:i&SrSSKJrJr SSKJr SSKrSSKJ r J r SSK J r SSK Jr \"S S 55r\R 4S jr"S S \5r"SS\5r"SS\5r"SS\5r"SS\5r"SS\5r\\\\\S.rg)zM Module contains classes for invertible (and differentiable) link functions. )ABCabstractmethod) dataclassN)expitlogit)gmean)softmaxcJ\rSrSr%\\S'\\S'\\S'\\S'SrSrSr g ) Intervallowhigh low_inclusivehigh_inclusivecURUR:a&[SURSURS35eg)zCheck that low <= highz#One must have low <= high; got low=z, high=.N)rr ValueError)selfs U/srv/projetos/modelo_ml_acdoc/venv/lib/python3.13/site-packages/sklearn/_loss/link.py __post_init__Interval.__post_init__s? 88dii 5dhhZwtyykQRS  cUR(a![R"XR5nO [R"XR5n[R "U5(dgUR (a![R"XR5nO [R"XR5n[[R "U55$)zTest whether all values of x are in interval range. Parameters ---------- x : ndarray Array whose elements are tested to be in interval range. Returns ------- result : bool F) rnp greater_equalrgreaterallr less_equalrlessbool)rxrrs rincludesInterval.includess   ""1hh/C**Q)Cvvc{{   ==II.D771ii(DBFF4L!!rN) __name__ __module__ __qualname____firstlineno__float__annotations__r!rr#__static_attributes__r%rrr r s" J K"rr cS[R"U5R-nUR[R*:XaSnO;URS:aURSU- -U-nOURSU--U-nUR [R:XaSnX44$UR S:aUR SU--U- nX44$UR SU- -U- nX44$)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)rfinfoepsrinfr)intervaldtyper1rrs r_inclusive_low_highr5<s rxx"" "C||w  lla#g&,lla#g&,}} 9  }}C(3. 9}}C(3. 9rc\rSrSrSrSr\"\R*\RSS5r \ SSj5r \ SSj5r Sr g) BaseLinkXaAbstract 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. FNcg)aCompute 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 rlink BaseLink.linknrcg)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_predictionr<s rinverseBaseLink.inverser?rr%N)r&r'r(r)__doc__ is_multiclassr rr2interval_y_predrr=rCr,r%rrr7r7XsP M wu=O  *  rr7c&\rSrSrSrSSjr\rSrg) IdentityLinkz"The identity link function g(x)=x.Nc<Ub[R"X!5 U$U$rE)rcopytor:s rr=IdentityLink.links ? IIc "JMrr%rE)r&r'r(r)rFr=rCr,r%rrrJrJs,GrrJcV\rSrSrSr\"S\RSS5rS Sjr S Sjr Sr g) LogLinkz"The log link function g(x)=log(x).rFNc*[R"XS9$Nr<)rlogr:s rr= LogLink.linksvvf&&rc*[R"XS9$rS)rexprAs rrCLogLink.inversesvvn..rr%rE) r&r'r(r)rFr rr2rHr=rCr,r%rrrPrPs#,q"&&%7O'/rrPcB\rSrSrSr\"SSSS5rS SjrS SjrS r g) LogitLinkz&The logit link function g(x)=logit(x).rr/FNc[XS9$rSrr:s rr=LogitLink.links V%%rc[XS9$rSrrAs rrCLogitLink.inverses ^--rr%rE r&r'r(r)rFr rHr=rCr,r%rrr[r[s0q!UE2O&.rr[cB\rSrSrSr\"SSSS5rS SjrS SjrS r g) HalfLogitLinkzRHalf the logit link function g(x)=1/2 * logit(x). Used for the exponential loss. rr/FNc"[XS9nUS-nU$)NrTg?r^r:s rr=HalfLogitLink.linksF$ s  rc [SU-U5$)Nr rarAs rrCHalfLogitLink.inversesQ'--rr%rErcr%rrreres# q!UE2O .rrecL\rSrSrSrSr\"SSSS5rSrS S jr S S jr S r g) 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/Fc\U[R"USS9SS2[R4- $)Nr/axis)rmeannewaxis)rrBs rsymmetrize_raw_prediction*MultinomialLogit.symmetrize_raw_predictions%Q ?2:: NNNrNcn[USS9n[R"XSS2[R4- US9$)Nr/rorT)rrrUrr)rr;r<gms rr=MultinomialLogit.links/ 6 "vvf!RZZ-00c::rc`Uc [USS9$[R"X!5 [USS9 U$)NT)copyF)r rrMrAs rrCMultinomialLogit.inverse s/ ;>5 5 IIc * Ce $Jrr%rE) r&r'r(r)rFrGr rHrsr=rCr,r%rrrlrls/+ZMq!UE2OO; rrl)identityrUr half_logitmultinomial_logit)rFabcrr dataclassesrnumpyr scipy.specialrr scipy.statsr utils.extmathr r float64r5r7rJrPr[rerl_LINKSr%rrrs $!&# '"'" '"T)+ 8@ s@ F 8  /h / . ..H."?x?F  )  r