Mpj?SrSSKJrJr SSKJr SSKJr SSKJ r SSK J r J r J r SSKJr \"SS 55rS r"S S \5r"S S\5r"SS\5r"SS\5r"SS\5r"SS\5r\\\\\S.rg)zM Module contains classes for invertible (and differentiable) link functions. )ABCabstractmethod) dataclass)ulp)gmean)_expit_logit get_namespacesoftmaxcJ\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 N/var/www/html/pdf-tiff/venv/lib/python3.13/site-packages/sklearn/_loss/link.py __post_init__Interval.__post_init__s? 88dii 5dhhZwtyykQRS  c[U5up#UR(aURXR5nOUR XR5nUR U5(dgUR (aURXR5nOURXR5n[UR U55$)zTest whether all values of x are in interval range. Parameters ---------- x : ndarray Array whose elements are tested to be in interval range. Returns ------- result : bool F) r r greater_equalrgreaterallr less_equalrlessbool)rxxp_rrs rincludesInterval.includes sa    ""1hh/C**Q)Cvvc{{   ==II.D771ii(DBFF4L!!rN) __name__ __module__ __qualname____firstlineno__float__annotations__r"rr&__static_attributes__r(rrrrs" J K"rrcS[S5-nUR[S5*:XaSnO;URS:aURSU- -U-nOURSU--U-nUR[S5:XaSnO;URS:aURSU--U- nOURSU- -U- n[U5[U54$)zGenerate values low and high to be within the interval range. This is used in tests only. Returns ------- low, high : tuple of floats The returned values low and high lie within the interval. infg _rg _B)rrr-r)intervalepsrrs r_inclusive_low_highr6>s s1v+C||e }$  lla#g&,lla#g&,}}e $  }}C(3.}}C(3. :uT{ ""rcl\rSrSrSrSr\"\"S5*\"S5SS5r\ S5r \ S5r Sr g) BaseLinkZaAbstract 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. Fr3cg)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. Returns ------- array Output array, element-wise link function. Nr(ry_preds rlink BaseLink.linkprcg)aJCompute 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). Returns ------- array Output array, element-wise inverse link function. Nr(rraw_predictions rinverseBaseLink.inverser?rr(N) r)r*r+r,__doc__ is_multiclassrr-interval_y_predrr=rCr/r(rrr8r8ZsP M e }eElE5IO  "  rr8c"\rSrSrSrSr\rSrg) IdentityLinkz"The identity link function g(x)=x.cU$Nr(r;s rr=IdentityLink.links rr(N)r)r*r+r,rEr=rCr/r(rrrIrIs,GrrIcF\rSrSrSr\"S\"S5SS5rSrSr Sr g ) LogLinkz"The log link function g(x)=log(x).rr3Fc>[U5up#URU5$rL)r log)rr<r$r%s rr= LogLink.linksf%vvf~rc>[U5up#URU5$rL)r exprrBr$r%s rrCLogLink.inversesn-vvn%%rr(N) r)r*r+r,rErr-rGr=rCr/r(rrrOrOs#,q%,u=O&rrOc:\rSrSrSr\"SSSS5rSrSrSr g ) LogitLinkz&The logit link function g(x)=logit(x).rr2Fc[U5$rLr r;s rr=LogitLink.links f~rc[U5$rLrrAs rrCLogitLink.inverses n%%rr(N r)r*r+r,rErrGr=rCr/r(rrrYrYs0q!UE2O&rrYc:\rSrSrSr\"SSSS5rSrSrSr g ) HalfLogitLinkzRHalf the logit link function g(x)=1/2 * logit(x). Used for the exponential loss. rr2FcS[U5-$)Ng?r\r;s rr=HalfLogitLink.linksVF^##rc[SU-5$)Nr_rAs rrCHalfLogitLink.inversesa.())rr(Nrar(rrrcrcs# q!UE2O$*rrccD\rSrSrSrSr\"SSSS5rSrSr S r 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 Trr2FcN[U5up#XRUSS9SS2S4- $Nr2)axis)r meanrVs rsymmetrize_raw_prediction*MultinomialLogit.symmetrize_raw_predictions-n-Q ?4 HHHrcd[U5up#[USS9nURXSS2S4- 5$rn)r rrR)rr<r$r%gms rr=MultinomialLogit.links4f% 6 "vvf!T'{*++rc[U5$rLr rAs rrCMultinomialLogit.inverses ~&&rr(N) r)r*r+r,rErFrrGrqr=rCr/r(rrrkrks/+ZMq!UE2OI, 'rrk)identityrRlogit half_logitmultinomial_logitN)rEabcrr dataclassesrmathr scipy.statsrsklearn.utils._array_apirr r sklearn.utils.extmathr rr6r8rIrOrYrcrk_LINKSr(rrrs$!BB) ("(" ("V#88 s8 v8 &h & & & *H *<'x<'@  )  r