Module Expr Str Import alias identifier ImportFrom alias alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias ImportFrom alias ClassDef bases NameLoad body Expr Str FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad Num Str body If CompareIs NameLoad NameLoad body Assign NameStore Call AttributeLoad NameLoad attr If UnaryOpNot Call NameLoad NameLoad AttributeLoad NameLoad attr body Print Str Expr Call AttributeLoad Call NameLoad NameLoad NameLoad attr NameLoad keyword NameLoad Assign AttributeStore NameLoad attr Call NameLoad Str NameLoad Call NameLoad Expr Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr If Call NameLoad NameLoad AttributeLoad NameLoad attr body Assign AttributeStore NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults NameLoad body Raise Call NameLoad Str Return BinOpDiv NameLoad Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults NameLoad body Return AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam defaults body Assign AttributeStore AttributeLoad NameLoad attr attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults NameLoad body Return Call AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad body Expr Str Assign NameStore BinOpDiv Num BinOpAdd BinOpDiv Num AttributeLoad NameLoad attr NameLoad Assign NameStore BinOpMult NameLoad BinOpAdd BinOpDiv NameLoad AttributeLoad NameLoad attr NameLoad Assign NameStore BinOpAdd AttributeLoad NameLoad attr BinOpDiv Num NameLoad Assign NameStore BinOpMult BinOpDiv Num Call AttributeLoad NameLoad attr BinOpMult BinOpMult Num AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr BinOpDiv BinOpMult Num BinOpPow BinOpSub NameLoad BinOpDiv NameLoad NameLoad Num NameLoad Return TupleLoad NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad NameLoad body If NameLoad body If CompareEq AttributeLoad NameLoad attr Num body AugAssignAdd NameStore BinOpMult Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num AttributeLoad NameLoad attr If CompareEq AttributeLoad NameLoad attr Num body AugAssignAdd NameStore Call AttributeLoad NameLoad attr BinOpMult Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num AttributeLoad NameLoad attr orelse AugAssignAdd NameStore AttributeLoad NameLoad attr Return TupleLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults body Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad body Return BinOpAdd AttributeLoad NameLoad attr BinOpPow NameLoad Num decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad body Return ListComp BinOpAdd BinOpMult Call AttributeLoad AttributeLoad NameLoad attr attr BinOpDiv NameLoad Num Call AttributeLoad NameLoad attr BinOpAdd NameLoad AttributeLoad NameLoad attr NameLoad comprehension NameStore NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad body Expr Str Return Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad NameLoad Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad body Expr Str Assign NameStore Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr Return BinOpSub BinOpSub BinOpMult UnaryOpUSub BinOpDiv Num BinOpMult Num AttributeLoad NameLoad attr BinOpPow BinOpSub NameLoad NameLoad Num BinOpMult Num NameLoad BinOpMult Num Call AttributeLoad NameLoad attr BinOpMult Num AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad body Expr Str Assign NameStore BinOpDiv Num AttributeLoad NameLoad attr Assign NameStore BinOpSub BinOpMult NameLoad NameLoad BinOpMult NameLoad NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad body Expr Str Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Assign NameStore BinOpMult UnaryOpUSub BinOpDiv Num AttributeLoad NameLoad attr Call AttributeLoad NameLoad attr TupleLoad NameLoad NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad body Expr Str Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Assign NameStore Call AttributeLoad NameLoad attr TupleLoad NameLoad NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad body Expr Str Assign NameStore BinOpSub NameLoad NameLoad Assign NameStore BinOpDiv Num