 0.0516
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0325
Epoch 40/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0537
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0324
Epoch 41/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0534
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0318
Epoch 42/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0503
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0312
Epoch 43/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0488
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0308
Epoch 44/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0513
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0303
Epoch 45/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0467
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0301
Epoch 46/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0443
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0295
Epoch 47/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0430
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0290
Epoch 48/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 15ms/step - loss: 0.0410
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0287
Epoch 49/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0396
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0283
Epoch 50/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0386
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0282
Epoch 51/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m2s[0m 91ms/step - loss: 0.0371
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0277
Epoch 52/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0374
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0273
Epoch 53/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0351
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0271
Epoch 54/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0328
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0266
Epoch 55/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0317
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0262
Epoch 56/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0321
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0258
Epoch 57/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0276
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0250
Epoch 58/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0276
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0244
Epoch 59/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0267
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0239
Epoch 60/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0244
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0238
Epoch 61/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0262
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0232
Epoch 62/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0228
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0236
Epoch 63/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0224
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0228
Epoch 64/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0186
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0226
Epoch 65/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0182
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0222
Epoch 66/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 18ms/step - loss: 0.0194
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0221
Epoch 67/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 18ms/step - loss: 0.0182
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 1ms/step - loss: 0.0222
Epoch 68/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0179
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0219
Epoch 69/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0156
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0216
Epoch 70/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0159
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0214
Epoch 71/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0149
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0211
Epoch 72/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0159
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0211
Epoch 73/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0146
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0208
Epoch 74/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 15ms/step - loss: 0.0147
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0207
Epoch 75/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0153
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0207
Epoch 76/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0140
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0206
Epoch 77/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 31ms/step - loss: 0.0143
[1m30/32[0m [32mββββββββββββββββββ[0m[37mββ[0m [1m0s[0m 2ms/step - loss: 0.0171
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0202
Epoch 78/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 18ms/step - loss: 0.0148
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0205
Epoch 79/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0142
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0202
Epoch 80/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0146
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0201
Epoch 81/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0145
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0202
Epoch 82/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0142
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0200
Epoch 83/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 18ms/step - loss: 0.0143
