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Instantiate an object of a derived class using the information
in input_dict (built by the to_dict method of the derived class).
More specifically, after reading the derived class from input_dict,
it calls the method _build_from_input_dict of the derived class.
Note: This method should n... |
Convert the object into a json serializable dictionary.
Note: It uses the private method _save_to_input_dict of the parent.
:return dict: json serializable dictionary containing the needed information to instantiate the object
def to_dict(self):
"""
Convert the object into a json seri... |
Builds a kernel for an Intrinsic Coregionalization Model
:input_dim: Input dimensionality (does not include dimension of indices)
:num_outputs: Number of outputs
:param kernel: kernel that will be multiplied by the coregionalize kernel (matrix B).
:type kernel: a GPy kernel
:param W_rank: number tu... |
Builds a kernel for an Linear Coregionalization Model
:input_dim: Input dimensionality (does not include dimension of indices)
:num_outputs: Number of outputs
:param kernel: kernel that will be multiplied by the coregionalize kernel (matrix B).
:type kernel: a GPy kernel
:param W_rank: number tuple... |
Builds a kernel for an Intrinsic Coregionalization Model
:input_dim: Input dimensionality
:num_outputs: Number of outputs
:param kernel: kernel that will be multiplied by the coregionalize kernel (matrix B).
:type kernel: a GPy kernel
:param W_rank: number tuples of the corregionalization parameter... |
Kernel function applied on inputs X and X2.
In the stationary case there is an inner function depending on the
distances from X to X2, called r.
K(X, X2) = K_of_r((X-X2)**2)
def K(self, X, X2=None):
"""
Kernel function applied on inputs X and X2.
In the stationary case ... |
compute the derivative of K wrt X going through X
def dK_dr_via_X(self, X, X2):
"""
compute the derivative of K wrt X going through X
"""
#a convenience function, so we can cache dK_dr
return self.dK_dr(self._scaled_dist(X, X2)) |
Compute the Euclidean distance between each row of X and X2, or between
each pair of rows of X if X2 is None.
def _unscaled_dist(self, X, X2=None):
"""
Compute the Euclidean distance between each row of X and X2, or between
each pair of rows of X if X2 is None.
"""
#X, =... |
Efficiently compute the scaled distance, r.
..math::
r = \sqrt( \sum_{q=1}^Q (x_q - x'q)^2/l_q^2 )
Note that if thre is only one lengthscale, l comes outside the sum. In
this case we compute the unscaled distance first (in a separate
function for caching) and divide by leng... |
Given the derivative of the objective wrt the covariance matrix
(dL_dK), compute the gradient wrt the parameters of this kernel,
and store in the parameters object as e.g. self.variance.gradient
def update_gradients_full(self, dL_dK, X, X2=None, reset=True):
"""
Given the derivative of ... |
Specially intended for the Grid regression case.
Given the computed log likelihood derivates, update the corresponding
kernel and likelihood gradients.
Useful for when gradients have been computed a priori.
def update_gradients_direct(self, dL_dVar, dL_dLen):
"""
Specially inten... |
Compute the elementwise inverse of the distance matrix, expecpt on the
diagonal, where we return zero (the distance on the diagonal is zero).
This term appears in derviatives.
def _inv_dist(self, X, X2=None):
"""
Compute the elementwise inverse of the distance matrix, expecpt on the
... |
Given the derivative of the objective wrt K (dL_dK), compute the derivative wrt X
def gradients_X(self, dL_dK, X, X2=None):
"""
Given the derivative of the objective wrt K (dL_dK), compute the derivative wrt X
"""
if use_stationary_cython:
return self._gradients_X_cython(dL_... |
Given the derivative of the objective K(dL_dK), compute the second derivative of K wrt X and X2:
returns the full covariance matrix [QxQ] of the input dimensionfor each pair or vectors, thus
the returned array is of shape [NxNxQxQ].
..math:
\frac{\partial^2 K}{\partial X2 ^2} = - \... |
Given the derivative of the objective dL_dK, compute the second derivative of K wrt X:
..math:
\frac{\partial^2 K}{\partial X\partial X}
..returns:
dL2_dXdX: [NxQxQ]
def gradients_XX_diag(self, dL_dK_diag, X):
"""
Given the derivative of the objective dL_dK, comp... |
Return the state space representation of the covariance.
def sde(self):
"""
Return the state space representation of the covariance.
"""
variance = float(self.variance.values)
lengthscale = float(self.lengthscale.values)
foo = np.sqrt(3.)/lengthscale
F = np.a... |
Return the Gram matrix of the vector of functions F with respect to the RKHS norm. The use of this function is limited to input_dim=1.
:param F: vector of functions
:type F: np.array
:param F1: vector of derivatives of F
:type F1: np.array
:param F2: vector of second derivatives... |
Convert the object into a json serializable dictionary.
Note: It uses the private method _save_to_input_dict of the parent.
:return dict: json serializable dictionary containing the needed information to instantiate the object
def to_dict(self):
"""
Convert the object into a json seri... |
Convenience function for returning back fixed_inputs where the other inputs
are fixed using fix_routine
:param model: model
:type model: Model
:param non_fixed_inputs: dimensions of non fixed inputs
:type non_fixed_inputs: list
:param fix_routine: fixing routine to use, 'mean', 'median', 'zero'
... |
Infer the distribution of X for the new observed data *Y_new*.
:param model: the GPy model used in inference
:type model: GPy.core.Model
:param Y_new: the new observed data for inference
:type Y_new: numpy.ndarray
:param optimize: whether to optimize the location of new X (True by default)
:typ... |
Return the state space representation of the covariance.
Note! For Sparse GP inference too small or two high values of lengthscale
lead to instabilities. This is because Qc are too high or too low
and P_inf are not full rank. This effect depends on approximatio order.
For N = 10... |
Return the state space representation of the covariance.
def sde(self):
"""
Return the state space representation of the covariance.
"""
variance = float(self.variance.values)
lengthscale = float(self.lengthscale)
F = np.array(((-1.0/lengthscale,),))
L = np.ar... |
Likelihood function given link(f)
:param link_f: latent variables link(f)
:type link_f: Nx1 array
:param y: data
:type y: Nx1 array
:param Y_metadata: Y_metadata which is not used in weibull distribution
:returns: likelihood evaluated for this point
:rtype: floa... |
Log Likelihood Function given link(f)
.. math::
\\ln p(y_{i}|\lambda(f_{i})) = \\alpha_{i}\\log \\beta - \\log \\Gamma(\\alpha_{i}) + (\\alpha_{i} - 1)\\log y_{i} - \\beta y_{i}\\\\
\\alpha_{i} = \\beta y_{i}
:param link_f: latent variables (link(f))
:type link_f: Nx1 a... |
Gradient of the log likelihood function at y, given link(f) w.r.t link(f)
.. math::
\\frac{d \\ln p(y_{i}|\\lambda(f_{i}))}{d\\lambda(f)} = \\beta (\\log \\beta y_{i}) - \\Psi(\\alpha_{i})\\beta\\\\
\\alpha_{i} = \\beta y_{i}
:param link_f: latent variables (f)
:type li... |
Hessian at y, given link(f), w.r.t link(f)
i.e. second derivative logpdf at y given link(f_i) and link(f_j) w.r.t link(f_i) and link(f_j)
The hessian will be 0 unless i == j
.. math::
\\frac{d^{2} \\ln p(y_{i}|\lambda(f_{i}))}{d^{2}\\lambda(f)} = -\\beta^{2}\\frac{d\\Psi(\\alpha_{i... |
Third order derivative log-likelihood function at y given link(f) w.r.t link(f)
.. math::
\\frac{d^{3} \\ln p(y_{i}|\lambda(f_{i}))}{d^{3}\\lambda(f)} = -\\beta^{3}\\frac{d^{2}\\Psi(\\alpha_{i})}{d\\alpha_{i}}\\\\
\\alpha_{i} = \\beta y_{i}
:param link_f: latent variables link(... |
First order derivative derivative of loglikelihood wrt r:shape parameter
:param link_f: latent variables link(f)
:type link_f: Nx1 array
:param y: data
:type y: Nx1 array
:param Y_metadata: Y_metadata which is not used in gamma distribution
:returns: third derivative of ... |
Returns a set of samples of observations conditioned on a given value of latent variable f.
:param gp: latent variable
def samples(self, gp, Y_metadata=None):
"""
Returns a set of samples of observations conditioned on a given value of latent variable f.
:param gp: latent variable
... |
The first phase of inference:
Compute: log-likelihood, dL_dKmm
Cached intermediate results: Kmm, KmmInv,
def inference_likelihood(self, kern, X, Z, likelihood, Y):
"""
The first phase of inference:
Compute: log-likelihood, dL_dKmm
Cached intermediate results: Kmm, KmmI... |
The second phase of inference: Computing the derivatives over a minibatch of Y
Compute: dL_dpsi0, dL_dpsi1, dL_dpsi2, dL_dthetaL
return a flag showing whether it reached the end of Y (isEnd)
def inference_minibatch(self, kern, X, Z, likelihood, Y):
"""
The second phase of inference: Com... |
The second phase of inference: Computing the derivatives over a minibatch of Y
Compute: dL_dpsi0, dL_dpsi1, dL_dpsi2, dL_dthetaL
return a flag showing whether it reached the end of Y (isEnd)
def inference_minibatch(self, kern, X, Z, likelihood, Y, Zp):
"""
The second phase of inference:... |
Convert the object into a json serializable dictionary.
Note: It uses the private method _save_to_input_dict of the parent.
:return dict: json serializable dictionary containing the needed information to instantiate the object
def to_dict(self):
"""
Convert the object into a json seri... |
Specially intended for Grid regression.
def get_one_dimensional_kernel(self, dim):
"""
Specially intended for Grid regression.
"""
oneDkernel = GridRBF(input_dim=1, variance=self.variance.copy(), originalDimensions=dim)
return oneDkernel |
Load in a data set of marker points from the Ohio State University C3D motion capture files (http://accad.osu.edu/research/mocap/mocap_data.htm).
def load_text_data(dataset, directory, centre=True):
"""Load in a data set of marker points from the Ohio State University C3D motion capture files (http://accad.osu.edu... |
Parse data from Ohio State University text mocap files (http://accad.osu.edu/research/mocap/mocap_data.htm).
def parse_text(file_name):
"""Parse data from Ohio State University text mocap files (http://accad.osu.edu/research/mocap/mocap_data.htm)."""
# Read the header
fid = open(file_name, 'r')
point_... |
Read a file detailing which markers should be connected to which for motion capture data.
def read_connections(file_name, point_names):
"""Read a file detailing which markers should be connected to which for motion capture data."""
connections = []
fid = open(file_name, 'r')
line=fid.readline()
wh... |
Take a tree and set the children according to the parents.
Takes a tree structure which lists the parents of each vertex
and computes the children for each vertex and places them in.
def find_children(self):
"""Take a tree and set the children according to the parents.
Takes a tree st... |
Take a tree and set the parents according to the children
Takes a tree structure which lists the children of each vertex
and computes the parents for each vertex and places them in.
def find_parents(self):
"""Take a tree and set the parents according to the children
Takes a tree struc... |
Finds the index of the root node of the tree.
def find_root(self):
"""Finds the index of the root node of the tree."""
self.find_parents()
index = 0
while len(self.vertices[index].parents)>0:
index = self.vertices[index].parents[0]
return index |
Give the index associated with a given vertex id.
def get_index_by_id(self, id):
"""Give the index associated with a given vertex id."""
for i in range(len(self.vertices)):
if self.vertices[i].id == id:
return i
raise ValueError('Reverse look up of id failed.') |
Give the index associated with a given vertex name.
def get_index_by_name(self, name):
"""Give the index associated with a given vertex name."""
for i in range(len(self.vertices)):
if self.vertices[i].name == name:
return i
raise ValueError('Reverse look up of name f... |
Order vertices in the graph such that parents always have a lower index than children.
def order_vertices(self):
"""Order vertices in the graph such that parents always have a lower index than children."""
ordered = False
while ordered == False:
for i in range(len(self.vert... |
Swap two vertices in the tree structure array.
swap_vertex swaps the location of two vertices in a tree structure array.
:param tree: the tree for which two vertices are to be swapped.
:param i: the index of the first vertex to be swapped.
:param j: the index of the second vertex to be... |
Remove discontinuities in angle channels so that they don't cause artifacts in algorithms that rely on the smoothness of the functions.
def smooth_angle_channels(self, channels):
"""Remove discontinuities in angle channels so that they don't cause artifacts in algorithms that rely on the smoothness of the func... |
Loads an ASF file into a skeleton structure.
:param file_name: The file name to load in.
def load_skel(self, file_name):
"""
Loads an ASF file into a skeleton structure.
:param file_name: The file name to load in.
"""
fid = open(file_name, 'r')
sel... |
Read bone data from an acclaim skeleton file stream.
def read_bonedata(self, fid):
"""Read bone data from an acclaim skeleton file stream."""
bone_count = 0
lin = self.read_line(fid)
while lin[0]!=':':
parts = lin.split()
if parts[0] == 'begin':
... |
Read channels from an acclaim file.
def read_channels(self, fid):
"""Read channels from an acclaim file."""
bones = [[] for i in self.vertices]
num_channels = 0
for vertex in self.vertices:
num_channels = num_channels + len(vertex.meta['channels'])
lin = self.read_l... |
Read documentation from an acclaim skeleton file stream.
def read_documentation(self, fid):
"""Read documentation from an acclaim skeleton file stream."""
lin = self.read_line(fid)
while lin[0] != ':':
self.documentation.append(lin)
lin = self.read_line(fid)
ret... |
Read hierarchy information from acclaim skeleton file stream.
def read_hierarchy(self, fid):
"""Read hierarchy information from acclaim skeleton file stream."""
lin = self.read_line(fid)
while lin != 'end':
parts = lin.split()
if lin != 'begin':
... |
Read a line from a file string and check it isn't either empty or commented before returning.
def read_line(self, fid):
"""Read a line from a file string and check it isn't either empty or commented before returning."""
lin = '#'
while lin[0] == '#':
lin = fid.readline().strip()
... |
Read the root node from an acclaim skeleton file stream.
def read_root(self, fid):
"""Read the root node from an acclaim skeleton file stream."""
lin = self.read_line(fid)
while lin[0] != ':':
parts = lin.split()
if parts[0]=='order':
... |
Loads an acclaim skeleton format from a file stream.
def read_skel(self, fid):
"""Loads an acclaim skeleton format from a file stream."""
lin = self.read_line(fid)
while lin:
if lin[0]==':':
if lin[1:]== 'name':
lin = self.read_line(fid)
... |
Read units from an acclaim skeleton file stream.
def read_units(self, fid):
"""Read units from an acclaim skeleton file stream."""
lin = self.read_line(fid)
while lin[0] != ':':
parts = lin.split()
if parts[0]=='mass':
self.mass = float... |
Get indices for the skeleton from the channels when loading in channel data.
def resolve_indices(self, index, start_val):
"""Get indices for the skeleton from the channels when loading in channel data."""
channels = self.vertices[index].meta['channels']
base_channel = start_val
rot_in... |
Set the meta information at each vertex to contain the correct matrices C and Cinv as prescribed by the rotations and rotation orders.
def set_rotation_matrices(self):
"""Set the meta information at each vertex to contain the correct matrices C and Cinv as prescribed by the rotations and rotation orders."""
... |
Compute the diagonal of the covariance matrix for X.
def Kdiag(self, X):
"""Compute the diagonal of the covariance matrix for X."""
X_prod = self._comp_prod(X)
return self.variance*four_over_tau*np.arcsin(X_prod/(X_prod+1.)) |
Derivative of the covariance with respect to the parameters.
def update_gradients_full(self, dL_dK, X, X2=None):
"""Derivative of the covariance with respect to the parameters."""
dvar, dw, db = self._comp_grads(dL_dK, X, X2)[:3]
self.variance.gradient = dvar
self.weight_variance.gradie... |
Derivative of the covariance matrix with respect to X
def gradients_X(self, dL_dK, X, X2):
"""Derivative of the covariance matrix with respect to X"""
return self._comp_grads(dL_dK, X, X2)[3] |
Derivative of the covariance matrix with respect to X
def gradients_X_X2(self, dL_dK, X, X2):
"""Derivative of the covariance matrix with respect to X"""
return self._comp_grads(dL_dK, X, X2)[3:] |
return the value of the parameters.
def _get_params(self):
"""return the value of the parameters."""
return np.hstack((self.varianceU,self.varianceY, self.lengthscaleU,self.lengthscaleY)) |
set the value of the parameters.
def _set_params(self, x):
"""set the value of the parameters."""
