## 1 Introduction  
Anomaly detection [1; 2; 3] in machine learning refers to the task of identifying data points, events, or observations that deviate significantly from the expected or typical patterns in a dataset. Anomalies are also referred to as outliers, deviations, or exceptions. This process is critical in many real-world applications because anomalies often represent critical, rare, or unexpected events, such as system failures, fraud, or unusual behaviors.  
There are different types of anomaly detection. Point anomaly is a single data point that is considered anomalous if it differs significantly from the rest of the data. For example, in a dataset of daily sales, one day has unusually high or low sales compared to other days. In the case of contextual anomalies, a data point is anomalous within a specific context, even if it might not be anomalous in general. For example, a high temperature may be normal in summer but anomalous in winter. Collective anomalies are a group of data points that are anomalous if they deviate from the overall dataset pattern, even if individual data points may not be anomalous by themselves, for example, series of small fraudulent transactions that are each individually not alarming but collectively may indicate fraud.  
In machine learning there are three general approaches to anomaly detection, depending on the training data type that is available:  
* Supervised anomaly detection--In this approach, the dataset contains labeled examples of normal and anomalous data. Supervised learning algorithms are trained to classify future data points as normal or anomalous. Example: Fraud detection in credit card transactions where labeled fraudulent and non-fraudulent transactions are available.  
* Semi-supervised anomaly detection--In this scenario, the model is trained only on normal data, and when applying the model to new data anything that significantly deviates from the learned normal pattern is flagged as an anomaly. Example: Predictive maintenance of industrial equipment where the system only learns normal operational data.
* Unsupervised anomaly detection--In this method, the training dataset does not have labeled anomalies, but it is assumed that the anomalies are there in the training set. The algorithm identifies anomalies based on deviations from the normal distribution or patterns of the data. Example: Network intrusion detection where the system learns to recognize unusual network traffic without any prior knowledge of attacks.  
There are numerous examples of applications of anomaly detection models, such as fraud detection (identifying fraudulent activities in credit card transactions, insurance claims, or financial statements) [4; 5; 6], network security (detecting unusual network traffic patterns that may indicate cyber-attacks or unauthorized access) [7; 8; 9; 10], healthcare (identifying abnormal patient conditions or rare diseases based on medical records and health data) [11; 12; 13; 14], manufacturing (detecting faults or defects in production lines, equipment, or sensors to enable predictive maintenance) [15; 16; 17; 18], finance (monitoring stock price fluctuations or market behaviors to detect irregular activities or insider trading) [19; 20; 21], autonomous vehicles (detecting unusual sensor readings or behaviors that may indicate malfunctioning sensors or dangerous driving conditions) [22; 23; 24], and many others.