Course 1: Data Science Foundations

Data Science Foundations covers multivariate statistics, linear factor models, and estimation of high-dimensional location and dispersion.

In particular, this course covers the following topics:

Multivariate distributions and notable classes: elliptical, exponential, discrete, mixtures
The “mean-covariance/linear” ecosystem: mean vector, covariance matrix, ellipsoid, affine equivariance, correlation, linear prediction, whitening
Estimation of the “mean-covariance/linear” ecosystem: historical, maximum likelihood, Bayesian, random matrix theory and shrinkage
Linear factor models: regression, principal component analysis, factor analysis, cross-sectional models

After the course you will obtain a Statement of Completion. Furthermore, you can choose to complete an optional code-based project that will count as one of the two Practical Projects towards the ARPM Certification.

Distributions

• Elliptical distributions

• Scenario-probability distributions

• Exponential family distributions

• Mixture distributions

• