NaiveBayes models

Function	Works
`tidypredict_fit()`, `tidypredict_sql()`, `parse_model()`	✔
`tidypredict_to_column()`	✗
`tidypredict_test()`	✗
`tidypredict_interval()`, `tidypredict_sql_interval()`	✗
`parsnip`	✔

klaR::NaiveBayes() and naivebayes::naive_bayes() fit naive Bayes classifiers. Predicting with such a model multiplies the prior probability of each class by one conditional density per predictor, and then normalizes those products into posterior probabilities. Working on the log scale turns the products into sums, which makes the posterior probabilities the softmax of the summed log densities.

Numeric predictors contribute a normal log density, and categorical predictors contribute a case_when() lookup of the conditional probability of the observed level. naivebayes::naive_bayes() additionally supports Poisson densities for integer predictors when fit with usepoisson = TRUE. Kernel density estimates cannot be expressed this way, so models fit with usekernel = TRUE are not supported.

Because these models predict one probability per outcome class, tidypredict_fit() returns a named list of expressions, one for each class, rather than a single expression. Since the output is a list, tidypredict_to_column() and tidypredict_test() are not supported.

`tidypredict_` functions

model <- klaR::NaiveBayes(Species ~ ., data = iris)

Create the R formulas, one per class

fit <- tidypredict_fit(model)
names(fit)
#> [1] "setosa"     "versicolor" "virginica"
fit[["setosa"]]
#> exp(-1.09861228866811 + (1.04273391328984 - ((Sepal.Length - 
#>     5.006)^2/0.248497959183673)) + (0.970049249016581 - ((Sepal.Width - 
#>     3.428)^2/0.287379591836735)) + (1.75063290136911 - ((Petal.Length - 
#>     1.462)^2/0.0603183673469388)) + (2.25012937537181 - ((Petal.Width - 
#>     0.246)^2/0.0222122448979592)))/(exp(-1.09861228866811 + (1.04273391328984 - 
#>     ((Sepal.Length - 5.006)^2/0.248497959183673)) + (0.970049249016581 - 
#>     ((Sepal.Width - 3.428)^2/0.287379591836735)) + (1.75063290136911 - 
#>     ((Petal.Length - 1.462)^2/0.0603183673469388)) + (2.25012937537181 - 
#>     ((Petal.Width - 0.246)^2/0.0222122448979592))) + exp(-1.09861228866811 + 
#>     (0.661316888138019 - ((Sepal.Length - 5.936)^2/0.532865306122449)) + 
#>     (1.15900478165984 - ((Sepal.Width - 2.77)^2/0.196938775510204)) + 
#>     (0.755212012346146 - ((Petal.Length - 4.26)^2/0.441632653061225)) + 
#>     (1.620738119938 - ((Petal.Width - 1.326)^2/0.0782122448979592))) + 
#>     exp(-1.09861228866811 + (0.452746052315965 - ((Sepal.Length - 
#>         6.588)^2/0.808685714285714)) + (1.13166256707153 - ((Sepal.Width - 
#>         2.974)^2/0.208008163265306)) + (0.594398019628377 - ((Petal.Length - 
#>         5.552)^2/0.609175510204082)) + (1.29225751662055 - ((Petal.Width - 
#>         2.026)^2/0.150865306122449))))

Add the predictions to the original table

library(dplyr)

iris %>%
  mutate(!!!tidypredict_fit(model)) %>%
  glimpse()
#> Rows: 150
#> Columns: 8
#> $ Sepal.Length <dbl> 5.1, 4.9, 4.7, 4.6, 5.0, 5.4, 4.6, 5.0, 4.4, 4.9…
#> $ Sepal.Width  <dbl> 3.5, 3.0, 3.2, 3.1, 3.6, 3.9, 3.4, 3.4, 2.9, 3.1…
#> $ Petal.Length <dbl> 1.4, 1.4, 1.3, 1.5, 1.4, 1.7, 1.4, 1.5, 1.4, 1.5…
#> $ Petal.Width  <dbl> 0.2, 0.2, 0.2, 0.2, 0.2, 0.4, 0.3, 0.2, 0.2, 0.1…
#> $ Species      <fct> setosa, setosa, setosa, setosa, setosa, setosa, …
#> $ setosa       <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, …
#> $ versicolor   <dbl> 2.981309e-18, 3.169312e-17, 2.367113e-18, 3.0696…
#> $ virginica    <dbl> 2.152373e-25, 6.938030e-25, 7.240956e-26, 8.6906…