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 1ms/step - loss: 0.0198
Epoch 84/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0143
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0201
Epoch 85/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0138
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0198
Epoch 86/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 19ms/step - loss: 0.0147
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0198
Epoch 87/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0147
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 1ms/step - loss: 0.0200
Epoch 88/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0139
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0199
Epoch 89/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0144
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0199
Epoch 90/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0142
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0196
Epoch 91/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0140
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0196
Epoch 92/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0136
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0195
Epoch 93/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 18ms/step - loss: 0.0145
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0189
Epoch 94/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0138
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0192
Epoch 95/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 18ms/step - loss: 0.0143
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0187
Epoch 96/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0148
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0193
Epoch 97/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0148
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0186
Epoch 98/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 16ms/step - loss: 0.0129
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0192
Epoch 99/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 18ms/step - loss: 0.0159
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0181
Epoch 100/100
[1m 1/32[0m [37mββββββββββββββββββββ[0m [1m0s[0m 17ms/step - loss: 0.0137
[1m32/32[0m [32mββββββββββββββββββββ[0m[37m[0m [1m0s[0m 2ms/step - loss: 0.0195
[1m 1/313[0m [37mββββββββββββββββββββ[0m [1m19s[0m 63ms/step - loss: 0.0147
[1m 50/313[0m [32mβββ[0m[37mβββββββββββββββββ[0m [1m0s[0m 1ms/step - loss: 0.0341
[1m101/313[0m [32mββββββ[0m[37mββββββββββββββ[0m [1m0s[0m 1ms/step - loss: 0.0303
[1m148/313[0m [32mβββββββββ[0m[37mβββββββββββ[0m [1m0s[0m 1ms/step - loss: 0.0287
[1m169/313[0m [32mββββββββββ[0m[37mββββββββββ[0m [1m0s[0m 1ms/step - loss: 0.0283
[1m188/313[0m [32mββββββββββββ[0m[37mββββββββ[0m [1m0s[0m 1ms/step - loss: 0.0280
[1m212/313[0m [32mβββββββββββββ[0m[37mβββββββ[0m [1m0s[0m 1ms/step - loss: 0.0276
[1m232/313[0m [32mββββββββββββββ[0m[37mββββββ[0m [1m0s[0m 2ms/step - loss: 0.0273
[1m259/313[0m [32mββββββββββββββββ[0m[37mββββ[0m [1m0s[0m 2ms/step - loss: 0.0272
[1m282/313[0m [32mββββββββββββββββββ[0m[37mββ[0m [1m0s[0m 2ms/step - loss: 0.0270
[1m302/313[0m [32mβββββββββββββββββββ[0m[37mβ[0m [1m0s[0m 2ms/step - loss: 0.0269
[1m313/313[0m [32mββββββββββββββββββββ[0m[37m[0m [1m1s[0m 2ms/step - loss: 0.0254
0.025420546531677246
PDP
Uncorrelated setting
Global PDP
pdp = effector.PDP(data=X_uncor_train, model=model_uncor, schema={"feature_names": ['x1','x2','x3'], "target_name": "Y"})
pdp.plot(feature=0, centering=True, show_avg_output=False, heterogeneity="ice", y_limits=[-5, 5])
pdp.plot(feature=1, centering=True, show_avg_output=False, heterogeneity="ice", y_limits=[-5, 5])
pdp.plot(feature=2, centering=True, show_avg_output=False, heterogeneity="ice", y_limits=[-5, 5])
Feature importance and one-click explanation
Beyond the plots, every global effect exposes importances() (the dispersion of the
mean effect, the \(\mu\)-twin of heterogeneity), and effector.explain(...) produces a
self-contained Report in one call.
# per-feature importance = dispersion of the mean effect (mu-twin of heterogeneity)
print("importances:", np.round(pdp.importances(), 3))
# one-click auto-explanation -> Report (serializable; self-contained HTML)
report = effector.explain(
X_uncor_train, model_uncor, method="pdp",
schema={"feature_names": ['x1', 'x2', 'x3'], "target_name": "Y"},
nof_instances="all",
)
report.show()
# the whole notebook, in one page: the report published with this example
from pathlib import Path
_out = Path("reports") / "04_regional_effects_real_f"
_out.mkdir(parents=True, exist_ok=True)
report.to_html(_out / "report_pdp.html")
importances: [0.024 0.002 0.585]
[effector] global effects (GAM) -> 11.0% of the model's variance
regional effects (CALM) -> 99.3%
ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
PDP report Β· target: Y
ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
DATA & MODEL
ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
instances 1,000
features 3 Β· 3 continuous
model output mean 0.0708 Β· std 1.79 Β· range [-3.65, 3.92]
EXPLAINED VARIANCE
ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
step split on solo ΞRΒ² RΒ² heter
ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
GAM (all features global) β β 11.0% β
+ x1 x3 +88.3% +88.3% 99.3% 1.69 β 0.08
ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
FINAL 99.3%
REJECTED SPLITS min gain 1.0%
ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
feature split on solo ΞRΒ² reason
ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
β x3 x1 +83.2% -80.1% redundant
β redundant: it would explain variance on its own (see solo),
but the accepted splits already account for it.
FEATURES ranked, in the selected snapshot
ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
feature importance heter #regions
ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
x1 1.6690 ββββββββββββββββββ 0.0781 4
x3 0.5849 ββββββ 1.6876 1
ββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ
the features above carry 100% of the total importance mass
Feature 0 - Full partition tree:
π³ Full Tree Structure:
βββββββββββββββββββββββ
x1 πΉ [id: 0 | heter: 1.69 | inst: 1000 | w: 1.00]
x3 < -0.00 πΉ [id: 1 | heter: 0.19 | inst: 498 | w: 0.50]
x3 < -0.10 πΉ [id: 2 | heter: 0.02 | inst: 450 | w: 0.45]
-0.10 β€ x3 < -0.00 πΉ [id: 3 | heter: 0.53 | inst: 48 | w: 0.05]
x3 β₯ -0.00 πΉ [id: 4 | heter: 0.24 | inst: 502 | w: 0.50]
-0.00 β€ x3 < 0.10 πΉ [id: 5 | heter: 0.63 | inst: 50 | w: 0.05]
x3 β₯ 0.10 πΉ [id: 6 | heter: 0.03 | inst: 452 | w: 0.45]
--------------------------------------------------
Feature 0 - Statistics per tree level:
π³ Tree Summary:
βββββββββββββββββ
Level 0πΉheter: 1.69
Level 1πΉheter: 0.21 | π»1.47 (87.42%)
Level 2πΉheter: 0.08 | π»0.13 (63.16%)
/home/givasile/github/packages/effector/effector/report.py:606: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.
fig.tight_layout()
Feature triage
Survey all features at once: effector.plot_triage β importance right, heterogeneity up; the top-right corner is the to-do list for find_regions.
effector.plot_triage(pdp)
Regional PDP
pdp = effector.PDP(
data=X_uncor_train, model=model_uncor,
schema={"feature_names": ['x1', 'x2', 'x3']},
axis_limits=np.array([[-1, 1], [-1, 1], [-1, 1]]).T,
nof_instances="all",
)
pdp.fit("all", centering=True)
finder = effector.space_partitioning.Best(min_heterogeneity_decrease_pcg=0.3, numerical_features_grid_size=10)
# plural form: one search per feature in a single call -> {feature_name: Partition}
parts = pdp.find_regions(features="all", finder=finder)
partitions = {feat: parts[name] for feat, name in enumerate(['x1', 'x2', 'x3'])}
partitions[0].show()
Feature 0 - Full partition tree:
π³ Full Tree Structure:
βββββββββββββββββββββββ
x1 πΉ [id: 0 | heter: 1.69 | inst: 1000 | w: 1.00]
x3 < 0.00 πΉ [id: 1 | heter: 0.22 | inst: 500 | w: 0.50]
x3 < -0.20 πΉ [id: 2 | heter: 0.01 | inst: 405 | w: 0.41]
-0.20 β€ x3 < 0.00 πΉ [id: 3 | heter: 0.46 | inst: 95 | w: 0.10]
x3 β₯ 0.00 πΉ [id: 4 | heter: 0.21 | inst: 500 | w: 0.50]
0.00 β€ x3 < 0.20 πΉ [id: 5 | heter: 0.43 | inst: 106 | w: 0.11]
x3 β₯ 0.20 πΉ [id: 6 | heter: 0.02 | inst: 394 | w: 0.39]
--------------------------------------------------
Feature 0 - Statistics per tree level:
π³ Tree Summary:
βββββββββββββββββ
Level 0πΉheter: 1.69
Level 1πΉheter: 0.21 | π»1.47 (87.30%)
Level 2πΉheter: 0.10 | π»0.11 (51.26%)
# plot the two level-1 subregions (region idx == old node_idx)
part = partitions[0]
for r in part:
if r.level == 1:
part.plot(r.idx, heterogeneity="ice", y_limits=[-5, 5])
partitions[1].show()
Feature 1 - Full partition tree:
No splits found for feature 1
--------------------------------------------------
Feature 1 - Statistics per tree level:
No splits found for feature 1
partitions[2].show()
Feature 2 - Full partition tree:
π³ Full Tree Structure:
βββββββββββββββββββββββ
x3 πΉ [id: 0 | heter: 1.69 | inst: 1000 | w: 1.00]
x1 < 0.00 πΉ [id: 1 | heter: 0.84 | inst: 494 | w: 0.49]
x1 < -0.40 πΉ [id: 2 | heter: 0.52 | inst: 301 | w: 0.30]
-0.40 β€ x1 < 0.00 πΉ [id: 3 | heter: 0.34 | inst: 193 | w: 0.19]
x1 β₯ 0.00 πΉ [id: 4 | heter: 0.83 | inst: 506 | w: 0.51]
0.00 β€ x1 < 0.40 πΉ [id: 5 | heter: 0.35 | inst: 199 | w: 0.20]
x1 β₯ 0.40 πΉ [id: 6 | heter: 0.50 | inst: 307 | w: 0.31]
--------------------------------------------------
Feature 2 - Statistics per tree level:
π³ Tree Summary:
βββββββββββββββββ
Level 0πΉheter: 1.69
Level 1πΉheter: 0.83 | π»0.85 (50.66%)
Level 2πΉheter: 0.44 | π»0.39 (46.70%)
part = partitions[2]
for r in part:
if r.level == 1:
part.plot(r.idx, heterogeneity="ice", centering=True, y_limits=[-5, 5])
Back on the triage plane, partitions= (the dict returned by the plural find_regions) turns it into a before/after story: an arrow runs from each feature's global point to each of its leaf points. Leaves of a good partition land right and down β more decisive, less heterogeneous.
effector.plot_triage(pdp, partitions={"x1": parts["x1"], "x3": parts["x3"]})
Conclusion
For the Global PDP:
- the average effect of \(x_1\) is \(0\) with some heterogeneity implied by the interaction with \(x_1\). The heterogeneity is expressed with two opposite lines; \(-3x_1\) when \(x_1 \leq 0\) and \(3x_1\) when \(x_1 >0\)
- the average effect of \(x_2\) to be \(0\) without heterogeneity
- the average effect of \(x_3\) to be \(x_3\) with some heterogeneity due to the interaction with \(x_1\). The heterogeneity is expressed with a discontinuity around \(x_3=0\), with either a positive or a negative offset depending on the value of \(x_1^i\)
For the Regional PDP:
- For \(x_1\), the algorithm finds two regions, one for \(x_3 \leq 0\) and one for \(x_3 > 0\)
- when \(x_3>0\) the effect is \(3x_1\)
- when \(x_3 \leq 0\), the effect is \(-3x_1\)
- For \(x_2\) the algorithm does not find any subregion
- For \(x_3\), there is a change in the offset:
- when \(x_1>0\) the line is \(x_3 - 3x_1^i\) in the first half and \(x_3 + 3x_1^i\) later
- when \(x_1<0\) the line is \(x_3 + 3x_1^i\) in the first half and \(x_3 - 3x_1^i\) later
Correlated setting
Global PDP
pdp = effector.PDP(data=X_cor_train, model=model_cor, schema={"feature_names": ['x1','x2','x3'], "target_name": "Y"})
pdp.plot(feature=0, centering=True, show_avg_output=False, heterogeneity="ice", y_limits=[-5, 5])
pdp.plot(feature=1, centering=True, show_avg_output=False, heterogeneity="ice", y_limits=[-5, 5])
pdp.plot(feature=2, centering=True, show_avg_output=False, heterogeneity="ice", y_limits=[-5, 5])
Regional-PDP
pdp = effector.PDP(
data=X_cor_train, model=model_cor,
schema={"feature_names": ['x1', 'x2', 'x3']},
axis_limits=np.array([[-1, 1], [-1, 1], [-1, 1]]).T,
nof_instances="all",
)
pdp.fit("all", centering=True)
finder = effector.space_partitioning.Best(min_heterogeneity_decrease_pcg=0.4, numerical_features_grid_size=10)
partitions = {feat: pdp.find_regions(feat, finder=finder) for feat in range(3)}
partitions[0].show()
Feature 0 - Full partition tree:
π³ Full Tree Structure:
βββββββββββββββββββββββ
x1 πΉ [id: 0 | heter: 1.46 | inst: 900 | w: 1.00]
x3 < 0.00 πΉ [id: 1 | heter: 0.21 | inst: 436 | w: 0.48]
x3 β₯ 0.00 πΉ [id: 2 | heter: 0.27 | inst: 464 | w: 0.52]
0.00 β€ x3 < 0.20 πΉ [id: 3 | heter: 0.28 | inst: 115 | w: 0.13]
x3 β₯ 0.20 πΉ [id: 4 | heter: 0.02 | inst: 349 | w: 0.39]
--------------------------------------------------
Feature 0 - Statistics per tree level:
π³ Tree Summary:
βββββββββββββββββ
Level 0πΉheter: 1.46
Level 1πΉheter: 0.24 | π»1.22 (83.76%)
Level 2πΉheter: 0.05 | π»0.19 (80.94%)
part = partitions[0]
for r in part:
if r.level == 1:
part.plot(r.idx, heterogeneity="ice", centering=True, y_limits=[-5, 5])
partitions[1].show()
Feature 1 - Full partition tree:
No splits found for feature 1
--------------------------------------------------
Feature 1 - Statistics per tree level:
No splits found for feature 1
partitions[2].show()
Feature 2 - Full partition tree:
π³ Full Tree Structure:
βββββββββββββββββββββββ
