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158 | def exp_learning(
name="Exponential Learning",
resolution=100,
minimum_trial=1,
minimum_initial_value=0,
maximum_initial_value=0.5,
lr=0.03,
p_asymptotic=1.0,
):
"""
Exponential Learning
Args:
p_asymptotic: additive bias on constant multiplier
lr: learning rate
maximum_initial_value: upper bound for initial p value
minimum_initial_value: lower bound for initial p value
minimum_trial: upper bound for exponential constant
name: name of the experiment
resolution: number of allowed values for stimulus
"""
maximum_trial = resolution
params = dict(
name="Exponential Learning",
resolution=resolution,
minimum_trial=minimum_trial,
maximum_trial=maximum_trial,
minimum_initial_value=minimum_initial_value,
maximum_initial_value=maximum_initial_value,
lr=lr,
p_asymptotic=p_asymptotic,
)
p_initial = IV(
name="P_asymptotic",
allowed_values=np.linspace(
minimum_initial_value, maximum_initial_value, resolution
),
value_range=(minimum_initial_value, maximum_initial_value),
units="performance",
variable_label="Asymptotic Performance",
type=ValueType.REAL,
)
trial = IV(
name="trial",
allowed_values=np.linspace(minimum_trial, maximum_trial, resolution),
value_range=(minimum_trial, maximum_trial),
units="trials",
variable_label="Trials",
type=ValueType.REAL,
)
performance = DV(
name="performance",
value_range=(0, p_asymptotic),
units="performance",
variable_label="Performance",
type=ValueType.REAL,
)
variables = VariableCollection(
independent_variables=[p_initial, trial],
dependent_variables=[performance],
)
def run(
conditions: Union[pd.DataFrame, np.ndarray, np.recarray],
added_noise: float = 0.01,
random_state: Optional[int] = None,
):
rng = np.random.default_rng(random_state)
X = np.array(conditions)
Y = np.zeros((X.shape[0], 1))
# exp learning function according to
# Heathcote, A., Brown, S., & Mewhort, D. J. (2000). The power law repealed:
# The case for an exponential law of practice. Psychonomic bulletin & review, 7(2), 185–207.
# Thurstone, L. L. (1919). The learning curve equation.
# Psy- chological Monographs, 26(3), i.
for idx, x in enumerate(X):
p_initial_exp = x[0]
trial_exp = x[1]
y = (
p_asymptotic
- (p_asymptotic - p_initial_exp) * np.exp(-lr * trial_exp)
+ rng.random.normal(0, added_noise)
)
Y[idx] = y
return Y
ground_truth = partial(run, added_noise=0.0)
def domain():
p_initial_values = variables.independent_variables[0].allowed_values
trial_values = variables.independent_variables[1].allowed_values
X = np.array(np.meshgrid(p_initial_values, trial_values)).T.reshape(-1, 2)
return X
def plotter(
model=None,
):
import matplotlib.pyplot as plt
P_0_list = [0, 0.25, 0.5]
for P_0 in P_0_list:
X = np.zeros((len(trial.allowed_values), 2))
X[:, 0] = P_0
X[:, 1] = trial.allowed_values
y = ground_truth(X, std=0)
plt.plot(trial, y, label=f"$P_0 = {P_0}$ (Original)")
if model is not None:
y = model.predict(X)
plt.plot(trial, y, label=f"$P_0 = {P_0}$ (Recovered)", linestyle="--")
x_limit = [0, variables.independent_variables[1].value_range[1]]
y_limit = [0, 1]
x_label = "Trial $t$"
y_label = "Performance $P_n$"
plt.xlim(x_limit)
plt.ylim(y_limit)
plt.xlabel(x_label, fontsize="large")
plt.ylabel(y_label, fontsize="large")
plt.legend(loc=4, fontsize="medium")
plt.title("Exponential Learning", fontsize="x-large")
plt.show()
collection = SyntheticExperimentCollection(
name=name,
description=exp_learning.__doc__,
variables=variables,
run=run,
ground_truth=ground_truth,
domain=domain,
plotter=plotter,
params=params,
factory_function=exp_learning,
)
return collection
|