Class WeightedTau
public class WeightedTau extends CorrelationIndex
Given two scores vectors for a list of items,
this class provides a method to compute efficiently the weighted τ
using an ExchangeWeigher
.
Instances of this class are immutable. At creation time you can specify a
weigher that turns indices into weights, and
whether to combine weights additively or multiplicatively.
Readymade weighers include HYPERBOLIC_WEIGHER
, which is the weigher of choice. Alternatives include
LOGARITHMIC_WEIGHER
and QUADRATIC_WEIGHER
.
Additional methods inherited from CorrelationIndex
make it possible to
compute directly the weighted τ bewteen two files, to bound the number of significant digits, or
to reverse the standard association between scores and ranks (by default,
a larger score corresponds to a higher rank, i.e., to a smaller rank index; the largest score gets
rank 0).
The weighted τ is defined as follows: consider a rank function ρ (returning natural numbers or ∞) that provides a ground truth—it tells us which elements are more or less important. Consider also a weight function w(−, −) associating with each pair of ranks a nonnegative real number. We define the rankweighted τ by
The weight function can be specified by giving a weigher f (e.g., HYPERBOLIC_WEIGHER
) and a combination
strategy, which can be additive or multiplicative.
The weight of the exchange between i and j
is then f(i) ● f(j), where ● is the chosen combinator.
Now, consider the rank function ρ_{r, s} induced by the lexicographical order by r and s. We define
In particular, the (additive) hyperbolic τ is defined by the weight function h(i) = 1 / (i + 1) combined additively:
The methods inherited from CorrelationIndex
compute the formula above using the provided weigher
and combination method. A readymade instance HYPERBOLIC
can be used to compute the additive hyperbolic τ. An
ad hoc method can instead compute τ_{ρ,w}.
A main method is provided for commandline usage.

Nested Class Summary
Nested Classes Modifier and Type Class Description static class
WeightedTau.AbstractWeigher

Field Summary
Fields Modifier and Type Field Description static WeightedTau
HYPERBOLIC
A singleton instance of the symmetric hyperbolic additive τ.static Int2DoubleFunction
HYPERBOLIC_WEIGHER
A hyperbolic weigher (the default one).static Int2DoubleFunction
LOGARITHMIC_WEIGHER
A logarithmic weigher.static Int2DoubleFunction
QUADRATIC_WEIGHER
A quadratic weigher.static Int2DoubleFunction
ZERO_WEIGHER
A constant zero weigher. 
Constructor Summary
Constructors Constructor Description WeightedTau()
Create an additive hyperbolic τ.WeightedTau(Int2DoubleFunction weigher)
Create an additive weighted τ using the specified weigher.WeightedTau(Int2DoubleFunction weigher, boolean multiplicative)
Create an additive or multiplicative weighted τ using the specified weigher and combination strategy. 
Method Summary
Modifier and Type Method Description double
compute(double[] v0, double[] v1)
Computes the symmetrized weighted τ between two score vectors.double
compute(double[] v0, double[] v1, int[] rank)
Computes the weighted τ between two score vectors, given a reference rank.static void
main(String[] arg)
Methods inherited from class it.unimi.dsi.law.stat.CorrelationIndex
compute, compute, compute, compute, computeDoubles, computeDoubles, computeDoubles, computeDoubles, computeFloats, computeFloats, computeFloats, computeFloats, computeInts, computeInts, computeLongs, computeLongs, loadAsDoubles, parseInputTypes

Field Details

HYPERBOLIC_WEIGHER
A hyperbolic weigher (the default one). Rank x has weight 1 / (x + 1). 
QUADRATIC_WEIGHER
A quadratic weigher. Rank x has weight 1 / (x + 1)^{2}. 
LOGARITHMIC_WEIGHER
A logarithmic weigher. Rank x has weight 1 / ln(x + e). 
ZERO_WEIGHER
A constant zero weigher. 
HYPERBOLIC
A singleton instance of the symmetric hyperbolic additive τ.


Constructor Details

WeightedTau
public WeightedTau()Create an additive hyperbolic τ. 
WeightedTau
Create an additive weighted τ using the specified weigher. Parameters:
weigher
 a weigher.

WeightedTau
Create an additive or multiplicative weighted τ using the specified weigher and combination strategy. Parameters:
weigher
 a weigher.multiplicative
 if true, weights are combined multiplicatively, rather than additively.


Method Details

compute
public double compute(double[] v0, double[] v1)Computes the symmetrized weighted τ between two score vectors. Specified by:
compute
in classCorrelationIndex
 Parameters:
v0
 the first score vector.v1
 the second score vector. Returns:
 the symmetric weighted τ.

compute
public double compute(double[] v0, double[] v1, int[] rank)Computes the weighted τ between two score vectors, given a reference rank.Note that this method must be called with some care. More precisely, the two arguments should be built onthefly in the method call, and not stored in variables, as the first argument array will be
null
'd during the execution of this method to free some memory: if the array is referenced elsewhere the garbage collector will not be able to collect it. Parameters:
v0
 the first score vector.v1
 the second score vector.rank
 the “ground truth” ranking used to weight exchanges, ornull
to use the ranking induced lexicographically byv1
andv0
as ground truth. Returns:
 the weighted τ.

main
