Quantile regions

Fit source points with fit(), then request a region with T.quantile_region(coverage=0.9). See the guide for the construction and a worked example.

radius is the largest included reference-centre radius. labels are the zero-based labels of the included cells.

Transport.quantile_region(coverage)

Return the smallest quantile region reaching the requested coverage.

\[\Omega_r=\{z:\|T(z)\|\leq r\},\qquad J_r=\{j:\|m_j\|\leq r\}.\]

coverage is a probability in [0, 1], not the radius r. Choose the smallest r >= 0 with \(|J_r|/(n+1)\) at least this probability. Under exchangeability and almost-sure uniqueness of the augmented assignment, the region covers the next observation with probability region.coverage, averaging over fitted observations and the next candidate, not conditional on one fitted sample.

Equal-radius cells enter together, so achieved coverage can exceed the request. Selecting every cell gives the whole space, even for a request below 1. Requires the default reference-cell construction.

class yemale.ot.QuantileRegion

A finite-sample union of source cells selected by reference radius.

radius

Reference-centre radius cutoff defining the region.

Type:

float

labels

Zero-based labels of the included reference cells.

Type:

numpy.ndarray

property coverage

Fraction of reference cells included in the region.

Under the assumptions in quantile_region, this is the next observation’s marginal coverage, not coverage conditional on the fit.

contains(point)

Return whether each point belongs to the region.

halfspaces()

Return (A, b) for every closed source cell in the region.

Density regions

law.density_region(mass=0.9) selects points by density. Its mass is a numerical integral, not a future-data coverage guarantee. Smooth maps offer the same operation on their unnormalized density; see Smoothing.

threshold is the density cutoff. mass is the numerical mass included at that cutoff.

class yemale.ot.DensityRegion

Points whose density reaches a cutoff, including ties.

Build with density_region on a law or smooth map. mass estimates the included density integral, not the coverage of future observations.

mass

Estimated density integral over the region, including cutoff ties.

Type:

float

property threshold

Density cutoff; membership is compared in log space.

contains(points)

Return membership for one point or a batch, preserving batch axes.