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train | Weibull.dlogpdf_dlink | 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... | GPy/likelihoods/weibull.py | def dlogpdf_dlink(self, link_f, y, Y_metadata=None):
"""
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} = \... | def dlogpdf_dlink(self, link_f, y, Y_metadata=None):
"""
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} = \... | [
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train | Weibull.d2logpdf_dlink2 | 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)
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.. math::
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"""
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_{... | def d2logpdf_dlink2(self, link_f, y, Y_metadata=None):
"""
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)
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train | Weibull.d3logpdf_dlink3 | 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}}\\\\
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"""
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}}\\\\
... | def d3logpdf_dlink3(self, link_f, y, Y_metadata=None):
"""
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}}\\\\
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train | Weibull.dlogpdf_dlink_dr | First order derivative derivative of loglikelihood wrt r:shape parameter
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:type y: Nx1 array
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First order derivative derivative of loglikelihood wrt r:shape parameter
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First order derivative derivative of loglikelihood wrt r:shape parameter
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:type link_f: Nx1 array
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train | Weibull.samples | Returns a set of samples of observations conditioned on a given value of latent variable f.
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:param gp: latent variable
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train | VarDTC_minibatch.inference_likelihood | The first phase of inference:
Compute: log-likelihood, dL_dKmm
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train | VarDTC_minibatch.inference_minibatch | The second phase of inference: Computing the derivatives over a minibatch of Y
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train | VarDTC_minibatch_IBPLFM.inference_minibatch | The second phase of inference: Computing the derivatives over a minibatch of Y
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train | RBF.to_dict | Convert the object into a json serializable dictionary.
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train | RBF.get_one_dimensional_kernel | Specially intended for Grid regression. | GPy/kern/src/rbf.py | def get_one_dimensional_kernel(self, dim):
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train | load_text_data | 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). | GPy/util/mocap.py | def load_text_data(dataset, directory, centre=True):
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train | parse_text | Parse data from Ohio State University text mocap files (http://accad.osu.edu/research/mocap/mocap_data.htm). | GPy/util/mocap.py | def parse_text(file_name):
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# Read the header
fid = open(file_name, 'r')
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connections[-1][0]... | def read_connections(file_name, point_names):
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train | tree.find_root | Finds the index of the root node of the tree. | GPy/util/mocap.py | def find_root(self):
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train | tree.get_index_by_id | Give the index associated with a given vertex id. | GPy/util/mocap.py | def get_index_by_id(self, id):
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train | tree.get_index_by_name | Give the index associated with a given vertex name. | GPy/util/mocap.py | def get_index_by_name(self, name):
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train | tree.order_vertices | Order vertices in the graph such that parents always have a lower index than children. | GPy/util/mocap.py | def order_vertices(self):
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train | tree.swap_vertices | Swap two vertices in the tree structure array.
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train | skeleton.smooth_angle_channels | Remove discontinuities in angle channels so that they don't cause artifacts in algorithms that rely on the smoothness of the functions. | GPy/util/mocap.py | def smooth_angle_channels(self, channels):
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train | acclaim_skeleton.load_skel | Loads an ASF file into a skeleton structure.
