UgLdZddlmZmZddlmZddlZddlm Z m Z ddl m Z ddl mZeGd d Zejfd ZGd d eZGddeZGddeZGddeZGddeZGddeZeeeeedZdS)zM Module contains classes for invertible (and differentiable) link functions. )ABCabstractmethod) dataclassN)expitlogit)gmean)softmaxcDeZdZUeed<eed<eed<eed<dZdZdS)Intervallowhigh low_inclusivehigh_inclusivecf|j|jkr td|jd|jddS)zCheck that low <= highz#One must have low <= high; got low=z, high=.N)r r ValueError)selfs Q/var/www/surfInsights/venv3-11/lib/python3.11/site-packages/sklearn/_loss/link.py __post_init__zInterval.__post_init__sE 8di  SdhSStySSS  c`|jrtj||j}ntj||j}tj|sdS|jrtj||j}ntj ||j}ttj|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) rnp greater_equalr greaterallr less_equalrlessbool)rxr rs rincludeszInterval.includess   *"1dh//CC*Q))Cvc{{ 5   )=DI..DD71di((DBF4LL!!!rN)__name__ __module__ __qualname__float__annotations__rrr!rrr r s^ JJJ KKK"""""rr cTdtj|jz}|jtj krd}n,|jdkr|jd|z z|z}n|jd|zz|z}|jtjkrd}n,|jdkr|jd|zz|z }n|jd|z z|z }||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)rfinfoepsr infr)intervaldtyper,r rs r_inclusive_low_highr0<s rx" "C|w   la#g&,la#g&,}   }C(3.}C(3. 9rcxeZdZdZdZeej ejddZe ddZ e 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. FNcdS)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. Nr'ry_predouts rlinkz BaseLink.linknrcdS)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. Nr'rraw_predictionr6s rinversezBaseLink.inverser8rN) r"r#r$__doc__ is_multiclassr rr-interval_y_predrr7r<r'rrr2r2Xs  M hwu==O   ^ *   ^   rr2ceZdZdZddZeZdS) IdentityLinkz"The identity link function g(x)=x.Nc8|tj|||S|Sr=)rcopytor4s rr7zIdentityLink.links# ? Ic6 " " "JMrr=)r"r#r$r>r7r<r'rrrBrBs/,,GGGrrBcHeZdZdZedejddZddZddZ dS)LogLinkz"The log link function g(x)=log(x).rFNc.tj||SNr6)rlogr4s rr7z LogLink.linksvf#&&&&rc.tj||SrH)rexpr:s rr<zLogLink.inversesvn#....rr=) r"r#r$r>r rr-r@r7r<r'rrrFrFsY,,hq"&%77O''''//////rrFc>eZdZdZeddddZddZddZdS) LogitLinkz&The logit link function g(x)=logit(x).rr*FNc$t||SrHrr4s rr7zLogitLink.linksV%%%%rc$t||SrHrr:s rr<zLogitLink.inverses^----rr=r"r#r$r>r r@r7r<r'rrrNrNsW00hq!UE22O&&&&......rrNc>eZdZdZeddddZddZddZdS) HalfLogitLinkzZHalf the logit link function g(x)=1/2 * logit(x). Used for the exponential loss. rr*FNc2t||}|dz}|S)NrIg?rPr4s rr7zHalfLogitLink.links"F$$$ s  rc(td|z|S)Nr rRr:s rr<zHalfLogitLink.inversesQ'---rr=rSr'rrrUrUs] hq!UE22O ......rrUcHeZdZdZdZeddddZdZd dZd 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." 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