Real world use case

Below, we use the mini-gpr package to fit a model to the airfoil self-noise dataset.

import pandas as pd

url = "https://archive.ics.uci.edu/ml/machine-learning-databases/00291/airfoil_self_noise.dat"

inputs = [
    "frequency",
    "angle_of_attack",
    "chord_length",
    "free_stream_velocity",
    "suction_side_displacement_thickness",
]
output = "scaled_sound_pressure_level"
cols = inputs + [output]

df = pd.read_csv(url, sep=r"\t|\s+", header=None, names=cols, engine="python")
df

	frequency	angle_of_attack	chord_length	free_stream_velocity	suction_side_displacement_thickness	scaled_sound_pressure_level
0	800	0.0	0.3048	71.3	0.002663	126.201
1	1000	0.0	0.3048	71.3	0.002663	125.201
2	1250	0.0	0.3048	71.3	0.002663	125.951
3	1600	0.0	0.3048	71.3	0.002663	127.591
4	2000	0.0	0.3048	71.3	0.002663	127.461
...	...	...	...	...	...	...
1498	2500	15.6	0.1016	39.6	0.052849	110.264
1499	3150	15.6	0.1016	39.6	0.052849	109.254
1500	4000	15.6	0.1016	39.6	0.052849	106.604
1501	5000	15.6	0.1016	39.6	0.052849	106.224
1502	6300	15.6	0.1016	39.6	0.052849	104.204

1503 rows × 6 columns

# take a random 500 training points, and use the rest for testing
train = df.sample(500)
test = df.drop(train.index)
len(train), len(test)

(500, 1003)

from sklearn.preprocessing import StandardScaler

input_scaler = StandardScaler()
output_scaler = StandardScaler()

X = input_scaler.fit_transform(train[inputs])
y = output_scaler.fit_transform(train[[output]])

from mini_gpr.kernels import RBF
from mini_gpr.models import GPR

model = GPR(RBF(sigma=[0.05] * 5), noise=0.1)
model.fit(X, y)

import matplotlib.pyplot as plt

%config InlineBackend.figure_format = 'svg'

raw_pred_train = model.predict(X)
pred_train = output_scaler.inverse_transform(
    raw_pred_train.reshape(-1, 1)
).flatten()

raw_pred_test = model.predict(input_scaler.transform(test[inputs]))
pred_test = output_scaler.inverse_transform(
    raw_pred_test.reshape(-1, 1)
).flatten()

plt.figure(figsize=(3, 3))
plt.plot(pred_test, test[output], ".r", label="test set")
plt.plot(pred_train, train[output], ".k", label="training set")
plt.axline((pred_train[0], pred_train[0]), slope=1, color="k", ls="--", lw=1)
plt.xlabel("Predicted (dB)")
plt.ylabel("True (dB)")
plt.legend(bbox_to_anchor=(1.05, 0.5), loc="center left", markerscale=2);

from mini_gpr.opt import maximise_log_likelihood, optimise_model

best_model = optimise_model(
    model, maximise_log_likelihood, X, y, optimise_noise=True
)
best_model.kernel.params

{'sigma': [0.3196713784422319,
  1.6818896267717998,
  1.3924475424814566,
  0.05,
  0.7961265272752749],
 'scale': 1.246932649911396}

raw_pred_train = best_model.predict(X)
pred_train = output_scaler.inverse_transform(
    raw_pred_train.reshape(-1, 1)
).flatten()

raw_pred_test = best_model.predict(input_scaler.transform(test[inputs]))
pred_test = output_scaler.inverse_transform(
    raw_pred_test.reshape(-1, 1)
).flatten()

plt.figure(figsize=(3, 3))
plt.plot(pred_test, test[output], ".r", label="test set")
plt.plot(pred_train, train[output], ".k", label="training set")
plt.axline((pred_train[0], pred_train[0]), slope=1, color="k", ls="--", lw=1)
plt.xlabel("Predicted (dB)")
plt.ylabel("True (dB)")
plt.legend(bbox_to_anchor=(1.05, 0.5), loc="center left", markerscale=2)

<matplotlib.legend.Legend at 0x12b6ff090>