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Therefore with regards to this test data, the cumulative weight is >= 50% when y = 4. Therefore: Median = 4 For all the samples, we can get the total error by summing: Absolute(Median - y) * weight I.e., total error = (Absolute(4 - 3) * 0.1) + (Absolute(4 - 3) * 0.3) + (Absolute(4 - 4) * 1.0) + (Absolute(4 - 6) * 0.6) + (Absolute(4 - 7) * 0.3) = 2.5 Impurity = Total error / total weight = 2.5 / 2.3 = 1.08695652173913 ------------------ From this root node, the next best split is between X values of 3 and 5. Thus, we have left and right child nodes: LEFT RIGHT ------------------ ------------------ | X | y | weight | | X | y | weight | ------------------ ------------------ | 3 | 3 | 0.1 | | 5 | 3 | 0.3 | | 3 | 6 | 0.6 | | 8 | 4 | 1.0 | ------------------ | 5 | 7 | 0.3 | |sum wt:| 0.7 | ------------------ ------------------ |sum wt:| 1.6 | ------------------ Impurity is found in the same way: Left node Median = 6 Total error = (Absolute(6 - 3) * 0.1) + (Absolute(6 - 6) * 0.6) = 0.3 Left Impurity = Total error / total weight = 0.3 / 0.7 = 0.428571428571429 ------------------- Likewise for Right node: Right node Median = 4 Total error = (Absolute(4 - 3) * 0.3) + (Absolute(4 - 4) * 1.0) + (Absolute(4 - 7) * 0.3) = 1.2 Right Impurity = Total error / total weight = 1.2 / 1.6 = 0.75 ------ ## Second toy dataset: ------------------ | X | y | weight | ------------------ | 1 | 1 | 3 | | 2 | 1 | 3 | | 3 | 3 | 2 | | 4 | 1 | 1 | | 5 | 2 | 2 | ------------------ |sum wt:| 11 | ------------------ The weighted median is 1 Total error = Absolute(1 - 3) * 2 + Absolute(1 - 2) * 2 = 6 The best split is between X values of 2 and 3, with: - left node being the first 2 data points, both with y=1 => AE and impurity is 0 - right node being the last 3 data points, weighted median is 2. 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F/c[R"[R5nSn[R"XS9nXR 5/nUH n[ X$US9 M [ R"[SS9 [ X SS9 SSS5 USS2SS2SS24[R"U54H:n[ R"[SS9 [ UUURS9 SSS5 M< [ R"[S S9 [ UR[R5UUS9 SSS5 g!,(df  N=f!,(df  M=f!,(df  g=f) N)r?r=rQr)rexpected_shapezWrong shape.+value arrayr )r=rQr=zvalue array.+C-contiguouszvalue array.+incompatible dtype) ryrrrqrr&rrrr rr.r/)rr value_ndarrayrrproblematic_arrs rtest_check_value_ndarrayr  s&XXbjj)NNHH^BM$&A&A&CDN ^  z)C D   E *!Q(3R5F5F}5UV ]]:-H I -.44 J IW z)J K   ,))  L K E D J I L Ks$8 D8 E )E8 E E  E)c[n[R"SUS9nU[U5[ U5/nUUVs/sH+o3R UR R55PM- sn- nUH n[XS9 M [R"[SS9 [R"SUS9n[X@S9 SSS5 [R"[SS9 USSS2n[X@S9 SSS5 UR RR5VVVs0sH unupgXV_M nnnnUR5n [RU S '[R "[!U R#55[!U R%55S .5n UR U 5n[R"[S S9 [X@S9 SSS5 UR5n [R&U S '[R "[!U R#55[!U R%55S .5n UR U 5n[R"[S S9 [X@S9 SSS5 gs snf!,(df  GN=f!,(df  GN=fs snnnf!,(df  N=f!,(df  g=f) N)r?r)rzWrong dimensions.+node arrayr )r?rQznode array.+C-contiguousrQr|rznode array.+incompatible dtyper)r ryrqrrr.rrr%rrrrrrrrr rr) rrvalid_node_ndarraysrproblematic_node_ndarrayrrrA dtype_dictrrs rtest_check_node_ndarrayr, sLN88D7L *<8,\: 8K8K 399))+,8K#LH# z)G H#%88F.#I 4T I z)C D#/!#4 4T E7C6H6H6O6O6U6U6WX6W"2$ $+6WJX __&N"$((N;~**,-$~?T?T?V:WXI ,229= z)I J4T K __&N#%::N< ~**,-$~?T?T?V:WXI ,229= z)I J4T K JM I H E DY K J K Js;2I>JJJ' J.+ J? J J$. J<? K Splitterc d[RRS5nSnS[R"SS/[RS9pC[ S"X45nU"XRSSUS S 9n[ R"U5n[ R"U5nURU:Xde[X5(deg ) z&Check that splitters are serializable.rrHrQr@rr5r?rON) monotonic_cst) ryrrJrr<rrmrnrorr) rr0rr?rkrrsplitter_serialize splitter_backs rtest_splitter_serializabler` s ))   #CLbhh1vRWW=yV$Y:I CDQHh/LL!34M  % % 55 5 m . .. .rc[URS55n[SS9nUR[[ 5 [ R"X!5 [ R"USS9n[URURS5 g)z`Check that Trees can be deserialized with read only buffers. Non-regression test for gh-25584. z clf.joblibrrr) mmap_modez?The trees of the original and loaded classifiers are not equal.N) strjoinrrrrrrrrr)tmpdir pickle_pathr loaded_clfs r/test_tree_deserialization_from_read_only_bufferrr sf fkk,/0K a 0CGGGW KK!8J Irc0[R"SS/SS//5n[R"SS/5nU"SS9RX5 U"SS9nSn[R"[ US9 UR"X5 SSS5 g!,(df  g=f)z`Check that an error is raised when min_sample_split=1. non-regression test for issue gh-25481. rr=rS)rzb'min_samples_split' .* must be an int in the range \[2, inf\) or a float in the range \(0.0, 1.0\]r N)ryrrrrr)r'rerfr msgs rtest_min_sample_split_1_errorr  s 1a&1a&!"A !QA 3##A) ! $D 0 z -  . - -s +B Bc[R"/SQ/5Rn[R"/SQ5n[SSUS9nUR X5 UR [R //5n[U[R"USS5/5 USSnUSSn[SSUS9nUR XV5 UR [R //5n[U[R"US S5/5 g) z=Check missing values goes to correct node during predictions. rr=rQr@rPrrM  rrBr2rBr4r4rRg?g@rr=rrANrCr>) ryrrrrrr rr)rrerfdtcrX_equaly_equals r;test_missing_values_best_splitter_on_equal_nodes_no_missingr) s 01244A >?A R1 RCGGAM[[266( $FFRWWQrsV_-.fGfG R1 RCGGG[[266( $FFRWWWRS\234rcp[R"/SQ/5Rn[R"/SQ5n[USUS9nUR X#5 UR R SnUR RSnUR RUnUR RUnXx:n UR RUSn UR RUSn UR[R//5n U (a [X5 g[X5 g)zCheck missing values go to the correct node during predictions for ExtraTree. Since ETC use random splits, we use different seeds to verify that the left/right node is chosen correctly when the splits occur. r"r%r=rrN) ryrrrrrrxrwrSrrr r) rr}rerfetrrr left_samples right_samples went_left y_pred_left y_pred_rightrs r=test_missing_values_random_splitter_on_equal_nodes_no_missingr1 s 01244A >?A $!y QCGGAM((+J))**1-K9944Z@LII55kBM,I))//*-a0K99??;/2L[[266( $F , -rrr5cSn[R"[R/S-/SQ-/5Rn[R"U/S-S/S--S/S--5n[ SSUS9nUR X#5 [R"[RSS //5RnUR U5n[XaSS/5 g ) zITest when missing values are uniquely present in a class among 3 classes.rr<)rr=rQr@rPrrMr#r=rQrrr@r#Nryrr rrrrr,)rmissing_values_classrerfr&r y_nan_preds r/test_missing_values_best_splitter_three_classesr6 s 266(Q,!;;<=??A &'!+qcAg5a?@A bA SCGGAM XX2' ( * *FV$Jz!Q#?@rc[R"[R/S-/SQ-/5Rn[R"S/S-S/S--5n[ SSUS9nUR X5 [R"[RS [R//5RnUR U5n[U/S Q5 g ) zMissing values spanning only one class at fit-time must make missing values at predict-time be classified has belonging to this class.r<rr=rQr@r<r?rr=rNrrQrr?)rr=rNr3rrerfr&rrs r)test_missing_values_best_splitter_to_leftr: s 266(Q,!334577A !qA37"#A bA SCGGAM XX266*+ , . .F [[ Fvy)rc[R"[R/S-/SQ-/5Rn[R"S/S-S/S--S/S--5n[ SSUS9nUR X5 [R"[RSS //5RnUR U5n[U/S Q5 g ) zMissing values and non-missing values sharing one class at fit-time must make missing values at predict-time be classified has belonging to this class.r<r8r=rrQrrrTg333333@rNr3r9s r*test_missing_values_best_splitter_to_rightr< s 266(Q,!334577A !qA37"aS1W,-A bA SCGGAM XXS)* + - -F [[ Fvy)rc [R"SSSS[RSSSS[R/ /5Rn[R"S /S-S/S--5n[ S SUS 9nUR X5 [R"[RS S //5RnUR U5n[U/SQ5 g)zNCheck behavior of missing value when there is one missing value in each class.r=rQr@r?rHr_r[<rrrgffffff@gA@rNr3r9s r>test_missing_values_best_splitter_missing_both_classes_has_nanr? s 1aArvvr2r2rvv>?@BBA !qA37"#A bA SCGGAM XXT*+ , . .F [[ Fvy)rr r c t[R"SSSS[RSSSS[R/ /5Rn[R"S /S-S/S--5nUbU"U5n[R "[ S S 9 UR"X#5 S S S 5 g !,(df  g =f) z4Check unsupported configurations for missing values.r=rQr@r?rHr_r[r>rNzInput X contains NaNr )ryrr rrrrr)r4r rerfs rtest_missing_value_errorsrA s 1aArvvr2r2rvv>?@BBA !qA37"#A# Q  z)? @  A @ @s B)) B7cD[RR5[Rp![R USSS2S4'[R USSS2S4'U"SSS9nUR X5 URU5nUS :R5(deg) z5Smoke test for poisson regression and missing values.Nr?rrNrCr:rrrX) rhrrrryr rrr)r'rerfrrs rtest_missing_values_poissonrC- s ==   qAcc1fIAcc2gJ  4CGGAM [[^F cM    rcB[R"U0UD6up#US:nX#4$)N)r make_friedman1)argsrrerfs rmake_friedman1_classificationrH= s)  " "D 3F 3DA BA 4Krzmake_data, Tree, tolerancegQ?gQ?gQ?sample_weight_trainrcNSupVU"UUSUS9upxUR5n [RRU5n [RXR SS/UR SS/S9'[XUS 9uppUS :Xa$[R"U R S 5nOS nS nU"UUS9nURXUS9 URX5n[[5U"UUS95nURX5 URX5nUU-U:dSU<SUSU35eg )zFCheck that trees can deal with missing values have decent performance.)rrHrS)r]r^noiser\FTrZrrarrrrNrHrrzscore_native_tree=z + z! should be strictly greater than ) rryrrJr choicerrrrrrr ) make_datar'rIr tolerancer]r^rerf X_missingr0X_missing_trainX_missing_testrrrr native_treescore_native_treetree_with_imputerscore_tree_with_imputers r!test_missing_values_is_resiliencerWC sT(&I '  DAI ))   2 3CGIvvIjj%QWWc jCD7G#584OWf$ 5 5a 89  I9KLKOOOMOJ#)).A% @RS/3/55nM y (+B B   c)- # $ & BrzTree, expected_scoreg333333?g(\?c&[RRS5nSnURUS4S9n[R"[R "US-5[R "US-5/5nURSS/USS /S 9nUR5R[5nX)X'URUS9n [RX'XS S 2S 4'U"US 9n [XUS S9R5n X:d SUSU 35eg )z@Check the tree learns when only the missing value is predictive.rrr_r`rQFTgffffff?rUrLNr?r)cvzExpected CV score: z but got )ryrrJstandard_normalrrqrrMrr.boolr rr) r'expected_scorerr0r]rerf X_random_masky_mask X_predictiver tree_cv_scores r test_missing_value_is_predictivera s ))   "CI )R1A a0"'')q.2IJKAJJt}9t JMM VVX__T "F#22F&&I&6L66LadG / 0D$DQ15::[SS9R[R[R5n[SS9R[R[R5n[ R "U5n[ R "U5nX#:Xdegr,)rrrgrrrmrn)tree1tree2pickle1pickle2s rtest_deterministic_picklerk sj # 2 6 6tyy$++ NE " 2 6 6tyy$++ NEll5!Gll5!G   rrer?rNcURSS5n[R"S5nU"X#S9RX5n[ U5RURSS5U5nUR R n[US:5(dUR55eU[La:[UR R SSUR R SS5 [R"UR RS:HUR RS:H-5n[UR R US5 g) aCheck that we properly handle missing values in regression trees using a toy dataset. The regression targeted by this test was that we were not reinitializing the criterion when it comes to the number of missing values. Therefore, the value of the critetion (i.e. MSE) was completely wrong. This test check that the MSE is null when there is a single sample in the leaf. Non-regression test for: https://github.com/scikit-learn/scikit-learn/issues/28254 https://github.com/scikit-learn/scikit-learn/issues/28316 rCr=rNrrNrQrX)rryrrrrrrrrr flatnonzerorxr}) r'rerrrfr tree_refr leaves_idxs r'test_regression_tree_missing_values_toyrp s 6 "aA ! A ) E I I! ODT{qyyQ/3Hzz""H x1}  -x||~-  $$ ++BQ/1H1H!1LM  ! !R 'DJJ,E,E,JKJDJJ'' 3S9rc[RRU5nSn[R"U[RS9R SS5n[R USS2SS24'URU5 [R"U5n[USS9RX45nURRn[US:5(dU5eg) NrMrrCr=ir?rr) ryrrJrrrr rrrrrr)rr0r]rerfr rs r-test_regression_extra_tree_missing_values_toyrr s ))   2 3CI )2::.66r1=AAcdAgJKKN )A += K O OPQ UDzz""H x1}  'x' rc[R"SS9up[RR S5nUR 5nUR [R"S[RS9USS2S/4S- S 9R[5n[RX4'[X1S S 9upVpv[R"/S Q[RS 9n[SSSS9n U R"XXXx5 [!U R"R$S:5(de[R&"U R"R(S:HU R"R*S:H-5n [-U R"R$U S5 g)aCheck that we properly handle missing values in classification trees using a toy dataset. The test is more involved because we use a case where we detected a regression in a random forest. We therefore define the seed and bootstrap indices to detect one of the non-frequent regression. Here, we check that the impurity is null or positive in the leaves. Non-regression test for: https://github.com/scikit-learn/scikit-learn/issues/28254 T) return_X_yr)r=r<)rrNrQrP)nr r)prQQ'a[&.ervYRrMrErwIJ3/kKnr_r$h9r$rO#MZrr|rv^rzrP]rrrr#rvrmrrHrrr\4r_rrPrPrrr#r#rrrr[r}Nr#rirrrr#frrvr}r=rrM rrjrr>8rr>UrwrxPr?rNrTr@r@Lrrr@riHnrrrCr=rX)r load_irisryrrJrrrrr.r[r rrrrrrrrmrxr}r) rerfr0rPmaskrrArrr ros r+test_classification_tree_missing_values_toyr sJ    .DA ))   #CI << ''bhh /1QV9q=   fTl ffIO-iLGhhXXG "&z D HHW w/0 tzz""a' ( (( (  ! !R 'DJJ,E,E,JKJDJJ'' 3S9rc[SSS9nUR"[R[R5 [ R "UR5n[URXR5n[ R"URR[ RS9nSUS'[X RU5 URRS:XdeURS:Xde[ R""[$5 ['URR(UR(5 SSS5 ['URR(SUR(S5 [URXR5n[ R"URR[ RS9nSUSS&[X RU5 URRS:XdeURS:XdUR5e['URR(UR(5 g!,(df  GN=f)zHTest pruning a tree with the Python caller of the Cythonized prune tree.rr=rrr@N)rrrgrrry atleast_1drrn_features_in_rFrqrruuint8r#rrAssertionErrorr,rr rk pruned_treeleave_in_subtrees rtest_build_pruned_tree_pyr6 s !qA >DHHTYY $ doo.IT00)__MKxx 5 5RXXFQ+zz3CD :: A %% %  ! !Q && & ~ &4::++[->->? 'tzz''*K,=,=a,@AT00)__MKxx 5 5RXXFQR+zz3CD :: A %% %  ! !Q &> (>(>> &tzz''):):; ' &s +I I c[SSS9nUR"[R[R5 [ R "UR5n[URXR5n[ R"URR[ RS9nSUS'[R "["SS9 [%X RU5 SSS5 g!,(df  g=f)z8Test pruning a tree does not result in an infinite loop.rr=rrz,Node has reached a leaf in the original treer N)rrrgrrryrrrrrFrqrrurrrrr#rs r$test_build_pruned_tree_infinite_looprU s "qA >DHHTYY $ doo.IT00)__MKxx 5 5RXXFQ H  k::7GH   s C// C=cN[RRS5nURSSSS9R [R 5n[R "U/S-5n[R"S[RS9n[X#S5 /S Qn[X45 g ) zNon-regression test for gh-30554. Using log2 and log in sort correctly sorts feature_values, but the tie breaking is different which can results in placing samples in a different order. rrX$@rH)locscalerar?rr)2r(r[r_rHrx1r-r$rr?rMr})r=r#rQrrrrvrr@!rN$r|rrr<rEr",rrr%rrPr{0rN) ryr default_rngnormalr.r/rrr<rr,)r0somefeature_valuesrexpected_sampless rtest_sort_log2_buildrg s ))   #C ::#T: 3 : :2:: FD^^TFQJ/Nii"''*G ^b) w1rc^SmS U4Sjjn[RRU5nSHnURUS4S9nURU5nUSURSS5--n[R"U5nU"XEU5 U"U[R "U5U5 U"XER 5S-U5 U"XEUS S 9 URU5nU"XEU5 U"XEUS S 9 M g ) aw Test the main bit of logic of the MAE(RegressionCriterion) class (used by DecisionTreeRegressor(criterion="absolute_error")). The implementation of the criterion relies on an efficient precomputation of left/right children absolute error for each split. This test verifies this part of the computation, in case of major refactor of the MAE class, it can be safely removed. c UR5R5n[SURS-5Vs/sHn[ USUUSUSSS9PM nn[ [SURS-5U5VVs/sH5up$[ R"USUU- 5USU-R5PM7 nnn[ R"U5[ R"U54$s snfs snnf)Nr=rTaverage) rrrRrar3zipryrr~r)rfwrmediansmerrorss rcompute_prefix_abs_errors_naiveUtest_absolute_errors_precomputation_function..compute_prefix_abs_errors_naive s GGINN 1affqj) ) !2A"1r4 @)  E!QVVaZ0': :VVAbqEAI 2A & + + -:  xx'!222  s C)>URSnU(aUS- S4OSU4n[XU/UQUP76upgXnXn U(aUSSS2nU SSS2n T "X5upU(aU SSS2n U SSS2n [XjSS9 [X{SS9 g)Nrr=rCgdy=)atol)rrr) rfrrreverserurG abs_errorsry_sortedw_sorted abs_errors_medians_rs rassert_same_resultsItest_absolute_errors_precomputation_function..assert_same_results s GGAJ%Ar{Aq6rCrFrIrKrgrwrrrrrrrrrrrrrrrrrrrrsortedrL intersectionrrrrrrr rrrrr"r*r/r6rHrTr r`rbrfr\rerzr|rRrrrrrrrrrrrr rrrr r)r1r6r:r<r?rArCrHrFrWrarrrerkr rprrrrrrrrrr)r s0rrs  ..  ,)))(-( F*;  C.2/( 57%O5.  3,  & 4    ((56<94:@>>@74545?@A84544/ 8 P 6 "XBx"bAq6Aq6Aq6:"X1v1v iiA t{{''( IIdO kk$   ! ! # x++, d# //$'     v}}))*kk$  d# !!$ %DDbR l ###1 $' \S !   15  1$RTJRRT ))$++ .mm(//:KKfmm4 W-[1$<8$84% H5$8488G$8 4 $N X X!1!1!34n5,65,*F* $y'89n56:!1!1!34 ,- ./ +, )*  <5 < 4 W 2L>-KFB8 v+1,1..9W:/W &*: z+G,G..9:/EP0f !!#^ 4 !!#^ 4@%@%F=( E*8Z1h30+,N,,N^+ , +$K$(Y%5%5%78+9+( -?"!*&Rl3   6 46 fS->-K-KI-V&WXZ$=>.?Y. l3$WX.90::Y40:f<E<493D$<E~ VW ,D,$)2C,DnU$WX.9::Y:"l3!3~~#FHP4HPV  +,,, ++dVn-DE$F,$$+G,G..9G:/GB&+,,,:+.90:,0J;Z+8+dVn-DE F $ vc(--/*k:-FFG&<>Q%RS AT AHMMO4&;=O%PQ AR5 A . :%P+fh%78+dVn-D~-UVW9,4&RS!1!1!34 >5T >q*&+&B'0T"8:M!NOq!f-G.PG,(2(4?$?"I-,-6@$ B1Uho,,.0@0G0G0IJ / /&!1!1!345*&GH5I52q*&GH.I+.By&&9: A; Ay&&9: *; *y&&9: *; * y&&9: *; *+dVn-DE (89%56 F !1!1!34 !5 !    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