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train | acclaim_skeleton.read_bonedata | Read bone data from an acclaim skeleton file stream. | GPy/util/mocap.py | def read_bonedata(self, fid):
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train | acclaim_skeleton.read_channels | Read channels from an acclaim file. | GPy/util/mocap.py | def read_channels(self, fid):
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train | acclaim_skeleton.read_documentation | Read documentation from an acclaim skeleton file stream. | GPy/util/mocap.py | def read_documentation(self, fid):
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train | acclaim_skeleton.read_hierarchy | Read hierarchy information from acclaim skeleton file stream. | GPy/util/mocap.py | def read_hierarchy(self, fid):
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train | acclaim_skeleton.read_line | Read a line from a file string and check it isn't either empty or commented before returning. | GPy/util/mocap.py | def read_line(self, fid):
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train | acclaim_skeleton.read_root | Read the root node from an acclaim skeleton file stream. | GPy/util/mocap.py | def read_root(self, fid):
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train | MLP.gradients_X | Derivative of the covariance matrix with respect to X | GPy/kern/src/mlp.py | def gradients_X(self, dL_dK, X, X2):
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train | MLP.gradients_X_X2 | Derivative of the covariance matrix with respect to X | GPy/kern/src/mlp.py | def gradients_X_X2(self, dL_dK, X, X2):
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train | ODE_1._get_params | return the value of the parameters. | GPy/kern/src/todo/ODE_1.py | def _get_params(self):
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train | ODE_1.K | Compute the covariance matrix between X and X2. | GPy/kern/src/todo/ODE_1.py | def K(self, X, X2, target):
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train | ODE_1.Kdiag | Compute the diagonal of the covariance matrix associated to X. | GPy/kern/src/todo/ODE_1.py | def Kdiag(self, X, target):
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train | GaussianGridInference.inference | Returns a GridPosterior class containing essential quantities of the posterior | GPy/inference/latent_function_inference/gaussian_grid_inference.py | def inference(self, kern, X, likelihood, Y, Y_metadata=None):
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train | Constant.to_dict | Convert the object into a json serializable dictionary.
Note: It uses the private method _save_to_input_dict of the parent.
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"""
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
"""
input_dict = sup... | def to_dict(self):
"""
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
"""
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train | StudentT.update_gradients | Pull out the gradients, be careful as the order must match the order
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"""
Pull out the gradients, be careful as the order must match the order
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train | StudentT.pdf_link | 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}}
... | GPy/likelihoods/student_t.py | def pdf_link(self, inv_link_f, y, Y_metadata=None):
"""
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} - \\lamb... | def pdf_link(self, inv_link_f, y, Y_metadata=None):
"""
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} - \\lamb... | [
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train | StudentT.logpdf_link | 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... | GPy/likelihoods/student_t.py | def logpdf_link(self, inv_link_f, y, Y_metadata=None):
"""
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(... | def logpdf_link(self, inv_link_f, y, Y_metadata=None):
"""
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(... | [
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train | StudentT.dlogpdf_dlink | 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... | GPy/likelihoods/student_t.py | def dlogpdf_dlink(self, inv_link_f, y, Y_metadata=None):
"""
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}
... | def dlogpdf_dlink(self, inv_link_f, y, Y_metadata=None):
"""
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}
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train | StudentT.d2logpdf_dlink2 | 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)
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"""
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... | def d2logpdf_dlink2(self, inv_link_f, y, Y_metadata=None):
"""
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)
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.. math::
\\frac{d^{2} \\ln p... | [
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train | StudentT.d3logpdf_dlink3 | 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... | GPy/likelihoods/student_t.py | def d3logpdf_dlink3(self, inv_link_f, y, Y_metadata=None):
"""
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}... | def d3logpdf_dlink3(self, inv_link_f, y, Y_metadata=None):
"""
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}... | [
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train | StudentT.dlogpdf_link_dvar | 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})}
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"""
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^{... | def dlogpdf_link_dvar(self, inv_link_f, y, Y_metadata=None):
"""
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^{... | [
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train | StudentT.dlogpdf_dlink_dvar | 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}
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... | GPy/likelihoods/student_t.py | def dlogpdf_dlink_dvar(self, inv_link_f, y, Y_metadata=None):
"""
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})... | def dlogpdf_dlink_dvar(self, inv_link_f, y, Y_metadata=None):
"""
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})... | [
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train | StudentT.d2logpdf_dlink2_dvar | 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}}
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"""
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_{... | def d2logpdf_dlink2_dvar(self, inv_link_f, y, Y_metadata=None):
"""
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_{... | [
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train | StudentT.samples | Returns a set of samples of observations based on a given value of the latent variable.
:param gp: latent variable | GPy/likelihoods/student_t.py | 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
"""
orig_shape = gp.shape
gp = gp.flatten()
#FIXME: Very slow as we are computing a new random variable ... | def samples(self, gp, Y_metadata=None):
"""
Returns a set of samples of observations based on a given value of the latent variable.
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orig_shape = gp.shape
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train | SparseGPMiniBatch._inner_parameters_changed | 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
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The dic... | GPy/models/sparse_gp_minibatch.py | def _inner_parameters_changed(self, kern, X, Z, likelihood, Y, Y_metadata, Lm=None, dL_dKmm=None, psi0=None, psi1=None, psi2=None, **kwargs):
"""
This is the standard part, which usually belongs in parameters_changed.
For automatic handling of subsampling (such as missing_data, stochastics etc.... | def _inner_parameters_changed(self, kern, X, Z, likelihood, Y, Y_metadata, Lm=None, dL_dKmm=None, psi0=None, psi1=None, psi2=None, **kwargs):
"""
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train | Gaussian.moments_match_ep | Moments match of the marginal approximation in EP algorithm
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train | Gaussian.pdf_link | Likelihood function given link(f)
.. math::
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"""
Likelihood function given link(f)
.. math::
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:param link_f: late... | def pdf_link(self, link_f, y, Y_metadata=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}
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train | Gaussian.logpdf_link | Log likelihood function given link(f)
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\\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}
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"""
Log likelihood function given link(f)
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Log likelihood function given link(f)
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train | Gaussian.dlogpdf_dlink | 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}))
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:param link_f: latent variables link(f)
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Gradient of the pdf at y, given link(f) w.r.t link(f)
.. math::
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train | Gaussian.d2logpdf_dlink2 | Hessian at y, given link_f, w.r.t link_f.
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.. math::
\\frac{d^{2} \\ln p(y_{i}|\\lambda(f_{i}))}{d^{2}f} = -\\frac{1}{\\sigma^{2}}
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"""
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}|\... | def d2logpdf_dlink2(self, link_f, y, Y_metadata=None):
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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)
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train | Gaussian.d3logpdf_dlink3 | 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
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"""
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_... | def d3logpdf_dlink3(self, link_f, y, Y_metadata=None):
"""
Third order derivative log-likelihood function at y given link(f) w.r.t link(f)
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train | Gaussian.dlogpdf_link_dvar | 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}}
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"""
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_... | def dlogpdf_link_dvar(self, link_f, y, Y_metadata=None):
"""
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_... | [
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train | Gaussian.dlogpdf_dlink_dvar | 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
... | GPy/likelihoods/gaussian.py | def dlogpdf_dlink_dvar(self, link_f, y, Y_metadata=None):
"""
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}))
... | def dlogpdf_dlink_dvar(self, link_f, y, Y_metadata=None):
"""
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}))
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train | Gaussian.d2logpdf_dlink2_dvar | 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)
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"""
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}}
:par... | def d2logpdf_dlink2_dvar(self, link_f, y, Y_metadata=None):
"""
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}}
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train | Gaussian.samples | Returns a set of samples of observations based on a given value of the latent variable.
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"""
Returns a set of samples of observations based on a given value of the latent variable.
:param gp: latent variable
"""
orig_shape = gp.shape
gp = gp.flatten()
#orig_shape = gp.shape
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orig_shape = gp.shape
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train | Gaussian.log_predictive_density | assumes independence | GPy/likelihoods/gaussian.py | 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 | def log_predictive_density(self, y_test, mu_star, var_star, Y_metadata=None):
"""
assumes independence
"""
v = var_star + self.variance
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This is useful if we wish to change our existing data but maintain the same model
:param X: input observations
:type X: np.ndarray
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... | def set_XY(self, X=None, Y=None):
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Set the input / output data of the model
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:param X: input observations
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In order to predict without adding in the likelihood give
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... | GPy/core/gp.py | def predict(self, Xnew, full_cov=False, Y_metadata=None, kern=None,
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"""
Predict the function(s) at the new point(s) Xnew. This includes the
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train | GP.predict_noiseless | Convenience function to predict the underlying function of the GP (often
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prediction function.
This is most likely what you want to use for your predictions.
:param Xnew: The points at which to make a prediction
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"""
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 ... | def predict_noiseless(self, Xnew, full_cov=False, Y_metadata=None, kern=None):
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train | GP.predict_quantiles | 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
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"""
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)
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Get the predictive quantiles around the prediction at X
:param X: The points at which to make a prediction
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train | GP.predictive_gradients | Compute the derivatives of the predicted latent function with respect
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derivatives of the mean and variance. Resulting arrays are sized:
dmu_dX* -- [N*, Q ,D], where D is the number of output in this GP
... | GPy/core/gp.py | def predictive_gradients(self, Xnew, kern=None):
"""
Compute the derivatives of the predicted latent function with respect
to X*
Given a set of points at which to predict X* (size [N*,Q]), compute the
derivatives of the mean and variance. Resulting arrays are sized:
... | def predictive_gradients(self, Xnew, kern=None):
"""
Compute the derivatives of the predicted latent function with respect
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Given a set of points at which to predict X* (size [N*,Q]), compute the
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train | GP.predict_jacobian | Compute the derivatives of the posterior of the GP.
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"""
Compute the derivatives of the posterior of the GP.
Given a set of points at which to predict X* (size [N*,Q]), compute the
mean and variance of the derivative. Resulting arrays are sized:
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train | GP.predict_wishart_embedding | Predict the wishart embedding G of the GP. This is the density of the
input of the GP defined by the probabilistic function mapping f.
G = J_mean.T*J_mean + output_dim*J_cov.
:param array-like Xnew: The points at which to evaluate the magnification.
:param :py:class:`~GPy.kern.Kern` ker... | GPy/core/gp.py | def predict_wishart_embedding(self, Xnew, kern=None, mean=True, covariance=True):
"""
Predict the wishart embedding G of the GP. This is the density of the
input of the GP defined by the probabilistic function mapping f.
G = J_mean.T*J_mean + output_dim*J_cov.
:param array-like ... | def predict_wishart_embedding(self, Xnew, kern=None, mean=True, covariance=True):
"""
Predict the wishart embedding G of the GP. This is the density of the
input of the GP defined by the probabilistic function mapping f.
G = J_mean.T*J_mean + output_dim*J_cov.
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train | GP.predict_magnification | Predict the magnification factor as
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:param bool covariance: whether to include the covariance of the wishart embedding.
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"""
Predict the magnification factor as
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Predict the magnification factor as
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train | GP.posterior_samples_f | Samples the posterior GP at the points X.
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:type X: np.ndarray (Nnew x self.input_dim)
:param size: the number of a posteriori samples.
:type size: int.
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:param X: The points at which to take the samples.
:type X: np.ndarray (Nnew x self.input_dim)
:param size: the number of a posteriori samples.
:type size: int.
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Samples the posterior GP at the points X.
:param X: The points at which to take the samples.
:type X: np.ndarray (Nnew x self.input_dim)
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train | GP.posterior_samples | Samples the posterior GP at the points X.
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:param size: the number of a posteriori samples.
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Samples the posterior GP at the points X.
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train | GP.optimize | Optimize the model using self.log_likelihood and self.log_likelihood_gradient, as well as self.priors.
kwargs are passed to the optimizer. They can be:
:param max_iters: maximum number of function evaluations
:type max_iters: int
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"""
Optimize the model using self.log_likelihood and self.log_likelihood_gradient, as well as self.priors.
kwargs are passed to the optimizer. They can be:
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Optimize the model using self.log_likelihood and self.log_likelihood_gradient, as well as self.priors.
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train | GP.infer_newX | Infer X for the new observed data *Y_new*.
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:type Y_new: numpy.ndarray
:param optimize: whether to optimize the location of new X (True by default)
:type optimize: boolean
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: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)
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Infer X for the new observed data *Y_new*.