x3 πΉ [id: 0 | heter: 1.46 | inst: 900 | w: 1.00]
x1 < 0.00 πΉ [id: 1 | heter: 0.72 | inst: 463 | w: 0.51]
x1 < -0.40 πΉ [id: 2 | heter: 0.39 | inst: 246 | w: 0.27]
-0.40 β€ x1 < 0.00 πΉ [id: 3 | heter: 0.33 | inst: 217 | w: 0.24]
x1 β₯ 0.00 πΉ [id: 4 | heter: 0.75 | inst: 437 | w: 0.49]
0.00 β€ x1 < 0.40 πΉ [id: 5 | heter: 0.32 | inst: 189 | w: 0.21]
x1 β₯ 0.40 πΉ [id: 6 | heter: 0.48 | inst: 248 | w: 0.28]
--------------------------------------------------
Feature 2 - Statistics per tree level:
π³ Tree Summary:
βββββββββββββββββ
Level 0πΉheter: 1.46
Level 1πΉheter: 0.74 | π»0.72 (49.52%)
Level 2πΉheter: 0.39 | π»0.35 (47.69%)
part = partitions[2]
for r in part:
if r.level == 1:
part.plot(r.idx, heterogeneity="ice", centering=True, y_limits=[-5, 5])
Conclusion
(RH)ALE
def model_uncor_jac(x):
x_tensor = tf.convert_to_tensor(x, dtype=tf.float32)
with tf.GradientTape() as t:
t.watch(x_tensor)
pred = model_uncor(x_tensor)
grads = t.gradient(pred, x_tensor)
return grads.numpy()
def model_cor_jac(x):
x_tensor = tf.convert_to_tensor(x, dtype=tf.float32)
with tf.GradientTape() as t:
t.watch(x_tensor)
pred = model_cor(x_tensor)
grads = t.gradient(pred, x_tensor)
return grads.numpy()
Uncorrelated setting
Global RHALE
rhale = effector.RHALE(data=X_uncor_train, model=model_uncor, model_jac=model_uncor_jac, schema={"feature_names": ['x1','x2','x3'], "target_name": "Y"})
binning_method = effector.axis_partitioning.Fixed(10, min_points_per_bin=0)
rhale.fit(features="all", binning_method=binning_method, centering=True)
rhale.plot(feature=0, centering=True, heterogeneity="std", show_avg_output=False, y_limits=[-5, 5], dy_limits=[-5, 5])
rhale.plot(feature=1, centering=True, heterogeneity="std", show_avg_output=False, y_limits=[-5, 5], dy_limits=[-5, 5])
rhale.plot(feature=2, centering=True, heterogeneity="std", show_avg_output=False, y_limits=[-5, 5], dy_limits=[-5, 5])
Regional RHALE
rhale = effector.RHALE(
data=X_uncor_train, model=model_uncor, model_jac=model_uncor_jac,
schema={"feature_names": ['x1', 'x2', 'x3']},
axis_limits=np.array([[-1, 1], [-1, 1], [-1, 1]]).T,
nof_instances="all",
)
binning_method = effector.axis_partitioning.Fixed(11, min_points_per_bin=0)
rhale.fit("all", binning_method=binning_method, centering=True)
finder = effector.space_partitioning.Best(min_heterogeneity_decrease_pcg=0.6, numerical_features_grid_size=10)
partitions = {feat: rhale.find_regions(feat, finder=finder) for feat in range(3)}
partitions[0].show()
Feature 0 - Full partition tree:
π³ Full Tree Structure:
βββββββββββββββββββββββ
x1 πΉ [id: 0 | heter: 1.68 | inst: 1000 | w: 1.00]
x3 < 0.00 πΉ [id: 1 | heter: 0.30 | inst: 500 | w: 0.50]
x3 β₯ 0.00 πΉ [id: 2 | heter: 0.35 | inst: 500 | w: 0.50]
--------------------------------------------------
Feature 0 - Statistics per tree level:
π³ Tree Summary:
βββββββββββββββββ
Level 0πΉheter: 1.68
Level 1πΉheter: 0.33 | π»1.35 (80.56%)
part = partitions[0]
for r in part:
if r.level == 1:
part.plot(r.idx, heterogeneity="std", centering=True, y_limits=[-5, 5])
partitions[1].show()
Feature 1 - Full partition tree:
No splits found for feature 1
--------------------------------------------------
Feature 1 - Statistics per tree level:
No splits found for feature 1
partitions[2].show()
Feature 2 - Full partition tree:
No splits found for feature 2
--------------------------------------------------
Feature 2 - Statistics per tree level:
No splits found for feature 2
Conclusion
Correlated setting
Global RHALE
rhale = effector.RHALE(data=X_cor_train, model=model_cor, model_jac=model_cor_jac, schema={"feature_names": ['x1','x2','x3'], "target_name": "Y"})
binning_method = effector.axis_partitioning.Fixed(10, min_points_per_bin=0)
rhale.fit(features="all", binning_method=binning_method, centering=True)
rhale.plot(feature=0, centering=True, heterogeneity="std", show_avg_output=False, y_limits=[-5, 5], dy_limits=[-5, 5])
rhale.plot(feature=1, centering=True, heterogeneity="std", show_avg_output=False, y_limits=[-5, 5], dy_limits=[-5, 5])
rhale.plot(feature=2, centering=True, heterogeneity="std", show_avg_output=False, y_limits=[-5, 5], dy_limits=[-5, 5])
Regional RHALE
rhale = effector.RHALE(
data=X_cor_train, model=model_cor, model_jac=model_cor_jac,
schema={"feature_names": ['x1', 'x2', 'x3']},
axis_limits=np.array([[-1, 1], [-1, 1], [-1, 1]]).T,
nof_instances="all",
)
binning_method = effector.axis_partitioning.Fixed(11, min_points_per_bin=0)
rhale.fit("all", binning_method=binning_method, centering=True)
finder = effector.space_partitioning.Best(min_heterogeneity_decrease_pcg=0.6, numerical_features_grid_size=10)
partitions = {feat: rhale.find_regions(feat, finder=finder) for feat in range(3)}
partitions[0].show()
Feature 0 - Full partition tree:
π³ Full Tree Structure:
βββββββββββββββββββββββ
x1 πΉ [id: 0 | heter: 0.86 | inst: 900 | w: 1.00]
x3 < 0.00 πΉ [id: 1 | heter: 0.25 | inst: 436 | w: 0.48]
x3 β₯ 0.00 πΉ [id: 2 | heter: 0.30 | inst: 464 | w: 0.52]
--------------------------------------------------
Feature 0 - Statistics per tree level:
π³ Tree Summary:
βββββββββββββββββ
Level 0πΉheter: 0.86
Level 1πΉheter: 0.28 | π»0.58 (67.75%)
partitions[1].show()
Feature 1 - Full partition tree:
No splits found for feature 1
--------------------------------------------------
Feature 1 - Statistics per tree level:
No splits found for feature 1
partitions[2].show()
Feature 2 - Full partition tree:
No splits found for feature 2
--------------------------------------------------
Feature 2 - Statistics per tree level:
No splits found for feature 2
Conclusion
SHAP DP
Uncorrelated setting
Global SHAP DP
shap = effector.ShapDP(data=X_uncor_train, model=model_uncor, schema={"feature_names": ['x1', 'x2', 'x3'], "target_name": "Y"})
binning_method = effector.axis_partitioning.Fixed(nof_bins=5, min_points_per_bin=0)
shap.fit(features="all", binning_method=binning_method, centering=True)
shap.plot(feature=0, centering=True, heterogeneity="shap_values", show_avg_output=False, y_limits=[-3, 3])
shap.plot(feature=1, centering=True, heterogeneity="shap_values", show_avg_output=False, y_limits=[-3, 3])
