In some fields, class probability predictions must meet certain standards before a firm decision can be made using them. If they fail these standards, the prediction can be marked as equivocal, which just means that you are unsure of the true result. You might want to further investigate these equivocal values, or rerun whatever process generated them before proceeding.
For example, in a binary model, if a prediction returned probability values of 52% Yes and 48% No, are you really sure that that isn’t just random noise? In this case, you could use a buffer surrounding a threshold of 50% to determine whether or not your model is sure of its predictions, and mark values you are unsure about as equivocal.
Another example could come from a Bayesian perspective, where each prediction comes with a probability distribution. Your model might predict 80% Yes, but could have a standard deviation around that of +/- 20%. In this case, you could set a maximum allowed standard deviation as the cutoff of whether or not to mark values as equivocal.
To work with these equivocal zones, probably provides a new class for hard class predictions that is very similar to a factor, but allows you to mark certain values as equivocal.
<- factor(c("Yes", "No", "Yes", "Yes")) x # Create a class_pred object from a factor class_pred(x) #>  Yes No Yes Yes #> Levels: No Yes #> Reportable: 100% # Say you aren't sure about that 2nd "Yes" value. # You could mark it as equivocal. class_pred(x, which = 3) #>  Yes No [EQ] Yes #> Levels: No Yes #> Reportable: 75%
The reportable rate is the fraction of values that are not equivocal, relative to the total number. Above, you can see that the reportable rate started at 100%, but as soon as a single value was marked equivocal, that value dropped to 75%. In fields where equivocal zones are used, there is often a tradeoff between marking values as equivocal and keeping a certain minimum reportable rate.
Generally, you won’t create these
directly, but will instead create them indirectly through converting
class probabilities into class predictions with
library(dplyr) data("segment_logistic") segment_logistic#> # A tibble: 1,010 × 3 #> .pred_poor .pred_good Class #> * <dbl> <dbl> <fct> #> 1 0.986 0.0142 poor #> 2 0.897 0.103 poor #> 3 0.118 0.882 good #> 4 0.102 0.898 good #> 5 0.991 0.00914 poor #> 6 0.633 0.367 good #> 7 0.770 0.230 good #> 8 0.00842 0.992 good #> 9 0.995 0.00458 poor #> 10 0.765 0.235 poor #> # … with 1,000 more rows # Convert probabilities into predictions # > 0.5 = good # < 0.5 = poor <- segment_logistic %>% segment_logistic_thresh mutate( .pred = make_two_class_pred( estimate = .pred_good, levels = levels(Class), threshold = 0.5 ) ) segment_logistic_thresh#> # A tibble: 1,010 × 4 #> .pred_poor .pred_good Class .pred #> <dbl> <dbl> <fct> <clss_prd> #> 1 0.986 0.0142 poor poor #> 2 0.897 0.103 poor poor #> 3 0.118 0.882 good good #> 4 0.102 0.898 good good #> 5 0.991 0.00914 poor poor #> 6 0.633 0.367 good poor #> 7 0.770 0.230 good poor #> 8 0.00842 0.992 good good #> 9 0.995 0.00458 poor poor #> 10 0.765 0.235 poor poor #> # … with 1,000 more rows
buffer is used, an equivocal zone is created around
the threshold of
threshold +/- buffer and any values inside
the zone are automatically marked as equivocal.
# Convert probabilities into predictions # x > 0.55 = good # x < 0.45 = poor # 0.45 < x < 0.55 = equivocal <- segment_logistic %>% segment_pred mutate( .pred = make_two_class_pred( estimate = .pred_good, levels = levels(Class), threshold = 0.5, buffer = 0.05 ) ) %>% segment_pred count(.pred) #> # A tibble: 3 × 2 #> .pred n #> <clss_prd> <int> #> 1 [EQ] 45 #> 2 good 340 #> 3 poor 625 %>% segment_pred summarise(reportable = reportable_rate(.pred)) #> # A tibble: 1 × 1 #> reportable #> <dbl> #> 1 0.955
Equivocal values in
class_pred objects are converted to
NA when the object is converted to a factor. It’s also
worth noting that the
[EQ] label is not treated as a
%>% segment_pred mutate(.pred_fct = as.factor(.pred)) %>% count(.pred, .pred_fct) #> # A tibble: 3 × 3 #> .pred .pred_fct n #> <clss_prd> <fct> <int> #> 1 [EQ] <NA> 45 #> 2 good good 340 #> 3 poor poor 625 levels(segment_pred$.pred) #>  "good" "poor"
NA behavior feeds into how probably can be used
with yardstick. Generally, equivocal values are removed completely from
performance evaluation. So converting them to
NA and then
leaving the default
na_rm = TRUE in any yardstick metric
removes them from consideration.
library(yardstick) #> For binary classification, the first factor level is assumed to be the event. #> Use the argument `event_level = "second"` to alter this as needed. # No equivocal zone %>% segment_logistic_thresh mutate(.pred_fct = as.factor(.pred)) %>% precision(Class, .pred_fct) #> # A tibble: 1 × 3 #> .metric .estimator .estimate #> <chr> <chr> <dbl> #> 1 precision binary 0.680 # Equivocal zone %>% segment_pred mutate(.pred_fct = as.factor(.pred)) %>% precision(Class, .pred_fct) #> # A tibble: 1 × 3 #> .metric .estimator .estimate #> <chr> <chr> <dbl> #> 1 precision binary 0.694
As seen above, removing equivocal values using a simple threshold generally improves performance because the values your model is most unsure about are removed. But don’t be fooled! You should give those cases extra consideration, and remember that your reportable rate has decreased by removing them. In production, you’ll likely have to do something with those predictions!