:param Y_new: the new observed data for inference
:type Y_new: numpy.ndarray
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train | GP.log_predictive_density | Calculation of the log predictive density
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:param x_test: test locations (x_{*})
:type x_test: (Nx1) array
:param y_test: test observations (y_{*})
:type y_test: (Nx1) array
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"""
Calculation of the log predictive density
.. math:
p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\mu_{*}\\sigma^{2}_{*})
:param x_test: test locations (x_{*})
:type x_test: (Nx1) array
:param y_test... | def log_predictive_density(self, x_test, y_test, Y_metadata=None):
"""
Calculation of the log predictive density
.. math:
p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\mu_{*}\\sigma^{2}_{*})
:param x_test: test locations (x_{*})
:type x_test: (Nx1) array
:param y_test... | [
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train | GP.log_predictive_density_sampling | Calculation of the log predictive density by sampling
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p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\mu_{*}\\sigma^{2}_{*})
:param x_test: test locations (x_{*})
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Calculation of the log predictive density by sampling
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p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\mu_{*}\\sigma^{2}_{*})
:param x_test: test locations (x_{*})
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"""
Calculation of the log predictive density by sampling
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p(y_{*}|D) = p(y_{*}|f_{*})p(f_{*}|\mu_{*}\\sigma^{2}_{*})
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train | GP.posterior_covariance_between_points | Computes the posterior covariance between points.
:param X1: some input observations
:param X2: other input observations | GPy/core/gp.py | def posterior_covariance_between_points(self, X1, X2):
"""
Computes the posterior covariance between points.
:param X1: some input observations
:param X2: other input observations
"""
return self.posterior.covariance_between_points(self.kern, self.X, X1, X2) | def posterior_covariance_between_points(self, X1, X2):
"""
Computes the posterior covariance between points.
:param X1: some input observations
:param X2: other input observations
"""
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train | generate_dims_coords | Generate default dimensions and coordinates for a variable.
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----------
shape : tuple[int]
Shape of the variable
var_name : str
Name of the variable. Used in the default name, if necessary
dims : list
List of dimensions for the variable
coords : dict[str] -> li... | arviz/data/base.py | def generate_dims_coords(shape, var_name, dims=None, coords=None, default_dims=None):
"""Generate default dimensions and coordinates for a variable.
Parameters
----------
shape : tuple[int]
Shape of the variable
var_name : str
Name of the variable. Used in the default name, if neces... | def generate_dims_coords(shape, var_name, dims=None, coords=None, default_dims=None):
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Parameters
----------
shape : tuple[int]
Shape of the variable
var_name : str
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train | numpy_to_data_array | Convert a numpy array to an xarray.DataArray.
The first two dimensions will be (chain, draw), and any remaining
dimensions will be "shape".
If the numpy array is 1d, this dimension is interpreted as draw
If the numpy array is 2d, it is interpreted as (chain, draw)
If the numpy array is 3 or more di... | arviz/data/base.py | def numpy_to_data_array(ary, *, var_name="data", coords=None, dims=None):
"""Convert a numpy array to an xarray.DataArray.
The first two dimensions will be (chain, draw), and any remaining
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"""Convert a numpy array to an xarray.DataArray.
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train | dict_to_dataset | Convert a dictionary of numpy arrays to an xarray.Dataset.
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data : dict[str] -> ndarray
Data to convert. Keys are variable names.
attrs : dict
Json serializable metadata to attach to the dataset, in addition to defaults.
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Parameters
----------
data : dict[str] -> ndarray
Data to convert. Keys are variable names.
attrs : dict
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----------
data : dict[str] -> ndarray
Data to convert. Keys are variable names.
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train | make_attrs | Make standard attributes to attach to xarray datasets.
Parameters
----------
attrs : dict (optional)
Additional attributes to add or overwrite
Returns
-------
dict
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Parameters
----------
attrs : dict (optional)
Additional attributes to add or overwrite
Returns
-------
dict
attrs
"""
default_attrs = {"created_at": datetime.datetim... | def make_attrs(attrs=None, library=None):
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attrs : dict (optional)
Additional attributes to add or overwrite
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-------
dict
attrs
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train | get_data_home | Return the path of the arviz data dir.
This folder is used by some dataset loaders to avoid downloading the
data several times.
By default the data dir is set to a folder named 'arviz_data' in the
user home folder.
