Course Name: Multivariate Data Analysis (MDA)
Participants: BSc Mathematics and Data Science students of Sorbonne University
Faculty Name: Dr. Tanujit Chakraborty, Assistant Professor of Statistics at Sorbonne University AD and Sorbonne Center for AI (SCAI)
Timeline : January to May | Total Teaching : 45 Sessions (20 Theory + 5 Tutorials + 20 Practicals)
The key details of the courses are given below:
Theoretical class notes (written on boards) are available under the folder Handwritten Classnotes
Tutorial Exercises are available under the folder Tutorial Worksheets
Slides, Data, and Code are available under the Practical Slides and Codes folder.
In case you want to recap the basics of probability and statistics, check the Basic Probability and Statistics (Recap) folder.
Happy Learning! Share your feedback at ctanujit@gmail.com
Course Objectives: Predictive models are essential tools used daily in corporate practice and decision-making. This course aims to give students a general overview of the statistical methods used to analyze multivariate data. In particular, the course covers the statistical tools needed to extract relevant information from any dataset. The course presents several standard techniques, including univariate and multivariate regression, principal components analysis, factor analysis, and multifactor analysis. Students are expected to understand how these methods work, how to apply them to a new dataset, and how to interpret the outputs of different algorithms.
Course Syllabus: Topics to be covered in this course include
- Introduction to MDA
- Recap of Descriptive Statistics
- Recap of Probability and Sampling Distributions
- Basics of Statistical Inference and ANOVA
- Basics of R and RStudio
- Relationship Analysis
- Multiple Linear Regression
- Model Selection
- Multicollinearity
- Shrinkage Methods: Ridge, LASSO, and Elastic Net
- Model Adequacy Checking
- Nonlinear Regression Analysis
- Transformations and Generalized Linear Models
- Autoregression Analysis
- Logistic Regression
- Singular Value Decomposition
- Principal Component Analysis
- Factor Analysis and Market Basket Analysis
- Linear Discriminant Analysis and QDA
- Implementations in RStudio
Evaluation Components: The evaluation components for the Multivariate Data Analytics (MDA) course will be as follows:
- Kaggle Competition/Project - 50%; 2) Mid-Term Exam - 25%; 3) End Term Test - 50%.
Textbooks and References:
• Friedman J, Hastie T, Tibshirani R. (2017). The Elements of Statistical Learning. Springer series in statistics. Link: web.stanford.edu/~hastie/ElemStatLearn/
• Gareth, J, Witten D, Hastie T, and Tibshirani R. (2021). An introduction to statistical learning: with applications in R. Springer. Link: https://www.statlearning.com/
• Rencher, A.C. and Christensen, W.F. (2012). Methods of Multivariate Analysis. 3rd Edition. An Introduction to Stochastic Modeling. Wiley.
• Wickham, H. and Garrett, G. (2016). R for Data Science. O'Reilly Media, Inc.
• Healy, Kieran. Data visualization: a practical introduction. (2018). Princeton University Press.
Some Interesting Papers For Reading:
• The Two Cultures - Statistical Modeling: The Two Cultures (2001): doi.org/10.1214/ss/1009213726
• Data Science - 50 Years of Data Science (2017): https://www.tandfonline.com/doi/full/10.1080/10618600.2017.1384734
• Future - The future of statistics and data science (2018): https://www.sciencedirect.com/science/article/pii/S0167715218300877
• Statistics Vs Machine Learning - Prediction, Estimation, and Attribution (2020): https://statprize.org/pdfs/materials/2019Efron-presentation.pdf
• Statistics - What are the most important statistical ideas of the past 50 years? (2021): https://arxiv.org/pdf/2012.00174
