# Outlier Detection for Multivariate Time Series Using Dynamic Bayesian Networks
## 5 Conclusions  
The presence of outliers can severely distort data analysis and, consequently, hamper statistical model identification. Outlier detection has become a very challenging task in many application fields. For example, in medical scans, outliers elicit abnormal or \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Experiment** & **TP** & **FP** & **TN** & **FN** & **PPV** & **TPR** & **ACC** & **F\({}_{1}\)** \\ \hline \(D_{7}\) & 24 & 41 & 1102 & 106 & 0.37 & 0.18 & 0.88 & 0.25 \\ \(D_{8}\) & 98 & 45 & 1098 & 32 & 0.69 & 0.75 & 0.94 & 0.72 \\ \(D_{9}\) & 90 & 42 & 1101 & 40 & 0.68 & 0.69 & 0.94 & 0.69 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of pen digits outlier detection experiments. Figure 9: Transition outlierness for mortality datasets of 5 (**a**) and 6 (**b**) variables using a third-order tDBN (\(m=3\)) with one inter-slice connectivity per node (\(p=1\)). Dataset (**a**) is comprised by 5 variables (\(n=5\)) representing mortality rates of males with ages 20, 30, 40, 60 and 80. Dataset (**b**) includes the same variables as (**a**) with the addition of a variable representing the mortality rate of males aged 10 (\(n=6\)). Transitions are arranged by year and classified as anomalous (red) and normal (green). Major wars and epidemics which affected France in the selected years are exhibited. changed patterns, and therefore, their detection may help detect certain types of diseases. When following-up patients, detecting patient outliers governed by abnormal temporal patterns can advance pharmaceutical or medical research. Still, versatile and automatic outlier detection methods for MTS are almost inexistent, with scarce available algorithms and software. The developed system, known as METEOR, utilizes a sliding window mechanism to uncover contextual anomalies with temporal and inter-variable dependencies arising from portions and entire MTS, oblivious in the existing literature. Observations are scored with respect to a modeled DBN, adjustable to both stationary and non-stationary scenarios. A widely available web application [20] is deployed to assist an analyst in their specific endeavour along with a user-friendly interface and tutorial. A diverse set of applications has benefited from the former, presenting an adaptable outlier detection system previously nonexistent, ranging from pre-processing to score-analysis. METEOR showed promising results when employed in synthetic and real data in quite different domains: it detected unusually behaved sections in ECG; it detected abnormal youth mortality during Spanish flu epidemics; and recognized that digit 7 more commonly resembles digit 1 than digits 8 and 9. Moreover, a comparison with a PST technique that independently looks at each variable, as in the univariate case, showed that PST does not detect outliers discovered by METEOR due to relationships between subjects becoming identical. Possible future research could consist in augmenting the tDBN algorithm with the employment of change-point mechanisms in the case of non-stationarity as well as the study of additional pre-processing and score-analysis mechanisms capable of better-capturing data's underlying features. Application of METEOR to the analysis of clinical data is also a promising future development. Indeed, METEOR is perfectly suited for multivariate time series analysis stored in electronic medical records (with patients' follow-up). This data is becoming increasingly common in chronic conditions such as rheumatic disorders and dementia, and also cancer. [PERSON] implemented the algorithms, performed the computational experiments and wrote the first draft of the manuscript (all authors made the required updates). [PERSON] and [PERSON] conceived the study, supervised the research, results and manuscript. All authors read and approved the final manuscript.