Add A3I anomaly detection intro

src/year2/artificial-intelligence-in-industry/sections/_anomaly_detection.tex

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+\chapter{Anomaly detection: Taxi calls}
+
+\begin{description}
+    \item[Anomaly] \marginnote{Anomaly}
+        Event that deviates from the usual pattern.
+
+    \item[Time series] \marginnote{Time series}
+        Data with an ordering (e.g., chronological).
+\end{description}
+
+
+
+\section{Data}
+
+The dataset is a time series and it is a \texttt{DataFrame} with the following fields:
+\begin{descriptionlist}
+    \item[\texttt{timestamp}] with a 30 minutes granularity.
+    \item[\texttt{value}] number of calls.
+\end{descriptionlist}
+
+The label is a \texttt{Series} containing the timestamps of the anomalies.
+
+An additional \texttt{DataFrame} contains information about the time window in which the anomalies happen:
+\begin{descriptionlist}
+    \item[\texttt{begin}] acceptable moment from which an anomaly can be detected.
+    \item[\texttt{end}] acceptable moment from which there are no anomalies anymore.
+\end{descriptionlist}
+
+\begin{figure}[H]
+    \centering
+    \includegraphics[width=0.7\linewidth]{./img/_ad_taxi_data.pdf}
+    \caption{Plot of the time series, anomalies, and windows}
+\end{figure}
+
+
+
+\section{Approaches}
+
+
+\subsection{Gaussian assumption}
+
+Assuming that the data follows a Gaussian distribution, mean and variance can be used to determine anomalies through a threshold. $z$-score can also be used.
+
+
+\subsection{Characterize data distribution}
+
+Classify a data point as an anomaly if it is too unlikely.
+
+\begin{description}
+    \item[Formalization] 
+        Given a random variable $X$ with values $x$ to represent the number of taxi calls, we want to find its probability density function (PDF) $f(x)$.
+
+        An anomaly is determined whether:
+        \[ f(x) \leq \varepsilon \]
+        where $\varepsilon$ is a threshold.
+
+        \begin{remark}
+            The PDF can be reasonably used even though the dataset is discrete if its data points are sufficiently fine-grained.
+        \end{remark}
+\end{description}