Bases: Objective
Computes the B-optimal design metric.
Refer to the following paper for more details
- Approximate Sequential Optimization for Informative Path Planning [Ott et al., 2024]
B-optimality minimizes the trace of the inverse of the covariance matrix
\(-Tr(K(X, X)^{-1})\). Since optimization
algorithms typically minimize a function, this objective returns
\(Tr(K(X, X)^{-1})\), which is then maximized.
Source code in sgptools/objectives.py
| class BOptimal(Objective):
"""
Computes the B-optimal design metric.
Refer to the following paper for more details:
- Approximate Sequential Optimization for Informative Path Planning [Ott et al., 2024]
B-optimality minimizes the trace of the inverse of the covariance matrix
$-Tr(K(X, X)^{-1})$. Since optimization
algorithms typically minimize a function, this objective returns
$Tr(K(X, X)^{-1})$, which is then maximized.
"""
def __call__(self, X: tf.Tensor) -> tf.Tensor:
"""
Computes the trace of the inverse of the covariance matrix $Tr(K(X, X)^{-1})$.
Args:
X (tf.Tensor): The input points (e.g., sensing locations) for which
the objective is to be computed. Shape: (M, D).
Returns:
tf.Tensor: The computed B-optimal metric value.
Usage:
```python
import gpflow
import numpy as np
# Assume kernel is defined
# X_objective = np.random.rand(100, 2) # Not used by B-Optimal but required by base class
# kernel = gpflow.kernels.SquaredExponential()
# noise_variance = 0.1
b_optimal_objective = BOptimal(
X_objective=X_objective,
kernel=kernel,
noise_variance=noise_variance
)
X_sensing = tf.constant(np.random.rand(10, 2), dtype=tf.float64)
b_optimal_value = b_optimal_objective(X_sensing)
```
"""
# K(X, X)
K_X_X = self.kernel(X)
inv_K_X_X = tf.linalg.inv(self.jitter_fn(K_X_X))
trace_inv_K_X_X = tf.linalg.trace(inv_K_X_X)
return trace_inv_K_X_X
|
Computes the trace of the inverse of the covariance matrix \(Tr(K(X, X)^{-1})\).
Parameters:
| Name |
Type |
Description |
Default |
X
|
Tensor
|
The input points (e.g., sensing locations) for which
the objective is to be computed. Shape: (M, D).
|
required
|
Returns:
| Type |
Description |
Tensor
|
tf.Tensor: The computed B-optimal metric value.
|
Usage
import gpflow
import numpy as np
# Assume kernel is defined
# X_objective = np.random.rand(100, 2) # Not used by B-Optimal but required by base class
# kernel = gpflow.kernels.SquaredExponential()
# noise_variance = 0.1
b_optimal_objective = BOptimal(
X_objective=X_objective,
kernel=kernel,
noise_variance=noise_variance
)
X_sensing = tf.constant(np.random.rand(10, 2), dtype=tf.float64)
b_optimal_value = b_optimal_objective(X_sensing)
Source code in sgptools/objectives.py
| def __call__(self, X: tf.Tensor) -> tf.Tensor:
"""
Computes the trace of the inverse of the covariance matrix $Tr(K(X, X)^{-1})$.
Args:
X (tf.Tensor): The input points (e.g., sensing locations) for which
the objective is to be computed. Shape: (M, D).
Returns:
tf.Tensor: The computed B-optimal metric value.
Usage:
```python
import gpflow
import numpy as np
# Assume kernel is defined
# X_objective = np.random.rand(100, 2) # Not used by B-Optimal but required by base class
# kernel = gpflow.kernels.SquaredExponential()
# noise_variance = 0.1
b_optimal_objective = BOptimal(
X_objective=X_objective,
kernel=kernel,
noise_variance=noise_variance
)
X_sensing = tf.constant(np.random.rand(10, 2), dtype=tf.float64)
b_optimal_value = b_optimal_objective(X_sensing)
```
"""
# K(X, X)
K_X_X = self.kernel(X)
inv_K_X_X = tf.linalg.inv(self.jitter_fn(K_X_X))
trace_inv_K_X_X = tf.linalg.trace(inv_K_X_X)
return trace_inv_K_X_X
|