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1 | | -""" |
| 1 | +r""" |
2 | 2 | ======================================= |
3 | 3 | Robust vs Empirical covariance estimate |
4 | 4 | ======================================= |
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12 | 12 | ---------------------------------------- |
13 | 13 | The Minimum Covariance Determinant estimator is a robust, high-breakdown point |
14 | 14 | (i.e. it can be used to estimate the covariance matrix of highly contaminated |
15 | | -datasets, up to :math:`\\frac{n_samples - n_features-1}{2}` outliers) estimator of |
16 | | -covariance. The idea is to find :math:`\\frac{n_samples+n_features+1}{2}` |
| 15 | +datasets, up to |
| 16 | +:math:`\frac{n_\text{samples} - n_\text{features}-1}{2}` outliers) estimator of |
| 17 | +covariance. The idea is to find |
| 18 | +:math:`\frac{n_\text{samples} + n_\text{features}+1}{2}` |
17 | 19 | observations whose empirical covariance has the smallest determinant, yielding |
18 | 20 | a "pure" subset of observations from which to compute standards estimates of |
19 | 21 | location and covariance. After a correction step aiming at compensating the |
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31 | 33 |
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32 | 34 | - The mean and the empirical covariance of the full dataset, which break |
33 | 35 | down as soon as there are outliers in the data set |
34 | | -- The robust MCD, that has a low error provided n_samples > 5 * n_features |
| 36 | +- The robust MCD, that has a low error provided |
| 37 | + :math:`n_\text{samples} > 5n_\text{features}` |
35 | 38 | - The mean and the empirical covariance of the observations that are known |
36 | 39 | to be good ones. This can be considered as a "perfect" MCD estimation, |
37 | 40 | so one can trust our implementation by comparing to this case. |
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