432 lines
18 KiB
Python
432 lines
18 KiB
Python
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"""
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Created on Sat May 19 15:53:21 2018
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Author: Josef Perktold
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License: BSD-3
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"""
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from collections import defaultdict
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import numpy as np
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from statsmodels.base._penalties import SCADSmoothed
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class ScreeningResults:
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"""Results for Variable Screening
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Note: Indices except for exog_idx and in the iterated case also
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idx_nonzero_batches are based on the combined [exog_keep, exog] array.
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Attributes
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----------
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results_final : instance
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Results instance returned by the final fit of the penalized model, i.e.
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after trimming exog with params below trimming threshold.
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results_pen : results instance
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Results instance of the penalized model before trimming. This includes
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variables from the last forward selection
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idx_nonzero
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index of exog columns in the final selection including exog_keep
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idx_exog
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index of exog columns in the final selection for exog candidates, i.e.
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without exog_keep
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idx_excl
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idx of excluded exog based on combined [exog_keep, exog] array. This is
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the complement of idx_nonzero
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converged : bool
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True if the iteration has converged and stopped before maxiter has been
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reached. False if maxiter has been reached.
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iterations : int
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number of iterations in the screening process. Each iteration consists
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of a forward selection step and a trimming step.
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history : dict of lists
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results collected for each iteration during the screening process
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'idx_nonzero' 'params_keep'].append(start_params)
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history['idx_added'].append(idx)
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The ScreeningResults returned by `screen_exog_iterator` has additional
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attributes:
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idx_nonzero_batches : ndarray 2-D
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Two-dimensional array with batch index in the first column and variable
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index withing batch in the second column. They can be used jointly as
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index for the data in the exog_iterator.
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exog_final_names : list[str]
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'var<bidx>_<idx>' where `bidx` is the batch index and `idx` is the
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index of the selected column withing batch `bidx`.
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history_batches : dict of lists
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This provides information about the selected variables within each
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batch during the first round screening
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'idx_nonzero' is based ond the array that includes exog_keep, while
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'idx_exog' is the index based on the exog of the batch.
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"""
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def __init__(self, screener, **kwds):
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self.screener = screener
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self.__dict__.update(**kwds)
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class VariableScreening:
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"""Ultra-high, conditional sure independence screening
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This is an adjusted version of Fan's sure independence screening.
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Parameters
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----------
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model : instance of penalizing model
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examples: GLMPenalized, PoissonPenalized and LogitPenalized.
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The attributes of the model instance `pen_weight` and `penal` will be
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ignored.
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pen_weight : None or float
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penalization weight use in SCAD penalized MLE
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k_add : int
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number of exog to add during expansion or forward selection
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see Notes section for tie handling
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k_max_add : int
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maximum number of variables to include during variable addition, i.e.
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forward selection. default is 30
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threshold_trim : float
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threshold for trimming parameters to zero, default is 1e-4
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k_max_included : int
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maximum total number of variables to include in model.
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ranking_attr : str
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This determines the result attribute or model method that is used for
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the ranking of exog to include. The availability of attributes depends
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on the model.
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Default is 'resid_pearson', 'model.score_factor' can be used in GLM.
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ranking_project : bool
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If ranking_project is True, then the exog candidates for inclusion are
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first projected on the already included exog before the computation
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of the ranking measure. This brings the ranking measure closer to
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the statistic of a score test for variable addition.
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Notes
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-----
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Status: experimental, tested only on a limited set of models and
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with a limited set of model options.
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Tie handling: If there are ties at the decision threshold, then all those
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tied exog columns are treated in the same way. During forward selection
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all exog columns with the same boundary value are included. During
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elimination, the tied columns are not dropped. Consequently, if ties are
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present, then the number of included exog can be larger than specified
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by k_add, k_max_add and k_max_included.
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The screening algorithm works similar to step wise regression. Each
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iteration of the screening algorithm includes a forward selection step
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where variables are added to the model, and a backwards selection step
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where variables are removed. In contrast to step wise regression, we add
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a fixed number of variables at each forward selection step. The
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backwards selection step is based on SCAD penalized estimation and
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trimming of variables with estimated coefficients below a threshold.
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The tuning parameters can be used to adjust the number of variables to add
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and to include depending on the size of the dataset.
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There is currently no automatic tuning parameter selection. Candidate
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explanatory variables should be standardized or should be on a similar
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scale because penalization and trimming are based on the absolute values
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of the parameters.
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TODOs and current limitations:
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freq_weights are not supported in this. Candidate ranking uses
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moment condition with resid_pearson or others without freq_weights.
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pearson_resid: GLM resid_pearson does not include freq_weights.
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variable names: do we keep track of those? currently made-up names
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currently only supports numpy arrays, no exog type check or conversion
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currently only single columns are selected, no terms (multi column exog)
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"""
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def __init__(self, model, pen_weight=None, use_weights=True, k_add=30,
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k_max_add=30, threshold_trim=1e-4, k_max_included=20,
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ranking_attr='resid_pearson', ranking_project=True):
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self.model = model
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self.model_class = model.__class__
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self.init_kwds = model._get_init_kwds()
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# pen_weight and penal are explicitly included
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# TODO: check what we want to do here
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self.init_kwds.pop('pen_weight', None)
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self.init_kwds.pop('penal', None)
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self.endog = model.endog
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self.exog_keep = model.exog
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self.k_keep = model.exog.shape[1]
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self.nobs = len(self.endog)
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self.penal = self._get_penal()
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if pen_weight is not None:
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self.pen_weight = pen_weight
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else:
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self.pen_weight = self.nobs * 10
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# option for screening algorithm
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self.use_weights = use_weights
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self.k_add = k_add
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self.k_max_add = k_max_add
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self.threshold_trim = threshold_trim
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self.k_max_included = k_max_included
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self.ranking_attr = ranking_attr
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self.ranking_project = ranking_project
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def _get_penal(self, weights=None):
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"""create new Penalty instance
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"""
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return SCADSmoothed(0.1, c0=0.0001, weights=weights)
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def ranking_measure(self, res_pen, exog, keep=None):
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"""compute measure for ranking exog candidates for inclusion
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"""
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endog = self.endog
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if self.ranking_project:
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assert res_pen.model.exog.shape[1] == len(keep)
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ex_incl = res_pen.model.exog[:, keep]
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exog = exog - ex_incl.dot(np.linalg.pinv(ex_incl).dot(exog))
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if self.ranking_attr == 'predicted_poisson':
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# I keep this for more experiments
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# TODO: does it really help to change/trim params
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# we are not reestimating with trimmed model
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p = res_pen.params.copy()
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if keep is not None:
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p[~keep] = 0
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predicted = res_pen.model.predict(p)
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# this is currently hardcoded for Poisson
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resid_factor = (endog - predicted) / np.sqrt(predicted)
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elif self.ranking_attr[:6] == 'model.':
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# use model method, this is intended for score_factor
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attr = self.ranking_attr.split('.')[1]
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resid_factor = getattr(res_pen.model, attr)(res_pen.params)
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if resid_factor.ndim == 2:
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# for score_factor when extra params are in model
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resid_factor = resid_factor[:, 0]
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mom_cond = np.abs(resid_factor.dot(exog))**2
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else:
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# use results attribute
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resid_factor = getattr(res_pen, self.ranking_attr)
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mom_cond = np.abs(resid_factor.dot(exog))**2
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return mom_cond
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def screen_exog(self, exog, endog=None, maxiter=100, method='bfgs',
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disp=False, fit_kwds=None):
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"""screen and select variables (columns) in exog
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Parameters
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----------
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exog : ndarray
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candidate explanatory variables that are screened for inclusion in
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the model
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endog : ndarray (optional)
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use a new endog in the screening model.
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This is not tested yet, and might not work correctly
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maxiter : int
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number of screening iterations
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method : str
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optimization method to use in fit, needs to be only of the gradient
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optimizers
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disp : bool
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display option for fit during optimization
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Returns
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-------
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res_screen : instance of ScreeningResults
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The attribute `results_final` contains is the results instance
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with the final model selection.
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`idx_nonzero` contains the index of the selected exog in the full
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exog, combined exog that are always kept plust exog_candidates.
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see ScreeningResults for a full description
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"""
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model_class = self.model_class
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if endog is None:
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# allow a different endog than used in model
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endog = self.endog
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x0 = self.exog_keep
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k_keep = self.k_keep
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x1 = exog
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k_current = x0.shape[1]
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# TODO: remove the need for x, use x1 separately from x0
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# needs change to idx to be based on x1 (candidate variables)
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x = np.column_stack((x0, x1))
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nobs, k_vars = x.shape
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fkwds = fit_kwds if fit_kwds is not None else {}
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fit_kwds = {'maxiter': 200, 'disp': False}
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fit_kwds.update(fkwds)
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history = defaultdict(list)
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idx_nonzero = np.arange(k_keep, dtype=int)
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keep = np.ones(k_keep, np.bool_)
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idx_excl = np.arange(k_keep, k_vars)
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mod_pen = model_class(endog, x0, **self.init_kwds)
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# do not penalize initial estimate
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mod_pen.pen_weight = 0
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res_pen = mod_pen.fit(**fit_kwds)
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start_params = res_pen.params
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converged = False
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idx_old = []
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for it in range(maxiter):
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# candidates for inclusion in next iteration
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x1 = x[:, idx_excl]
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mom_cond = self.ranking_measure(res_pen, x1, keep=keep)
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assert len(mom_cond) == len(idx_excl)
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mcs = np.sort(mom_cond)[::-1]
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idx_thr = min((self.k_max_add, k_current + self.k_add, len(mcs)))
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threshold = mcs[idx_thr]
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# indices of exog in current expansion model
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idx = np.concatenate((idx_nonzero, idx_excl[mom_cond > threshold]))
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start_params2 = np.zeros(len(idx))
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start_params2[:len(start_params)] = start_params
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if self.use_weights:
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weights = np.ones(len(idx))
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weights[:k_keep] = 0
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# modify Penalty instance attached to self
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# damgerous if res_pen is reused
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self.penal.weights = weights
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mod_pen = model_class(endog, x[:, idx], penal=self.penal,
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pen_weight=self.pen_weight,
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**self.init_kwds)
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res_pen = mod_pen.fit(method=method,
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start_params=start_params2,
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warn_convergence=False, skip_hessian=True,
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**fit_kwds)
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keep = np.abs(res_pen.params) > self.threshold_trim
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# use largest params to keep
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if keep.sum() > self.k_max_included:
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# TODO we can use now np.partition with partial sort
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thresh_params = np.sort(np.abs(res_pen.params))[
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-self.k_max_included]
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keep2 = np.abs(res_pen.params) > thresh_params
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keep = np.logical_and(keep, keep2)
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# Note: idx and keep are for current expansion model
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# idx_nonzero has indices of selected variables in full exog
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keep[:k_keep] = True # always keep exog_keep
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idx_nonzero = idx[keep]
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if disp:
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print(keep)
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print(idx_nonzero)
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# x0 is exog of currently selected model, not used in iteration
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# x0 = x[:, idx_nonzero]
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k_current = len(idx_nonzero)
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start_params = res_pen.params[keep]
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# use mask to get excluded indices
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mask_excl = np.ones(k_vars, dtype=bool)
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mask_excl[idx_nonzero] = False
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idx_excl = np.nonzero(mask_excl)[0]
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history['idx_nonzero'].append(idx_nonzero)
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history['keep'].append(keep)
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history['params_keep'].append(start_params)
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history['idx_added'].append(idx)
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if (len(idx_nonzero) == len(idx_old) and
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(idx_nonzero == idx_old).all()):
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converged = True
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break
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idx_old = idx_nonzero
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# final esimate
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# check that we still have exog_keep
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assert np.all(idx_nonzero[:k_keep] == np.arange(k_keep))
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if self.use_weights:
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weights = np.ones(len(idx_nonzero))
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weights[:k_keep] = 0
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# create new Penalty instance to avoide sharing attached penal
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penal = self._get_penal(weights=weights)
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else:
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penal = self.penal
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mod_final = model_class(endog, x[:, idx_nonzero],
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penal=penal,
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pen_weight=self.pen_weight,
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**self.init_kwds)
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res_final = mod_final.fit(method=method,
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start_params=start_params,
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warn_convergence=False,
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**fit_kwds)
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# set exog_names for final model
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|
|
xnames = ['var%4d' % ii for ii in idx_nonzero]
|
||
|
|
res_final.model.exog_names[k_keep:] = xnames[k_keep:]
|
||
|
|
|
||
|
|
res = ScreeningResults(self,
|
||
|
|
results_pen = res_pen,
|
||
|
|
results_final = res_final,
|
||
|
|
idx_nonzero = idx_nonzero,
|
||
|
|
idx_exog = idx_nonzero[k_keep:] - k_keep,
|
||
|
|
idx_excl = idx_excl,
|
||
|
|
history = history,
|
||
|
|
converged = converged,
|
||
|
|
iterations = it + 1 # it is 0-based
|
||
|
|
)
|
||
|
|
return res
|
||
|
|
|
||
|
|
def screen_exog_iterator(self, exog_iterator):
|
||
|
|
"""
|
||
|
|
batched version of screen exog
|
||
|
|
|
||
|
|
This screens variables in a two step process:
|
||
|
|
|
||
|
|
In the first step screen_exog is used on each element of the
|
||
|
|
exog_iterator, and the batch winners are collected.
|
||
|
|
|
||
|
|
In the second step all batch winners are combined into a new array
|
||
|
|
of exog candidates and `screen_exog` is used to select a final
|
||
|
|
model.
|
||
|
|
|
||
|
|
Parameters
|
||
|
|
----------
|
||
|
|
exog_iterator : iterator over ndarrays
|
||
|
|
|
||
|
|
Returns
|
||
|
|
-------
|
||
|
|
res_screen_final : instance of ScreeningResults
|
||
|
|
This is the instance returned by the second round call to
|
||
|
|
`screen_exog`. Additional attributes are added to provide
|
||
|
|
more information about the batched selection process.
|
||
|
|
The index of final nonzero variables is
|
||
|
|
`idx_nonzero_batches` which is a 2-dimensional array with batch
|
||
|
|
index in the first column and variable index within batch in the
|
||
|
|
second column. They can be used jointly as index for the data
|
||
|
|
in the exog_iterator.
|
||
|
|
see ScreeningResults for a full description
|
||
|
|
"""
|
||
|
|
k_keep = self.k_keep
|
||
|
|
# res_batches = []
|
||
|
|
res_idx = []
|
||
|
|
exog_winner = []
|
||
|
|
exog_idx = []
|
||
|
|
for ex in exog_iterator:
|
||
|
|
res_screen = self.screen_exog(ex, maxiter=20)
|
||
|
|
# avoid storing res_screen, only for debugging
|
||
|
|
# res_batches.append(res_screen)
|
||
|
|
res_idx.append(res_screen.idx_nonzero)
|
||
|
|
exog_winner.append(ex[:, res_screen.idx_nonzero[k_keep:] - k_keep])
|
||
|
|
exog_idx.append(res_screen.idx_nonzero[k_keep:] - k_keep)
|
||
|
|
|
||
|
|
exog_winner = np.column_stack(exog_winner)
|
||
|
|
res_screen_final = self.screen_exog(exog_winner, maxiter=20)
|
||
|
|
|
||
|
|
exog_winner_names = ['var%d_%d' % (bidx, idx)
|
||
|
|
for bidx, batch in enumerate(exog_idx)
|
||
|
|
for idx in batch]
|
||
|
|
|
||
|
|
idx_full = [(bidx, idx)
|
||
|
|
for bidx, batch in enumerate(exog_idx)
|
||
|
|
for idx in batch]
|
||
|
|
ex_final_idx = res_screen_final.idx_nonzero[k_keep:] - k_keep
|
||
|
|
final_names = np.array(exog_winner_names)[ex_final_idx]
|
||
|
|
res_screen_final.idx_nonzero_batches = np.array(idx_full)[ex_final_idx]
|
||
|
|
res_screen_final.exog_final_names = final_names
|
||
|
|
history = {'idx_nonzero': res_idx,
|
||
|
|
'idx_exog': exog_idx}
|
||
|
|
res_screen_final.history_batches = history
|
||
|
|
return res_screen_final
|