Theorist Tutorial¶

Theorists are classes designed to automate the construction of interpretable models from data. AutoRA theorists are implemented as sklearn regressors and can be used with the fit and predict methods.

In order to use a theorist, you must first install the corresponding theorist package. Some theorists are installed by default when you install autora. Once a theorist is installed, you can instantiate it and use it as you would any other sklearn regressor. That is, you can call the fit function of the theorist by passing in experimental conditions and corresponding observations, and then call the predict function to generate predicted observations for novel experimental conditions using the discovered model.

The following tutorial demonstrates how to use the BMSRegressor (Guimerà et al., 2020, in Sci. Adv.)–a theorist that can discover an interpretable equation relating the independent variables of an experiment (experiment conditions) to predicted dependent variables (observations).

In [ ]:

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

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

After importing the necessary modules,

In [ ]:

from autora.theorist.bms import BMSRegressor
import numpy as np
import matplotlib.pyplot as plt

from autora.theorist.bms import BMSRegressor import numpy as np import matplotlib.pyplot as plt

we begin by generating data with a ground-truth equation, $y = \sin(x) + x^3$.

In [ ]:

x = np.expand_dims(np.linspace(start=-1, stop=1, num=500), 1)
y = np.power(x, 3) + np.sin(x)

x = np.expand_dims(np.linspace(start=-1, stop=1, num=500), 1) y = np.power(x, 3) + np.sin(x)

Then we set up the BMS regressor with our chosen meta parameters. In this case, we will specify the number of epochs as well as temperatures (ts). Note, BMS also allows users to specify unique priors over the operations considered in the search space (prior_par), but in this simple example we will stick with those priors implemented by the original authors, Guimerà et al. (2020).

In [ ]:

temperatures = [1.0] + [1.04**k for k in range(1, 20)]

bms_estimator = BMSRegressor(
    epochs=500,
    ts=temperatures,
)

temperatures = [1.0] + [1.04**k for k in range(1, 20)] bms_estimator = BMSRegressor( epochs=500, ts=temperatures, )

With our regressor initialized, we can call the fit method to discover an equation for our data and then use the predict method to generate predictions using our discovered equation.

In [ ]:

bms_estimator.fit(x,y)
y_pred = bms_estimator.predict(x)

bms_estimator.fit(x,y) y_pred = bms_estimator.predict(x)

INFO:autora.theorist.bms.regressor:BMS fitting started
100%|██████████| 500/500 [04:47<00:00,  1.74it/s]
INFO:autora.theorist.bms.regressor:BMS fitting finished

Finally, we can plot the results.

In [ ]:

# plot out the ground truth versus predicted responses
plt.figure()
plt.plot(x, y, "o")
plt.plot(x, y_pred, "-")
plt.show()

# plot out the ground truth versus predicted responses plt.figure() plt.plot(x, y, "o") plt.plot(x, y_pred, "-") plt.show()

In this simple case, the algorithm finds an equation with a perfect fit.