View source: R/hausdInterval.R
hausdInterval | R Documentation |
hausdInterval
computes a confidence interval for the Hausdorff distance between a point cloud X
and the underlying manifold from which X
was sampled. See Details and References.
hausdInterval( X, m, B = 30, alpha = 0.05, parallel = FALSE, printProgress = FALSE)
X |
an n by d matrix of coordinates of sampled points. |
m |
the size of the subsamples. |
B |
the number of subsampling iterations. The default value is |
alpha |
|
parallel |
logical: if |
printProgress |
if |
For B
times, the subsampling algorithm subsamples m
points of X
(without replacement) and computes the Hausdorff distance between the original sample X
and the subsample. The result is a sequence of B
values. Let q be the (1-alpha
) quantile of these values and let c = 2 * q. The interval [0, c] is a valid (1-alpha
) confidence interval for the Hausdorff distance between X
and the underlying manifold, as proven in (Fasy, Lecci, Rinaldo, Wasserman, Balakrishnan, and Singh, 2013, Theorem 3).
The function hausdInterval
returns a number c. The confidence interval is [0, c].
Fabrizio Lecci
Fasy BT, Lecci F, Rinaldo A, Wasserman L, Balakrishnan S, Singh A (2013). "Statistical Inference For Persistent Homology: Confidence Sets for Persistence Diagrams." (arXiv:1303.7117). Annals of Statistics.
bootstrapBand
X <- circleUnif(1000) interval <- hausdInterval(X, m = 800) print(interval)
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.