Basic Usage¶

The goal of this notebook is to demonstrate the usage of the mixture_sample function, which combines different sampling strategies to select experimental conditions. The mixture_sample function takes a pool of experimental conditions, a temperature parameter, a list of samplers with their weights, a dictionary of parameters for the samplers, and an optional number of samples to return.

We begin with importing the necessary packages.

In [ ]:

# Uncomment the following lines when running on Google Colab
# !pip install "autora[experimentalits-mixture]"
# !pip install "autora[experimentalist-falsification]"
# !pip install "autora[experimentalist-novelty]"

# Uncomment the following lines when running on Google Colab # !pip install "autora[experimentalits-mixture]" # !pip install "autora[experimentalist-falsification]" # !pip install "autora[experimentalist-novelty]"

In [1]:

---------------------------------------------------------------------------
ModuleNotFoundError                       Traceback (most recent call last)
<ipython-input-1-5feb8d753802> in <module>
----> 1 from autora.experimentalist.sampler.mixture import mixture_sample

ModuleNotFoundError: No module named 'autora'

In [132]:

from autora.experimentalist.mixture import mixture_sample
from autora.experimentalist.falsification import falsification_sample, falsification_score_sample
from autora.experimentalist.novelty import novelty_sampler, novelty_score_sample
import numpy as np
import matplotlib.pyplot as plt

from sklearn.linear_model import LinearRegression

from autora.experimentalist.mixture import mixture_sample from autora.experimentalist.falsification import falsification_sample, falsification_score_sample from autora.experimentalist.novelty import novelty_sampler, novelty_score_sample import numpy as np import matplotlib.pyplot as plt from sklearn.linear_model import LinearRegression

Example: Sampling fom a Sine Function¶

In this example, we will consider ground truth in a form of the sine function. We will then use mixture_sampler to choose experimental conditions according to the 1) novelty strategy with different degrees of randomness and 2) a mixture of novelty and falsification strategies.

First, we define the experiment conditions $X$ and the observations $Y$. We consider a domain of $X \in [0, 2\pi]$.

In [138]:

# Define the domain
x = np.linspace(0, 2*np.pi, 100)
# Compute the values of the sine function at the points in the domain
y = np.sin(x)

# Create the plot
plt.figure(figsize=(8, 6))
plt.plot(x, y, "-")

# Add labels and title
plt.xlabel('x')
plt.ylabel('sin(x)')
plt.title('Ground truth')

# Display the plot
plt.show()

# Define the domain x = np.linspace(0, 2*np.pi, 100) # Compute the values of the sine function at the points in the domain y = np.sin(x) # Create the plot plt.figure(figsize=(8, 6)) plt.plot(x, y, "-") # Add labels and title plt.xlabel('x') plt.ylabel('sin(x)') plt.title('Ground truth') # Display the plot plt.show()

Mixture sampler using the novelty strategy¶

Now, we can try to use a mixture sampler to sample using the novelty strategy with different levels of randomness.

In [139]:

new_X = np.linspace(0, 2 * np.pi, 100)
# old points
X = np.linspace(0, 0.5, 50)
Y = np.sin(X)

params = {
    "novelty": {"reference_conditions": X},
}

new_X = np.linspace(0, 2 * np.pi, 100) # old points X = np.linspace(0, 0.5, 50) Y = np.sin(X) params = { "novelty": {"reference_conditions": X}, }

Low temperature: points are sampled deterministically.¶

In [140]:

selected_conditions = mixture_sample(
    conditions=new_X,
    temperature=0.01,
    samplers=[[novelty_score_sample, "novelty", [0.8, 0.2]]],
    params=params,
    num_samples=10
)

selected_conditions = mixture_sample( conditions=new_X, temperature=0.01, samplers=[[novelty_score_sample, "novelty", [0.8, 0.2]]], params=params, num_samples=10 )

In [141]:

selected_conditions

selected_conditions

Out[141]:

array([6.28318531, 6.21971879, 6.15625227, 6.09278575, 6.02931923,
       5.96585272, 5.9023862 , 5.83891968, 5.77545316, 5.71198664])

In [143]:

# Define the domain
x = np.linspace(0, 2*np.pi, 100)

# Compute the values of the sine function at the points in the domain
y = np.sin(x)

# Create the plot
plt.figure(figsize=(8, 6))
plt.plot(x, y, "-")
plt.plot(X, Y, "bo")

# Add vertical lines at the sampled x-values
for val in selected_conditions:
    plt.axvline(x=val, color='black')

# Add labels and title
plt.xlabel('x')
plt.ylabel('sin(x)')
plt.title('Ground Truth, Training Data, and Sampled Conditions')

# Display the plot
plt.grid(True)
plt.show()

# Define the domain x = np.linspace(0, 2*np.pi, 100) # Compute the values of the sine function at the points in the domain y = np.sin(x) # Create the plot plt.figure(figsize=(8, 6)) plt.plot(x, y, "-") plt.plot(X, Y, "bo") # Add vertical lines at the sampled x-values for val in selected_conditions: plt.axvline(x=val, color='black') # Add labels and title plt.xlabel('x') plt.ylabel('sin(x)') plt.title('Ground Truth, Training Data, and Sampled Conditions') # Display the plot plt.grid(True) plt.show()

High temperature: randomness is added to the sampling process.¶

In [144]:

selected_conditions = mixture_sample(
    conditions=new_X,
    temperature=2,
    samplers=[[novelty_score_sample, "novelty", [0.8, 0.2]]],
    params=params,
    num_samples=10
)

selected_conditions = mixture_sample( conditions=new_X, temperature=2, samplers=[[novelty_score_sample, "novelty", [0.8, 0.2]]], params=params, num_samples=10 )

In [145]:

selected_conditions

selected_conditions

Out[145]:

array([2.66559377, 5.45812057, 5.33118753, 6.21971879, 0.6981317 ,
       5.58505361, 6.28318531, 5.26772102, 3.99839065, 4.95038842])

In [146]:

# Define the domain
x = np.linspace(0, 2*np.pi, 100)

# Compute the values of the sine function at the points in the domain
y = np.sin(x)

# Create the plot
plt.figure(figsize=(8, 6))
plt.plot(x, y, "-")
plt.plot(X, Y, "bo")

# Add vertical lines at the sampled x-values
for val in selected_conditions:
    plt.axvline(x=val, color='black')

# Add labels and title
plt.xlabel('x')
plt.ylabel('sin(x)')
plt.title('Ground Truth, Training Data, and Sampled Conditions')

# Display the plot
plt.grid(True)
plt.show()

# Define the domain x = np.linspace(0, 2*np.pi, 100) # Compute the values of the sine function at the points in the domain y = np.sin(x) # Create the plot plt.figure(figsize=(8, 6)) plt.plot(x, y, "-") plt.plot(X, Y, "bo") # Add vertical lines at the sampled x-values for val in selected_conditions: plt.axvline(x=val, color='black') # Add labels and title plt.xlabel('x') plt.ylabel('sin(x)') plt.title('Ground Truth, Training Data, and Sampled Conditions') # Display the plot plt.grid(True) plt.show()

Mixture experimentalist combining novelty and falsification¶

In [147]:

model = LinearRegression()
model.fit(X.reshape(-1, 1), Y)

model = LinearRegression() model.fit(X.reshape(-1, 1), Y)

Out[147]:

LinearRegression()

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.

Now, we have new conditions to choose sampling from!

In [148]:

new_X = np.linspace(0, 2 * np.pi, 100)

params = {
    "novelty": {"reference_conditions": X},
    "falsification": {"reference_conditions": X, "reference_observations": Y, "model": model}
}

new_X = np.linspace(0, 2 * np.pi, 100) params = { "novelty": {"reference_conditions": X}, "falsification": {"reference_conditions": X, "reference_observations": Y, "model": model} }

In [149]:

selected_conditions = mixture_sample(
    conditions=new_X,
    temperature=0.01,
    samplers=[[novelty_score_sample, "novelty", [0.7, 0.1]], [falsification_score_sample, "falsification", [0.5, 0]]],
    params=params,
    num_samples=10
)

selected_conditions = mixture_sample( conditions=new_X, temperature=0.01, samplers=[[novelty_score_sample, "novelty", [0.7, 0.1]], [falsification_score_sample, "falsification", [0.5, 0]]], params=params, num_samples=10 )

In [150]:

selected_conditions

selected_conditions

Out[150]:

array([0.57119866, 0.63466518, 0.6981317 , 0.50773215, 0.76159822,
       0.82506474, 6.28318531, 0.88853126, 6.21971879, 6.09278575])

In [151]:

x = np.linspace(0, 2*np.pi, 100)

# Compute the values of the sine function at the points in the domain
y = np.sin(x)

# Create the plot
plt.figure(figsize=(8, 6))
plt.plot(x, y, "-")
plt.plot(X, Y, "bo")

# Add vertical lines at the sampled x-values
for val in selected_conditions:
    plt.axvline(x=val, color='black')

# Add labels and title
plt.xlabel('x')
plt.ylabel('sin(x)')
plt.title('Ground Truth, Training Data, and Sampled Conditions')

# Display the plot
plt.grid(True)
plt.show()

x = np.linspace(0, 2*np.pi, 100) # Compute the values of the sine function at the points in the domain y = np.sin(x) # Create the plot plt.figure(figsize=(8, 6)) plt.plot(x, y, "-") plt.plot(X, Y, "bo") # Add vertical lines at the sampled x-values for val in selected_conditions: plt.axvline(x=val, color='black') # Add labels and title plt.xlabel('x') plt.ylabel('sin(x)') plt.title('Ground Truth, Training Data, and Sampled Conditions') # Display the plot plt.grid(True) plt.show()

In [ ]: