Skip to contents

Find tautologies or "almost tautologies" in a dataset

Source: R/dig_tautologies.R
dig_tautologies.Rd

This function finds tautologies (data-driven axioms) in a dataset, i.e., rules of the form {a1 & a2 & ... & an} => {c} where a1, a2, ..., an are antecedents and c is a consequent that holds with very high confidence. Such rules can serve as axioms for pruning further pattern searches: the resulting list of rules can be passed directly to the excluded argument of dig(), dig_associations(), or related functions via parse_condition(result$antecedent, result$consequent).

The search is performed by iteratively searching for rules with increasing length of the antecedent. Rules found in previous iterations are used as axioms (the excluded argument) in the next iteration, so that rules whose consequent can already be deduced from a shorter antecedent are not reported again.

Usage

dig_tautologies(
  x,
  antecedent = everything(),
  consequent = everything(),
  disjoint = var_names(colnames(x)),
  max_length = Inf,
  min_coverage = 0,
  min_support = 0,
  min_confidence = 0,
  contingency_table = deprecated(),
  t_norm = "goguen",
  max_results = Inf,
  verbose = FALSE,
  threads = 1
)

Arguments

x

a matrix or data frame with data to search in. The matrix must be numeric (double) or logical. If x is a data frame then each column must be either numeric (double) or logical.

antecedent

a tidyselect expression (see tidyselect syntax) specifying the columns to use in the antecedent (left) part of the rules

consequent

a tidyselect expression (see tidyselect syntax) specifying the columns to use in the consequent (right) part of the rules

disjoint

an atomic vector of size equal to the number of columns of x that specifies the groups of predicates: if some elements of the disjoint vector are equal, then the corresponding columns of x will NOT be present together in a single condition. If x is prepared with partition(), using the var_names() function on x's column names is a convenient way to create the disjoint vector.

max_length

The maximum length, i.e., the maximum number of predicates in the antecedent, of a rule to be generated. If equal to Inf, the maximum length is limited only by the number of available predicates.

min_coverage

the minimum coverage of a rule in the dataset x. (See Description for the definition of coverage.)

min_support

the minimum support of a rule in the dataset x. (See Description for the definition of support.)

min_confidence

the minimum confidence of a rule in the dataset x. (See Description for the definition of confidence.)

contingency_table

(Deprecated.) A logical value indicating whether to provide a contingency table for each rule. If TRUE, the columns pp, pn, np, and nn are added to the output table. These columns contain the number of rows satisfying the antecedent and the consequent, the antecedent but not the consequent, the consequent but not the antecedent, and neither the antecedent nor the consequent, respectively.

t_norm

a t-norm used to compute conjunction of weights. It must be one of "goedel" (minimum t-norm), "goguen" (product t-norm), or "lukas" (Łukasiewicz t-norm).

max_results

the maximum number of generated conditions to execute the callback function on. If the number of found conditions exceeds max_results, the function stops generating new conditions and returns the results. To avoid long computations during the search, it is recommended to set max_results to a reasonable positive value. Setting max_results to Inf will generate all possible conditions.

verbose

a logical value indicating whether to print progress messages.

threads

the number of threads to use for parallel computation.

Value

An S3 object which is an instance of associations and nugget classes and which is a tibble with found tautologies in the format equal to the output of dig_associations().

Author

Michal Burda

Examples

d <- partition(mtcars, .breaks = 2)
dig_tautologies(d,
                antecedent = everything(),
                consequent = everything(),
                max_length = 3,
                min_confidence = 0.99)
#> # A tibble: 575 × 13
#>    antecedent  consequent support confidence coverage conseq_support  lift count
#>    <chr>       <chr>        <dbl>      <dbl>    <dbl>          <dbl> <dbl> <dbl>
#>  1 {gear=(-In… {carb=(-I…   0.844          1    0.844          0.938  1.07    27
#>  2 {am=(-Inf;… {carb=(-I…   0.594          1    0.594          0.938  1.07    19
#>  3 {am=(-Inf;… {gear=(-I…   0.594          1    0.594          0.844  1.19    19
#>  4 {cyl=(-Inf… {disp=(-I…   0.562          1    0.562          0.562  1.78    18
#>  5 {cyl=(-Inf… {hp=(-Inf…   0.562          1    0.562          0.781  1.28    18
#>  6 {cyl=(-Inf… {wt=(-Inf…   0.562          1    0.562          0.656  1.52    18
#>  7 {disp=(-In… {hp=(-Inf…   0.562          1    0.562          0.781  1.28    18
#>  8 {disp=(-In… {wt=(-Inf…   0.562          1    0.562          0.656  1.52    18
#>  9 {disp=(-In… {cyl=(-In…   0.562          1    0.562          0.562  1.78    18
#> 10 {vs=(-Inf;… {qsec=(-I…   0.562          1    0.562          0.719  1.39    18
#> # ℹ 565 more rows
#> # ℹ 5 more variables: antecedent_length <int>, pp <dbl>, pn <dbl>, np <dbl>,
#> #   nn <dbl>