Novelty Experimentalist

The novelty experimentalist identifies experimental conditions ${\overrightarrow{x}}^{\prime }\in X^{\prime }$ with respect to a pairwise distance metric applied to existing experimental conditions $\overrightarrow{x}\in X$:

$$\underset{{\overrightarrow{x}}^{\prime }}{\arg max}f(d(\overrightarrow{x},{\overrightarrow{x}}^{\prime }))$$

where $f$ is an integration function applied to all pairwise distances.

Example

For instance, the integration function $f(x)=min(x)$ and distance function $d(x,x^{\prime })=|x-x^{\prime }|$ identifies condition ${\overrightarrow{x}}^{\prime }$ with the greatest minimal Euclidean distance to all existing conditions in $\overrightarrow{x}\in X$.

$$\underset{\overrightarrow{x}}{\arg max}\underset{i}{min}(\sum _{j=1}^n(x_{i,j}-x_{i,j}^{\prime }{)}^2)$$

To illustrate this sampling strategy, consider the following four experimental conditions that were already probed:

$x_{i,0}$	$x_{i,1}$	$x_{i,2}$
0	0	0
1	0	0
0	1	0
0	0	1

Fruthermore, let's consider the following three candidate conditions $X^{\prime }$:

$x_{i,0}^{\prime }$	$x_{i,1}^{\prime }$	$x_{i,2}^{\prime }$
1	1	1
2	2	2
3	3	3

If the novelty experimentalist is tasked to identify two novel conditions, it will select the last two candidate conditions $x_{1,j}^{\prime }$ and $x_{2,j}^{\prime }$ because they have the greatest minimal distance to all existing conditions $x_{i,j}$:

Example Code

import numpy as np
from autora.experimentalist.novelty import novelty_sample, novelty_score_sample

# Specify X and X'
X = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]])
X_prime = np.array([[1, 1, 1], [2, 2, 2], [3, 3, 3]])

# Here, we choose to identify two novel conditions
n = 2
X_sampled = novelty_sample(conditions=X_prime, reference_conditions=X, num_samples=n)

# We may also obtain samples along with their z-scored novelty scores  
(X_sampled, scores) = novelty_score_sample(conditions=X_prime, reference_conditions=X, num_samples=n)