Expected Value Theory¶

In [1]:

# Uncomment the following line when running on Google Colab
# !pip install "autora"

# Uncomment the following line when running on Google Colab # !pip install "autora"

The expected value theory experiment has to be initialized with a specific formula and effects.

In [2]:

import numpy as np
from autora.experiment_runner.synthetic.economics.expected_value_theory import expected_value_theory

s = expected_value_theory()

import numpy as np from autora.experiment_runner.synthetic.economics.expected_value_theory import expected_value_theory s = expected_value_theory()

Check the docstring to get information about the model

In [3]:

help(expected_value_theory)

help(expected_value_theory)

Help on function expected_value_theory in module autora.experiment_runner.synthetic.economics.expected_value_theory:

expected_value_theory(name='Expected Value Theory', choice_temperature: float = 0.1, value_lambda: float = 0.5, resolution=10, minimum_value=-1, maximum_value=1)
    Expected Value Theory
    
    Parameters:
        name:
        choice_temperature:
        value_lambda:
        resolution:
        minimum_value:
        maximum_value:
        Examples:
            >>> s = expected_value_theory()
            >>> s.run(np.array([[1,2,.1,.9]]), random_state=42)
               V_A  P_A  V_B  P_B  choose_A
            0  1.0  2.0  0.1  0.9  0.999938

... or use the describe function:

In [4]:

from autora.experiment_runner.synthetic.utilities import describe

print(describe(s))

from autora.experiment_runner.synthetic.utilities import describe print(describe(s))

    Expected Value Theory

    Parameters:
        name:
        choice_temperature:
        value_lambda:
        resolution:
        minimum_value:
        maximum_value:
        Examples:
            >>> s = expected_value_theory()
            >>> s.run(np.array([[1,2,.1,.9]]), random_state=42)
               V_A  P_A  V_B  P_B  choose_A
            0  1.0  2.0  0.1  0.9  0.999938
    

The synthetic experiement s has properties like the name of the experiment:

In [5]:

s.name

s.name

Out[5]:

'Expected Value Theory'

... a valid variables description:

In [6]:

s.variables

s.variables

Out[6]:

VariableCollection(independent_variables=[IV(name='V_A', value_range=(-1, 1), allowed_values=array([-1.        , -0.77777778, -0.55555556, -0.33333333, -0.11111111,
        0.11111111,  0.33333333,  0.55555556,  0.77777778,  1.        ]), units='dollar', type=<ValueType.REAL: 'real'>, variable_label='Value of Option A', rescale=1, is_covariate=False), IV(name='P_A', value_range=(0, 1), allowed_values=array([0.        , 0.11111111, 0.22222222, 0.33333333, 0.44444444,
       0.55555556, 0.66666667, 0.77777778, 0.88888889, 1.        ]), units='probability', type=<ValueType.REAL: 'real'>, variable_label='Probability of Option A', rescale=1, is_covariate=False), IV(name='V_B', value_range=(-1, 1), allowed_values=array([-1.        , -0.77777778, -0.55555556, -0.33333333, -0.11111111,
        0.11111111,  0.33333333,  0.55555556,  0.77777778,  1.        ]), units='dollar', type=<ValueType.REAL: 'real'>, variable_label='Value of Option B', rescale=1, is_covariate=False), IV(name='P_B', value_range=(0, 1), allowed_values=array([0.        , 0.11111111, 0.22222222, 0.33333333, 0.44444444,
       0.55555556, 0.66666667, 0.77777778, 0.88888889, 1.        ]), units='probability', type=<ValueType.REAL: 'real'>, variable_label='Probability of Option B', rescale=1, is_covariate=False)], dependent_variables=[DV(name='choose_A', value_range=(0, 1), allowed_values=None, units='probability', type=<ValueType.PROBABILITY: 'probability'>, variable_label='Probability of Choosing Option A', rescale=1, is_covariate=False)], covariates=[])

... now we can generate the full domain of the data

In [7]:

x = s.domain()
x

x = s.domain() x

Out[7]:

array([[-1.        , -0.77777778, -0.55555556, -0.33333333],
       [-0.11111111,  0.11111111,  0.33333333,  0.55555556],
       [ 0.77777778,  1.        ,  0.        ,  0.11111111],
       [ 0.22222222,  0.33333333,  0.44444444,  0.55555556],
       [ 0.66666667,  0.77777778,  0.88888889,  1.        ],
       [-1.        , -0.77777778, -0.55555556, -0.33333333],
       [-0.11111111,  0.11111111,  0.33333333,  0.55555556],
       [ 0.77777778,  1.        ,  0.        ,  0.11111111],
       [ 0.22222222,  0.33333333,  0.44444444,  0.55555556],
       [ 0.66666667,  0.77777778,  0.88888889,  1.        ]])

... the experiment_runner which can be called to generate experimental results:

In [8]:

experiment_data = s.run(x)
experiment_data

experiment_data = s.run(x) experiment_data

Out[8]:

	V_A	P_A	V_B	P_B	choose_A
0	-1.000000	-0.777778	-0.555556	-0.333333	0.942923
1	-0.111111	0.111111	0.333333	0.555556	0.225084
2	0.777778	1.000000	0.000000	0.111111	0.980658
3	0.222222	0.333333	0.444444	0.555556	0.311833
4	0.666667	0.777778	0.888889	1.000000	0.120028
5	-1.000000	-0.777778	-0.555556	-0.333333	0.945268
6	-0.111111	0.111111	0.333333	0.555556	0.267370
7	0.777778	1.000000	0.000000	0.111111	0.975918
8	0.222222	0.333333	0.444444	0.555556	0.232454
9	0.666667	0.777778	0.888889	1.000000	0.113917

... a function to plot the ground truth (no noise):

In [9]:

s.plotter()

s.plotter()

... against a fitted model if it exists:

In [10]:

from sklearn.linear_model import LinearRegression
ivs = [iv.name for iv in s.variables.independent_variables]
dvs = [dv.name for dv in s.variables.dependent_variables]
X = experiment_data[ivs]
y = experiment_data[dvs]
model = LinearRegression().fit(X, y)
s.plotter(model)

from sklearn.linear_model import LinearRegression ivs = [iv.name for iv in s.variables.independent_variables] dvs = [dv.name for dv in s.variables.dependent_variables] X = experiment_data[ivs] y = experiment_data[dvs] model = LinearRegression().fit(X, y) s.plotter(model)

/Users/younesstrittmatter/Documents/GitHub/AutoRA/autora-synthetic/venv/lib/python3.11/site-packages/sklearn/base.py:464: UserWarning: X does not have valid feature names, but LinearRegression was fitted with feature names
  warnings.warn(
/Users/younesstrittmatter/Documents/GitHub/AutoRA/autora-synthetic/venv/lib/python3.11/site-packages/sklearn/base.py:464: UserWarning: X does not have valid feature names, but LinearRegression was fitted with feature names
  warnings.warn(
/Users/younesstrittmatter/Documents/GitHub/AutoRA/autora-synthetic/venv/lib/python3.11/site-packages/sklearn/base.py:464: UserWarning: X does not have valid feature names, but LinearRegression was fitted with feature names
  warnings.warn(

We can wrap this functions to use with the state logic of AutoRA: First, we create the state with the variables:

In [11]:

from autora.state import StandardState, on_state, experiment_runner_on_state, estimator_on_state
from autora.experimentalist.grid import grid_pool
from autora.experimentalist.random import random_sample

# We can get the variables from the runner
variables = s.variables

# With the variables, we initialize a StandardState
state = StandardState(variables)

from autora.state import StandardState, on_state, experiment_runner_on_state, estimator_on_state from autora.experimentalist.grid import grid_pool from autora.experimentalist.random import random_sample # We can get the variables from the runner variables = s.variables # With the variables, we initialize a StandardState state = StandardState(variables)

Wrap the experimentalists in on_state function to use them on state:

In [12]:

# Wrap the functions to use on state
# Experimentalists:
pool_on_state = on_state(grid_pool, output=['conditions'])
sample_on_state = on_state(random_sample, output=['conditions'])

state = pool_on_state(state)
state = sample_on_state(state, num_samples=2)
print(state.conditions)

# Wrap the functions to use on state # Experimentalists: pool_on_state = on_state(grid_pool, output=['conditions']) sample_on_state = on_state(random_sample, output=['conditions']) state = pool_on_state(state) state = sample_on_state(state, num_samples=2) print(state.conditions)

           V_A       P_A       V_B       P_B
5093  0.111111  0.000000  1.000000  0.333333
4839 -0.111111  0.888889 -0.333333  1.000000

Wrap the runner with the experiment_runner_on_state wrapper to use it on state:

In [13]:

# Runner:
run_on_state = experiment_runner_on_state(s.run)
state = run_on_state(state)

state.experiment_data

# Runner: run_on_state = experiment_runner_on_state(s.run) state = run_on_state(state) state.experiment_data

Out[13]:

	V_A	P_A	V_B	P_B	choose_A
239	-1.000000	0.222222	-0.333333	1.0	0.625000
7580	0.555556	0.555556	0.777778	0.0	0.780558

Wrap the regressor with the estimator_on_state wrapper:

In [14]:

theorist = LinearRegression()
theorist_on_state = estimator_on_state(theorist)

state = theorist_on_state(state)
# Access the last model:
model = state.models[-1]


print(f"rt = "
      f"{model.coef_[0][0]:.2f}*V_A "
      f"{model.coef_[0][1]:.2f}*P_A "
      f"{model.coef_[0][2]:.2f}*V_B "
      f"{model.coef_[0][3]:.2f}*P_B "
      f"{model.intercept_[0]:+.2f} ")

theorist = LinearRegression() theorist_on_state = estimator_on_state(theorist) state = theorist_on_state(state) # Access the last model: model = state.models[-1] print(f"rt = " f"{model.coef_[0][0]:.2f}*V_A " f"{model.coef_[0][1]:.2f}*P_A " f"{model.coef_[0][2]:.2f}*V_B " f"{model.coef_[0][3]:.2f}*P_B " f"{model.intercept_[0]:+.2f} ")

rt = 0.05*V_A 0.01*P_A 0.04*V_B -0.03*P_B +0.72 

In [ ]: