Pushing the docs to dev/ for branch: master, commit 7bc20c0e5013bd79f257c0ea5abdf6d6d8d8f269

Author: sklearn-ci

dev/_downloads/auto_examples_jupyter.zip

@@ -15,7 +15,7 @@
       "cell_type": "markdown",
       "metadata": {},
       "source": [
-        "\n# Robust vs Empirical covariance estimate\n\n\nThe usual covariance maximum likelihood estimate is very sensitive to the\npresence of outliers in the data set. In such a case, it would be better to\nuse a robust estimator of covariance to guarantee that the estimation is\nresistant to \"erroneous\" observations in the data set.\n\nMinimum Covariance Determinant Estimator\n----------------------------------------\nThe Minimum Covariance Determinant estimator is a robust, high-breakdown point\n(i.e. it can be used to estimate the covariance matrix of highly contaminated\ndatasets, up to\n$\\frac{n_\\text{samples} - n_\\text{features}-1}{2}$ outliers) estimator of\ncovariance. The idea is to find\n$\\frac{n_\\text{samples} + n_\\text{features}+1}{2}$\nobservations whose empirical covariance has the smallest determinant, yielding\na \"pure\" subset of observations from which to compute standards estimates of\nlocation and covariance. After a correction step aiming at compensating the\nfact that the estimates were learned from only a portion of the initial data,\nwe end up with robust estimates of the data set ___location and covariance.\n\nThe Minimum Covariance Determinant estimator (MCD) has been introduced by\nP.J.Rousseuw in [1]_.\n\nEvaluation\n----------\nIn this example, we compare the estimation errors that are made when using\nvarious types of ___location and covariance estimates on contaminated Gaussian\ndistributed data sets:\n\n- The mean and the empirical covariance of the full dataset, which break\n  down as soon as there are outliers in the data set\n- The robust MCD, that has a low error provided\n  $n_\\text{samples} > 5n_\\text{features}$\n- The mean and the empirical covariance of the observations that are known\n  to be good ones. This can be considered as a \"perfect\" MCD estimation,\n  so one can trust our implementation by comparing to this case.\n\n\nReferences\n----------\n.. [1] P. J. Rousseeuw. Least median of squares regression. Journal of American\n    Statistical Ass., 79:871, 1984.\n.. [2] Johanna Hardin, David M Rocke. The distribution of robust distances.\n    Journal of Computational and Graphical Statistics. December 1, 2005,\n    14(4): 928-946.\n.. [3] Zoubir A., Koivunen V., Chakhchoukh Y. and Muma M. (2012). Robust\n    estimation in signal processing: A tutorial-style treatment of\n    fundamental concepts. IEEE Signal Processing Magazine 29(4), 61-80.\n\n\n"
+        "\n# Robust vs Empirical covariance estimate\n\n\nThe usual covariance maximum likelihood estimate is very sensitive to the\npresence of outliers in the data set. In such a case, it would be better to\nuse a robust estimator of covariance to guarantee that the estimation is\nresistant to \"erroneous\" observations in the data set. [1]_, [2]_\n\nMinimum Covariance Determinant Estimator\n----------------------------------------\nThe Minimum Covariance Determinant estimator is a robust, high-breakdown point\n(i.e. it can be used to estimate the covariance matrix of highly contaminated\ndatasets, up to\n$\\frac{n_\\text{samples} - n_\\text{features}-1}{2}$ outliers) estimator of\ncovariance. The idea is to find\n$\\frac{n_\\text{samples} + n_\\text{features}+1}{2}$\nobservations whose empirical covariance has the smallest determinant, yielding\na \"pure\" subset of observations from which to compute standards estimates of\nlocation and covariance. After a correction step aiming at compensating the\nfact that the estimates were learned from only a portion of the initial data,\nwe end up with robust estimates of the data set ___location and covariance.\n\nThe Minimum Covariance Determinant estimator (MCD) has been introduced by\nP.J.Rousseuw in [3]_.\n\nEvaluation\n----------\nIn this example, we compare the estimation errors that are made when using\nvarious types of ___location and covariance estimates on contaminated Gaussian\ndistributed data sets:\n\n- The mean and the empirical covariance of the full dataset, which break\n  down as soon as there are outliers in the data set\n- The robust MCD, that has a low error provided\n  $n_\\text{samples} > 5n_\\text{features}$\n- The mean and the empirical covariance of the observations that are known\n  to be good ones. This can be considered as a \"perfect\" MCD estimation,\n  so one can trust our implementation by comparing to this case.\n\n\nReferences\n----------\n.. [1] Johanna Hardin, David M Rocke. The distribution of robust distances.\n    Journal of Computational and Graphical Statistics. December 1, 2005,\n    14(4): 928-946.\n.. [2] Zoubir A., Koivunen V., Chakhchoukh Y. and Muma M. (2012). Robust\n    estimation in signal processing: A tutorial-style treatment of\n    fundamental concepts. IEEE Signal Processing Magazine 29(4), 61-80.\n.. [3] P. J. Rousseeuw. Least median of squares regression. Journal of American\n    Statistical Ass., 79:871, 1984.\n\n\n"
       ]
     },
     {

dev/_downloads/auto_examples_python.zip

@@ -6,7 +6,7 @@
 The usual covariance maximum likelihood estimate is very sensitive to the
 presence of outliers in the data set. In such a case, it would be better to
 use a robust estimator of covariance to guarantee that the estimation is
-resistant to "erroneous" observations in the data set.
+resistant to "erroneous" observations in the data set. [1]_, [2]_
 
 Minimum Covariance Determinant Estimator
 ----------------------------------------
@@ -23,7 +23,7 @@
 we end up with robust estimates of the data set ___location and covariance.
 
 The Minimum Covariance Determinant estimator (MCD) has been introduced by
-P.J.Rousseuw in [1]_.
+P.J.Rousseuw in [3]_.
 
 Evaluation
 ----------
@@ -42,14 +42,14 @@
 
 References
 ----------
-.. [1] P. J. Rousseeuw. Least median of squares regression. Journal of American
-    Statistical Ass., 79:871, 1984.
-.. [2] Johanna Hardin, David M Rocke. The distribution of robust distances.
+.. [1] Johanna Hardin, David M Rocke. The distribution of robust distances.
     Journal of Computational and Graphical Statistics. December 1, 2005,
     14(4): 928-946.
-.. [3] Zoubir A., Koivunen V., Chakhchoukh Y. and Muma M. (2012). Robust
+.. [2] Zoubir A., Koivunen V., Chakhchoukh Y. and Muma M. (2012). Robust
     estimation in signal processing: A tutorial-style treatment of
     fundamental concepts. IEEE Signal Processing Magazine 29(4), 61-80.
+.. [3] P. J. Rousseeuw. Least median of squares regression. Journal of American
+    Statistical Ass., 79:871, 1984.
 
 """
 print(__doc__)