pyuncertainnumber.calibration.data_peeling.scenario

Solution to the scenario optimization problem for enclosing sets.

A scenario optimization inputs (1) a table of observations i.e. an (nxd) array, and (2) a shape.

In general, a scenario program should output three data structures:

  1. A list of integers pointing to the support vectors in the data set;

  2. A data structure representing the set if parametric, e.g. a box, a circle, an ellipse.

  3. A function or object representing the optimal set. For example, the function/method returns true if evaluated inside the set and false otherwise.

Attributes

bet

Functions

minimal_enclosing_hyperbox(x)

Inputs

is_inside_box(x, abox)

x: (nxd) array

epsLU(k, N, bet)

Port of the MATLAB code provided by the Authors.

Module Contents

pyuncertainnumber.calibration.data_peeling.scenario.minimal_enclosing_hyperbox(x)

Inputs x: (nxd) array, where n is the size of the data, and d is the number of dimensions of the box

Outputs active_scenarios: list[int], a list of integers pointing to the corresponding active scenarios in the dataset box: 2xd array, an enclosing box of dimension d.

pyuncertainnumber.calibration.data_peeling.scenario.is_inside_box(x, abox)

x: (nxd) array abox: (dx2) array, or list[list[2 float]] ex.: [[0,1],[3,8],[1,9]] <- a.k.a. interval iterable

pyuncertainnumber.calibration.data_peeling.scenario.epsLU(k, N, bet)

Port of the MATLAB code provided by the Authors.

%% Reference Article % Title Risk and complexity in scenario optimization % Authors S. Garatti and ·M. C. Campi % Journal Mathematical Programming % DOI https://doi.org/10.1007/s10107-019-01446-4

% This function provide the lower and upper reliability parameter for a % convex program as defined in Eq (14) of the refernced paper

% N= number of samples % k = Number of scenarios delta_i for which zeta_i geq 0, i.e. f(x,delta_i) geq 0 % beta = confidence parameter (e.g. very high confidence beta=10^-8)

pyuncertainnumber.calibration.data_peeling.scenario.bet = 0.1