BinOpPow AttributeLoad NameLoad attr Num Assign NameStore BinOpAdd BinOpDiv Num AttributeLoad NameLoad attr BinOpMult BinOpMult Num NameLoad Call AttributeLoad NameLoad attr NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad body Expr Str Assign NameStore BinOpDiv Num BinOpPow AttributeLoad NameLoad attr Num Assign NameStore BinOpAdd BinOpMult UnaryOpUSub NameLoad NameLoad BinOpMult NameLoad NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad body Expr Str Assign NameStore BinOpDiv Num BinOpPow AttributeLoad NameLoad attr Num Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Num Assign NameStore BinOpMult Call AttributeLoad NameLoad attr TupleLoad NameLoad NameLoad NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad body Assign NameStore Call AttributeLoad NameLoad attr TupleLoad AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num SubscriptLoad AttributeLoad NameLoad attr Index Num Assign SubscriptStore NameLoad ExtSlice Index Num Slice Slice Call AttributeLoad NameLoad attr NameLoad NameLoad keyword NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad body Assign NameStore Call AttributeLoad NameLoad attr TupleLoad AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num SubscriptLoad AttributeLoad NameLoad attr Index Num Assign SubscriptStore NameLoad ExtSlice Index Num Slice Slice Call AttributeLoad NameLoad attr NameLoad NameLoad keyword NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam defaults NameLoad body Assign NameStore Call AttributeLoad NameLoad attr TupleLoad AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num SubscriptLoad AttributeLoad NameLoad attr Index Num Assign SubscriptStore NameLoad ExtSlice Index Num Slice Slice Call AttributeLoad NameLoad attr NameLoad NameLoad keyword NameLoad Return NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Return Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam defaults body Expr Str Return AttributeLoad NameLoad attr decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults NameLoad body Expr Str Assign NameStore AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad NameLoad attr Assign NameStore Call AttributeLoad NameLoad attr ListComp Call AttributeLoad AttributeLoad NameLoad attr attr Call AttributeLoad AttributeLoad NameLoad attr attr NameLoad keyword Call AttributeLoad NameLoad attr AttributeLoad NameLoad attr keyword Num comprehension NameStore NameLoad Return Call AttributeLoad NameLoad attr NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad body Expr Str Assign NameStore BinOpAdd NameLoad AttributeLoad NameLoad attr Return BinOpSub BinOpSub BinOpMult Num Call AttributeLoad NameLoad attr BinOpMult Num AttributeLoad NameLoad attr BinOpMult Num Call AttributeLoad NameLoad attr NameLoad BinOpDiv BinOpMult Num Call AttributeLoad NameLoad attr BinOpSub NameLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam NameParam defaults NameLoad NameLoad body If UnaryOpNot Call NameLoad AttributeLoad NameLoad attr AttributeLoad NameLoad attr body Return Call AttributeLoad Call NameLoad NameLoad NameLoad attr keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad keyword NameLoad Assign NameStore Call NameLoad AttributeLoad NameLoad attr Assign NameStore BinOpSub BinOpSub BinOpMult Num Call AttributeLoad NameLoad attr BinOpMult Num AttributeLoad NameLoad attr BinOpMult Num Call AttributeLoad NameLoad attr NameLoad BinOpDiv BinOpMult Num BinOpSub BinOpAdd BinOpAdd Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad NameLoad BinOpMult BinOpMult Num NameLoad NameLoad NameLoad Assign NameStore BinOpDiv BinOpSub NameLoad NameLoad NameLoad Assign NameStore BinOpMult Call AttributeLoad NameLoad attr NameLoad BinOpDiv Num NameLoad Assign NameStore BinOpAdd BinOpDiv Num NameLoad BinOpDiv BinOpMult Num BinOpSub BinOpAdd BinOpAdd Call AttributeLoad NameLoad attr NameLoad Call AttributeLoad NameLoad attr NameLoad NameLoad BinOpMult BinOpMult Num NameLoad NameLoad BinOpPow NameLoad Num Return TupleLoad NameLoad NameLoad NameLoad Call AttributeLoad NameLoad attr Num SubscriptLoad AttributeLoad NameLoad attr Index Num SubscriptLoad AttributeLoad NameLoad attr Index Num decorator_list decorator_list ClassDef bases NameLoad body FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad Num Str body If CompareIs NameLoad NameLoad body Assign NameStore Call AttributeLoad NameLoad attr If UnaryOpNot Call NameLoad NameLoad AttributeLoad NameLoad attr body Print Str Expr Call AttributeLoad Call NameLoad NameLoad NameLoad attr NameLoad BinOpMult Call AttributeLoad NameLoad attr AttributeLoad SubscriptLoad NameLoad Index Str attr NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam defaults NameLoad body Return SubscriptLoad NameLoad Index SubscriptLoad NameLoad Index Str decorator_list FunctionDef arguments args NameParam NameParam defaults NameLoad body Return SubscriptLoad AttributeLoad NameLoad attr Index Call AttributeLoad SubscriptLoad NameLoad Index Str attr decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad NameLoad body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Call AttributeLoad SubscriptLoad NameLoad Index Str attr If NameLoad body If CompareEq AttributeLoad NameLoad attr Num body AugAssignAdd NameStore BinOpMult Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num NameLoad If CompareEq AttributeLoad NameLoad attr Num body AugAssignAdd NameStore Call AttributeLoad NameLoad attr BinOpMult Call AttributeLoad NameLoad attr SubscriptLoad AttributeLoad NameLoad attr Index Num NameLoad orelse AugAssignAdd NameStore NameLoad Return TupleLoad NameLoad NameLoad decorator_list FunctionDef arguments args NameParam NameParam NameParam NameParam NameParam defaults NameLoad body Assign NameStore SubscriptLoad AttributeLoad NameLoad attr Index Call AttributeLoad SubscriptLoad NameLoad Index Str attr Return ListComp BinOpAdd BinOpMult Call AttributeLoad AttributeLoad NameLoad attr attr BinOpDiv NameLoad Num Call AttributeLoad NameLoad attr BinOpAdd NameLoad NameLoad NameLoad comprehension NameStore NameLoad decorator_list decorator_list
N/A N/A 
A lot of this code assumes that the link function is the identity.

I think laplace code is okay, but I'm quite sure that the EP moments will only work if the link is identity.

Furthermore, exact Guassian inference can only be done for the identity link, so we should be asserting so for all calls which relate to that.

James 11/12/13
 N/A numpy np scipy stats special N/A link_functions likelihood Likelihood core.parameterization Param paramz.transformations Logexp scipy stats Gaussian N/A Likelihood N/A N/A 
    Gaussian likelihood

    .. 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 variance: variance value of the Gaussian distribution
    :param N: Number of data points
    :type N: int
     __init__ N/A N/A self gp_link variance name N/A None 1.0 Gaussian_noise N/A N/A N/A gp_link None N/A N/A gp_link N/A N/A link_functions Identity N/A N/A N/A isinstance gp_link N/A link_functions Identity N/A N/A Warning, Exact inference is not implemeted for non-identity link functions,            if you are not already, ensure Laplace inference_method is used N/A N/A N/A N/A super Gaussian self __init__ gp_link name name N/A N/A self variance N/A Param variance variance N/A Logexp N/A N/A N/A self link_parameter N/A self variance N/A N/A isinstance gp_link N/A link_functions Identity N/A N/A N/A self log_concave True N/A betaY N/A N/A self Y Y_metadata N/A None N/A N/A N/A RuntimeError Please notify the GPy developers, this should not happen N/A N/A Y N/A N/A self gaussian_variance Y_metadata N/A gaussian_variance N/A N/A self Y_metadata N/A None N/A N/A N/A self variance N/A update_gradients N/A N/A self grad N/A N/A N/A N/A N/A self variance gradient grad N/A exact_inference_gradients N/A N/A self dL_dKdiag Y_metadata N/A None N/A N/A N/A N/A dL_dKdiag sum N/A _preprocess_values N/A N/A self Y N/A N/A N/A 
        Check if the values of the observations correspond to the values
        assumed by the likelihood function.
