Metrics on davethehuman.com

accuracy

Tue, 29 Sep 2026 00:00:00 +0000

Accuracy is the ratio of the correctly classified observations. In binary classification settings, it checks the sum of TP and TN over all the predictions:

$$ \mathrm{Accuracy} = \frac{TP + TN}{TP + TN + FP + FN} $$

It is very important to use this metric on datasets that do not suffer from class imbalance; for example, a model that always predicts “False” on a dataset having 99.9% of False observations will have a very high 0.999 accuracy score but it won’t be meaningful for detecting the True observations.

classification metrics

Tue, 29 Sep 2026 00:00:00 +0000

When building a classifier we want to minimize the number of misclassified observations. In binary cases, we talk about true positives, false positives, true negatives and false negatives that can be visualized in a confusion matrix:

The main classification metrics are:

Their usage depends on the classification task.

euclidean distance

Tue, 29 Sep 2026 00:00:00 +0000

The Euclidean distance is the measure of the true straight-line distance between two points in a Euclidean space. It is the geometric distance you would measure with a ruler, representing the shortest path between those points.

The Formula
#

$$ d(p, q) = \sqrt{\sum_{i=1}^{n} (q_i - p_i)^2} $$

In a 2D Space, for two points $P_1(x_1, y_1)$ and $P_2(x_2, y_2)$:

F1-score

Tue, 29 Sep 2026 00:00:00 +0000

F1-score (also called harmonic mean) is a metric that takes into account both precision and recall:

$$ \mathrm{F1} = \frac{2*Precision*Recall}{Precision + Recall} $$

It is widely used in NLP and it balances precision and recall, handling class imbalance and highlighting poor performance on minority classes.

FN

Tue, 29 Sep 2026 00:00:00 +0000

In binary classification, a False Negative (FN) is a misclassification of the model that assigns a “False” label to an observation whose label is actually “True”.

Used in the classification metrics.

FP

Tue, 29 Sep 2026 00:00:00 +0000

In binary classification, a False Positive (FP) is a misclassification of the model that assigns a “True” label to an observation whose actual label is “False”.

Used in the classification metrics.

FPR

Tue, 29 Sep 2026 00:00:00 +0000

False Positive Rate (FPR) is the ratio of the negative observations that are classified as positives (how many FP over the sum of FP and FN):

$$ \mathrm{FPR} = \frac{FP}{FP + TN} $$

It is used in ROC-AUC.

precision

Tue, 29 Sep 2026 00:00:00 +0000

Precision is the ratio of the observation classified as positives that are actually positives. In binary classification settings, it takes the number of TP and divides it by the sum of TP and FP:

$$ \mathrm{Precision} = \frac{TP}{TP + FP} $$

While recall uses in the denominator the total number of observations that are actually positives, precision uses the total number of observations that are classified as positives.

This metric is useful in cases of class imbalance and when the false positive creates severe inconvenience, financial loss or user distrust; a typical task where precision is used as a metric is spam detection.

recall

Tue, 29 Sep 2026 00:00:00 +0000

Recall is the ratio of the positive observations that are actually classified as positives. In binary classification setting, it takes the number of TP and divides it by the sum of TP and FN:

$$ \mathrm{Recall} = \frac{TP}{TP + FN} $$

It is also called sensitivity or true positive rate. the correctly classified observations.

While precision uses in the denominator the total number of observations classified as positives, recall uses the total number of observations that are actual positives.

RSS

Tue, 29 Sep 2026 00:00:00 +0000

The Residual Sum of Squares (RSS) is the loss function used in Linear Regression to find the weights.

$$ \operatorname{RSS} = \sum_{i=1}^{n} (y_i - \hat{y}_i)^2, \qquad \hat{y}_i = \beta_0 + x_i^{\mathsf{T}}\beta $$

It is also the core error metric used to build and optimize regression decision trees by selecting the best split that results in the lowest total RSS for the resulting child nodes:

$$RSS = \sum_{i \in R_1} (y_i - \hat{y}_{R_1})^2 + \sum_{i \in R_2} (y_i - \hat{y}_{R_2})^2$$

sensitivity

Tue, 29 Sep 2026 00:00:00 +0000

See recall.

TN

Tue, 29 Sep 2026 00:00:00 +0000

In binary classification, a True Negative (TN) is a correct classification of the model that assigns a “False” label to an observation whose label is “False”.

Used in the classification metrics.

TP

Tue, 29 Sep 2026 00:00:00 +0000

In binary classification, a True Positive (TP) is a correct classification of the model that assigns a “True” label to an observation whose label is “True”.

Used in the classification metrics.

TPR

Tue, 29 Sep 2026 00:00:00 +0000

See recall.

Metrics on davethehuman.com

accuracy

classification metrics

euclidean distance

The Formula #

F1-score

FN

FP

FPR

precision

recall

RSS

sensitivity

TN

TP

TPR

The Formula
#