shap.plot(feature=2, centering=True, heterogeneity="shap_values", show_avg_output=False, y_limits=[-3, 3])
Regional SHAP-DP
shap = effector.ShapDP(
data=X_uncor_train, model=model_uncor,
schema={"feature_names": ['x1', 'x2', 'x3']},
axis_limits=np.array([[-1, 1], [-1, 1], [-1, 1]]).T,
nof_instances="all",
)
binning_method = effector.axis_partitioning.Fixed(nof_bins=5, min_points_per_bin=0)
shap.fit("all", binning_method=binning_method, centering=True)
finder = effector.space_partitioning.Best(min_heterogeneity_decrease_pcg=0.6, numerical_features_grid_size=10)
partitions = {feat: shap.find_regions(feat, finder=finder) for feat in range(3)}
partitions[0].show()
Feature 0 - Full partition tree:
π³ Full Tree Structure:
βββββββββββββββββββββββ
x1 πΉ [id: 0 | heter: 0.88 | inst: 1000 | w: 1.00]
x3 < 0.00 πΉ [id: 1 | heter: 0.20 | inst: 500 | w: 0.50]
x3 β₯ 0.00 πΉ [id: 2 | heter: 0.17 | inst: 500 | w: 0.50]
--------------------------------------------------
Feature 0 - Statistics per tree level:
π³ Tree Summary:
βββββββββββββββββ
Level 0πΉheter: 0.88
Level 1πΉheter: 0.19 | π»0.69 (78.68%)
part = partitions[0]
for r in part:
if r.level == 1:
part.plot(r.idx, heterogeneity="std", centering=True, y_limits=[-5, 5])
partitions[1].show()
Feature 1 - Full partition tree:
No splits found for feature 1
--------------------------------------------------
Feature 1 - Statistics per tree level:
No splits found for feature 1
partitions[2].show()
Feature 2 - Full partition tree:
No splits found for feature 2
--------------------------------------------------
Feature 2 - Statistics per tree level:
No splits found for feature 2
Conclusion
Correlated setting
Global SHAP-DP
shap = effector.ShapDP(data=X_cor_train, model=model_cor, schema={"feature_names": ['x1', 'x2', 'x3'], "target_name": "Y"})
binning_method = effector.axis_partitioning.Fixed(nof_bins=5, min_points_per_bin=0)
shap.fit(features="all", binning_method=binning_method, centering=True)
shap.plot(feature=0, centering=True, heterogeneity="shap_values", show_avg_output=False, y_limits=[-3, 3])
shap.plot(feature=1, centering=True, heterogeneity="shap_values", show_avg_output=False, y_limits=[-3, 3])
shap.plot(feature=2, centering=True, heterogeneity="shap_values", show_avg_output=False, y_limits=[-3, 3])
Regional SHAP
shap = effector.ShapDP(
data=X_cor_train, model=model_cor,
schema={"feature_names": ['x1', 'x2', 'x3']},
axis_limits=np.array([[-1, 1], [-1, 1], [-1, 1]]).T,
nof_instances="all",
)
binning_method = effector.axis_partitioning.Fixed(nof_bins=5, min_points_per_bin=0)
shap.fit("all", binning_method=binning_method, centering=True)
finder = effector.space_partitioning.Best(min_heterogeneity_decrease_pcg=0.6, numerical_features_grid_size=10)
partitions = {feat: shap.find_regions(feat, finder=finder) for feat in range(3)}
partitions[0].show()
partitions[1].show()
partitions[2].show()
Feature 0 - Full partition tree:
No splits found for feature 0
--------------------------------------------------
Feature 0 - Statistics per tree level:
No splits found for feature 0
Feature 1 - Full partition tree:
No splits found for feature 1
