Bases: Kernel
Stack kernel class for combining multiple Gaussian Process (GP) kernels additively.
The Stack class defines a kernel that combines multiple input kernels by stacking them together.
This additive combination allows for capturing a more complex covariance structure by summing the
contributions from each individual kernel.
Parameters:
-
parts
(List[Kernel])
–
A list of kernel objects to be combined additively.
Examples:
Creating and using a Stack kernel:
from geostat.kernel import Stack, SquaredExponential, Noise
# Create individual kernels
kernel1 = SquaredExponential(sill=1.0, range=2.0)
kernel2 = Noise(nugget=0.1)
# Combine kernels using the Stack class
stacked_kernel = Stack(parts=[kernel1, kernel2])
locs1 = np.array([[0.0], [1.0], [2.0]])
locs2 = np.array([[0.0], [1.0], [2.0]])
covariance_matrix = stacked_kernel({'locs1': locs1, 'locs2': locs2})
Adding another kernel to an existing Stack:
kernel3 = SquaredExponential(sill=0.5, range=1.0)
combined_stack = stacked_kernel + kernel3
Notes:
- The
call method computes the sum of all covariance matrices generated by the stacked kernels.
- The
vars method gathers parameters from all input kernels, making them accessible for optimization.
- The
Stack kernel is useful for building complex models where multiple covariance structures need to be
combined additively, enabling richer and more flexible GP models.
Source code in src/geostat/kernel.py
| class Stack(Kernel):
"""
Stack kernel class for combining multiple Gaussian Process (GP) kernels additively.
The `Stack` class defines a kernel that combines multiple input kernels by stacking them together.
This additive combination allows for capturing a more complex covariance structure by summing the
contributions from each individual kernel.
Parameters:
parts (List[Kernel]):
A list of kernel objects to be combined additively.
Examples:
Creating and using a `Stack` kernel:
```python
from geostat.kernel import Stack, SquaredExponential, Noise
# Create individual kernels
kernel1 = SquaredExponential(sill=1.0, range=2.0)
kernel2 = Noise(nugget=0.1)
# Combine kernels using the Stack class
stacked_kernel = Stack(parts=[kernel1, kernel2])
locs1 = np.array([[0.0], [1.0], [2.0]])
locs2 = np.array([[0.0], [1.0], [2.0]])
covariance_matrix = stacked_kernel({'locs1': locs1, 'locs2': locs2})
```
Adding another kernel to an existing `Stack`:
```python
kernel3 = SquaredExponential(sill=0.5, range=1.0)
combined_stack = stacked_kernel + kernel3
```
Examples: Notes:
- The `call` method computes the sum of all covariance matrices generated by the stacked kernels.
- The `vars` method gathers parameters from all input kernels, making them accessible for optimization.
- The `Stack` kernel is useful for building complex models where multiple covariance structures need to be
combined additively, enabling richer and more flexible GP models.
"""
def __init__(self, parts: List[Kernel]):
self.parts = parts
super().__init__({}, dict(locs1='locs1', locs2='locs2', parts=parts))
def vars(self):
return {k: p for part in self.parts for k, p in part.vars().items()}
def __add__(self, other):
if isinstance(other, Kernel):
return Stack(self.parts + [other])
def call(self, e):
return tf.reduce_sum(e['parts'], axis=0)
def report(self):
return ' '.join(part.report(p) for part in self.parts)
|