assert x.size == self.num_params
self.varianceU = x[0]
self.varianceY = x[1]
self.lengthscaleU = x[2]
self.lengthscaleY = x[3] |
Compute the covariance matrix between X and X2.
def K(self, X, X2, target):
"""Compute the covariance matrix between X and X2."""
if X2 is None: X2 = X
# i1 = X[:,1]
# i2 = X2[:,1]
# X = X[:,0].reshape(-1,1)
# X2 = X2[:,0].reshape(-1,1)
dist = np.abs(X - X2.T)
... |
Compute the diagonal of the covariance matrix associated to X.
def Kdiag(self, X, target):
"""Compute the diagonal of the covariance matrix associated to X."""
ly=1/self.lengthscaleY
lu=np.sqrt(3)/self.lengthscaleU
#ly=self.lengthscaleY
#lu=self.lengthscaleU
k1 ... |
derivative of the covariance matrix with respect to the parameters.
def _param_grad_helper(self, dL_dK, X, X2, target):
"""derivative of the covariance matrix with respect to the parameters."""
if X2 is None: X2 = X
dist = np.abs(X - X2.T)
ly=1/self.lengthscaleY
lu=np.sqrt(3)/s... |
Returns a GridPosterior class containing essential quantities of the posterior
def inference(self, kern, X, likelihood, Y, Y_metadata=None):
"""
Returns a GridPosterior class containing essential quantities of the posterior
"""
N = X.shape[0] #number of training points
D = X.sh... |
Convert the object into a json serializable dictionary.
Note: It uses the private method _save_to_input_dict of the parent.
:return dict: json serializable dictionary containing the needed information to instantiate the object
def to_dict(self):
"""
Convert the object into a json seri... |
Pull out the gradients, be careful as the order must match the order
in which the parameters are added
def update_gradients(self, grads):
"""
Pull out the gradients, be careful as the order must match the order
in which the parameters are added
"""
self.sigma2.gradient =... |
Likelihood function given link(f)
.. math::
p(y_{i}|\\lambda(f_{i})) = \\frac{\\Gamma\\left(\\frac{v+1}{2}\\right)}{\\Gamma\\left(\\frac{v}{2}\\right)\\sqrt{v\\pi\\sigma^{2}}}\\left(1 + \\frac{1}{v}\\left(\\frac{(y_{i} - \\lambda(f_{i}))^{2}}{\\sigma^{2}}\\right)\\right)^{\\frac{-v+1}{2}}
... |
Log Likelihood Function given link(f)
.. math::
\\ln p(y_{i}|\lambda(f_{i})) = \\ln \\Gamma\\left(\\frac{v+1}{2}\\right) - \\ln \\Gamma\\left(\\frac{v}{2}\\right) - \\ln \\sqrt{v \\pi\\sigma^{2}} - \\frac{v+1}{2}\\ln \\left(1 + \\frac{1}{v}\\left(\\frac{(y_{i} - \lambda(f_{i}))^{2}}{\\sigma^{2}}\\r... |
Gradient of the log likelihood function at y, given link(f) w.r.t link(f)
.. math::
\\frac{d \\ln p(y_{i}|\lambda(f_{i}))}{d\\lambda(f)} = \\frac{(v+1)(y_{i}-\lambda(f_{i}))}{(y_{i}-\lambda(f_{i}))^{2} + \\sigma^{2}v}
:param inv_link_f: latent variables (f)
:type inv_link_f: Nx1 ar... |
Hessian at y, given link(f), w.r.t link(f)
i.e. second derivative logpdf at y given link(f_i) and link(f_j) w.r.t link(f_i) and link(f_j)
The hessian will be 0 unless i == j
.. math::
\\frac{d^{2} \\ln p(y_{i}|\lambda(f_{i}))}{d^{2}\\lambda(f)} = \\frac{(v+1)((y_{i}-\lambda(f_{i}))... |
Third order derivative log-likelihood function at y given link(f) w.r.t link(f)
.. math::
\\frac{d^{3} \\ln p(y_{i}|\lambda(f_{i}))}{d^{3}\\lambda(f)} = \\frac{-2(v+1)((y_{i} - \lambda(f_{i}))^3 - 3(y_{i} - \lambda(f_{i})) \\sigma^{2} v))}{((y_{i} - \lambda(f_{i})) + \\sigma^{2} v)^3}
:par... |
Gradient of the log-likelihood function at y given f, w.r.t variance parameter (t_noise)
.. math::
\\frac{d \\ln p(y_{i}|\lambda(f_{i}))}{d\\sigma^{2}} = \\frac{v((y_{i} - \lambda(f_{i}))^{2} - \\sigma^{2})}{2\\sigma^{2}(\\sigma^{2}v + (y_{i} - \lambda(f_{i}))^{2})}
:param inv_link_f: late... |
Derivative of the dlogpdf_dlink w.r.t variance parameter (t_noise)
.. math::
\\frac{d}{d\\sigma^{2}}(\\frac{d \\ln p(y_{i}|\lambda(f_{i}))}{df}) = \\frac{-2\\sigma v(v + 1)(y_{i}-\lambda(f_{i}))}{(y_{i}-\lambda(f_{i}))^2 + \\sigma^2 v)^2}