         N/A Y N/A moments_match_ep N/A N/A self data_i tau_i v_i Y_metadata_i N/A None N/A N/A 
        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)
         N/A sigma2_hat N/A 1.0 N/A N/A 1.0 N/A self variance tau_i N/A mu_hat N/A sigma2_hat N/A N/A data_i N/A self variance v_i N/A sum_var N/A N/A self variance N/A 1.0 tau_i N/A Z_hat N/A N/A 1.0 N/A N/A np sqrt N/A N/A 2.0 N/A np pi sum_var N/A N/A np exp N/A N/A -0.5 N/A N/A data_i N/A v_i tau_i 2.0 sum_var N/A N/A Z_hat mu_hat sigma2_hat N/A predictive_values N/A N/A self mu var full_cov Y_metadata N/A False None N/A N/A full_cov N/A N/A N/A N/A var ndim 2 N/A N/A var N/A N/A N/A np eye N/A N/A var shape N/A 0 N/A self variance N/A N/A N/A var ndim 3 N/A N/A var N/A N/A np atleast_3d N/A N/A N/A np eye N/A N/A var shape N/A 0 N/A self variance N/A N/A var N/A self variance N/A N/A mu var N/A predictive_mean N/A N/A self mu sigma N/A N/A N/A mu N/A predictive_variance N/A N/A self mu sigma predictive_mean N/A None N/A N/A N/A N/A self variance N/A sigma 2 N/A predictive_quantiles N/A N/A self mu var quantiles Y_metadata N/A None N/A N/A N/A N/A N/A N/A N/A N/A stats norm ppf N/A q 100.0 N/A N/A np sqrt N/A var N/A self variance mu N/A q quantiles N/A pdf_link N/A N/A self link_f y Y_metadata N/A None N/A N/A 
        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 y: data
        :type y: Nx1 array
        :param Y_metadata: Y_metadata not used in gaussian
        :returns: likelihood evaluated for this point
        :rtype: float
         N/A N/A N/A np exp N/A N/A np sum N/A N/A np log N/A N/A N/A stats norm pdf y link_f N/A N/A np sqrt N/A self variance N/A logpdf_link N/A N/A self link_f y Y_metadata N/A None N/A N/A 
        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
        :param y: data
        :type y: Nx1 array
        :param Y_metadata: Y_metadata not used in gaussian
        :returns: log likelihood evaluated for this point
        :rtype: float
         N/A ln_det_cov N/A N/A np log N/A self variance N/A N/A N/A N/A N/A N/A 1.0 N/A 2 N/A self variance N/A N/A y link_f 2 N/A 0.5 ln_det_cov N/A 0.5 N/A N/A np log N/A 2.0 N/A np pi N/A dlogpdf_dlink N/A N/A self link_f y Y_metadata N/A None N/A N/A 
        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
        :param Y_metadata: Y_metadata not used in gaussian
        :returns: gradient of log likelihood evaluated at points link(f)
        :rtype: Nx1 array
         N/A s2_i N/A 1.0 N/A self variance N/A grad N/A N/A s2_i y N/A s2_i link_f N/A grad N/A d2logpdf_dlink2 N/A N/A self link_f y Y_metadata N/A None N/A N/A 
        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: latent variables link(f)
        :type link_f: Nx1 array
        :param y: data
        :type y: Nx1 array
        :param Y_metadata: Y_metadata not used in gaussian
        :returns: Diagonal of log hessian matrix (second derivative of log likelihood evaluated at points link(f))
        :rtype: Nx1 array

        .. Note::
            Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases
            (the distribution for y_i depends only on link(f_i) not on link(f_(j!=i))
         N/A N N/A N/A y shape N/A 0 N/A D N/A N/A link_f shape N/A 1 N/A hess N/A N/A N/A 1.0 N/A self variance N/A N/A np ones N/A N D N/A hess N/A d3logpdf_dlink3 N/A N/A self link_f y Y_metadata N/A None N/A N/A 
        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
        :param Y_metadata: Y_metadata not used in gaussian
        :returns: third derivative of log likelihood evaluated at points link(f)
        :rtype: Nx1 array
         N/A N N/A N/A y shape N/A 0 N/A D N/A N/A link_f shape N/A 1 N/A d3logpdf_dlink3 N/A N/A np zeros N/A N D N/A d3logpdf_dlink3 N/A dlogpdf_link_dvar N/A N/A self link_f y Y_metadata N/A None N/A N/A 
        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)
        :type link_f: Nx1 array
        :param y: data
        :type y: Nx1 array
        :param Y_metadata: Y_metadata not used in gaussian
        :returns: derivative of log likelihood evaluated at points link(f) w.r.t variance parameter
        :rtype: float
         N/A e N/A y link_f N/A s_4 N/A 1.0 N/A N/A self variance 2 N/A dlik_dsigma N/A N/A -0.5 N/A self variance N/A N/A 0.5 s_4 N/A N/A np square e N/A dlik_dsigma N/A dlogpdf_dlink_dvar N/A N/A self link_f y Y_metadata N/A None N/A N/A 
        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
        :param y: data
        :type y: Nx1 array
        :param Y_metadata: Y_metadata not used in gaussian
        :returns: derivative of log likelihood evaluated at points link(f) w.r.t variance parameter
        :rtype: Nx1 array
         N/A s_4 N/A 1.0 N/A N/A self variance 2 N/A dlik_grad_dsigma N/A N/A N/A s_4 y N/A s_4 link_f N/A dlik_grad_dsigma N/A d2logpdf_dlink2_dvar N/A N/A self link_f y Y_metadata N/A None N/A N/A 
        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
        :param y: data
        :type y: Nx1 array
        :param Y_metadata: Y_metadata not used in gaussian
        :returns: derivative of log hessian evaluated at points link(f_i) and link(f_j) w.r.t variance parameter
        :rtype: Nx1 array
         N/A s_4 N/A 1.0 N/A N/A self variance 2 N/A N N/A N/A y shape N/A 0 N/A D N/A N/A link_f shape N/A 1 N/A d2logpdf_dlink2_dvar N/A N/A N/A np ones N/A N D s_4 N/A d2logpdf_dlink2_dvar N/A dlogpdf_link_dtheta N/A N/A self f y Y_metadata N/A None N/A N/A dlogpdf_dtheta N/A N/A np zeros N/A N/A self size N/A N/A f shape N/A 0 N/A N/A f shape N/A 1 N/A N/A dlogpdf_dtheta N/A N/A 0 N/A N/A N/A N/A self dlogpdf_link_dvar f y Y_metadata Y_metadata N/A dlogpdf_dtheta N/A dlogpdf_dlink_dtheta N/A N/A self f y Y_metadata N/A None N/A N/A dlogpdf_dlink_dtheta N/A N/A np zeros N/A N/A self size N/A N/A f shape N/A 0 N/A N/A f shape N/A 1 N/A N/A dlogpdf_dlink_dtheta N/A N/A 0 N/A N/A N/A N/A self dlogpdf_dlink_dvar f y Y_metadata Y_metadata N/A dlogpdf_dlink_dtheta N/A d2logpdf_dlink2_dtheta N/A N/A self f y Y_metadata N/A None N/A N/A d2logpdf_dlink2_dtheta N/A N/A np zeros N/A N/A self size N/A N/A f shape N/A 0 N/A N/A f shape N/A 1 N/A N/A d2logpdf_dlink2_dtheta N/A N/A 0 N/A N/A N/A N/A self d2logpdf_dlink2_dvar f y Y_metadata Y_metadata N/A d2logpdf_dlink2_dtheta N/A _mean N/A N/A self gp N/A N/A N/A 
        Expected value of y under the Mass (or density) function p(y|f)

        .. math::
            E_{p(y|f)}[y]
         N/A N/A N/A N/A self gp_link transf gp N/A _variance N/A N/A self gp N/A N/A N/A 
        Variance of y under the Mass (or density) function p(y|f)

        .. math::
            Var_{p(y|f)}[y]
         N/A N/A self variance N/A samples N/A N/A self gp Y_metadata N/A None N/A N/A 
        Returns a set of samples of observations based on a given value of the latent variable.

