Revision

**291ae6c7dbfcbded27c604f136982a5067d14b8e**authored by thevincentadam on**20 January 2020, 12:17:20 UTC**, committed by thevincentadam on**20 January 2020, 12:17:20 UTC****1 parent**5dc31b8

sums.py

```
import itertools
from functools import reduce
import tensorflow as tf
from .. import kernels
from .. import mean_functions as mfn
from ..inducing_variables import InducingPoints
from ..probability_distributions import DiagonalGaussian, Gaussian, MarkovGaussian
from . import dispatch
from .expectations import expectation
NoneType = type(None)
@dispatch.expectation.register(Gaussian, kernels.Sum, NoneType, NoneType, NoneType)
def _E(p, kernel, _, __, ___, nghp=None):
r"""
Compute the expectation:
<\Sum_i diag(Ki_{X, X})>_p(X)
- \Sum_i Ki_{.,.} :: Sum kernel
:return: N
"""
exps = [expectation(p, k, nghp=nghp) for k in kernel.kernels]
return reduce(tf.add, exps)
@dispatch.expectation.register(Gaussian, kernels.Sum, InducingPoints, NoneType, NoneType)
def _E(p, kernel, inducing_variable, _, __, nghp=None):
r"""
Compute the expectation:
<\Sum_i Ki_{X, Z}>_p(X)
- \Sum_i Ki_{.,.} :: Sum kernel
:return: NxM
"""
exps = [expectation(p, (k, inducing_variable), nghp=nghp) for k in kernel.kernels]
return reduce(tf.add, exps)
@dispatch.expectation.register(Gaussian, (mfn.Linear, mfn.Identity, mfn.Constant), NoneType, kernels.Sum,
InducingPoints)
def _E(p, mean, _, kernel, inducing_variable, nghp=None):
r"""
Compute the expectation:
expectation[n] = <m(x_n)^T (\Sum_i Ki_{x_n, Z})>_p(x_n)
- \Sum_i Ki_{.,.} :: Sum kernel
:return: NxQxM
"""
exps = [expectation(p, mean, (k, inducing_variable), nghp=nghp) for k in kernel.kernels]
return reduce(tf.add, exps)
@dispatch.expectation.register(MarkovGaussian, mfn.Identity, NoneType, kernels.Sum, InducingPoints)
def _E(p, mean, _, kernel, inducing_variable, nghp=None):
r"""
Compute the expectation:
expectation[n] = <x_{n+1} (\Sum_i Ki_{x_n, Z})>_p(x_{n:n+1})
- \Sum_i Ki_{.,.} :: Sum kernel
:return: NxDxM
"""
exps = [expectation(p, mean, (k, inducing_variable), nghp=nghp) for k in kernel.kernels]
return reduce(tf.add, exps)
@dispatch.expectation.register((Gaussian, DiagonalGaussian), kernels.Sum, InducingPoints, kernels.Sum, InducingPoints)
def _E(p, kern1, feat1, kern2, feat2, nghp=None):
r"""
Compute the expectation:
expectation[n] = <(\Sum_i K1_i_{Z1, x_n}) (\Sum_j K2_j_{x_n, Z2})>_p(x_n)
- \Sum_i K1_i_{.,.}, \Sum_j K2_j_{.,.} :: Sum kernels
:return: NxM1xM2
"""
crossexps = []
if kern1 == kern2 and feat1 == feat2: # avoid duplicate computation by using transposes
for i, k1 in enumerate(kern1.kernels):
crossexps.append(expectation(p, (k1, feat1), (k1, feat1), nghp=nghp))
for k2 in kern1.kernels[:i]:
eKK = expectation(p, (k1, feat1), (k2, feat2), nghp=nghp)
eKK += tf.linalg.adjoint(eKK)
crossexps.append(eKK)
else:
for k1, k2 in itertools.product(kern1.kernels, kern2.kernels):
crossexps.append(expectation(p, (k1, feat1), (k2, feat2), nghp=nghp))
return reduce(tf.add, crossexps)
```

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