From b919ebfe0c23dbb1dc5a9ad2f76ebdbf10911061 Mon Sep 17 00:00:00 2001 From: jasonfan1997 Date: Tue, 29 Oct 2024 14:38:58 -0400 Subject: [PATCH] Adding reference --- docs/build/doctrees/environment.pickle | Bin 156578 -> 156974 bytes .../nbsphinx/notebooks/validation.ipynb | 50 ++++++++---- .../doctrees/notebooks/validation.doctree | Bin 32088 -> 33416 bytes .../_sources/notebooks/validation.ipynb.txt | 50 ++++++++---- docs/build/html/index.html | 1 + docs/build/html/notebooks/validation.html | 48 ++++++----- docs/build/html/notebooks/validation.ipynb | 50 ++++++++---- docs/build/html/objects.inv | Bin 3039 -> 3050 bytes docs/build/html/searchindex.js | 2 +- docs/build/latex/calzone.aux | 2 + docs/build/latex/calzone.fdb_latexmk | 54 ++++++------- docs/build/latex/calzone.log | 76 +++++++++--------- docs/build/latex/calzone.out | 19 ++--- docs/build/latex/calzone.pdf | Bin 1447119 -> 1448130 bytes docs/build/latex/calzone.tex | 49 +++++++---- docs/build/latex/calzone.toc | 1 + 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a/docs/build/doctrees/nbsphinx/notebooks/validation.ipynb b/docs/build/doctrees/nbsphinx/notebooks/validation.ipynb index 20b05f7..0aa6e96 100644 --- a/docs/build/doctrees/nbsphinx/notebooks/validation.ipynb +++ b/docs/build/doctrees/nbsphinx/notebooks/validation.ipynb @@ -24,22 +24,20 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Difference for uniform/histogram binning:\n", + "Difference for equal-width binning:\n", "Reliability difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", "Confidence difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", "\n", - "Difference for quantile/equal frequency binning:\n", - "Reliability difference: [1.e-05 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00\n", - " 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]\n", - "Confidence difference: [1.e-05 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00\n", - " 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]\n" + "Difference for equal-count binning:\n", + "Reliability difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", + "Confidence difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n" ] } ], @@ -51,17 +49,21 @@ "### loading the data\n", "wellcal_dataloader = data_loader(data_path=\"../../../example_data/simulated_welldata.csv\")\n", "\n", + "###scikit-learn implementation\n", "scikit_reliability_H,scikit_confidence_H = calibration_curve(wellcal_dataloader.labels,wellcal_dataloader.probs[:,1],n_bins=15,strategy='uniform',pos_label=1)\n", "scikit_reliability_C,scikit_confidence_C = calibration_curve(wellcal_dataloader.labels,wellcal_dataloader.probs[:,1],n_bins=15,strategy='quantile',pos_label=1)\n", + "\n", + "### calzone implementation\n", "calzone_reliability_H,calzone_confindence_H,bin_edge_H,bin_count_H = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=15, class_to_plot=1, is_equal_freq=False)\n", "calzone_reliability_C,calzone_confindence_C,bin_edge_C,bin_count_C = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=15, class_to_plot=1, is_equal_freq=True)\n", "\n", - "print(\"Difference for uniform/histogram binning:\")\n", - "print(\"Reliability difference:\", np.round(np.abs(scikit_reliability_H - calzone_reliability_H), 5))\n", - "print(\"Confidence difference:\", np.round(np.abs(scikit_confidence_H - calzone_confindence_H), 5))\n", - "print(\"\\nDifference for quantile/equal frequency binning:\")\n", - "print(\"Reliability difference:\", np.round(np.abs(scikit_reliability_C - calzone_reliability_C), 5))\n", - "print(\"Confidence difference:\", np.round(np.abs(scikit_confidence_C - calzone_confindence_C), 5))" + "###showing the difference between the two implementations\n", + "print(\"Difference for equal-width binning:\")\n", + "print(\"Reliability difference:\", np.round(np.abs(scikit_reliability_H - calzone_reliability_H), 4))\n", + "print(\"Confidence difference:\", np.round(np.abs(scikit_confidence_H - calzone_confindence_H), 4))\n", + "print(\"\\nDifference for equal-count binning:\")\n", + "print(\"Reliability difference:\", np.round(np.abs(scikit_reliability_C - calzone_reliability_C), 4))\n", + "print(\"Confidence difference:\", np.round(np.abs(scikit_confidence_C - calzone_confindence_C), 4))" ] }, { @@ -82,7 +84,7 @@ }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -100,13 +102,14 @@ "calzone_reliability_topclass_H,calzone_confindence_topclass_H,bin_edge_topclass_H,bin_count_topclass_H = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=15, class_to_plot=None, is_equal_freq=False)\n", "calzone_reliability_topclass_C,calzone_confindence_topclass_C,bin_edge_topclass_C,bin_count_topclass_C = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=15, class_to_plot=None, is_equal_freq=True)\n", "\n", + "### compare MAPIE and calzone equal-width binning\n", "print(\"MAPIE topclass ECE-H:\",top_label_ece(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins = 15,split_strategy='uniform'))\n", "print(\"calzone topclass ECE-H:\",calculate_ece_mce(calzone_reliability_topclass_H,calzone_confindence_topclass_H,bin_count_topclass_H)[0])\n" ] }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -119,6 +122,7 @@ } ], "source": [ + "### compare MAPIE and calzone equal-count binning\n", "print(\"MAPIE topclass ECE-C:\",top_label_ece(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins = 15,split_strategy='quantile'))\n", "print(\"calzone topclass ECE-C:\",calculate_ece_mce(calzone_reliability_topclass_C,calzone_confindence_topclass_C,bin_count_topclass_C)[0])\n" ] @@ -132,7 +136,7 @@ }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -145,6 +149,7 @@ } ], "source": [ + "### compare the Z statistics\n", "print(\"MAPIE Z statistic\", spiegelhalter_statistic(wellcal_dataloader.labels,wellcal_dataloader.probs[:,1]))\n", "print(\"calzone Z statistic\", spiegelhalter_z_test(wellcal_dataloader.labels,wellcal_dataloader.probs)[0])" ] @@ -233,6 +238,19 @@ "source": [ "We see that the test statistics are the same. The R package doesn't allow user input degree of freedom so the p-value is different as expected." ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## reference\n", + "\n", + "Taquet, V., Blot, V., Morzadec, T., Lacombe, L., & Brunel, N. (2022). MAPIE: an open-source library for distribution-free uncertainty quantification. arXiv preprint arXiv:2207.12274.\n", + "\n", + "Pedregosa, F., Varoquaux, Ga\"el, Gramfort, A., Michel, V., Thirion, B., Grisel, O., … others. (2011). Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12(Oct), 2825–2830.\n", + "\n", + "Lele, S. R., Keim, J. L., & Solymos, P. (2017). Resource selection (probability) functions for use-availability data. Package ‘ResourceSelection’, Version 0.3-2." + ] } ], "metadata": { diff --git a/docs/build/doctrees/notebooks/validation.doctree b/docs/build/doctrees/notebooks/validation.doctree index 0f72e5028b117b238dd9eb7100ef2065b1210e17..cb0e3f9f90f235337c31f8ac4cb8512272944b9c 100644 GIT binary patch delta 3152 zcmds3Uu+ab81Hwz_DZp|wgqa%>p-=%c)hmEl|pF|O0iH{di@Jh3+&y^v3uRyJ$Cn6 zuh3jEqL7@Dbc%opf#0Q8$6QeOECK4Y6sy<;%#23IAow@6^R}v6fo_yJz z`R1FM@Av)Y_sv|s4g2?*Qif6v4Ze6b<-BDM*Hb+rSb9c;RS|PHN4~OLFg2wbk+e#% z78Vw2Zn0O?OC`*!G7|j(3H!0E^SY?W#)Vm{VL>`|LT+9fP-J|ELpu2*C)Y@S)CVir zN`lfa$~%!RVB`_KUaVr-jgbrM{TRzpv)-@Vv4lnjADKTJ?+Wr#X}{>v1#&FMNv>xv z00&9WT}PU8Sj(65__&W-3CcS4k)q>#hNGlp9Nd=w4JdFJQtmu}T2j!xmV7aHKPaSS zUfz@}?L~#;>cW?%WF=Z$1f0N#xpc8@ZXEdB0ne z?^@=PzZY1hJK0L=3hJSS?QeC_{p%->kylYs;xV~<0<@wy^yx2QL<&0q1moJ1M@=by zp+M*(*Vb2)PZwu^W_-E$34oCCYcVpzZt~;$R@h6fth8sEyO$gdMajmrnQVbw(=63VGy&--Ht?v z4pLC_=CXRq)cpXAYIg#lK>@<_=jMQMW0jCjlU|t^5$WA<-1=u?G^`wLMH(wMEKC0B#r`Y)k0f4M%y$xxGqwQxCWRSeh*C0fG zH(SZ2P7h=mOS+x{$R^IsZKgb+sVg_W-@G9i78%y=uK|jU>(B22uoGe1ElVZPOq){( z%k<&xmrN^}zuk!Jm}`OOh_!p$IiUuCH)_R3dL&7$m`6_dMj=2p_5KBY%)xk1dK+NR za3IgX@*4pA&IQT<4wCX+x8aEKv>F09#zKLU$t)F**Xa25kYL$2vUg-~ zq?krFoJuYh*}_${c`!98NkBrfuuxbe6gHoRpi5{hi8-c3KI!0h1+i{JU3MF)la%pR zv!V|09_+TE4r*`W-HP9ZX@ho(P@Ni-v1CJ=?5LP4=eQDkOdi!#A4mycxl~hvD!oO* zlIT)-HH26l@K7dI(G_HuRH;|R7zOD~qw2gU>mfw%5?L3$qC0wt*%7a95&IA=i2;?4 z$GX)VS6*eW;J7M>J&yjK@rP#$V21G*-wVJbStp`ok<8At@cZmo#TlDI)HhD-QSnYi z<8A0!N<$Z~Dl}=q7i_43U&QEWP>>(k$PhbxN*(9-N zCW#%rE3xl1VTnqs-HzHQBO9^kx1mP+xYXJeDdbl)8*;`7s-pbR%*NzJX~b?OCsZ6z z6&LRkB~cHRATJdbGiy=Z1vOmChx>R@8h1b*Ugzz|$-8^`otU11Bk>j6;|q=r9i>dr zW5E_Lw=XT_CJ38exM5Zf9w6SChdar_XS4v4&x@8YfmuF`@j$MuudR*iY`ijlOe-T6 z=CA^q)iV-FsH?n?O<&@5y!N@F` z_hUU2z#6O1zN^&XfbS!E10V1WnAtZHwXlf?fR@?eMj+U!Sj?{(R@@1YZYh d4bn-zPS#==f{_fbqUf@s9y4R`nDZ+BxzI*m(FtN&I6{()g%bj-y*QZ86yODga9 z#mhT1nr~iuw51)cS|cXGYmP?ir zyBa@dUzEscqLartG4OL1t!)hoqfpHpC|)iYgy&eZ>y>YOK{5*E0PlTAUoL6^m>_Yw z(*R#EP8WsucYgp8-YA&_hFmRuBZd{&v#%Fg@uMUTv-a0Q2pQO)2uv8z;&Vx`V`DD1 z>q8(4&*&2cD#(uVVn2u{XY@}1HV{K)8$c==Dp~wg^_s~P%p_9umZ&hGdK7YI&AwMh zGEhO)YT__y0cyx_T_Hdn4%e|Lx7?&*cxd?sP9GxX$Q2-Ce&kQ|ZEyX+gL&OrLNYqa;0Ns3 B^-ll* diff --git a/docs/build/html/_sources/notebooks/validation.ipynb.txt b/docs/build/html/_sources/notebooks/validation.ipynb.txt index 20b05f7..0aa6e96 100644 --- a/docs/build/html/_sources/notebooks/validation.ipynb.txt +++ b/docs/build/html/_sources/notebooks/validation.ipynb.txt @@ -24,22 +24,20 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Difference for uniform/histogram binning:\n", + "Difference for equal-width binning:\n", "Reliability difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", "Confidence difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", "\n", - "Difference for quantile/equal frequency binning:\n", - "Reliability difference: [1.e-05 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00\n", - " 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]\n", - "Confidence difference: [1.e-05 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00\n", - " 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]\n" + "Difference for equal-count binning:\n", + "Reliability difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n", + "Confidence difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n" ] } ], @@ -51,17 +49,21 @@ "### loading the data\n", "wellcal_dataloader = data_loader(data_path=\"../../../example_data/simulated_welldata.csv\")\n", "\n", + "###scikit-learn implementation\n", "scikit_reliability_H,scikit_confidence_H = calibration_curve(wellcal_dataloader.labels,wellcal_dataloader.probs[:,1],n_bins=15,strategy='uniform',pos_label=1)\n", "scikit_reliability_C,scikit_confidence_C = calibration_curve(wellcal_dataloader.labels,wellcal_dataloader.probs[:,1],n_bins=15,strategy='quantile',pos_label=1)\n", + "\n", + "### calzone implementation\n", "calzone_reliability_H,calzone_confindence_H,bin_edge_H,bin_count_H = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=15, class_to_plot=1, is_equal_freq=False)\n", "calzone_reliability_C,calzone_confindence_C,bin_edge_C,bin_count_C = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=15, class_to_plot=1, is_equal_freq=True)\n", "\n", - "print(\"Difference for uniform/histogram binning:\")\n", - "print(\"Reliability difference:\", np.round(np.abs(scikit_reliability_H - calzone_reliability_H), 5))\n", - "print(\"Confidence difference:\", np.round(np.abs(scikit_confidence_H - calzone_confindence_H), 5))\n", - "print(\"\\nDifference for quantile/equal frequency binning:\")\n", - "print(\"Reliability difference:\", np.round(np.abs(scikit_reliability_C - calzone_reliability_C), 5))\n", - "print(\"Confidence difference:\", np.round(np.abs(scikit_confidence_C - calzone_confindence_C), 5))" + "###showing the difference between the two implementations\n", + "print(\"Difference for equal-width binning:\")\n", + "print(\"Reliability difference:\", np.round(np.abs(scikit_reliability_H - calzone_reliability_H), 4))\n", + "print(\"Confidence difference:\", np.round(np.abs(scikit_confidence_H - calzone_confindence_H), 4))\n", + "print(\"\\nDifference for equal-count binning:\")\n", + "print(\"Reliability difference:\", np.round(np.abs(scikit_reliability_C - calzone_reliability_C), 4))\n", + "print(\"Confidence difference:\", np.round(np.abs(scikit_confidence_C - calzone_confindence_C), 4))" ] }, { @@ -82,7 +84,7 @@ }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -100,13 +102,14 @@ "calzone_reliability_topclass_H,calzone_confindence_topclass_H,bin_edge_topclass_H,bin_count_topclass_H = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=15, class_to_plot=None, is_equal_freq=False)\n", "calzone_reliability_topclass_C,calzone_confindence_topclass_C,bin_edge_topclass_C,bin_count_topclass_C = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=15, class_to_plot=None, is_equal_freq=True)\n", "\n", + "### compare MAPIE and calzone equal-width binning\n", "print(\"MAPIE topclass ECE-H:\",top_label_ece(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins = 15,split_strategy='uniform'))\n", "print(\"calzone topclass ECE-H:\",calculate_ece_mce(calzone_reliability_topclass_H,calzone_confindence_topclass_H,bin_count_topclass_H)[0])\n" ] }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -119,6 +122,7 @@ } ], "source": [ + "### compare MAPIE and calzone equal-count binning\n", "print(\"MAPIE topclass ECE-C:\",top_label_ece(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins = 15,split_strategy='quantile'))\n", "print(\"calzone topclass ECE-C:\",calculate_ece_mce(calzone_reliability_topclass_C,calzone_confindence_topclass_C,bin_count_topclass_C)[0])\n" ] @@ -132,7 +136,7 @@ }, { "cell_type": "code", - "execution_count": 45, + "execution_count": 5, "metadata": {}, "outputs": [ { @@ -145,6 +149,7 @@ } ], "source": [ + "### compare the Z statistics\n", "print(\"MAPIE Z statistic\", spiegelhalter_statistic(wellcal_dataloader.labels,wellcal_dataloader.probs[:,1]))\n", "print(\"calzone Z statistic\", spiegelhalter_z_test(wellcal_dataloader.labels,wellcal_dataloader.probs)[0])" ] @@ -233,6 +238,19 @@ "source": [ "We see that the test statistics are the same. The R package doesn't allow user input degree of freedom so the p-value is different as expected." ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## reference\n", + "\n", + "Taquet, V., Blot, V., Morzadec, T., Lacombe, L., & Brunel, N. (2022). MAPIE: an open-source library for distribution-free uncertainty quantification. arXiv preprint arXiv:2207.12274.\n", + "\n", + "Pedregosa, F., Varoquaux, Ga\"el, Gramfort, A., Michel, V., Thirion, B., Grisel, O., … others. (2011). Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12(Oct), 2825–2830.\n", + "\n", + "Lele, S. R., Keim, J. L., & Solymos, P. (2017). Resource selection (probability) functions for use-availability data. Package ‘ResourceSelection’, Version 0.3-2." + ] } ], "metadata": { diff --git a/docs/build/html/index.html b/docs/build/html/index.html index d8e30a3..f433cb0 100644 --- a/docs/build/html/index.html +++ b/docs/build/html/index.html @@ -180,6 +180,7 @@

Welcome to the documentation for calzoneReliability diagram
  • Expected calibration error and Z test
  • HL test
    • +
  • reference
  • calzone
  • calzone
    • @@ -103,7 +104,7 @@

    Validating metrics with external packages

    We will use scikit-learn’s calibration_curve function to calculate the reliability diagram

    -
    [1]:
+
    [2]:
 
    
 
    
 
    from calzone.utils import reliability_diagram,data_loader
@@ -113,17 +114,21 @@ 
    Reliability diagram### loading the data
 wellcal_dataloader = data_loader(data_path="../../../example_data/simulated_welldata.csv")
 
+###scikit-learn implementation
 scikit_reliability_H,scikit_confidence_H = calibration_curve(wellcal_dataloader.labels,wellcal_dataloader.probs[:,1],n_bins=15,strategy='uniform',pos_label=1)
 scikit_reliability_C,scikit_confidence_C = calibration_curve(wellcal_dataloader.labels,wellcal_dataloader.probs[:,1],n_bins=15,strategy='quantile',pos_label=1)
+
+### calzone implementation
 calzone_reliability_H,calzone_confindence_H,bin_edge_H,bin_count_H = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=15, class_to_plot=1, is_equal_freq=False)
 calzone_reliability_C,calzone_confindence_C,bin_edge_C,bin_count_C = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=15, class_to_plot=1, is_equal_freq=True)
 
-print("Difference for uniform/histogram binning:")
-print("Reliability difference:", np.round(np.abs(scikit_reliability_H - calzone_reliability_H), 5))
-print("Confidence difference:", np.round(np.abs(scikit_confidence_H - calzone_confindence_H), 5))
-print("\nDifference for quantile/equal frequency binning:")
-print("Reliability difference:", np.round(np.abs(scikit_reliability_C - calzone_reliability_C), 5))
-print("Confidence difference:", np.round(np.abs(scikit_confidence_C - calzone_confindence_C), 5))
+###showing the difference between the two implementations
+print("Difference for equal-width binning:")
+print("Reliability difference:", np.round(np.abs(scikit_reliability_H - calzone_reliability_H), 4))
+print("Confidence difference:", np.round(np.abs(scikit_confidence_H - calzone_confindence_H), 4))
+print("\nDifference for equal-count binning:")
+print("Reliability difference:", np.round(np.abs(scikit_reliability_C - calzone_reliability_C), 4))
+print("Confidence difference:", np.round(np.abs(scikit_confidence_C - calzone_confindence_C), 4))
    @@ -132,15 +137,13 @@

    Reliability diagram 
    -Difference for uniform/histogram binning:
+Difference for equal-width binning:
 Reliability difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 Confidence difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 
-Difference for quantile/equal frequency binning:
-Reliability difference: [1.e-05 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00
- 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
-Confidence difference: [1.e-05 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00
- 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
+Difference for equal-count binning:
+Reliability difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
+Confidence difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]

    We can see that the calzone package return the same Reliability diagram as the sckit-learn package. We will move to test the expected calibration error.

    @@ -149,7 +152,7 @@

    Reliability diagram

    We will use mapie package to validate some of the metrics in calzone. Description of mapie can be found here.

    -
    [43]:
+
    [3]:
 
    
 
    
 
    from mapie.metrics import spiegelhalter_p_value,top_label_ece,spiegelhalter_statistic
@@ -157,6 +160,7 @@ 
    Expected calibration error and Z testcalzone_reliability_topclass_H,calzone_confindence_topclass_H,bin_edge_topclass_H,bin_count_topclass_H = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=15, class_to_plot=None, is_equal_freq=False)
 calzone_reliability_topclass_C,calzone_confindence_topclass_C,bin_edge_topclass_C,bin_count_topclass_C = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=15, class_to_plot=None, is_equal_freq=True)
 
+### compare MAPIE and calzone equal-width binning
 print("MAPIE topclass ECE-H:",top_label_ece(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins = 15,split_strategy='uniform'))
 print("calzone topclass ECE-H:",calculate_ece_mce(calzone_reliability_topclass_H,calzone_confindence_topclass_H,bin_count_topclass_H)[0])
 
    
@@ -172,10 +176,11 @@ 
    Expected calibration error and Z test
-
    [40]:
+
    [4]:
 
    
 
    
-
    print("MAPIE topclass ECE-C:",top_label_ece(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins = 15,split_strategy='quantile'))
+
    ### compare MAPIE and calzone equal-count binning
+print("MAPIE topclass ECE-C:",top_label_ece(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins = 15,split_strategy='quantile'))
 print("calzone topclass ECE-C:",calculate_ece_mce(calzone_reliability_topclass_C,calzone_confindence_topclass_C,bin_count_topclass_C)[0])
 
    
 
    
@@ -191,10 +196,11 @@ 
    Expected calibration error and Z testmapie package incorrectly calculates the p-value by using a one-sided test. Therefore, we will only compare the test statistic but not the p-value.
    
 
    
-
    [45]:
+
    [5]:
 
    
 
    
-
    print("MAPIE Z statistic", spiegelhalter_statistic(wellcal_dataloader.labels,wellcal_dataloader.probs[:,1]))
+
    ### compare the Z statistics
+print("MAPIE Z statistic", spiegelhalter_statistic(wellcal_dataloader.labels,wellcal_dataloader.probs[:,1]))
 print("calzone Z statistic", spiegelhalter_z_test(wellcal_dataloader.labels,wellcal_dataloader.probs)[0])
 
    
 
    
@@ -281,6 +287,12 @@ 
    HL test
 
    
 
    We see that the test statistics are the same. The R package doesn’t allow user input degree of freedom so the p-value is different as expected.
    
 
+
    
+
    reference
    
+
    Taquet, V., Blot, V., Morzadec, T., Lacombe, L., & Brunel, N. (2022). MAPIE: an open-source library for distribution-free uncertainty quantification. arXiv preprint arXiv:2207.12274.
    
+
    Pedregosa, F., Varoquaux, Ga”el, Gramfort, A., Michel, V., Thirion, B., Grisel, O., … others. (2011). Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12(Oct), 2825–2830.
    
+
    Lele, S. R., Keim, J. L., & Solymos, P. (2017). Resource selection (probability) functions for use-availability data. Package ‘ResourceSelection’, Version 0.3-2.
    
+
    
 
 
 
diff --git a/docs/build/html/notebooks/validation.ipynb b/docs/build/html/notebooks/validation.ipynb
index 20b05f7..0aa6e96 100644
--- a/docs/build/html/notebooks/validation.ipynb
+++ b/docs/build/html/notebooks/validation.ipynb
@@ -24,22 +24,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Difference for uniform/histogram binning:\n",
+      "Difference for equal-width binning:\n",
       "Reliability difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
       "Confidence difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
       "\n",
-      "Difference for quantile/equal frequency binning:\n",
-      "Reliability difference: [1.e-05 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00\n",
-      " 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]\n",
-      "Confidence difference: [1.e-05 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00\n",
-      " 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]\n"
+      "Difference for equal-count binning:\n",
+      "Reliability difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
+      "Confidence difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n"
      ]
     }
    ],
@@ -51,17 +49,21 @@
     "### loading the data\n",
     "wellcal_dataloader = data_loader(data_path=\"../../../example_data/simulated_welldata.csv\")\n",
     "\n",
+    "###scikit-learn implementation\n",
     "scikit_reliability_H,scikit_confidence_H = calibration_curve(wellcal_dataloader.labels,wellcal_dataloader.probs[:,1],n_bins=15,strategy='uniform',pos_label=1)\n",
     "scikit_reliability_C,scikit_confidence_C = calibration_curve(wellcal_dataloader.labels,wellcal_dataloader.probs[:,1],n_bins=15,strategy='quantile',pos_label=1)\n",
+    "\n",
+    "### calzone implementation\n",
     "calzone_reliability_H,calzone_confindence_H,bin_edge_H,bin_count_H = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=15, class_to_plot=1, is_equal_freq=False)\n",
     "calzone_reliability_C,calzone_confindence_C,bin_edge_C,bin_count_C = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=15, class_to_plot=1, is_equal_freq=True)\n",
     "\n",
-    "print(\"Difference for uniform/histogram binning:\")\n",
-    "print(\"Reliability difference:\", np.round(np.abs(scikit_reliability_H - calzone_reliability_H), 5))\n",
-    "print(\"Confidence difference:\", np.round(np.abs(scikit_confidence_H - calzone_confindence_H), 5))\n",
-    "print(\"\\nDifference for quantile/equal frequency binning:\")\n",
-    "print(\"Reliability difference:\", np.round(np.abs(scikit_reliability_C - calzone_reliability_C), 5))\n",
-    "print(\"Confidence difference:\", np.round(np.abs(scikit_confidence_C - calzone_confindence_C), 5))"
+    "###showing the difference between the two implementations\n",
+    "print(\"Difference for equal-width binning:\")\n",
+    "print(\"Reliability difference:\", np.round(np.abs(scikit_reliability_H - calzone_reliability_H), 4))\n",
+    "print(\"Confidence difference:\", np.round(np.abs(scikit_confidence_H - calzone_confindence_H), 4))\n",
+    "print(\"\\nDifference for equal-count binning:\")\n",
+    "print(\"Reliability difference:\", np.round(np.abs(scikit_reliability_C - calzone_reliability_C), 4))\n",
+    "print(\"Confidence difference:\", np.round(np.abs(scikit_confidence_C - calzone_confindence_C), 4))"
    ]
   },
   {
@@ -82,7 +84,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 43,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
@@ -100,13 +102,14 @@
     "calzone_reliability_topclass_H,calzone_confindence_topclass_H,bin_edge_topclass_H,bin_count_topclass_H = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=15, class_to_plot=None, is_equal_freq=False)\n",
     "calzone_reliability_topclass_C,calzone_confindence_topclass_C,bin_edge_topclass_C,bin_count_topclass_C = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=15, class_to_plot=None, is_equal_freq=True)\n",
     "\n",
+    "### compare MAPIE and calzone equal-width binning\n",
     "print(\"MAPIE topclass ECE-H:\",top_label_ece(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins = 15,split_strategy='uniform'))\n",
     "print(\"calzone topclass ECE-H:\",calculate_ece_mce(calzone_reliability_topclass_H,calzone_confindence_topclass_H,bin_count_topclass_H)[0])\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -119,6 +122,7 @@
     }
    ],
    "source": [
+    "### compare MAPIE and calzone equal-count binning\n",
     "print(\"MAPIE topclass ECE-C:\",top_label_ece(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins = 15,split_strategy='quantile'))\n",
     "print(\"calzone topclass ECE-C:\",calculate_ece_mce(calzone_reliability_topclass_C,calzone_confindence_topclass_C,bin_count_topclass_C)[0])\n"
    ]
@@ -132,7 +136,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -145,6 +149,7 @@
     }
    ],
    "source": [
+    "### compare the Z statistics\n",
     "print(\"MAPIE Z statistic\", spiegelhalter_statistic(wellcal_dataloader.labels,wellcal_dataloader.probs[:,1]))\n",
     "print(\"calzone Z statistic\", spiegelhalter_z_test(wellcal_dataloader.labels,wellcal_dataloader.probs)[0])"
    ]
@@ -233,6 +238,19 @@
    "source": [
     "We see that the test statistics are the same. The R package doesn't allow user input degree of freedom so the p-value is different as expected."
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## reference\n",
+    "\n",
+    "Taquet, V., Blot, V., Morzadec, T., Lacombe, L., & Brunel, N. (2022). MAPIE: an open-source library for distribution-free uncertainty quantification. arXiv preprint arXiv:2207.12274.\n",
+    "\n",
+    "Pedregosa, F., Varoquaux, Ga\"el, Gramfort, A., Michel, V., Thirion, B., Grisel, O., … others. (2011). Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12(Oct), 2825–2830.\n",
+    "\n",
+    "Lele, S. R., Keim, J. L., & Solymos, P. (2017). Resource selection (probability) functions for use-availability data. Package ‘ResourceSelection’, Version 0.3-2."
+   ]
   }
  ],
  "metadata": {
diff --git a/docs/build/html/objects.inv b/docs/build/html/objects.inv
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zlxgQ}FY8>-l#ZMpS{FXtdhy#`i-S-%(Dm1Emr|Ql;e0y)

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+
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@@ -969,7 +969,7 @@ Package pdftex.def Info: mytable.png  used on input line 787.
 
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+
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@@ -1017,7 +1017,7 @@ ine 990.
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-
+
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+
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+
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 Chapter 11.
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+
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 Chapter 13.
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+[63] [64] [65] [66]
+Chapter 14.
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+Overfull \hbox (73.01103pt too wide) in paragraph at lines 4723--4727
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+Package atveryend Info: Empty hook `BeforeClearDocument' on input line 5371.
+Package atveryend Info: Empty hook `AfterLastShipout' on input line 5371.
  (./calzone.aux)
-Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 5354.
-Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 5354.
+Package atveryend Info: Executing hook `AtVeryEndDocument' on input line 5371.
+Package atveryend Info: Executing hook `AtEndAfterFileList' on input line 5371.
 
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 Here is how much of TeX's memory you used:
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- 318468 string characters out of 5920377
- 675207 words of memory out of 5000000
- 33630 multiletter control sequences out of 15000+600000
+ 19008 strings out of 481239
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@@ -1301,10 +1301,10 @@ fonts/type1/public/tex-gyre/qtmri.pfb>
-Output written on calzone.pdf (88 pages, 1447119 bytes).
+Output written on calzone.pdf (88 pages, 1448130 bytes).
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diff --git a/docs/build/latex/calzone.out b/docs/build/latex/calzone.out
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diff --git a/docs/build/latex/calzone.tex b/docs/build/latex/calzone.tex
index 3d43080..34235b3 100644
--- a/docs/build/latex/calzone.tex
+++ b/docs/build/latex/calzone.tex
@@ -3338,24 +3338,28 @@ \section{Reliability diagram}
 \begin{sphinxuseclass}{nbinput}
 {
 \begin{sphinxVerbatim}[commandchars=\\\{\}]
-\llap{\color{nbsphinxin}[1]:\,\hspace{\fboxrule}\hspace{\fboxsep}}\PYG{k+kn}{from} \PYG{n+nn}{calzone}\PYG{n+nn}{.}\PYG{n+nn}{utils} \PYG{k+kn}{import} \PYG{n}{reliability\PYGZus{}diagram}\PYG{p}{,}\PYG{n}{data\PYGZus{}loader}
+\llap{\color{nbsphinxin}[2]:\,\hspace{\fboxrule}\hspace{\fboxsep}}\PYG{k+kn}{from} \PYG{n+nn}{calzone}\PYG{n+nn}{.}\PYG{n+nn}{utils} \PYG{k+kn}{import} \PYG{n}{reliability\PYGZus{}diagram}\PYG{p}{,}\PYG{n}{data\PYGZus{}loader}
 \PYG{k+kn}{from} \PYG{n+nn}{calzone}\PYG{n+nn}{.}\PYG{n+nn}{metrics} \PYG{k+kn}{import} \PYG{n}{calculate\PYGZus{}ece\PYGZus{}mce}\PYG{p}{,}\PYG{n}{hosmer\PYGZus{}lemeshow\PYGZus{}test}
 \PYG{k+kn}{import} \PYG{n+nn}{numpy} \PYG{k}{as} \PYG{n+nn}{np}
 \PYG{k+kn}{from} \PYG{n+nn}{sklearn}\PYG{n+nn}{.}\PYG{n+nn}{calibration} \PYG{k+kn}{import} \PYG{n}{calibration\PYGZus{}curve}
 \PYG{c+c1}{\PYGZsh{}\PYGZsh{}\PYGZsh{} loading the data}
 \PYG{n}{wellcal\PYGZus{}dataloader} \PYG{o}{=} \PYG{n}{data\PYGZus{}loader}\PYG{p}{(}\PYG{n}{data\PYGZus{}path}\PYG{o}{=}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{../../../example\PYGZus{}data/simulated\PYGZus{}welldata.csv}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
 
+\PYG{c+c1}{\PYGZsh{}\PYGZsh{}\PYGZsh{}scikit\PYGZhy{}learn implementation}
 \PYG{n}{scikit\PYGZus{}reliability\PYGZus{}H}\PYG{p}{,}\PYG{n}{scikit\PYGZus{}confidence\PYGZus{}H} \PYG{o}{=} \PYG{n}{calibration\PYGZus{}curve}\PYG{p}{(}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{labels}\PYG{p}{,}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{probs}\PYG{p}{[}\PYG{p}{:}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{,}\PYG{n}{n\PYGZus{}bins}\PYG{o}{=}\PYG{l+m+mi}{15}\PYG{p}{,}\PYG{n}{strategy}\PYG{o}{=}\PYG{l+s+s1}{\PYGZsq{}}\PYG{l+s+s1}{uniform}\PYG{l+s+s1}{\PYGZsq{}}\PYG{p}{,}\PYG{n}{pos\PYGZus{}label}\PYG{o}{=}\PYG{l+m+mi}{1}\PYG{p}{)}
 \PYG{n}{scikit\PYGZus{}reliability\PYGZus{}C}\PYG{p}{,}\PYG{n}{scikit\PYGZus{}confidence\PYGZus{}C} \PYG{o}{=} \PYG{n}{calibration\PYGZus{}curve}\PYG{p}{(}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{labels}\PYG{p}{,}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{probs}\PYG{p}{[}\PYG{p}{:}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{,}\PYG{n}{n\PYGZus{}bins}\PYG{o}{=}\PYG{l+m+mi}{15}\PYG{p}{,}\PYG{n}{strategy}\PYG{o}{=}\PYG{l+s+s1}{\PYGZsq{}}\PYG{l+s+s1}{quantile}\PYG{l+s+s1}{\PYGZsq{}}\PYG{p}{,}\PYG{n}{pos\PYGZus{}label}\PYG{o}{=}\PYG{l+m+mi}{1}\PYG{p}{)}
+
+\PYG{c+c1}{\PYGZsh{}\PYGZsh{}\PYGZsh{} calzone implementation}
 \PYG{n}{calzone\PYGZus{}reliability\PYGZus{}H}\PYG{p}{,}\PYG{n}{calzone\PYGZus{}confindence\PYGZus{}H}\PYG{p}{,}\PYG{n}{bin\PYGZus{}edge\PYGZus{}H}\PYG{p}{,}\PYG{n}{bin\PYGZus{}count\PYGZus{}H} \PYG{o}{=} \PYG{n}{reliability\PYGZus{}diagram}\PYG{p}{(}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{labels}\PYG{p}{,}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{probs}\PYG{p}{,}\PYG{n}{num\PYGZus{}bins}\PYG{o}{=}\PYG{l+m+mi}{15}\PYG{p}{,} \PYG{n}{class\PYGZus{}to\PYGZus{}plot}\PYG{o}{=}\PYG{l+m+mi}{1}\PYG{p}{,} \PYG{n}{is\PYGZus{}equal\PYGZus{}freq}\PYG{o}{=}\PYG{k+kc}{False}\PYG{p}{)}
 \PYG{n}{calzone\PYGZus{}reliability\PYGZus{}C}\PYG{p}{,}\PYG{n}{calzone\PYGZus{}confindence\PYGZus{}C}\PYG{p}{,}\PYG{n}{bin\PYGZus{}edge\PYGZus{}C}\PYG{p}{,}\PYG{n}{bin\PYGZus{}count\PYGZus{}C} \PYG{o}{=} \PYG{n}{reliability\PYGZus{}diagram}\PYG{p}{(}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{labels}\PYG{p}{,}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{probs}\PYG{p}{,}\PYG{n}{num\PYGZus{}bins}\PYG{o}{=}\PYG{l+m+mi}{15}\PYG{p}{,} \PYG{n}{class\PYGZus{}to\PYGZus{}plot}\PYG{o}{=}\PYG{l+m+mi}{1}\PYG{p}{,} \PYG{n}{is\PYGZus{}equal\PYGZus{}freq}\PYG{o}{=}\PYG{k+kc}{True}\PYG{p}{)}
 
-\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{Difference for uniform/histogram binning:}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
-\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{Reliability difference:}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,} \PYG{n}{np}\PYG{o}{.}\PYG{n}{round}\PYG{p}{(}\PYG{n}{np}\PYG{o}{.}\PYG{n}{abs}\PYG{p}{(}\PYG{n}{scikit\PYGZus{}reliability\PYGZus{}H} \PYG{o}{\PYGZhy{}} \PYG{n}{calzone\PYGZus{}reliability\PYGZus{}H}\PYG{p}{)}\PYG{p}{,} \PYG{l+m+mi}{5}\PYG{p}{)}\PYG{p}{)}
-\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{Confidence difference:}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,} \PYG{n}{np}\PYG{o}{.}\PYG{n}{round}\PYG{p}{(}\PYG{n}{np}\PYG{o}{.}\PYG{n}{abs}\PYG{p}{(}\PYG{n}{scikit\PYGZus{}confidence\PYGZus{}H} \PYG{o}{\PYGZhy{}} \PYG{n}{calzone\PYGZus{}confindence\PYGZus{}H}\PYG{p}{)}\PYG{p}{,} \PYG{l+m+mi}{5}\PYG{p}{)}\PYG{p}{)}
-\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+se}{\PYGZbs{}n}\PYG{l+s+s2}{Difference for quantile/equal frequency binning:}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
-\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{Reliability difference:}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,} \PYG{n}{np}\PYG{o}{.}\PYG{n}{round}\PYG{p}{(}\PYG{n}{np}\PYG{o}{.}\PYG{n}{abs}\PYG{p}{(}\PYG{n}{scikit\PYGZus{}reliability\PYGZus{}C} \PYG{o}{\PYGZhy{}} \PYG{n}{calzone\PYGZus{}reliability\PYGZus{}C}\PYG{p}{)}\PYG{p}{,} \PYG{l+m+mi}{5}\PYG{p}{)}\PYG{p}{)}
-\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{Confidence difference:}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,} \PYG{n}{np}\PYG{o}{.}\PYG{n}{round}\PYG{p}{(}\PYG{n}{np}\PYG{o}{.}\PYG{n}{abs}\PYG{p}{(}\PYG{n}{scikit\PYGZus{}confidence\PYGZus{}C} \PYG{o}{\PYGZhy{}} \PYG{n}{calzone\PYGZus{}confindence\PYGZus{}C}\PYG{p}{)}\PYG{p}{,} \PYG{l+m+mi}{5}\PYG{p}{)}\PYG{p}{)}
+\PYG{c+c1}{\PYGZsh{}\PYGZsh{}\PYGZsh{}showing the difference between the two implementations}
+\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{Difference for equal\PYGZhy{}width binning:}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
+\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{Reliability difference:}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,} \PYG{n}{np}\PYG{o}{.}\PYG{n}{round}\PYG{p}{(}\PYG{n}{np}\PYG{o}{.}\PYG{n}{abs}\PYG{p}{(}\PYG{n}{scikit\PYGZus{}reliability\PYGZus{}H} \PYG{o}{\PYGZhy{}} \PYG{n}{calzone\PYGZus{}reliability\PYGZus{}H}\PYG{p}{)}\PYG{p}{,} \PYG{l+m+mi}{4}\PYG{p}{)}\PYG{p}{)}
+\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{Confidence difference:}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,} \PYG{n}{np}\PYG{o}{.}\PYG{n}{round}\PYG{p}{(}\PYG{n}{np}\PYG{o}{.}\PYG{n}{abs}\PYG{p}{(}\PYG{n}{scikit\PYGZus{}confidence\PYGZus{}H} \PYG{o}{\PYGZhy{}} \PYG{n}{calzone\PYGZus{}confindence\PYGZus{}H}\PYG{p}{)}\PYG{p}{,} \PYG{l+m+mi}{4}\PYG{p}{)}\PYG{p}{)}
+\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+se}{\PYGZbs{}n}\PYG{l+s+s2}{Difference for equal\PYGZhy{}count binning:}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{)}
+\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{Reliability difference:}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,} \PYG{n}{np}\PYG{o}{.}\PYG{n}{round}\PYG{p}{(}\PYG{n}{np}\PYG{o}{.}\PYG{n}{abs}\PYG{p}{(}\PYG{n}{scikit\PYGZus{}reliability\PYGZus{}C} \PYG{o}{\PYGZhy{}} \PYG{n}{calzone\PYGZus{}reliability\PYGZus{}C}\PYG{p}{)}\PYG{p}{,} \PYG{l+m+mi}{4}\PYG{p}{)}\PYG{p}{)}
+\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{Confidence difference:}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,} \PYG{n}{np}\PYG{o}{.}\PYG{n}{round}\PYG{p}{(}\PYG{n}{np}\PYG{o}{.}\PYG{n}{abs}\PYG{p}{(}\PYG{n}{scikit\PYGZus{}confidence\PYGZus{}C} \PYG{o}{\PYGZhy{}} \PYG{n}{calzone\PYGZus{}confindence\PYGZus{}C}\PYG{p}{)}\PYG{p}{,} \PYG{l+m+mi}{4}\PYG{p}{)}\PYG{p}{)}
 \end{sphinxVerbatim}
 }
 
@@ -3374,15 +3378,13 @@ \section{Reliability diagram}
 
 
 \begin{sphinxVerbatim}[commandchars=\\\{\}]
-Difference for uniform/histogram binning:
+Difference for equal-width binning:
 Reliability difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 Confidence difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 
-Difference for quantile/equal frequency binning:
-Reliability difference: [1.e-05 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00
- 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
-Confidence difference: [1.e-05 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00
- 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]
+Difference for equal-count binning:
+Reliability difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
+Confidence difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]
 \end{sphinxVerbatim}
 
 
@@ -3405,11 +3407,12 @@ \section{Expected calibration error and Z test}
 \begin{sphinxuseclass}{nbinput}
 {
 \begin{sphinxVerbatim}[commandchars=\\\{\}]
-\llap{\color{nbsphinxin}[43]:\,\hspace{\fboxrule}\hspace{\fboxsep}}\PYG{k+kn}{from} \PYG{n+nn}{mapie}\PYG{n+nn}{.}\PYG{n+nn}{metrics} \PYG{k+kn}{import} \PYG{n}{spiegelhalter\PYGZus{}p\PYGZus{}value}\PYG{p}{,}\PYG{n}{top\PYGZus{}label\PYGZus{}ece}\PYG{p}{,}\PYG{n}{spiegelhalter\PYGZus{}statistic}
+\llap{\color{nbsphinxin}[3]:\,\hspace{\fboxrule}\hspace{\fboxsep}}\PYG{k+kn}{from} \PYG{n+nn}{mapie}\PYG{n+nn}{.}\PYG{n+nn}{metrics} \PYG{k+kn}{import} \PYG{n}{spiegelhalter\PYGZus{}p\PYGZus{}value}\PYG{p}{,}\PYG{n}{top\PYGZus{}label\PYGZus{}ece}\PYG{p}{,}\PYG{n}{spiegelhalter\PYGZus{}statistic}
 \PYG{k+kn}{from} \PYG{n+nn}{calzone}\PYG{n+nn}{.}\PYG{n+nn}{metrics} \PYG{k+kn}{import} \PYG{n}{spiegelhalter\PYGZus{}z\PYGZus{}test}
 \PYG{n}{calzone\PYGZus{}reliability\PYGZus{}topclass\PYGZus{}H}\PYG{p}{,}\PYG{n}{calzone\PYGZus{}confindence\PYGZus{}topclass\PYGZus{}H}\PYG{p}{,}\PYG{n}{bin\PYGZus{}edge\PYGZus{}topclass\PYGZus{}H}\PYG{p}{,}\PYG{n}{bin\PYGZus{}count\PYGZus{}topclass\PYGZus{}H} \PYG{o}{=} \PYG{n}{reliability\PYGZus{}diagram}\PYG{p}{(}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{labels}\PYG{p}{,}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{probs}\PYG{p}{,}\PYG{n}{num\PYGZus{}bins}\PYG{o}{=}\PYG{l+m+mi}{15}\PYG{p}{,} \PYG{n}{class\PYGZus{}to\PYGZus{}plot}\PYG{o}{=}\PYG{k+kc}{None}\PYG{p}{,} \PYG{n}{is\PYGZus{}equal\PYGZus{}freq}\PYG{o}{=}\PYG{k+kc}{False}\PYG{p}{)}
 \PYG{n}{calzone\PYGZus{}reliability\PYGZus{}topclass\PYGZus{}C}\PYG{p}{,}\PYG{n}{calzone\PYGZus{}confindence\PYGZus{}topclass\PYGZus{}C}\PYG{p}{,}\PYG{n}{bin\PYGZus{}edge\PYGZus{}topclass\PYGZus{}C}\PYG{p}{,}\PYG{n}{bin\PYGZus{}count\PYGZus{}topclass\PYGZus{}C} \PYG{o}{=} \PYG{n}{reliability\PYGZus{}diagram}\PYG{p}{(}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{labels}\PYG{p}{,}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{probs}\PYG{p}{,}\PYG{n}{num\PYGZus{}bins}\PYG{o}{=}\PYG{l+m+mi}{15}\PYG{p}{,} \PYG{n}{class\PYGZus{}to\PYGZus{}plot}\PYG{o}{=}\PYG{k+kc}{None}\PYG{p}{,} \PYG{n}{is\PYGZus{}equal\PYGZus{}freq}\PYG{o}{=}\PYG{k+kc}{True}\PYG{p}{)}
 
+\PYG{c+c1}{\PYGZsh{}\PYGZsh{}\PYGZsh{} compare MAPIE and calzone equal\PYGZhy{}width binning}
 \PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{MAPIE topclass ECE\PYGZhy{}H:}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,}\PYG{n}{top\PYGZus{}label\PYGZus{}ece}\PYG{p}{(}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{labels}\PYG{p}{,}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{probs}\PYG{p}{,}\PYG{n}{num\PYGZus{}bins} \PYG{o}{=} \PYG{l+m+mi}{15}\PYG{p}{,}\PYG{n}{split\PYGZus{}strategy}\PYG{o}{=}\PYG{l+s+s1}{\PYGZsq{}}\PYG{l+s+s1}{uniform}\PYG{l+s+s1}{\PYGZsq{}}\PYG{p}{)}\PYG{p}{)}
 \PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{calzone topclass ECE\PYGZhy{}H:}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,}\PYG{n}{calculate\PYGZus{}ece\PYGZus{}mce}\PYG{p}{(}\PYG{n}{calzone\PYGZus{}reliability\PYGZus{}topclass\PYGZus{}H}\PYG{p}{,}\PYG{n}{calzone\PYGZus{}confindence\PYGZus{}topclass\PYGZus{}H}\PYG{p}{,}\PYG{n}{bin\PYGZus{}count\PYGZus{}topclass\PYGZus{}H}\PYG{p}{)}\PYG{p}{[}\PYG{l+m+mi}{0}\PYG{p}{]}\PYG{p}{)}
 
@@ -3446,7 +3449,8 @@ \section{Expected calibration error and Z test}
 \begin{sphinxuseclass}{nbinput}
 {
 \begin{sphinxVerbatim}[commandchars=\\\{\}]
-\llap{\color{nbsphinxin}[40]:\,\hspace{\fboxrule}\hspace{\fboxsep}}\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{MAPIE topclass ECE\PYGZhy{}C:}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,}\PYG{n}{top\PYGZus{}label\PYGZus{}ece}\PYG{p}{(}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{labels}\PYG{p}{,}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{probs}\PYG{p}{,}\PYG{n}{num\PYGZus{}bins} \PYG{o}{=} \PYG{l+m+mi}{15}\PYG{p}{,}\PYG{n}{split\PYGZus{}strategy}\PYG{o}{=}\PYG{l+s+s1}{\PYGZsq{}}\PYG{l+s+s1}{quantile}\PYG{l+s+s1}{\PYGZsq{}}\PYG{p}{)}\PYG{p}{)}
+\llap{\color{nbsphinxin}[4]:\,\hspace{\fboxrule}\hspace{\fboxsep}}\PYG{c+c1}{\PYGZsh{}\PYGZsh{}\PYGZsh{} compare MAPIE and calzone equal\PYGZhy{}count binning}
+\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{MAPIE topclass ECE\PYGZhy{}C:}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,}\PYG{n}{top\PYGZus{}label\PYGZus{}ece}\PYG{p}{(}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{labels}\PYG{p}{,}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{probs}\PYG{p}{,}\PYG{n}{num\PYGZus{}bins} \PYG{o}{=} \PYG{l+m+mi}{15}\PYG{p}{,}\PYG{n}{split\PYGZus{}strategy}\PYG{o}{=}\PYG{l+s+s1}{\PYGZsq{}}\PYG{l+s+s1}{quantile}\PYG{l+s+s1}{\PYGZsq{}}\PYG{p}{)}\PYG{p}{)}
 \PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{calzone topclass ECE\PYGZhy{}C:}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,}\PYG{n}{calculate\PYGZus{}ece\PYGZus{}mce}\PYG{p}{(}\PYG{n}{calzone\PYGZus{}reliability\PYGZus{}topclass\PYGZus{}C}\PYG{p}{,}\PYG{n}{calzone\PYGZus{}confindence\PYGZus{}topclass\PYGZus{}C}\PYG{p}{,}\PYG{n}{bin\PYGZus{}count\PYGZus{}topclass\PYGZus{}C}\PYG{p}{)}\PYG{p}{[}\PYG{l+m+mi}{0}\PYG{p}{]}\PYG{p}{)}
 
 \end{sphinxVerbatim}
@@ -3485,7 +3489,8 @@ \section{Expected calibration error and Z test}
 \begin{sphinxuseclass}{nbinput}
 {
 \begin{sphinxVerbatim}[commandchars=\\\{\}]
-\llap{\color{nbsphinxin}[45]:\,\hspace{\fboxrule}\hspace{\fboxsep}}\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{MAPIE Z statistic}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,} \PYG{n}{spiegelhalter\PYGZus{}statistic}\PYG{p}{(}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{labels}\PYG{p}{,}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{probs}\PYG{p}{[}\PYG{p}{:}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{)}\PYG{p}{)}
+\llap{\color{nbsphinxin}[5]:\,\hspace{\fboxrule}\hspace{\fboxsep}}\PYG{c+c1}{\PYGZsh{}\PYGZsh{}\PYGZsh{} compare the Z statistics}
+\PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{MAPIE Z statistic}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,} \PYG{n}{spiegelhalter\PYGZus{}statistic}\PYG{p}{(}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{labels}\PYG{p}{,}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{probs}\PYG{p}{[}\PYG{p}{:}\PYG{p}{,}\PYG{l+m+mi}{1}\PYG{p}{]}\PYG{p}{)}\PYG{p}{)}
 \PYG{n+nb}{print}\PYG{p}{(}\PYG{l+s+s2}{\PYGZdq{}}\PYG{l+s+s2}{calzone Z statistic}\PYG{l+s+s2}{\PYGZdq{}}\PYG{p}{,} \PYG{n}{spiegelhalter\PYGZus{}z\PYGZus{}test}\PYG{p}{(}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{labels}\PYG{p}{,}\PYG{n}{wellcal\PYGZus{}dataloader}\PYG{o}{.}\PYG{n}{probs}\PYG{p}{)}\PYG{p}{[}\PYG{l+m+mi}{0}\PYG{p}{]}\PYG{p}{)}
 \end{sphinxVerbatim}
 }
@@ -3644,6 +3649,18 @@ \section{HL test}
 \sphinxAtStartPar
 We see that the test statistics are the same. The R package doesn’t allow user input degree of freedom so the p\sphinxhyphen{}value is different as expected.
 
+
+\section{reference}
+\label{\detokenize{notebooks/validation:reference}}
+\sphinxAtStartPar
+Taquet, V., Blot, V., Morzadec, T., Lacombe, L., \& Brunel, N. (2022). MAPIE: an open\sphinxhyphen{}source library for distribution\sphinxhyphen{}free uncertainty quantification. arXiv preprint arXiv:2207.12274.
+
+\sphinxAtStartPar
+Pedregosa, F., Varoquaux, Ga”el, Gramfort, A., Michel, V., Thirion, B., Grisel, O., … others. (2011). Scikit\sphinxhyphen{}learn: Machine learning in Python. Journal of Machine Learning Research, 12(Oct), 2825\textendash{}2830.
+
+\sphinxAtStartPar
+Lele, S. R., Keim, J. L., \& Solymos, P. (2017). Resource selection (probability) functions for use\sphinxhyphen{}availability data. Package ‘ResourceSelection’, Version 0.3\sphinxhyphen{}2.
+
 \sphinxstepscope
 
 
diff --git a/docs/build/latex/calzone.toc b/docs/build/latex/calzone.toc
index c846221..fd33d62 100644
--- a/docs/build/latex/calzone.toc
+++ b/docs/build/latex/calzone.toc
@@ -54,6 +54,7 @@
 \contentsline {section}{\numberline {13.1}Reliability diagram}{63}{section.13.1}%
 \contentsline {section}{\numberline {13.2}Expected calibration error and Z test}{64}{section.13.2}%
 \contentsline {section}{\numberline {13.3}HL test}{65}{section.13.3}%
+\contentsline {section}{\numberline {13.4}reference}{66}{section.13.4}%
 \contentsline {chapter}{\numberline {14}calzone}{67}{chapter.14}%
 \contentsline {section}{\numberline {14.1}calzone package}{67}{section.14.1}%
 \contentsline {subsection}{\numberline {14.1.1}Submodules}{67}{subsection.14.1.1}%
diff --git a/docs/source/notebooks/validation.ipynb b/docs/source/notebooks/validation.ipynb
index 20b05f7..0aa6e96 100644
--- a/docs/source/notebooks/validation.ipynb
+++ b/docs/source/notebooks/validation.ipynb
@@ -24,22 +24,20 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "Difference for uniform/histogram binning:\n",
+      "Difference for equal-width binning:\n",
       "Reliability difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
       "Confidence difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
       "\n",
-      "Difference for quantile/equal frequency binning:\n",
-      "Reliability difference: [1.e-05 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00\n",
-      " 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]\n",
-      "Confidence difference: [1.e-05 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00\n",
-      " 0.e+00 0.e+00 0.e+00 0.e+00 0.e+00]\n"
+      "Difference for equal-count binning:\n",
+      "Reliability difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n",
+      "Confidence difference: [0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.]\n"
      ]
     }
    ],
@@ -51,17 +49,21 @@
     "### loading the data\n",
     "wellcal_dataloader = data_loader(data_path=\"../../../example_data/simulated_welldata.csv\")\n",
     "\n",
+    "###scikit-learn implementation\n",
     "scikit_reliability_H,scikit_confidence_H = calibration_curve(wellcal_dataloader.labels,wellcal_dataloader.probs[:,1],n_bins=15,strategy='uniform',pos_label=1)\n",
     "scikit_reliability_C,scikit_confidence_C = calibration_curve(wellcal_dataloader.labels,wellcal_dataloader.probs[:,1],n_bins=15,strategy='quantile',pos_label=1)\n",
+    "\n",
+    "### calzone implementation\n",
     "calzone_reliability_H,calzone_confindence_H,bin_edge_H,bin_count_H = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=15, class_to_plot=1, is_equal_freq=False)\n",
     "calzone_reliability_C,calzone_confindence_C,bin_edge_C,bin_count_C = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=15, class_to_plot=1, is_equal_freq=True)\n",
     "\n",
-    "print(\"Difference for uniform/histogram binning:\")\n",
-    "print(\"Reliability difference:\", np.round(np.abs(scikit_reliability_H - calzone_reliability_H), 5))\n",
-    "print(\"Confidence difference:\", np.round(np.abs(scikit_confidence_H - calzone_confindence_H), 5))\n",
-    "print(\"\\nDifference for quantile/equal frequency binning:\")\n",
-    "print(\"Reliability difference:\", np.round(np.abs(scikit_reliability_C - calzone_reliability_C), 5))\n",
-    "print(\"Confidence difference:\", np.round(np.abs(scikit_confidence_C - calzone_confindence_C), 5))"
+    "###showing the difference between the two implementations\n",
+    "print(\"Difference for equal-width binning:\")\n",
+    "print(\"Reliability difference:\", np.round(np.abs(scikit_reliability_H - calzone_reliability_H), 4))\n",
+    "print(\"Confidence difference:\", np.round(np.abs(scikit_confidence_H - calzone_confindence_H), 4))\n",
+    "print(\"\\nDifference for equal-count binning:\")\n",
+    "print(\"Reliability difference:\", np.round(np.abs(scikit_reliability_C - calzone_reliability_C), 4))\n",
+    "print(\"Confidence difference:\", np.round(np.abs(scikit_confidence_C - calzone_confindence_C), 4))"
    ]
   },
   {
@@ -82,7 +84,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 43,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
@@ -100,13 +102,14 @@
     "calzone_reliability_topclass_H,calzone_confindence_topclass_H,bin_edge_topclass_H,bin_count_topclass_H = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=15, class_to_plot=None, is_equal_freq=False)\n",
     "calzone_reliability_topclass_C,calzone_confindence_topclass_C,bin_edge_topclass_C,bin_count_topclass_C = reliability_diagram(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins=15, class_to_plot=None, is_equal_freq=True)\n",
     "\n",
+    "### compare MAPIE and calzone equal-width binning\n",
     "print(\"MAPIE topclass ECE-H:\",top_label_ece(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins = 15,split_strategy='uniform'))\n",
     "print(\"calzone topclass ECE-H:\",calculate_ece_mce(calzone_reliability_topclass_H,calzone_confindence_topclass_H,bin_count_topclass_H)[0])\n"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -119,6 +122,7 @@
     }
    ],
    "source": [
+    "### compare MAPIE and calzone equal-count binning\n",
     "print(\"MAPIE topclass ECE-C:\",top_label_ece(wellcal_dataloader.labels,wellcal_dataloader.probs,num_bins = 15,split_strategy='quantile'))\n",
     "print(\"calzone topclass ECE-C:\",calculate_ece_mce(calzone_reliability_topclass_C,calzone_confindence_topclass_C,bin_count_topclass_C)[0])\n"
    ]
@@ -132,7 +136,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {
@@ -145,6 +149,7 @@
     }
    ],
    "source": [
+    "### compare the Z statistics\n",
     "print(\"MAPIE Z statistic\", spiegelhalter_statistic(wellcal_dataloader.labels,wellcal_dataloader.probs[:,1]))\n",
     "print(\"calzone Z statistic\", spiegelhalter_z_test(wellcal_dataloader.labels,wellcal_dataloader.probs)[0])"
    ]
@@ -233,6 +238,19 @@
    "source": [
     "We see that the test statistics are the same. The R package doesn't allow user input degree of freedom so the p-value is different as expected."
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## reference\n",
+    "\n",
+    "Taquet, V., Blot, V., Morzadec, T., Lacombe, L., & Brunel, N. (2022). MAPIE: an open-source library for distribution-free uncertainty quantification. arXiv preprint arXiv:2207.12274.\n",
+    "\n",
+    "Pedregosa, F., Varoquaux, Ga\"el, Gramfort, A., Michel, V., Thirion, B., Grisel, O., … others. (2011). Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 12(Oct), 2825–2830.\n",
+    "\n",
+    "Lele, S. R., Keim, J. L., & Solymos, P. (2017). Resource selection (probability) functions for use-availability data. Package ‘ResourceSelection’, Version 0.3-2."
+   ]
   }
  ],
  "metadata": {