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02/23/12 22:47:51 (2 years ago)
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janezd <janez.demsar@…>
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Polished documentation for logistic regression

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  • docs/reference/rst/Orange.classification.logreg.rst

    r10246 r10346  
    99******************************** 
    1010 
    11 `Logistic regression <http://en.wikipedia.org/wiki/Logistic_regression>`_ 
    12 is a statistical classification methods that fits data to a logistic 
    13 function. Orange's implementation of algorithm 
    14 can handle various anomalies in features, such as constant variables and 
    15 singularities, that could make direct fitting of logistic regression almost 
    16 impossible. Stepwise logistic regression, which iteratively selects the most 
    17 informative features, is also supported. 
     11`Logistic regression 
     12<http://en.wikipedia.org/wiki/Logistic_regression>`_ is a statistical 
     13classification method that fits data to a logistic function. Orange 
     14provides various enhancement of the method, such as stepwise selection 
     15of variables and handling of constant variables and singularities. 
    1816 
    1917.. autoclass:: LogRegLearner 
     
    4442        that beta coefficients differ from 0.0. The probability is 
    4543        computed from squared Wald Z statistics that is distributed with 
    46         Chi-Square distribution. 
     44        chi-squared distribution. 
    4745 
    4846    .. attribute :: likelihood 
    4947 
    50         The probability of the sample (ie. learning examples) observed on 
    51         the basis of the derived model, as a function of the regression 
    52         parameters. 
     48        The likelihood of the sample (ie. learning data) given the 
     49        fitted model. 
    5350 
    5451    .. attribute :: fit_status 
    5552 
    56         Tells how the model fitting ended - either regularly 
    57         (:obj:`LogRegFitter.OK`), or it was interrupted due to one of beta 
    58         coefficients escaping towards infinity (:obj:`LogRegFitter.Infinity`) 
    59         or since the values didn't converge (:obj:`LogRegFitter.Divergence`). The 
    60         value tells about the classifier's "reliability"; the classifier 
    61         itself is useful in either case. 
     53        Tells how the model fitting ended, either regularly 
     54        (:obj:`LogRegFitter.OK`), or it was interrupted due to one of 
     55        beta coefficients escaping towards infinity 
     56        (:obj:`LogRegFitter.Infinity`) or since the values did not 
     57        converge (:obj:`LogRegFitter.Divergence`). 
     58 
     59        Although the model is functional in all cases, it is 
     60        recommended to inspect whether the coefficients of the model 
     61        if the fitting did not end normally. 
    6262 
    6363    .. method:: __call__(instance, result_type) 
     
    7878.. class:: LogRegFitter 
    7979 
    80     :obj:`LogRegFitter` is the abstract base class for logistic fitters. It 
    81     defines the form of call operator and the constants denoting its 
    82     (un)success: 
    83  
    84     .. attribute:: OK 
    85  
    86         Fitter succeeded to converge to the optimal fit. 
    87  
    88     .. attribute:: Infinity 
    89  
    90         Fitter failed due to one or more beta coefficients escaping towards infinity. 
    91  
    92     .. attribute:: Divergence 
    93  
    94         Beta coefficients failed to converge, but none of beta coefficients escaped. 
    95  
    96     .. attribute:: Constant 
    97  
    98         There is a constant attribute that causes the matrix to be singular. 
    99  
    100     .. attribute:: Singularity 
    101  
    102         The matrix is singular. 
     80    :obj:`LogRegFitter` is the abstract base class for logistic 
     81    fitters. Fitters can be called with a data table and return a 
     82    vector of coefficients and the corresponding statistics, or a 
     83    status signifying an error. The possible statuses are 
     84 
     85    .. attribute:: OK 
     86 
     87        Optimization converged 
     88 
     89    .. attribute:: Infinity 
     90 
     91        Optimization failed due to one or more beta coefficients 
     92        escaping towards infinity. 
     93 
     94    .. attribute:: Divergence 
     95 
     96        Beta coefficients failed to converge, but without any of beta 
     97        coefficients escaping toward infinity. 
     98 
     99    .. attribute:: Constant 
     100 
     101        The data is singular due to a constant variable. 
     102 
     103    .. attribute:: Singularity 
     104 
     105        The data is singular. 
    103106 
    104107 
    105108    .. method:: __call__(data, weight_id) 
    106109 
    107         Performs the fitting. There can be two different cases: either 
    108         the fitting succeeded to find a set of beta coefficients (although 
    109         possibly with difficulties) or the fitting failed altogether. The 
    110         two cases return different results. 
    111  
    112         `(status, beta, beta_se, likelihood)` 
    113             The fitter managed to fit the model. The first element of 
    114             the tuple, result, tells about the problems occurred; it can 
    115             be either :obj:`OK`, :obj:`Infinity` or :obj:`Divergence`. In 
    116             the latter cases, returned values may still be useful for 
    117             making predictions, but it's recommended that you inspect 
    118             the coefficients and their errors and make your decision 
    119             whether to use the model or not. 
    120  
    121         `(status, attribute)` 
    122             The fitter failed and the returned attribute is responsible 
    123             for it. The type of failure is reported in status, which 
    124             can be either :obj:`Constant` or :obj:`Singularity`. 
    125  
    126         The proper way of calling the fitter is to expect and handle all 
    127         the situations described. For instance, if fitter is an instance 
    128         of some fitter and examples contain a set of suitable examples, 
    129         a script should look like this:: 
     110        Fit the model and return a tuple with the fitted values and 
     111        the corresponding statistics or an error indicator. The two 
     112        cases differ by the tuple length and the status (the first 
     113        tuple element). 
     114 
     115        ``(status, beta, beta_se, likelihood)`` Fitting succeeded. The 
     116            first element, ``status`` is either :obj:`OK`, 
     117            :obj:`Infinity` or :obj:`Divergence`. In the latter cases, 
     118            returned values may still be useful for making 
     119            predictions, but it is recommended to inspect the 
     120            coefficients and their errors and decide whether to use 
     121            the model or not. 
     122 
     123        ``(status, variable)`` 
     124            The fitter failed due to the indicated 
     125            ``variable``. ``status`` is either :obj:`Constant` or 
     126            :obj:`Singularity`. 
     127 
     128        The proper way of calling the fitter is to handle both scenarios :: 
    130129 
    131130            res = fitter(examples) 
     
    141140 
    142141    The sole fitter available at the 
    143     moment. It is a C++ translation of `Alan Miller's logistic regression 
    144     code <http://users.bigpond.net.au/amiller/>`_. It uses Newton-Raphson 
     142    moment. This is a C++ translation of `Alan Miller's logistic regression 
     143    code <http://users.bigpond.net.au/amiller/>`_ that uses Newton-Raphson 
    145144    algorithm to iteratively minimize least squares error computed from 
    146     learning examples. 
     145    training data. 
    147146 
    148147 
     
    158157-------- 
    159158 
    160 The first example shows a very simple induction of a logistic regression 
    161 classifier (:download:`logreg-run.py <code/logreg-run.py>`). 
     159The first example shows a straightforward use a logistic regression (:download:`logreg-run.py <code/logreg-run.py>`). 
    162160 
    163161.. literalinclude:: code/logreg-run.py 
     
    210208 
    211209If :obj:`remove_singular` is set to 0, inducing a logistic regression 
    212 classifier would return an error:: 
     210classifier returns an error:: 
    213211 
    214212    Traceback (most recent call last): 
     
    221219    orange.KernelException: 'orange.LogRegLearner': singularity in workclass=Never-worked 
    222220 
    223 We can see that the attribute workclass is causing a singularity. 
     221The attribute variable which causes the singularity is ``workclass``. 
    224222 
    225223The example below shows how the use of stepwise logistic regression can help to 
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