prim

A scenario discovery oriented implementation of PRIM.

The implementation of prim provided here is data type aware, so categorical variables will be handled appropriately. It also uses a non-standard objective function in the peeling and pasting phase of the algorithm. This algorithm looks at the increase in the mean divided by the amount of data removed. So essentially, it uses something akin to the first order derivative of the original objective function.

The implementation is designed for interactive use in combination with the jupyter notebook.

class ema_workbench.analysis.prim.PRIMObjectiveFunctions(value, names=None, *values, module=None, qualname=None, type=None, start=1, boundary=None)

class ema_workbench.analysis.prim.Prim(x, y, threshold, obj_function=PRIMObjectiveFunctions.LENIENT1, peel_alpha=0.05, paste_alpha=0.05, mass_min=0.05, threshold_type=1, mode=RuleInductionType.BINARY, update_function='default')

Patient rule induction algorithm

The implementation of Prim is tailored to interactive use in the context of scenario discovery

Parameters:

• x (DataFrame) – the independent variables

• y (1d ndarray) – the dependent variable

• threshold (float) – the density threshold that a box has to meet

• obj_function ({LENIENT1, LENIENT2, ORIGINAL}) – the objective function used by PRIM. Defaults to a lenient objective function based on the gain of mean divided by the loss of mass.

• peel_alpha (float, optional) – parameter controlling the peeling stage (default = 0.05).

• paste_alpha (float, optional) – parameter controlling the pasting stage (default = 0.05).

• mass_min (float, optional) – minimum mass of a box (default = 0.05).

• threshold_type ({ABOVE, BELOW}) – whether to look above or below the threshold value

• mode ({RuleInductionType.BINARY, RuleInductionType.REGRESSION}, optional) – indicated whether PRIM is used for regression, or for scenario classification in which case y should be a binary vector

• {'default' (update_function =) – controls behavior of PRIM after having found a first box. use either the default behavior were all points are removed, or the procedure suggested by guivarch et al (2016) doi:10.1016/j.envsoft.2016.03.006 to simply set all points to be no longer of interest (only valid in binary mode).

• 'guivarch'} – controls behavior of PRIM after having found a first box. use either the default behavior were all points are removed, or the procedure suggested by guivarch et al (2016) doi:10.1016/j.envsoft.2016.03.006 to simply set all points to be no longer of interest (only valid in binary mode).

• optional – controls behavior of PRIM after having found a first box. use either the default behavior were all points are removed, or the procedure suggested by guivarch et al (2016) doi:10.1016/j.envsoft.2016.03.006 to simply set all points to be no longer of interest (only valid in binary mode).

See also

cart

property boxes

Property for getting a list of box limits

determine_coi(indices)

Given a set of indices on y, how many cases of interest are there in this set.

Parameters:

indices (ndarray) – a valid index for y

Returns:

the number of cases of interest.

Return type:

int

Raises:

ValueError – if threshold_type is not either ABOVE or BELOW

find_box()

Execute one iteration of the PRIM algorithm. That is, find one box, starting from the current state of Prim.

property stats

property for getting a list of dicts containing the statistics for each box

class ema_workbench.analysis.prim.PrimBox(prim, box_lims, indices)

A class that holds information for a specific box

coverage

coverage of currently selected box

Type:

float

density

density of currently selected box

Type:

float

mean

mean of currently selected box

Type:

float

res_dim

number of restricted dimensions of currently selected box

Type:

int

mass

mass of currently selected box

Type:

float

peeling_trajectory

stats for each box in peeling trajectory

Type:

DataFrame

box_lims

list of box lims for each box in peeling trajectory

Type:

list

by default, the currently selected box is the last box on the peeling trajectory, unless this is changed via PrimBox.select().

drop_restriction(uncertainty='', i=-1)

Drop the restriction on the specified dimension for box i

Parameters:

• i (int, optional) – defaults to the currently selected box, which defaults to the latest box on the trajectory

• uncertainty (str)

Replace the limits in box i with a new box where for the specified uncertainty the limits of the initial box are being used. The resulting box is added to the peeling trajectory.

inspect(i=None, style='table', ax=None, **kwargs)

Write the stats and box limits of the user specified box to standard out. If i is not provided, the last box will be printed

Parameters:

• i (int or list of ints, optional) – the index of the box, defaults to currently selected box

• style ({'table', 'graph', 'data'}) – the style of the visualization. ‘table’ prints the stats and boxlim. ‘graph’ creates a figure. ‘data’ returns a list of tuples, where each tuple contains the stats and the box_lims.

• ax (axes or list of axes instances, optional) – used in conjunction with graph style, allows you to control the axes on which graph is plotted if i is list, axes should be list of equal length. If axes is None, each i_j in i will be plotted in a separate figure.

• that (additional kwargs are passed to the helper function)

• graph (generates the table or)

resample(i=None, iterations=10, p=0.5)

Calculate resample statistics for candidate box i

Parameters:

• i (int, optional)

• iterations (int, optional)

• p (float, optional)

Return type:

DataFrame

select(i)

select an entry from the peeling and pasting trajectory and update the prim box to this selected box.

Parameters:

i (int) – the index of the box to select.

show_pairs_scatter(i=None, dims=None, diag_kind=DiagKind.KDE, upper='scatter', lower='contour', fill_subplots=True)

Make a pair wise scatter plot of all the restricted dimensions with color denoting whether a given point is of interest or not and the boxlims superimposed on top.

Parameters:

• i (int, optional)

• dims (list of str, optional) – dimensions to show, defaults to all restricted dimensions

• diag_kind ({DiagKind.KDE, DiagKind.CDF}) – Plot diagonal as kernel density estimate (‘kde’) or cumulative density function (‘cdf’).

• upper (string, optional) – Use either ‘scatter’, ‘contour’, or ‘hist’ (bivariate histogram) plots for upper and lower triangles. Upper triangle can also be ‘none’ to eliminate redundancy. Legend uses lower triangle style for markers.

• lower (string, optional) – Use either ‘scatter’, ‘contour’, or ‘hist’ (bivariate histogram) plots for upper and lower triangles. Upper triangle can also be ‘none’ to eliminate redundancy. Legend uses lower triangle style for markers.

• fill_subplots (Boolean, optional) – if True, subplots are resized to fill their respective axes. This removes unnecessary whitespace, but may be undesirable for some variable combinations.

Return type:

seaborn PairGrid

show_ppt()

show the peeling and pasting trajectory in a figure

show_tradeoff(cmap=<matplotlib.colors.ListedColormap object>, annotated=False)

Visualize the trade off between coverage and density. Color is used to denote the number of restricted dimensions.

Parameters:

• cmap (valid matplotlib colormap)

• annotated (bool, optional. Shows point labels if True.)

Return type:

a Figure instance

update(box_lims, indices)

update the box to the provided box limits.

Parameters:

• box_lims (DataFrame) – the new box_lims

• indices (ndarray) – the indices of y that are inside the box

write_ppt_to_stdout()

write the peeling and pasting trajectory to stdout

ema_workbench.analysis.prim.pca_preprocess(experiments, y, subsets=None, exclude={})

perform PCA to preprocess experiments before running PRIM

Pre-process the data by performing a pca based rotation on it. This effectively turns the algorithm into PCA-PRIM as described in Dalal et al (2013)

Parameters:

• experiments (DataFrame)

• y (ndarray) – one dimensional binary array

• subsets (dict, optional) – expects a dictionary with group name as key and a list of uncertainty names as values. If this is used, a constrained PCA-PRIM is executed

• exclude (list of str, optional) – the uncertainties that should be excluded from the rotation

Returns:

• rotated_experiments – DataFrame

• rotation_matrix – DataFrame

Raises:

RuntimeError – if mode is not binary (i.e. y is not a binary classification). if X contains non numeric columns

ema_workbench.analysis.prim.run_constrained_prim(experiments, y, issignificant=True, **kwargs)

Run PRIM repeatedly while constraining the maximum number of dimensions available in x

Improved usage of PRIM as described in Kwakkel (2019).

Parameters:

• x (DataFrame)

• y (numpy array)

• issignificant (bool, optional) – if True, run prim only on subsets of dimensions that are significant for the initial PRIM on the entire dataset.

• **kwargs (any additional keyword arguments are passed on to PRIM)

Return type:

PrimBox instance

ema_workbench.analysis.prim.setup_prim(results, classify, threshold, incl_unc=[], **kwargs)

Helper function for setting up the prim algorithm

Parameters:

• results (tuple) – tuple of DataFrame and dict with numpy arrays the return from perform_experiments().

• classify (str or callable) – either a string denoting the outcome of interest to use or a function.

• threshold (double) – the minimum score on the density of the last box on the peeling trajectory. In case of a binary classification, this should be between 0 and 1.

• incl_unc (list of str, optional) – list of uncertainties to include in prim analysis

• kwargs (dict) – valid keyword arguments for prim.Prim

Return type:

a Prim instance

Raises:

• PrimException – if data resulting from classify is not a 1-d array.

• TypeError – if classify is not a string or a callable.