h /dZddlmZmZddlmZddlZddlZddl m Z eddZ Gdd e Z Gd d e Z Gd de ZGdde ZGdde ZGdde ZeeeedZdS)z$ Distribution functions used in GLM )ABCMetaabstractmethod) namedtupleN)xlogyDistributionBoundary)value inclusivec\eZdZdZdZedZed dZdZd dZ d d Z d S) 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. ct|jtstd|jjrt j||jjSt j||jjS)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 DistributionBoundary) isinstance _lower_boundr TypeErrorr np greater_equalrgreater)selfys Z/var/www/html/Sam_Eipo/venv/lib/python3.11/site-packages/sklearn/_loss/glm_distribution.py in_y_rangez%ExponentialDispersionModel.in_y_range4sp$+-ABB M    & :#At'8'>?? ?:a!2!899 9cdS)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. Nry_preds r unit_variancez(ExponentialDispersionModel.unit_varianceHrFcdS)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_inputs r unit_deviancez(ExponentialDispersionModel.unit_deviance^rrc>d||z z||z 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)rrrs runit_deviance_derivativez3ExponentialDispersionModel.unit_deviance_derivativexs& QZ 4#5#5f#=#===rcXtj||||zS)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. )rsumr!rrrweightss rdeviancez#ExponentialDispersionModel.deviances),vg 2 21f = ==>>>rc4||||zS)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. )r$r(s rdeviance_derivativez.ExponentialDispersionModel.deviance_derivatives"66q&AAAArNF)r%) __name__ __module__ __qualname____doc__rrrr!r$r*r,rrrr r s8:::(  ^ *   ^ 2>>>$????0BBBBBBrr ) metaclassc^eZdZdZd dZedZejdZdZd dZ 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 numbersRealrformatrrInfr ValueErrorr<r9s rr8zTweedieDistribution.powers %.. XHOOPUVVWW W A:: 4bfW N N ND   ]]]]]]]]]Q %^^^^!^^^^^ 4Q$ G G GD   aZZ 4Q% H H HD    rc6tj||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. )rr8rs rrz!TweedieDistribution.unit_variancesx +++rFc|j}|rd|}|dkr+|dkrt|dzn|dkrnd|cxkrdkrnntdd|cxkrdkrFnnC|dks|dkrt|dznP|dkrC|dks|dkrt|dznt|dkr|dt jt j|dd|z d|z d|z zz |t j|d|z zd|z z z t j|d|z d|z z zz}n|dkr ||z dz}n|dkrtd|dkrdt |||z |z |zz}n|dkr$dt j||z ||z zdz z}nhdt j|d|z d|z d|z zz |t j|d|z zd|z z z t j|d|z d|z z zz}|S) rz>Mean Tweedie deviance error with power={} can only be used on rzstrictly positive y_pred.r%z;Tweedie deviance is only defined for power<=0 and power>=1.r>z,non-negative y and strictly positive y_pred.zstrictly positive y and y_pred.)r8rAanyrCrmaximumrlog)rrrr pmessagedevs rr!z!TweedieDistribution.unit_deviances 0 J  !PWW  1uuaK$$&&L$W/J%JKKKLaQ Qa!E;;==Vq[$5$5$7$7$"PPaF<<>>Rfk%6%6%8%8R$W/P%PQQQR! q55Aq))1q511a!eA5FGbhvq1u---Q78(61q5))QU34CC !VVv:!#CC UUM !VVuQF ++a/&89CC !VVrvfqj))AJ6:;CCAE""q1uQ&78bhvq1u---Q78(61q5))QU34C  rN)rr-) r.r/r0r1r:propertyr8setterrr!rrrr4r4s2X \\4 , , ,TTTTTTrr4c"eZdZdZfdZxZS)NormalDistributionz1Class for the Normal (aka Gaussian) distribution.cLtddS)Nrr7superr:r __class__s rr:zNormalDistribution.__init__W$ q!!!!!rr.r/r0r1r: __classcell__rTs@rrOrOTs>;;"""""""""rrOc"eZdZdZfdZxZS)PoissonDistributionz*Class for the scaled Poisson distribution.cLtddS)Nr%r7rQrSs rr:zPoissonDistribution.__init__^rUrrVrXs@rrZrZ[s>44"""""""""rrZc"eZdZdZfdZxZS)GammaDistributionz!Class for the Gamma distribution.cLtddS)Nr>r7rQrSs rr:zGammaDistribution.__init__erUrrVrXs@rr]r]bs>++"""""""""rr]c"eZdZdZfdZxZS)InverseGaussianDistributionz>Class for the scaled InverseGaussianDistribution distribution.cLtddS)Nr7rQrSs rr:z$InverseGaussianDistribution.__init__lrUrrVrXs@rr`r`is>HH"""""""""rr`)normalpoissongammazinverse-gaussian)r1abcrr collectionsrr?numpyr scipy.specialrrr r4rOrZr]r`EDM_DISTRIBUTIONSrrrrks('''''''"""""""z"8:PQQ\B\B\B\B\B7\B\B\B\B~[[[[[4[[[|""""",""""""""-""""""""+"""""""""5"""!" 3 r