JMI3 {praznik}

Third-order joint mutual information filter

Description

The method starts with two features: X_1 of a maximal mutual information with the decision Y, and X_2 of a maximal value of I(X_1,X_2;Y), as would be selected second by a regular JMI. Then, it greedily adds feature X with a maximal value of the following criterion:

J(X)=\frac{1}{2}\sum_{(U,W)\in S^2; U\neq W} I(X,U,W;Y),

where S is the set of already selected features.

Usage

JMI3(X, Y, k = 3, threads = 0)

Arguments

X

Attribute table, given as a data frame with either factors (preferred), booleans, integers (treated as categorical) or reals (which undergo automatic categorisation; see below for details). Single vector will be interpreted as a data.frame with one column. NAs are not allowed.

Y

Decision attribute; should be given as a factor, but other options are accepted, exactly like for attributes. NAs are not allowed.

k

Number of attributes to select. Must not exceed ncol(X).

threads

Number of threads to use; default value, 0, means all available to OpenMP.

Value

A list with two elements: selection, a vector of indices of the selected features in the selection order, and score, a vector of corresponding feature scores. Names of both vectors will correspond to the names of features in X. Both vectors will be at most of a length k, as the selection may stop sooner, even during initial selection, in which case both vectors will be empty.

Note

This method has a complexity of O(k^2\cdot m \cdot n), while other filters have O(k\cdot m \cdot n) — for larger k, it will be substantially slower. In the original paper, special shrinkage estimator of MI is used; in praznik, all algorithms use ML estimators, so is JMI3.

The method requires input to be discrete to use empirical estimators of distribution, and, consequently, information gain or entropy. To allow smoother user experience, praznik automatically coerces non-factor vectors in inputs, which requires additional time, memory and may yield confusing results – the best practice is to convert data to factors prior to feeding them in this function. Real attributes are cut into about 10 equally-spaced bins, following the heuristic often used in literature. Precise number of cuts depends on the number of objects; namely, it is n/3, but never less than 2 and never more than 10. Integers (which technically are also numeric) are treated as categorical variables (for compatibility with similar software), so in a very different way – one should be aware that an actually numeric attribute which happens to be an integer could be coerced into a n-level categorical, which would have a perfect mutual information score and would likely become a very disruptive false positive.

References

"Efficient feature selection using shrinkage estimators" K. Sechidis, L. Azzimonti, A. Pocock, G. Corani, J. Weatherall and G. Brown. Machine Learning, 108 (8-9), pp. 1261-1286 (2019)

Examples

## Not run: data(MadelonD)
JMI3(MadelonD$X,MadelonD$Y,20)
## End(Not run)