Summarize distributions with ROC curve
These functions help you perform a ROC ("Receiver Operating Characteristic")
analysis for one-dimensional linear classifier: values not more than some
threshold are classified as "negative", and more than threshold -
as "positive". Here input pair of pdqr-functions represent "true"
distributions of values with "negative" (f) and "positive" (g) labels.
summ_roc(f, g, n_grid = 1001) summ_rocauc(f, g, method = "expected") roc_plot(roc, ..., add_bisector = TRUE) roc_lines(roc, ...)
f |
A pdqr-function of any type and class. Represents "true" distribution of "negative" values. |
g |
A pdqr-function of any type and class. Represents "true" distribution of "positive" values. |
n_grid |
Number of points of ROC curve to be computed. |
method |
Method of computing ROC AUC. Should be one of "expected", "pessimistic", "optimistic" (see Details). |
roc |
A data frame representing ROC curve. Typically an output of
|
... |
Other arguments to be passed to |
add_bisector |
If |
ROC curve describes how well classifier performs under different thresholds. For all possible thresholds two classification metrics are computed which later form x and y coordinates of a curve:
False positive rate (FPR): proportion of "negative" distribution which was (incorrectly) classified as "positive". This is the same as one minus "specificity" (proportion of "negative" values classified as "negative").
True positive rate (TPR): proportion of "positive" distribution which was (correctly) classified as "positive". This is also called "sensitivity".
summ_roc() creates a uniform grid of decreasing n_grid values (so that
output points of ROC curve are ordered from left to right) covering range of
all meaningful thresholds. This range is computed as slightly extended range
of f and g supports (extension is needed to achieve extreme values of
"fpr" in presence of "discrete" type). Then FPR and TPR are computed for
every threshold.
summ_rocauc() computes a common general (without any particular threshold
in mind) diagnostic value of classifier, area under ROC curve ("ROC AUC"
or "AUROC"). Numerically it is equal to a probability of random variable with
distribution g being strictly greater than f plus possible correction
for functions being equal, with multiple ways to account for it. Method
"pessimistic" doesn't add correction, "expected" adds half of probability of
f and g being equal (which is default), "optimistic" adds full
probability. Note that this means that correction might be done only if
both input pdqr-functions have "discrete" type. See pdqr methods for "Ops" group generic family for more details on comparing
functions.
summ_roc() returns a data frame with n_grid rows and columns
"threshold" (grid of classification thresholds, ordered decreasingly), "fpr",
and "tpr" (corresponding false and true positive rates, ordered
non-decreasingly by "fpr").
summ_rocauc() returns single number representing area under the ROC curve.
roc_plot() and roc_lines() create plotting side effects.
summ_separation() for computing optimal separation threshold.
Other summary functions:
summ_center(),
summ_classmetric(),
summ_distance(),
summ_entropy(),
summ_hdr(),
summ_interval(),
summ_moment(),
summ_order(),
summ_prob_true(),
summ_pval(),
summ_quantile(),
summ_separation(),
summ_spread()
d_norm_1 <- as_d(dnorm) d_norm_2 <- as_d(dnorm, mean = 1) roc <- summ_roc(d_norm_1, d_norm_2) head(roc) # `summ_rocauc()` is equivalent to probability of `g > f` summ_rocauc(d_norm_1, d_norm_2) summ_prob_true(d_norm_2 > d_norm_1) # Plotting roc_plot(roc) roc_lines(summ_roc(d_norm_2, d_norm_1), col = "blue") # For "discrete" functions `summ_rocauc()` can produce different outputs d_dis_1 <- new_d(1:2, "discrete") d_dis_2 <- new_d(2:3, "discrete") summ_rocauc(d_dis_1, d_dis_2) summ_rocauc(d_dis_1, d_dis_2, method = "pessimistic") summ_rocauc(d_dis_1, d_dis_2, method = "optimistic") ## These methods correspond to different ways of plotting ROC curves roc <- summ_roc(d_dis_1, d_dis_2) ## Default line plot for "expected" method roc_plot(roc, main = "Different type of plotting ROC curve") ## Method "pessimistic" roc_lines(roc, type = "s", col = "blue") ## Method "optimistic" roc_lines(roc, type = "S", col = "green")
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