# similarity_measures_regression: Similarity Measure Infrastructure for Stability Assessment... In stablelearner: Stability Assessment of Statistical Learning Methods

## Description

Functions that provide objects with functionality used by `stability` to measure the similarity between numeric predictions of two results in regression problems.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13``` ``` edist() msdist() rmsdist() madist() qadist(p = 0.95) cprob(kappa = 0.1) rbfkernel() tanimoto() cosine() ccc() pcc() ```

## Arguments

 `p` A numeric value between 0 and 1 specifying the probability to which the sample quantile of the absolute distance between the predictions is computed. `kappa` A positive numeric value specifying the upper limit of the absolute distance between the predictions to which the coverage probability is computed.

## Details

The similarity measure functions provide objects that include functionality used by `stability` to measure the similarity between numeric predictions of two results in regression problems.

The `edist` (euclidean distance), `msdist` (mean squared distance), `rmsdist` (root mean squared distance), `madist` (mean absolute distance) and `qadist` (quantile of absolute distance) functions implement scale-variant distance measures that are unbounded.

The `cprob` (coverage probability), `rbfkernel` (gaussian radial basis function kernel), `tanimoto` (tanimoto coefficient) and `cosine` (cosine similarity) functions implement scale-variant distance measures that are bounded.

The `ccc` (concordance correlation coefficient) and `pcc` (pearson correlation coefficient) functions implement scale-invariant distance measures that are bounded between 0 and 1.

`stability`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54``` ```set.seed(0) library("partykit") airq <- subset(airquality, !is.na(Ozone)) m1 <- ctree(Ozone ~ ., data = airq[sample(1:nrow(airq), replace = TRUE),]) m2 <- ctree(Ozone ~ ., data = airq[sample(1:nrow(airq), replace = TRUE),]) p1 <- predict(m1) p2 <- predict(m2) ## euclidean distance m <- edist() m\$measure(p1, p2) ## mean squared distance m <- msdist() m\$measure(p1, p2) ## root mean squared distance m <- rmsdist() m\$measure(p1, p2) ## mean absolute istance m <- madist() m\$measure(p1, p2) ## quantile of absolute distance m <- qadist() m\$measure(p1, p2) ## coverage probability m <- cprob() m\$measure(p1, p2) ## gaussian radial basis function kernel m <- rbfkernel() m\$measure(p1, p2) ## tanimoto coefficient m <- tanimoto() m\$measure(p1, p2) ## cosine similarity m <- cosine() m\$measure(p1, p2) ## concordance correlation coefficient m <- ccc() m\$measure(p1, p2) ## pearson correlation coefficient m <- pcc() m\$measure(p1, p2) ```