The Swiss engineering master's degree

Many data sets are temporal by nature.  The course shows how to analyze time series of different domains and how to develop statistical models based on the data, in order to forecast future values or classify the time series into predefined categories. A probabilistic approach is emphasized, i.e. it is also discussed how to compute the uncertainty of the forecast which has been made.

The course adopts a practical approach: theoretical concepts are illustrated and applied in specific case studies. Students will also learn to identify the tools best suited for a given task.

The first part of the course presents techniques for analysis of time series. It starts from visualization techniques; then it shows techniques for characterizing trend and seasonality; eventually it present structured statistical approaches based on exponential smoothing and arima techniques. Several examples referring to real data sets are shown. The lab of this part are done using R.

In the second part of the course students learn how to analyze digital signals in different domains, i.e. time and spectral domain; they learn how to extract meaningful features from digital signals suitable for classification. Finally, they learn how to set up and learn statistical models, such as HMMs or DNNs, for recognizing and classifying time series. The lab of this part are done using Matlab.

Compétences préalables

Basic knowledge in statistics.
Programming with  scripting languages.

Objectifs d'apprentissage

• Students know how to visualize time series and how to characterize their main features.
• Students know how to evaluate forecast accuracy.
• Students know how to model trends, seasonalities and non-stationarities adopting exponential smoothing and ARIMA models.
• Students know how to perform model estimation, model selection and probabilistic prediction with these models.
• Students know different methods to analyse digital signals in different domains
• Students know how to extract important features used in speech processing
• Students learn to apply Bayes rule for classifying digital signals.
• Students can apply modern deep learning approaches to classify digital signals

Catégorie de module

Part 1: Forecasting sequential data (7 weeks)

• Time series graphics.
• Main features of time series.
• Assessment of the predictions.
• Exponential smoothing
• ARIMA models

Practical case studies in R.

Part 2: Analysis and classification of digital signals (7 weeks)

• Analysis of digital signals in different domains (1 week)
• Feature extraction (1 week)
• Modelling, classification & recognition of digital signals (5 weeks)
  • Classic Approaches: Dynamic Time Warping, Vector Quantization
  • Statistical modelling: Hidden Markov Models
  • Deep Learning Approaches

Practical case studies in Matlab.

Méthodes d'enseignement et d'apprentissage

• Ex cathedra
• Self study of literature / publications
• Practical exercises with computer

Bibliographie

Slides will be available covering the topics of the course.

In addition, recommended books are:

For forecasting:

R. Hyndman and G. Athanasopoulos., Forecasting: Principles and Practice, Springer, 2018 (online free textbook at https://otexts.org/fpp2/)

For digital signal processing:

X. Huang, A. Acero, H.-W. Hon:  Spoken Language Processing, Prentice Hall, 2001, ISBN 0-13-22616-5

L. R. Rabiner und B.-H. Juang, Fundamentals of Speech Recognition. Prentice Hall, 1993.

D. Yu und L. Deng, Automatic Speech Recognition: A Deep Learning Approach. Springer London, 2014.