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Outliers and anomalous values
  • Introduce the mathematical formalism necessary to understand some of the most used algorithms in Forecasting through regressions and time series.

  • Invite the student to understand the need and the advantages of regularization in linear regressions.

  • Motivate the use of time series as a method to correctly model some phenomena.

  • Teach the statistical and computational qualities of the proposed algorithms.

  • Introduce the concept of anomaly and those algorithms useful in its detection.


Course One: Time Series Anomalies and Regressions


Part I. Regularization

  • Ridge

  • Statistical qualities

  • Geometric interpretation and relationship with PCA

Part II Linear regression abnormalities

  • Regression abnormalities

  • Robust regression

  • Linear programming: a solution to robust regression


Part III Time series and anomaly detection

  • Basic definitions

  • Buys-Ballot model: relationship with regressions

  • Exponential smoothing

  • Anomaly detection


Course Two: Other Methods in Detecting Anomalies for Time Series



  • Moving average

  • White noise

  • Invitation to stochastic processes

  • Anomaly detection and ARIMA


Part II Mahalanobis distance and anomalies

  • Basic definitions

  • Geometric interpretation

  • DCM

  • Applications to anomaly detection

Part III. Time series anomalies via Elastic Search

  • Non-Gaussian distributions and other problems

  • Formal definition of the algorithm

  • Anomaly detection

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