vault backup: 2026-05-21 10:40:34

Running Start/CSB320 - Machine Learning Concepts/Class 4-23 (Model Validation & Evaluation).md

@@ -67,3 +67,14 @@ There are many ways to evaluate the performance of models. This is necessary to
 Loss functions are meant to quantify the difference between observed values and the predictions of a model. They can be used to minimize loss and improve model performance.
 ### Absolute Loss
 $$Y_{i} - \hat{Y}_{i}$$
+Used to measure the difference from the observed value and predicted value by the model.
+### Mean Absolute Error
+$$MAE=\frac{1}{n}\sum|\hat{Y}_{i} - Y_{i}|$$
+Calculates the average absolute loss of a model based on a training set of data. Is a metric that can be used to improve the accuracy of a model and train it. Should be minimized.
+
+Mean squared error is also used to penalize predictions that are further from observed values more heavily.
+$$MSE = \frac{1}{n}\sum(\hat{Y}_{i} - Y_{i})^2$$
+Since MSE produces a convex curve in the error metric it also allows the use of algorithms like gradient descent optimization to tune the weights of a model.
+### Log Loss
+$$L_{\log}(y_{i}, \hat{p}_{i}) = -(y_{i}\ln(\hat{p}_{i}) + (1-y_{i})\ln(1-\hat{p}_{i}))$$
+Log loss is used to optimize the weights of a logistic regression. MSE cannot be used since a logistic regression is not linear and the error with respect to weights does not have a clear minimum. This makes it challengin