Confirm that the results match the model’s predict() results

probs <- sapply(fit, \(f) rlang::eval_tidy(f, iris))
all.equal(unname(probs), unname(predict(model, iris)$posterior))
#> [1] TRUE

parsnip

parsnip fitted models are also supported by tidypredict:

library(parsnip)
library(discrim)

p_model <- naive_Bayes() %>%
  set_engine("klaR", usekernel = FALSE) %>%
  fit(Species ~ ., data = iris)

tidypredict_fit(p_model)[["virginica"]]
#> exp(-1.09861228866811 + (0.452746052315965 - ((Sepal.Length - 
#>     6.588)^2/0.808685714285714)) + (1.13166256707153 - ((Sepal.Width - 
#>     2.974)^2/0.208008163265306)) + (0.594398019628377 - ((Petal.Length - 
#>     5.552)^2/0.609175510204082)) + (1.29225751662055 - ((Petal.Width - 
#>     2.026)^2/0.150865306122449)))/(exp(-1.09861228866811 + (1.04273391328984 - 
#>     ((Sepal.Length - 5.006)^2/0.248497959183673)) + (0.970049249016581 - 
#>     ((Sepal.Width - 3.428)^2/0.287379591836735)) + (1.75063290136911 - 
#>     ((Petal.Length - 1.462)^2/0.0603183673469388)) + (2.25012937537181 - 
#>     ((Petal.Width - 0.246)^2/0.0222122448979592))) + exp(-1.09861228866811 + 
#>     (0.661316888138019 - ((Sepal.Length - 5.936)^2/0.532865306122449)) + 
#>     (1.15900478165984 - ((Sepal.Width - 2.77)^2/0.196938775510204)) + 
#>     (0.755212012346146 - ((Petal.Length - 4.26)^2/0.441632653061225)) + 
#>     (1.620738119938 - ((Petal.Width - 1.326)^2/0.0782122448979592))) + 
#>     exp(-1.09861228866811 + (0.452746052315965 - ((Sepal.Length - 
#>         6.588)^2/0.808685714285714)) + (1.13166256707153 - ((Sepal.Width - 
#>         2.974)^2/0.208008163265306)) + (0.594398019628377 - ((Petal.Length - 
#>         5.552)^2/0.609175510204082)) + (1.29225751662055 - ((Petal.Width - 
#>         2.026)^2/0.150865306122449))))

`naivebayes::naive_bayes()`

The naivebayes package is supported in the same way:

nb_model <- naivebayes::naive_bayes(Species ~ ., data = iris)

nb_fit <- tidypredict_fit(nb_model)
nb_fit[["setosa"]]
#> exp(-1.09861228866811 + (1.04273391328984 - ((Sepal.Length - 
#>     5.006)^2/0.248497959183673)) + (0.970049249016581 - ((Sepal.Width - 
#>     3.428)^2/0.287379591836735)) + (1.75063290136911 - ((Petal.Length - 
#>     1.462)^2/0.0603183673469388)) + (2.25012937537181 - ((Petal.Width - 
#>     0.246)^2/0.0222122448979592)))/(exp(-1.09861228866811 + (1.04273391328984 - 
#>     ((Sepal.Length - 5.006)^2/0.248497959183673)) + (0.970049249016581 - 
#>     ((Sepal.Width - 3.428)^2/0.287379591836735)) + (1.75063290136911 - 
#>     ((Petal.Length - 1.462)^2/0.0603183673469388)) + (2.25012937537181 - 
#>     ((Petal.Width - 0.246)^2/0.0222122448979592))) + exp(-1.09861228866811 + 
#>     (0.661316888138019 - ((Sepal.Length - 5.936)^2/0.532865306122449)) + 
#>     (1.15900478165984 - ((Sepal.Width - 2.77)^2/0.196938775510204)) + 
#>     (0.755212012346146 - ((Petal.Length - 4.26)^2/0.441632653061225)) + 
#>     (1.620738119938 - ((Petal.Width - 1.326)^2/0.0782122448979592))) + 
#>     exp(-1.09861228866811 + (0.452746052315965 - ((Sepal.Length - 
#>         6.588)^2/0.808685714285714)) + (1.13166256707153 - ((Sepal.Width - 
#>         2.974)^2/0.208008163265306)) + (0.594398019628377 - ((Petal.Length - 
#>         5.552)^2/0.609175510204082)) + (1.29225751662055 - ((Petal.Width - 
#>         2.026)^2/0.150865306122449))))

nb_probs <- sapply(nb_fit, \(f) rlang::eval_tidy(f, iris))
all.equal(
  unname(nb_probs),
  unname(predict(nb_model, iris[names(nb_model$tables)], type = "prob"))
)
#> [1] TRUE

The "naivebayes" parsnip engine works too, as long as usekernel = FALSE:

nb_p_model <- naive_Bayes() %>%
  set_engine("naivebayes", usekernel = FALSE) %>%
  fit(Species ~ ., data = iris)

tidypredict_fit(nb_p_model)[["virginica"]]
#> exp(-1.09861228866811 + (0.452746052315965 - ((Sepal.Length - 
#>     6.588)^2/0.808685714285714)) + (1.13166256707153 - ((Sepal.Width - 
#>     2.974)^2/0.208008163265306)) + (0.594398019628377 - ((Petal.Length - 
#>     5.552)^2/0.609175510204082)) + (1.29225751662055 - ((Petal.Width - 
#>     2.026)^2/0.150865306122449)))/(exp(-1.09861228866811 + (1.04273391328984 - 
#>     ((Sepal.Length - 5.006)^2/0.248497959183673)) + (0.970049249016581 - 
#>     ((Sepal.Width - 3.428)^2/0.287379591836735)) + (1.75063290136911 - 
#>     ((Petal.Length - 1.462)^2/0.0603183673469388)) + (2.25012937537181 - 
#>     ((Petal.Width - 0.246)^2/0.0222122448979592))) + exp(-1.09861228866811 + 
#>     (0.661316888138019 - ((Sepal.Length - 5.936)^2/0.532865306122449)) + 
#>     (1.15900478165984 - ((Sepal.Width - 2.77)^2/0.196938775510204)) + 
#>     (0.755212012346146 - ((Petal.Length - 4.26)^2/0.441632653061225)) + 
#>     (1.620738119938 - ((Petal.Width - 1.326)^2/0.0782122448979592))) + 
#>     exp(-1.09861228866811 + (0.452746052315965 - ((Sepal.Length - 
#>         6.588)^2/0.808685714285714)) + (1.13166256707153 - ((Sepal.Width - 
#>         2.974)^2/0.208008163265306)) + (0.594398019628377 - ((Petal.Length - 
#>         5.552)^2/0.609175510204082)) + (1.29225751662055 - ((Petal.Width - 
#>         2.026)^2/0.150865306122449))))

Parse model spec

Here is an example of the model spec:

pm <- parse_model(model)
str(pm, 2)
#> List of 3
#>  $ general    :List of 4
#>   ..$ model    : chr "NaiveBayes"
#>   ..$ version  : num 2
#>   ..$ type     : chr "naive_bayes"
#>   ..$ threshold: num 0.001
#>  $ classes    : chr [1:3] "setosa" "versicolor" "virginica"
#>  $ class_terms:List of 3
#>   ..$ :List of 2
#>   ..$ :List of 2
#>   ..$ :List of 2
#>  - attr(*, "class")= chr [1:3] "parsed_model" "pm_naive_bayes" "list"

tidypredict_ functions

parsnip

naivebayes::naive_bayes()

Parse model spec

`tidypredict_` functions

`naivebayes::naive_bayes()`