The components of a Random Planted Forest's prediction

Evaluates the components of a model at the rows of new_data: its intercept and one column per main effect and interaction. They are a functional decomposition of the prediction: for every row, the intercept plus the components equals the prediction. For a pruned model, the default of rpf(), these are its kept components.

Usage

predict_components(object, new_data, ...)

# S3 method for class 'rpf'
predict_components(
  object,
  new_data,
  max_interaction = NULL,
  predictors = NULL,
  ...
)

# S3 method for class 'rpf_pruned'
predict_components(
  object,
  new_data,
  max_interaction = NULL,
  predictors = NULL,
  ...
)

Arguments

object: [rpf | rpf_pruned]: A fitted rpf model, or a pruned one from prune_components() or rpf().
new_data: [data.frame | matrix]: New observations to predict.
...: Not currently used, but required for extensibility. Unknown arguments are an error.
max_interaction: [integer(1) | NULL: NULL]: Maximum degree of interactions to consider. NULL uses the max_interaction parameter from the rpf object. Must be between 1 (main effects only) and the max_interaction of the rpf object.
predictors: [character | NULL: NULL]: Vector of one or more names of the forest's predictors to extract components for. These are the columns the forest was fitted on: with a formula, its terms, such as log(x1). If NULL, all predictors and their interactions are returned, in the order of the fit's columns.

Value

A list with elements:

m (data.table): Components for each main effect and interaction term, representing the functional decomposition of the prediction. All components together with the intercept sum up to the prediction. For multiclass classification, the number of output columns is multiplied by the number of target_levels, the levels of the outcome: one column per component and level, named <component>__class:<level>. With loss = "logit" or "exponential" a component's columns sum to 0 across the levels, as the scores of predict() with type = "link" do.
intercept (numeric): Expected value of the prediction. For multiclass classification, one value per target level, named by target_levels.
x (data.table): The predictors selected by predictors, as the forest sees them in new_data (with a formula, its terms, such as log(x1)).
target_levels (character): For multiclass classification only: Vector of target levels which can be used to disassemble m, as names include both term and target level.
remainder (numeric): Only if m leaves out components of the forest: if predictors leaves out some of the forest's predictors, if max_interaction (lowered to the number of predictors) is below that of the rpf object, or if the forest was purified with a maxp_interaction below it (see purify()). The prediction minus intercept and m's row sums, so that the three sum to the prediction. For multiclass classification, one column per target level.

Details

Extracts all possible components up to max_interaction degrees, up to the value set when calling rpf(). The intercept is always included. Optionally predictors can be specified to only include components made of the given predictors; the sum of the other components is returned as remainder. If max_interaction is greater than length(predictors), the max_interaction will be lowered accordingly.

All components are evaluated in one pass over the rows of new_data. Components that the purified forest does not hold, such as sets of predictors that never appear together in a tree, are zero columns.

The components are only unique for a purified forest; purify() says how they are identified. An unpurified forest is purified in place on first use with the defaults of purify(). For other settings, such as more threads, call purify() before predict_components().

Note

Depending on the number of predictors and max_interaction, the number of components will increase drastically to sum(choose(ncol(new_data), seq_len(max_interaction))).

Pruned forests

For an rpf_pruned object from prune_components() or rpf(), m holds only the kept components, each scaled by its coefficient beta_S, and intercept is the pruned model's intercept alpha, so that they sum to predict() of the pruned model. Components that are not kept are absent, not zero columns. If predictors or max_interaction leave out kept components, their sum is returned as remainder.

Examples

# The default model: its kept components add up to its prediction
set.seed(1)
model <- rpf(mpg ~ wt + hp + cyl, data = mtcars)
components <- predict_components(model, mtcars[1:3, ])
components$m
#>            wt        hp        cyl
#>         <num>     <num>      <num>
#> 1:  0.3989752 0.2785334 -0.3703708
#> 2: -0.1242620 0.2785334 -0.3703708
#> 3:  1.6816513 1.1853078  2.4229759
components$intercept + rowSums(components$m)
#> [1] 20.50687 19.98363 25.48966
predict(model, mtcars[1:3, ])
#> # A tibble: 3 × 1
#>   .pred
#>   <dbl>
#> 1  20.5
#> 2  20.0
#> 3  25.5

# A forest: all its components up to its max_interaction
train <-  mtcars[1:20, 1:4]
test <-  mtcars[21:32, 1:4]

set.seed(23)
rpfit <- rpf(mpg ~ ., data = train, max_interaction = 3, n_families = 30, prune = FALSE)

# Extract all components, including main effects and interaction terms up to `max_interaction`
(components <- predict_components(rpfit, test))
#> $m
#>            cyl       disp         hp  cyl:disp      cyl:hp     disp:hp
#>          <num>      <num>      <num>     <num>       <num>       <num>
#>  1:  2.0588524  1.6373900  1.5625285 0.4989844 -0.24174939 -0.07853976
#>  2: -1.5316997 -1.2941107 -0.3316503 0.2765535  0.03790460  0.26998016
#>  3: -1.5316997 -1.2941107 -0.3316503 0.2765535  0.03790460  0.26998016
#>  4: -1.5316997 -1.2941107 -3.1737806 0.2765535 -0.28273580  0.13315752
#>  5: -1.5316997 -1.0895381 -0.5228127 0.2383035  0.07278092  0.41129734
#>  6:  2.0588524  3.1270869  3.0127215 0.8284196  0.29270117  0.84404186
#>  7:  2.0588524  1.6373900  3.0127215 0.4989844  0.29270117  0.48801491
#>  8:  2.0588524  3.1270869  0.4660429 0.8284196 -0.15597044 -0.16323737
#>  9: -1.5316997 -1.2941107 -3.1737806 0.2765535 -0.28273580  0.13315752
#> 10: -0.4691853  0.7975219 -0.5228127 0.1072327  0.15896496 -0.22308406
#> 11: -1.5316997 -1.2941107 -3.1737806 0.2765535 -0.28273580  0.13315752
#> 12:  2.0588524  1.6373900  1.1297472 0.4989844 -0.21032282 -0.01398476
#>     cyl:disp:hp
#>           <num>
#>  1: -0.03937451
#>  2:  0.02770790
#>  3:  0.02770790
#>  4:  0.01243666
#>  5:  0.02770790
#>  6:  0.08060198
#>  7: -0.04889802
#>  8:  0.07121579
#>  9:  0.01243666
#> 10:  0.01560123
#> 11:  0.01243666
#> 12: -0.04470784
#> 
#> $intercept
#> [1] 20.35293
#> 
#> $x
#>       cyl  disp    hp
#>     <num> <num> <num>
#>  1:     4 120.1    97
#>  2:     8 318.0   150
#>  3:     8 304.0   150
#>  4:     8 350.0   245
#>  5:     8 400.0   175
#>  6:     4  79.0    66
#>  7:     4 120.3    91
#>  8:     4  95.1   113
#>  9:     8 351.0   264
#> 10:     6 145.0   175
#> 11:     8 301.0   335
#> 12:     4 121.0   109
#> 
#> attr(,"class")
#> [1] "glex"           "rpf_components" "list"          

# sums to prediction
cbind(
  m_sum = rowSums(components$m) + components$intercept,
  prediction = predict(rpfit, test)
)
#>       m_sum    .pred
#> 1  25.75102 25.75102
#> 2  17.80761 17.80761
#> 3  17.80761 17.80761
#> 4  14.49275 14.49275
#> 5  17.95897 17.95897
#> 6  30.59735 30.59735
#> 7  28.29269 28.29269
#> 8  26.58534 26.58534
#> 9  14.49275 14.49275
#> 10 20.21717 20.21717
#> 11 14.49275 14.49275
#> 12 25.40889 25.40889

# Only get components with interactions of a lower degree, ignoring 3-way interactions
predict_components(rpfit, test, max_interaction = 2)
#> $m
#>            cyl       disp         hp  cyl:disp      cyl:hp     disp:hp
#>          <num>      <num>      <num>     <num>       <num>       <num>
#>  1:  2.0588524  1.6373900  1.5625285 0.4989844 -0.24174939 -0.07853976
#>  2: -1.5316997 -1.2941107 -0.3316503 0.2765535  0.03790460  0.26998016
#>  3: -1.5316997 -1.2941107 -0.3316503 0.2765535  0.03790460  0.26998016
#>  4: -1.5316997 -1.2941107 -3.1737806 0.2765535 -0.28273580  0.13315752
#>  5: -1.5316997 -1.0895381 -0.5228127 0.2383035  0.07278092  0.41129734
#>  6:  2.0588524  3.1270869  3.0127215 0.8284196  0.29270117  0.84404186
#>  7:  2.0588524  1.6373900  3.0127215 0.4989844  0.29270117  0.48801491
#>  8:  2.0588524  3.1270869  0.4660429 0.8284196 -0.15597044 -0.16323737
#>  9: -1.5316997 -1.2941107 -3.1737806 0.2765535 -0.28273580  0.13315752
#> 10: -0.4691853  0.7975219 -0.5228127 0.1072327  0.15896496 -0.22308406
#> 11: -1.5316997 -1.2941107 -3.1737806 0.2765535 -0.28273580  0.13315752
#> 12:  2.0588524  1.6373900  1.1297472 0.4989844 -0.21032282 -0.01398476
#> 
#> $intercept
#> [1] 20.35293
#> 
#> $x
#>       cyl  disp    hp
#>     <num> <num> <num>
#>  1:     4 120.1    97
#>  2:     8 318.0   150
#>  3:     8 304.0   150
#>  4:     8 350.0   245
#>  5:     8 400.0   175
#>  6:     4  79.0    66
#>  7:     4 120.3    91
#>  8:     4  95.1   113
#>  9:     8 351.0   264
#> 10:     6 145.0   175
#> 11:     8 301.0   335
#> 12:     4 121.0   109
#> 
#> $remainder
#>  [1] -0.03937451  0.02770790  0.02770790  0.01243666  0.02770790  0.08060198
#>  [7] -0.04889802  0.07121579  0.01243666  0.01560123  0.01243666 -0.04470784
#> 
#> attr(,"class")
#> [1] "glex"           "rpf_components" "list"          

# Only retrieve main effects
(main_effects <- predict_components(rpfit, test, max_interaction = 1))
#> $m
#>            cyl       disp         hp
#>          <num>      <num>      <num>
#>  1:  2.0588524  1.6373900  1.5625285
#>  2: -1.5316997 -1.2941107 -0.3316503
#>  3: -1.5316997 -1.2941107 -0.3316503
#>  4: -1.5316997 -1.2941107 -3.1737806
#>  5: -1.5316997 -1.0895381 -0.5228127
#>  6:  2.0588524  3.1270869  3.0127215
#>  7:  2.0588524  1.6373900  3.0127215
#>  8:  2.0588524  3.1270869  0.4660429
#>  9: -1.5316997 -1.2941107 -3.1737806
#> 10: -0.4691853  0.7975219 -0.5228127
#> 11: -1.5316997 -1.2941107 -3.1737806
#> 12:  2.0588524  1.6373900  1.1297472
#> 
#> $intercept
#> [1] 20.35293
#> 
#> $x
#>       cyl  disp    hp
#>     <num> <num> <num>
#>  1:     4 120.1    97
#>  2:     8 318.0   150
#>  3:     8 304.0   150
#>  4:     8 350.0   245
#>  5:     8 400.0   175
#>  6:     4  79.0    66
#>  7:     4 120.3    91
#>  8:     4  95.1   113
#>  9:     8 351.0   264
#> 10:     6 145.0   175
#> 11:     8 301.0   335
#> 12:     4 121.0   109
#> 
#> $remainder
#>  [1] 0.13932070 0.61214613 0.61214613 0.13941184 0.75008963 2.04576466
#>  [7] 1.23080242 0.58042762 0.13941184 0.05871484 0.13941184 0.22996894
#> 
#> attr(,"class")
#> [1] "glex"           "rpf_components" "list"          

# The difference is the combined contribution of interaction effects
cbind(
  m_sum = rowSums(main_effects$m) + main_effects$intercept,
  prediction = predict(rpfit, test)
)
#>       m_sum    .pred
#> 1  25.61170 25.75102
#> 2  17.19547 17.80761
#> 3  17.19547 17.80761
#> 4  14.35334 14.49275
#> 5  17.20888 17.95897
#> 6  28.55159 30.59735
#> 7  27.06189 28.29269
#> 8  26.00491 26.58534
#> 9  14.35334 14.49275
#> 10 20.15845 20.21717
#> 11 14.35334 14.49275
#> 12 25.17892 25.40889