U @|e /@sdZddlmZmZddlmZddlZddlZddl m Z eddZ Gdd d ed Z Gd d d e Z Gd dde ZGddde ZGddde ZGddde ZeeeedZdS)z$ Distribution functions used in GLM )ABCMetaabstractmethod) namedtupleN)xlogyDistributionBoundary)value inclusivec@sNeZdZdZddZeddZedddZd d Zdd d Z dddZ dS)ExponentialDispersionModela3Base class for reproductive Exponential Dispersion Models (EDM). The pdf of :math:`Y\sim \mathrm{EDM}(y_\textrm{pred}, \phi)` is given by .. math:: p(y| \theta, \phi) = c(y, \phi) \exp\left(\frac{\theta y-A(\theta)}{\phi}\right) = \tilde{c}(y, \phi) \exp\left(-\frac{d(y, y_\textrm{pred})}{2\phi}\right) with mean :math:`\mathrm{E}[Y] = A'(\theta) = y_\textrm{pred}`, variance :math:`\mathrm{Var}[Y] = \phi \cdot v(y_\textrm{pred})`, unit variance :math:`v(y_\textrm{pred})` and unit deviance :math:`d(y,y_\textrm{pred})`. Methods ------- deviance deviance_derivative in_y_range unit_deviance unit_deviance_derivative unit_variance References ---------- https://en.wikipedia.org/wiki/Exponential_dispersion_model. cCs@t|jtstd|jjr,t||jjSt||jjSdS)zReturns ``True`` if y is in the valid range of Y~EDM. Parameters ---------- y : array of shape (n_samples,) Target values. z;_lower_bound attribute must be of type DistributionBoundaryN) isinstance _lower_boundr TypeErrorrnp greater_equalrgreater)selfyr[/var/www/website-v5/atlas_env/lib/python3.8/site-packages/sklearn/_loss/glm_distribution.py in_y_range4s z%ExponentialDispersionModel.in_y_rangecCsdS)aCompute the unit variance function. The unit variance :math:`v(y_\textrm{pred})` determines the variance as a function of the mean :math:`y_\textrm{pred}` by :math:`\mathrm{Var}[Y_i] = \phi/s_i*v(y_\textrm{pred}_i)`. It can also be derived from the unit deviance :math:`d(y,y_\textrm{pred})` as .. math:: v(y_\textrm{pred}) = \frac{2}{ \frac{\partial^2 d(y,y_\textrm{pred})}{ \partialy_\textrm{pred}^2}}\big|_{y=y_\textrm{pred}} See also :func:`variance`. Parameters ---------- y_pred : array of shape (n_samples,) Predicted mean. Nrry_predrrr unit_varianceHsz(ExponentialDispersionModel.unit_varianceFcCsdS)Compute the unit deviance. The unit_deviance :math:`d(y,y_\textrm{pred})` can be defined by the log-likelihood as :math:`d(y,y_\textrm{pred}) = -2\phi\cdot \left(loglike(y,y_\textrm{pred},\phi) - loglike(y,y,\phi)\right).` Parameters ---------- y : array of shape (n_samples,) Target values. y_pred : array of shape (n_samples,) Predicted mean. check_input : bool, default=False If True raise an exception on invalid y or y_pred values, otherwise they will be propagated as NaN. Returns ------- deviance: array of shape (n_samples,) Computed deviance Nr)rrr check_inputrrr unit_deviance^sz(ExponentialDispersionModel.unit_deviancecCsd||||S)aCompute the derivative of the unit deviance w.r.t. y_pred. The derivative of the unit deviance is given by :math:`\frac{\partial}{\partialy_\textrm{pred}}d(y,y_\textrm{pred}) = -2\frac{y-y_\textrm{pred}}{v(y_\textrm{pred})}` with unit variance :math:`v(y_\textrm{pred})`. Parameters ---------- y : array of shape (n_samples,) Target values. y_pred : array of shape (n_samples,) Predicted mean. )r)rrrrrrunit_deviance_derivativexsz3ExponentialDispersionModel.unit_deviance_derivativecCst||||S)aCompute the deviance. The deviance is a weighted sum of the per sample unit deviances, :math:`D = \sum_i s_i \cdot d(y_i, y_\textrm{pred}_i)` with weights :math:`s_i` and unit deviance :math:`d(y,y_\textrm{pred})`. In terms of the log-likelihood it is :math:`D = -2\phi\cdot \left(loglike(y,y_\textrm{pred},\frac{phi}{s}) - loglike(y,y,\frac{phi}{s})\right)`. Parameters ---------- y : array of shape (n_samples,) Target values. y_pred : array of shape (n_samples,) Predicted mean. weights : {int, array of shape (n_samples,)}, default=1 Weights or exposure to which variance is inverse proportional. )r sumrrrrweightsrrrdeviancesz#ExponentialDispersionModel.deviancecCs||||S)aCompute the derivative of the deviance w.r.t. y_pred. It gives :math:`\frac{\partial}{\partial y_\textrm{pred}} D(y, \y_\textrm{pred}; weights)`. Parameters ---------- y : array, shape (n_samples,) Target values. y_pred : array, shape (n_samples,) Predicted mean. weights : {int, array of shape (n_samples,)}, default=1 Weights or exposure to which variance is inverse proportional. )rrrrrdeviance_derivativesz.ExponentialDispersionModel.deviance_derivativeN)F)r)r) __name__ __module__ __qualname____doc__rrrrrr!r"rrrrr s   r ) metaclassc@sFeZdZdZdddZeddZejddZdd Zdd d Z d S)TweedieDistributionaA class for the Tweedie distribution. A Tweedie distribution with mean :math:`y_\textrm{pred}=\mathrm{E}[Y]` is uniquely defined by it's mean-variance relationship :math:`\mathrm{Var}[Y] \propto y_\textrm{pred}^power`. Special cases are: ===== ================ Power Distribution ===== ================ 0 Normal 1 Poisson (1,2) Compound Poisson 2 Gamma 3 Inverse Gaussian Parameters ---------- power : float, default=0 The variance power of the `unit_variance` :math:`v(y_\textrm{pred}) = y_\textrm{pred}^{power}`. For ``0=1.T) r numbersRealr formatrr Infr ValueErrorr.r,rrrr+s cCst||jS)zCompute the unit variance of a Tweedie distribution v(y_ extrm{pred})=y_ extrm{pred}**power. Parameters ---------- y_pred : array of shape (n_samples,) Predicted mean. )r r+rrrrrs z!TweedieDistribution.unit_varianceFcCs|j}|rd|}|dkr6|dkrt|dn|dkr@nd|krTdkrbnn tdnpd|krvdkrnn&|dks|dkrt|dn2|dkr|dks|dkrt|dnt|dkr>dtt|dd|d|d||t|d|d|t|d|d|}n|dkrV||d}n|dkrjtdn|dkrdt|||||}n|dkrdt||||d}nXdt|d|d|d||t|d|d|t|d|d|}|S) rz>Mean Tweedie deviance error with power={} can only be used on rzstrictly positive y_pred.rz;Tweedie deviance is only defined for power<=0 and power>=1.r0z,non-negative y and strictly positive y_pred.zstrictly positive y and y_pred.)r+r3anyr5r maximumrlog)rrrrpmessagedevrrrrsd  &     z!TweedieDistribution.unit_devianceN)r)F) r#r$r%r&r-propertyr+setterrrrrrrr(s    r(cs eZdZdZfddZZS)NormalDistributionz1Class for the Normal (aka Gaussian) distribution.cstjdddS)Nrr*superr-r/ __class__rrr-WszNormalDistribution.__init__r#r$r%r&r- __classcell__rrrArr>Tsr>cs eZdZdZfddZZS)PoissonDistributionz*Class for the scaled Poisson distribution.cstjdddS)Nrr*r?r/rArrr-^szPoissonDistribution.__init__rCrrrArrE[srEcs eZdZdZfddZZS)GammaDistributionz!Class for the Gamma distribution.cstjdddS)Nr0r*r?r/rArrr-eszGammaDistribution.__init__rCrrrArrFbsrFcs eZdZdZfddZZS)InverseGaussianDistributionz>Class for the scaled InverseGaussianDistribution distribution.cstjdddS)Nr*r?r/rArrr-lsz$InverseGaussianDistribution.__init__rCrrrArrGisrG)normalpoissongammazinverse-gaussian)r&abcrr collectionsrr1numpyr scipy.specialrrr r(r>rErFrGZEDM_DISTRIBUTIONSrrrrs&