        :param gp: latent variable
         N/A orig_shape N/A gp shape N/A gp N/A N/A gp flatten N/A gp N/A N/A gp flatten N/A Ysim N/A N/A np array N/A N/A N/A N/A np random normal N/A N/A N/A self gp_link transf gpj scale N/A N/A np sqrt N/A self variance size 1 N/A gpj gp N/A N/A N/A Ysim reshape orig_shape N/A log_predictive_density N/A N/A self y_test mu_star var_star Y_metadata N/A None N/A N/A 
        assumes independence
         N/A v N/A var_star N/A self variance N/A N/A N/A N/A -0.5 N/A N/A np log N/A 2 N/A np pi N/A 0.5 N/A N/A np log v N/A N/A 0.5 N/A N/A np square N/A y_test mu_star v N/A variational_expectations N/A N/A self Y m v gh_points Y_metadata N/A None None N/A N/A N/A N/A isinstance N/A self gp_link N/A link_functions Identity N/A N/A N/A N/A N/A super Gaussian self variational_expectations Y Y m m v v gh_points gh_points Y_metadata Y_metadata N/A lik_var N/A float N/A self variance N/A F N/A N/A N/A -0.5 N/A N/A np log N/A 2 N/A np pi N/A 0.5 N/A N/A np log lik_var N/A N/A 0.5 N/A N/A N/A N/A N/A np square Y N/A N/A np square m v N/A N/A 2 m Y lik_var N/A dF_dmu N/A N/A Y m lik_var N/A dF_dv N/A N/A N/A np ones_like v N/A -0.5 lik_var N/A dF_dtheta N/A N/A -0.5 lik_var N/A N/A 0.5 N/A N/A N/A N/A N/A np square Y N/A N/A np square m v N/A N/A 2 m Y N/A lik_var 2 N/A N/A F dF_dmu dF_dv N/A N/A dF_dtheta reshape 1 N/A N/A Y shape N/A 0 N/A N/A Y shape N/A 1 N/A N/A HeteroscedasticGaussian N/A Gaussian N/A __init__ N/A N/A self Y_metadata gp_link variance name N/A None 1.0 het_Gauss N/A N/A N/A gp_link None N/A N/A gp_link N/A N/A link_functions Identity N/A N/A N/A isinstance gp_link N/A link_functions Identity N/A N/A Warning, Exact inference is not implemeted for non-identity link functions,            if you are not already, ensure Laplace inference_method is used N/A N/A N/A N/A super HeteroscedasticGaussian self __init__ gp_link N/A N/A N/A np ones N/A N/A Y_metadata N/A output_index shape variance name N/A exact_inference_gradients N/A N/A self dL_dKdiag Y_metadata N/A None N/A N/A N/A dL_dKdiag N/A N/A Y_metadata N/A output_index N/A gaussian_variance N/A N/A self Y_metadata N/A None N/A N/A N/A N/A self variance N/A N/A N/A N/A Y_metadata N/A output_index flatten N/A predictive_values N/A N/A self mu var full_cov Y_metadata N/A False None N/A N/A _s N/A N/A self variance N/A N/A N/A N/A Y_metadata N/A output_index flatten N/A full_cov N/A N/A N/A N/A var ndim 2 N/A N/A var N/A N/A N/A np eye N/A N/A var shape N/A 0 _s N/A N/A N/A var ndim 3 N/A N/A var N/A N/A np atleast_3d N/A N/A N/A np eye N/A N/A var shape N/A 0 _s N/A N/A var _s N/A N/A mu var N/A predictive_quantiles N/A N/A self mu var quantiles Y_metadata N/A None N/A N/A _s N/A N/A self variance N/A N/A N/A N/A Y_metadata N/A output_index flatten N/A N/A N/A N/A N/A N/A N/A stats norm ppf N/A q 100.0 N/A N/A np sqrt N/A var _s mu N/A q quantiles N/A N/A