Description Usage Arguments Details Value See Also Examples
Implementation of GPAV
(Generalized Pool-Adjacent Violators) algorithm.
(Burdakov et al., In: Di Pillo G, Roma M, editors. An O(n2) Algorithm for Isotonic Regression. Boston, MA: Springer US; 2006.
p. 25–33. Available from: https://doi.org/10.1007/0-387-30065-1_3
1 |
Y |
vector of scores relative to a single example. |
W |
vector of weight relative to a single example. If the vector |
adj |
adjacency matrix of the graph which must be sparse, logical and upper triangular. Number of columns of |
Given the constraints adjacency matrix of the graph, a vector of scores \hat{y} \in R^n and a vector of strictly positive
weights w \in R^n, the GPAV
algorithm returns a vector \bar{y} which is as close as possible, in the least-squares sense,
to the response vector \hat{y} and whose components are partially ordered in accordance with the constraints matrix adj
.
In other words, GPAV
solves the following problem:
\bar{y} = ≤ft\{ \begin{array}{l} \min ∑_{i \in N} (\hat{y}_i - \bar{y}_i )^2\\\\ \forall i, \quad j \in par(i) \Rightarrow \bar{y}_j ≥q \bar{y}_i \end{array} \right.
a list of 3 elements:
YFit
: a named vector with the scores of the classes corrected according to the GPAV
algorithm.
NOTE
: the classes of YFit
are topologically sorted, that is are in the same order of those of adj
.
blocks
: list of vectors, containing the partitioning of nodes (represented with an integer number) into blocks;
W
: vector of weights.
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