:param inv_link_f: latent variables inv_link_f
... |
Gradient of the hessian (d2logpdf_dlink2) w.r.t variance parameter (t_noise)
.. math::
\\frac{d}{d\\sigma^{2}}(\\frac{d^{2} \\ln p(y_{i}|\lambda(f_{i}))}{d^{2}f}) = \\frac{v(v+1)(\\sigma^{2}v - 3(y_{i} - \lambda(f_{i}))^{2})}{(\\sigma^{2}v + (y_{i} - \lambda(f_{i}))^{2})^{3}}
:param inv_li... |
Returns a set of samples of observations based on a given value of the latent variable.
:param gp: latent variable
def samples(self, gp, Y_metadata=None):
"""
Returns a set of samples of observations based on a given value of the latent variable.
:param gp: latent variable
"""... |
This is the standard part, which usually belongs in parameters_changed.
For automatic handling of subsampling (such as missing_data, stochastics etc.), we need to put this into an inner
loop, in order to ensure a different handling of gradients etc of different
subsets of data.
The dic... |
This is for automatic updates of values in the inner loop of missing
data handling. Both arguments are dictionaries and the values in
full_values will be updated by the current_gradients.
If a key from current_values does not exist in full_values, it will be
initialized to the value in ... |
Here you put the values, which were collected before in the right places.
E.g. set the gradients of parameters, etc.
def _outer_values_update(self, full_values):
"""
Here you put the values, which were collected before in the right places.
E.g. set the gradients of parameters, etc.
... |
If full_values has indices in values_indices, we might want to initialize
the full_values differently, so that subsetting is possible.
Here you can initialize the full_values for the values needed.
Keep in mind, that if a key does not exist in full_values when updating
values, it will ... |
Store the object into a json serializable dictionary
:param boolean save_data: if true, it adds the data self.X and self.Y to the dictionary
:return dict: json serializable dictionary containing the needed information to instantiate the object
def to_dict(self, save_data=True):
"""
Sto... |
Instantiate an SparseGPClassification object using the information
in input_dict (built by the to_dict method).
:param data: It is used to provide X and Y for the case when the model
was saved using save_data=False in to_dict method.
:type data: tuple(:class:`np.ndarray`, :class:`np.... |
Convert the object into a json serializable dictionary.
Note: It uses the private method _save_to_input_dict of the parent.
:return dict: json serializable dictionary containing the needed information to instantiate the object
def to_dict(self):
"""
Convert the object into a json seri... |
Moments match of the marginal approximation in EP algorithm
:param i: number of observation (int)
:param tau_i: precision of the cavity distribution (float)
:param v_i: mean/variance of the cavity distribution (float)
def moments_match_ep(self, data_i, tau_i, v_i, Y_metadata_i=None):
"... |
Likelihood function given link(f)
.. math::
\\ln p(y_{i}|\\lambda(f_{i})) = -\\frac{N \\ln 2\\pi}{2} - \\frac{\\ln |K|}{2} - \\frac{(y_{i} - \\lambda(f_{i}))^{T}\\sigma^{-2}(y_{i} - \\lambda(f_{i}))}{2}
:param link_f: latent variables link(f)
:type link_f: Nx1 array
:param ... |
Log likelihood function given link(f)
.. math::
\\ln p(y_{i}|\\lambda(f_{i})) = -\\frac{N \\ln 2\\pi}{2} - \\frac{\\ln |K|}{2} - \\frac{(y_{i} - \\lambda(f_{i}))^{T}\\sigma^{-2}(y_{i} - \\lambda(f_{i}))}{2}
:param link_f: latent variables link(f)
:type link_f: Nx1 array
:pa... |
Gradient of the pdf at y, given link(f) w.r.t link(f)
.. math::
\\frac{d \\ln p(y_{i}|\\lambda(f_{i}))}{d\\lambda(f)} = \\frac{1}{\\sigma^{2}}(y_{i} - \\lambda(f_{i}))
:param link_f: latent variables link(f)
:type link_f: Nx1 array
:param y: data
:type y: Nx1 array
... |
Hessian at y, given link_f, w.r.t link_f.
i.e. second derivative logpdf at y given link(f_i) link(f_j) w.r.t link(f_i) and link(f_j)
The hessian will be 0 unless i == j
.. math::
\\frac{d^{2} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{2}f} = -\\frac{1}{\\sigma^{2}}
:param link_f: ... |
Third order derivative log-likelihood function at y given link(f) w.r.t link(f)
.. math::
\\frac{d^{3} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{3}\\lambda(f)} = 0
:param link_f: latent variables link(f)
:type link_f: Nx1 array
:param y: data
:type y: Nx1 array
:par... |
Gradient of the log-likelihood function at y given link(f), w.r.t variance parameter (noise_variance)
.. math::
\\frac{d \\ln p(y_{i}|\\lambda(f_{i}))}{d\\sigma^{2}} = -\\frac{N}{2\\sigma^{2}} + \\frac{(y_{i} - \\lambda(f_{i}))^{2}}{2\\sigma^{4}}
:param link_f: latent variables link(f)
... |
Derivative of the dlogpdf_dlink w.r.t variance parameter (noise_variance)
.. math::
\\frac{d}{d\\sigma^{2}}(\\frac{d \\ln p(y_{i}|\\lambda(f_{i}))}{d\\lambda(f)}) = \\frac{1}{\\sigma^{4}}(-y_{i} + \\lambda(f_{i}))
:param link_f: latent variables link(f)
:type link_f: Nx1 array
... |
Gradient of the hessian (d2logpdf_dlink2) w.r.t variance parameter (noise_variance)
.. math::
\\frac{d}{d\\sigma^{2}}(\\frac{d^{2} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{2}\\lambda(f)}) = \\frac{1}{\\sigma^{4}}
:param link_f: latent variables link(f)
:type link_f: Nx1 array
:par... |
Returns a set of samples of observations based on a given value of the latent variable.
:param gp: latent variable
def samples(self, gp, Y_metadata=None):
"""
Returns a set of samples of observations based on a given value of the latent variable.
:param gp: latent variable
"""... |
assumes independence
def log_predictive_density(self, y_test, mu_star, var_star, Y_metadata=None):
"""
assumes independence
"""
v = var_star + self.variance
return -0.5*np.log(2*np.pi) -0.5*np.log(v) - 0.5*np.square(y_test - mu_star)/v |
Convert the object into a json serializable dictionary.
Note: It uses the private method _save_to_input_dict of the parent.
:param boolean save_data: if true, it adds the training data self.X and self.Y to the dictionary
:return dict: json serializable dictionary containing the needed informati... |
Set the input / output data of the model
This is useful if we wish to change our existing data but maintain the same model
:param X: input observations
:type X: np.ndarray
:param Y: output observations
:type Y: np.ndarray
def set_XY(self, X=None, Y=None):
"""
Se... |
Predict the function(s) at the new point(s) Xnew. This includes the
likelihood variance added to the predicted underlying function
(usually referred to as f).
In order to predict without adding in the likelihood give
`include_likelihood=False`, or refer to self.predict_noiseless().
... |
Convenience function to predict the underlying function of the GP (often
referred to as f) without adding the likelihood variance on the
prediction function.
This is most likely what you want to use for your predictions.
:param Xnew: The points at which to make a prediction
:ty... |
Get the predictive quantiles around the prediction at X
:param X: The points at which to make a prediction
:type X: np.ndarray (Xnew x self.input_dim)
:param quantiles: tuple of quantiles, default is (2.5, 97.5) which is the 95% interval
:type quantiles: tuple
:param kern: optio... |
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