Anomaly detection in machine learning refers to the identification of items, events, or observations that deviate significantly from the expected pattern in a dataset. These anomalies, also known as outliers, are often indicative of some sort of problem or unusual circumstance, and it's often important to be able to detect and investigate these anomalies.

suppose a data point is there p(x test), if p(x test)<Σ then the point can be said to be an anomaly,

if p(x test)≥Σ then the point is said to be an okay.

Gaussian Distribution :

The Gaussian distribution is given by:

μ → shows the graph peak point (graph peak will be created on that point)

σ → shows the width of the graph

Estimating Parameters for a Gaussian:

$\mu_i=\frac{1}{m}\sum_{j=1}^{m}x_i^{(j)}$

$\sigma_i^2=\frac{1}{m}\sum_{j=1}^{m}\left(x_i^{(j)}-\mu_i\right)^2$

Density Estimation :

Anomaly detection algorithm :

Anomaly detection vs. Supervised learning :