--------------------------------------------------
Feature 1 - Statistics per tree level:
No splits found for feature 1
Feature 2 - Full partition tree:
No splits found for feature 2
--------------------------------------------------
Feature 2 - Statistics per tree level:
No splits found for feature 2
Conclusion
Cross-method sanity check
The one-liner effector.explain with every engine this notebook's model
supports. Everything must run end to end; the closing table puts the reads
side by side. Where methods disagree β ranking, accepted splits, RΒ² β that is
a property of the data/model worth a closer look, not an error.
from pathlib import Path
_out = Path("reports") / "04_regional_effects_real_f"
_out.mkdir(parents=True, exist_ok=True)
# === cross-method sweep: effector.explain on every applicable engine ======
sweep_reports = {}
for _m in ["pdp", "ale", "rhale", "shapdp"]:
_kw = {"nof_instances": 300} if _m == "shapdp" else {}
print(f"--- {_m} " + "-" * 50)
sweep_reports[_m] = effector.explain(
X_uncor_train, model_uncor, None, method=_m, schema={"feature_names": ['x1','x2','x3'], "target_name": "Y"}, **_kw
)
if _m != "pdp": # the published report is the narrated one above
sweep_reports[_m].to_html(_out / f"report_{_m}.html")
print()
print(f"{'method':<8} {'ranking (plotted)':<44} {'GAM R2':>8} {'final R2':>9} splits")
for _m, _r in sweep_reports.items():
_rank = " > ".join(fr.name for fr in _r.features)
_ev = _r.explained_variance
if _ev:
_sp = "; ".join(f"{s['name']} on {s['on']}" for s in _ev["stages"]) or "none"
print(f"{_m:<8} {_rank:<44} {_ev['gam_r2']:>7.1%} {_ev['regional_r2']:>8.1%} {_sp}")
else:
print(f"{_m:<8} {_rank:<44} {'-':>7} {'-':>8} (derivative scale: no variance ledger)")
print(f"\nreports stored in {_out}/")
--- pdp --------------------------------------------------
[effector] global effects (GAM) -> 11.0% of the model's variance
regional effects (CALM) -> 99.3%
--- ale --------------------------------------------------
[effector] global effects (GAM) -> 10.5% of the model's variance
regional effects (CALM) -> 99.3%
/home/givasile/github/packages/effector/effector/report.py:606: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.
fig.tight_layout()
--- rhale --------------------------------------------------
[effector] global effects (GAM) -> 10.8% of the model's variance
regional effects (CALM) -> 99.3%
/home/givasile/github/packages/effector/effector/report.py:606: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.
fig.tight_layout()
--- shapdp --------------------------------------------------
[effector] global effects (GAM) -> 9.1% of the model's variance
regional effects (CALM) -> 98.6%
/home/givasile/github/packages/effector/effector/report.py:606: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect.
fig.tight_layout()
method ranking (plotted) GAM R2 final R2 splits
pdp x1 > x3 11.0% 99.3% x1 on x3
ale x1 > x3 10.5% 99.3% x1 on x3
rhale x1 > x3 10.8% 99.3% x1 on x3
shapdp x3 > x1 9.1% 98.6% x1 on x3; x3 on x1
reports stored in reports/04_regional_effects_real_f/