Alternatively, it can be set by the 'ARVIZ_DATA' environment
variable or progr... | arviz/data/datasets.py | def get_data_home(data_home=None):
"""Return the path of the arviz data dir.
This folder is used by some dataset loaders to avoid downloading the
data several times.
By default the data dir is set to a folder named 'arviz_data' in the
user home folder.
Alternatively, it can be set by the 'ARV... | def get_data_home(data_home=None):
"""Return the path of the arviz data dir.
This folder is used by some dataset loaders to avoid downloading the
data several times.
By default the data dir is set to a folder named 'arviz_data' in the
user home folder.
Alternatively, it can be set by the 'ARV... | [
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] | arviz-devs/arviz | python | https://github.com/arviz-devs/arviz/blob/d04d8da07f029fd2931f48d2f7f324cf393e5277/arviz/data/datasets.py#L68-L93 | [
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train | _sha256 | Calculate the sha256 hash of the file at path. | arviz/data/datasets.py | def _sha256(path):
"""Calculate the sha256 hash of the file at path."""
sha256hash = hashlib.sha256()
chunk_size = 8192
with open(path, "rb") as buff:
while True:
buffer = buff.read(chunk_size)
if not buffer:
break
sha256hash.update(buffer)
... | def _sha256(path):
"""Calculate the sha256 hash of the file at path."""
sha256hash = hashlib.sha256()
chunk_size = 8192
with open(path, "rb") as buff:
while True:
buffer = buff.read(chunk_size)
if not buffer:
break
sha256hash.update(buffer)
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train | load_arviz_data | Load a local or remote pre-made dataset.
Run with no parameters to get a list of all available models.
The directory to save to can also be set with the environement
variable `ARVIZ_HOME`. The checksum of the dataset is checked against a
hardcoded value to watch for data corruption.
Run `az.clear... | arviz/data/datasets.py | def load_arviz_data(dataset=None, data_home=None):
"""Load a local or remote pre-made dataset.
Run with no parameters to get a list of all available models.
The directory to save to can also be set with the environement
variable `ARVIZ_HOME`. The checksum of the dataset is checked against a
hardco... | def load_arviz_data(dataset=None, data_home=None):
"""Load a local or remote pre-made dataset.
Run with no parameters to get a list of all available models.
The directory to save to can also be set with the environement
variable `ARVIZ_HOME`. The checksum of the dataset is checked against a
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train | list_datasets | Get a string representation of all available datasets with descriptions. | arviz/data/datasets.py | def list_datasets():
"""Get a string representation of all available datasets with descriptions."""
lines = []
for name, resource in itertools.chain(LOCAL_DATASETS.items(), REMOTE_DATASETS.items()):
if isinstance(resource, LocalFileMetadata):
location = "local: {}".format(resource.filen... | def list_datasets():
"""Get a string representation of all available datasets with descriptions."""
lines = []
for name, resource in itertools.chain(LOCAL_DATASETS.items(), REMOTE_DATASETS.items()):
if isinstance(resource, LocalFileMetadata):
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train | _verify_names | Make sure var_names and arg_names are assigned reasonably.
This is meant to run before loading emcee objects into InferenceData.
In case var_names or arg_names is None, will provide defaults. If they are
not None, it verifies there are the right number of them.
Throws a ValueError in case validation f... | arviz/data/io_emcee.py | def _verify_names(sampler, var_names, arg_names):
"""Make sure var_names and arg_names are assigned reasonably.
This is meant to run before loading emcee objects into InferenceData.
In case var_names or arg_names is None, will provide defaults. If they are
not None, it verifies there are the right numb... | def _verify_names(sampler, var_names, arg_names):
"""Make sure var_names and arg_names are assigned reasonably.
This is meant to run before loading emcee objects into InferenceData.
In case var_names or arg_names is None, will provide defaults. If they are
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] | arviz-devs/arviz | python | https://github.com/arviz-devs/arviz/blob/d04d8da07f029fd2931f48d2f7f324cf393e5277/arviz/data/io_emcee.py#L6-L58 | [
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train | from_emcee | Convert emcee data into an InferenceData object.
