U 3d@sdZddlmZmZddlmZddlZddlm Z m Z ddl m Z ddl mZeGd d d Zejfd d ZGd ddeZGdddeZGdddeZGdddeZGdddeZeeeedZdS)zM Module contains classes for invertible (and differentiable) link functions. )ABCabstractmethod) dataclassN)expitlogit)gmean)softmaxc@s>eZdZUeed<eed<eed<eed<ddZddZd S) Intervallowhigh low_inclusivehigh_inclusivecCs*|j|jkr&td|jd|jddS)zCheck that low <= highz#One must have low <= high; got low=z, high=.N)r r ValueError)selfr6/tmp/pip-unpacked-wheel-zrfo1fqw/sklearn/_loss/link.py __post_init__s zInterval.__post_init__cCsd|jrt||j}nt||j}t|s2dS|jrHt||j}nt ||j}t t|S)zTest whether all values of x are in interval range. Parameters ---------- x : ndarray Array whose elements are tested to be in interval range. Returns ------- result : bool F) r npZ greater_equalr ZgreaterallrZ less_equalr Zlessbool)rxr r rrrincludess  zInterval.includesN)__name__ __module__ __qualname__float__annotations__rrrrrrrr s r cCsdt|j}|jtj kr$d}n0|jdkrB|jd||}n|jd||}|jtjkrfd}n0|jdkr|jd||}n|jd||}||fS)zGenerate values low and high to be within the interval range. This is used in tests only. Returns ------- low, high : tuple The returned values low and high lie within the interval. g _rg _B)rZfinfoepsr infr )intervalZdtyper!r r rrr_inclusive_low_high:s    r$c@sDeZdZdZdZeej ejddZe dddZ e d ddZ dS) BaseLinkaAbstract base class for differentiable, invertible link functions. Convention: - link function g: raw_prediction = g(y_pred) - inverse link h: y_pred = h(raw_prediction) For (generalized) linear models, `raw_prediction = X @ coef` is the so called linear predictor, and `y_pred = h(raw_prediction)` is the predicted conditional (on X) expected value of the target `y_true`. The methods are not implemented as staticmethods in case a link function needs parameters. FNcCsdS)aXCompute the link function g(y_pred). The link function maps (predicted) target values to raw predictions, i.e. `g(y_pred) = raw_prediction`. Parameters ---------- y_pred : array Predicted target values. out : array A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. Returns ------- out : array Output array, element-wise link function. Nrry_predoutrrrlinklsz BaseLink.linkcCsdS)aCompute the inverse link function h(raw_prediction). The inverse link function maps raw predictions to predicted target values, i.e. `h(raw_prediction) = y_pred`. Parameters ---------- raw_prediction : array Raw prediction values (in link space). out : array A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. Returns ------- out : array Output array, element-wise inverse link function. Nrrraw_predictionr(rrrinverseszBaseLink.inverse)N)N) rrr__doc__ is_multiclassr rr"interval_y_predrr)r,rrrrr%Vs r%c@seZdZdZdddZeZdS) IdentityLinkz"The identity link function g(x)=x.NcCs |dk rt|||S|SdS)N)rcopytor&rrrr)s zIdentityLink.link)N)rrrr-r)r,rrrrr0s r0c@s4eZdZdZedejddZd ddZd ddZ dS) LogLinkz"The log link function g(x)=log(x).rFNcCstj||dSNr()rlogr&rrrr)sz LogLink.linkcCstj||dSr3)rexpr*rrrr,szLogLink.inverse)N)N) rrrr-r rr"r/r)r,rrrrr2s r2c@s2eZdZdZeddddZd ddZd dd ZdS) LogitLinkz&The logit link function g(x)=logit(x).rr FNcCs t||dSr3)rr&rrrr)szLogitLink.linkcCs t||dSr3)rr*rrrr,szLogitLink.inverse)N)N)rrrr-r r/r)r,rrrrr7s r7c@s>eZdZdZdZeddddZddZd d d Zdd d Z dS)MultinomialLogitaThe symmetric multinomial logit function. Convention: - y_pred.shape = raw_prediction.shape = (n_samples, n_classes) Notes: - The inverse link h is the softmax function. - The sum is over the second axis, i.e. axis=1 (n_classes). We have to choose additional constraints in order to make y_pred[k] = exp(raw_pred[k]) / sum(exp(raw_pred[k]), k=0..n_classes-1) for n_classes classes identifiable and invertible. We choose the symmetric side constraint where the geometric mean response is set as reference category, see [2]: The symmetric multinomial logit link function for a single data point is then defined as raw_prediction[k] = g(y_pred[k]) = log(y_pred[k]/gmean(y_pred)) = log(y_pred[k]) - mean(log(y_pred)). Note that this is equivalent to the definition in [1] and implies mean centered raw predictions: sum(raw_prediction[k], k=0..n_classes-1) = 0. For linear models with raw_prediction = X @ coef, this corresponds to sum(coef[k], k=0..n_classes-1) = 0, i.e. the sum over classes for every feature is zero. Reference --------- .. [1] Friedman, Jerome; Hastie, Trevor; Tibshirani, Robert. "Additive logistic regression: a statistical view of boosting" Ann. Statist. 28 (2000), no. 2, 337--407. doi:10.1214/aos/1016218223. https://projecteuclid.org/euclid.aos/1016218223 .. [2] Zahid, Faisal Maqbool and Gerhard Tutz. "Ridge estimation for multinomial logit models with symmetric side constraints." Computational Statistics 28 (2013): 1017-1034. http://epub.ub.uni-muenchen.de/11001/1/tr067.pdf Trr FcCs |tj|ddddtjfS)Nr Zaxis)rZmeannewaxis)rr+rrrsymmetrize_raw_predictionsz*MultinomialLogit.symmetrize_raw_predictionNcCs,t|dd}tj||ddtjf|dS)Nr r9r4)rrr5r:)rr'r(Zgmrrrr)s zMultinomialLogit.linkcCs4|dkrt|ddSt||t|dd|SdS)NT)copyF)r rr1r*rrrr,s    zMultinomialLogit.inverse)N)N) rrrr-r.r r/r;r)r,rrrrr8s - r8)identityr5rZmultinomial_logit)r-abcrrZ dataclassesrZnumpyrZ scipy.specialrrZ scipy.statsrZ utils.extmathr r Zfloat64r$r%r0r2r7r8Z_LINKSrrrrs&   *C   C