Weber Fechner Example¶

Example file which shows some simple curve fitting using DARTSRegressor and some other estimators.

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# Uncomment the following lines when running on Google Colab
# !pip install "autora[theorist-darts]"

# Uncomment the following lines when running on Google Colab # !pip install "autora[theorist-darts]"

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from functools import partial

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from sklearn.linear_model import LinearRegression
from sklearn.model_selection import GridSearchCV
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import PolynomialFeatures

from autora.theorist.darts import DARTSRegressor
from autora.experiment_runner.synthetic.psychophysics.weber_fechner_law import weber_fechner_law

from functools import partial import matplotlib.pyplot as plt import numpy as np import pandas as pd from sklearn.linear_model import LinearRegression from sklearn.model_selection import GridSearchCV from sklearn.pipeline import make_pipeline from sklearn.preprocessing import PolynomialFeatures from autora.theorist.darts import DARTSRegressor from autora.experiment_runner.synthetic.psychophysics.weber_fechner_law import weber_fechner_law

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# %% Define some helper functions

def show_results_complete(
    data_: pd.DataFrame,
    estimator=None,
    show_results=True,
    projection="2d",
    label=None,
):
    """
    Function to plot input data (x_, y_) and the predictions of an estimator for the same x_.
    """
    if projection == "2d":
        plt.figure()
        data_.plot.scatter(
            "S1", "S2", c="difference_detected", cmap="viridis", zorder=10
        )
    elif projection == "3d":
        fig = plt.figure()
        ax = fig.add_subplot(projection="3d")
        ax.scatter(data_["S1"], data["S2"], data["difference_detected"])

        if estimator is not None:
            xs, ys = np.mgrid[0:5:0.2, 0:5:0.2]  # type: ignore

            zs = estimator.predict(np.column_stack((xs.ravel(), ys.ravel())))

            ax.plot_surface(xs, ys, zs.reshape(xs.shape), alpha=0.5)

    if label is not None:
        plt.title(label)

    if show_results:
        plt.show()

    return

# %% Define some helper functions def show_results_complete( data_: pd.DataFrame, estimator=None, show_results=True, projection="2d", label=None, ): """ Function to plot input data (x_, y_) and the predictions of an estimator for the same x_. """ if projection == "2d": plt.figure() data_.plot.scatter( "S1", "S2", c="difference_detected", cmap="viridis", zorder=10 ) elif projection == "3d": fig = plt.figure() ax = fig.add_subplot(projection="3d") ax.scatter(data_["S1"], data["S2"], data["difference_detected"]) if estimator is not None: xs, ys = np.mgrid[0:5:0.2, 0:5:0.2] # type: ignore zs = estimator.predict(np.column_stack((xs.ravel(), ys.ravel()))) ax.plot_surface(xs, ys, zs.reshape(xs.shape), alpha=0.5) if label is not None: plt.title(label) if show_results: plt.show() return

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# %% Load the data
s = weber_fechner_law(random_state=180, resolution=20)
X = s.domain()
y = s.experiment_runner(X)
data = pd.DataFrame(np.column_stack([X, y]), columns=["S1", "S2", "difference_detected"])

# %% Load the data s = weber_fechner_law(random_state=180, resolution=20) X = s.domain() y = s.experiment_runner(X) data = pd.DataFrame(np.column_stack([X, y]), columns=["S1", "S2", "difference_detected"])

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show_results = partial(show_results_complete, data_=data, projection="3d")
show_results(label="input data")

show_results = partial(show_results_complete, data_=data, projection="3d") show_results(label="input data")

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# %% Fit first using a super-simple linear regression

first_order_linear_estimator = LinearRegression()
first_order_linear_estimator.fit(X, y)

show_results(estimator=first_order_linear_estimator, label="1st order linear")

# %% Fit first using a super-simple linear regression first_order_linear_estimator = LinearRegression() first_order_linear_estimator.fit(X, y) show_results(estimator=first_order_linear_estimator, label="1st order linear")

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# %% Fit using a 0-3 order polynomial, getting the best fit for the data.
polynomial_estimator = GridSearchCV(
    make_pipeline(PolynomialFeatures(), LinearRegression(fit_intercept=False)),
    param_grid=dict(polynomialfeatures__degree=range(4)),
)
polynomial_estimator.fit(X, y)

show_results(estimator=polynomial_estimator, label="[0th-3rd]-order linear")

# %% Fit using a 0-3 order polynomial, getting the best fit for the data. polynomial_estimator = GridSearchCV( make_pipeline(PolynomialFeatures(), LinearRegression(fit_intercept=False)), param_grid=dict(polynomialfeatures__degree=range(4)), ) polynomial_estimator.fit(X, y) show_results(estimator=polynomial_estimator, label="[0th-3rd]-order linear")