Parameters
----------
sampler : emcee.EnsembleSampler
Fitted sampler from emcee.
var_names : list[str] (Optional)
A list of names for variables in the sampler
arg_names : list[str] (Optional)
A list of names for args in the sa... | arviz/data/io_emcee.py | def from_emcee(sampler=None, *, var_names=None, arg_names=None, coords=None, dims=None):
"""Convert emcee data into an InferenceData object.
Parameters
----------
sampler : emcee.EnsembleSampler
Fitted sampler from emcee.
var_names : list[str] (Optional)
A list of names for variable... | def from_emcee(sampler=None, *, var_names=None, arg_names=None, coords=None, dims=None):
"""Convert emcee data into an InferenceData object.
Parameters
----------
sampler : emcee.EnsembleSampler
Fitted sampler from emcee.
var_names : list[str] (Optional)
A list of names for variable... | [
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"InferenceData",
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] | arviz-devs/arviz | python | https://github.com/arviz-devs/arviz/blob/d04d8da07f029fd2931f48d2f7f324cf393e5277/arviz/data/io_emcee.py#L109-L269 | [
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train | EmceeConverter.posterior_to_xarray | Convert the posterior to an xarray dataset. | arviz/data/io_emcee.py | def posterior_to_xarray(self):
"""Convert the posterior to an xarray dataset."""
data = {}
for idx, var_name in enumerate(self.var_names):
# Use emcee3 syntax, else use emcee2
data[var_name] = (
self.sampler.get_chain()[(..., idx)].T
if has... | def posterior_to_xarray(self):
"""Convert the posterior to an xarray dataset."""
data = {}
for idx, var_name in enumerate(self.var_names):
# Use emcee3 syntax, else use emcee2
data[var_name] = (
self.sampler.get_chain()[(..., idx)].T
if has... | [
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] | arviz-devs/arviz | python | https://github.com/arviz-devs/arviz/blob/d04d8da07f029fd2931f48d2f7f324cf393e5277/arviz/data/io_emcee.py#L75-L85 | [
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train | EmceeConverter.observed_data_to_xarray | Convert observed data to xarray. | arviz/data/io_emcee.py | def observed_data_to_xarray(self):
"""Convert observed data to xarray."""
data = {}
for idx, var_name in enumerate(self.arg_names):
# Use emcee3 syntax, else use emcee2
data[var_name] = (
self.sampler.log_prob_fn.args[idx]
if hasattr(self.s... | def observed_data_to_xarray(self):
"""Convert observed data to xarray."""
data = {}
for idx, var_name in enumerate(self.arg_names):
# Use emcee3 syntax, else use emcee2
data[var_name] = (
self.sampler.log_prob_fn.args[idx]
if hasattr(self.s... | [
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] | arviz-devs/arviz | python | https://github.com/arviz-devs/arviz/blob/d04d8da07f029fd2931f48d2f7f324cf393e5277/arviz/data/io_emcee.py#L87-L97 | [
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train | from_tfp | Convert tfp data into an InferenceData object. | arviz/data/io_tfp.py | def from_tfp(
posterior=None,
*,
var_names=None,
model_fn=None,
feed_dict=None,
posterior_predictive_samples=100,
posterior_predictive_size=1,
observed=None,
coords=None,
dims=None
):
"""Convert tfp data into an InferenceData object."""
return TfpConverter(
... | def from_tfp(
posterior=None,
*,
var_names=None,
model_fn=None,
feed_dict=None,
posterior_predictive_samples=100,
posterior_predictive_size=1,
observed=None,
coords=None,
dims=None
):
"""Convert tfp data into an InferenceData object."""
return TfpConverter(
... | [
"Convert",
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"into",
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"InferenceData",
"object",
"."
] | arviz-devs/arviz | python | https://github.com/arviz-devs/arviz/blob/d04d8da07f029fd2931f48d2f7f324cf393e5277/arviz/data/io_tfp.py#L169-L192 | [
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",",
"observe... | d04d8da07f029fd2931f48d2f7f324cf393e5277 |
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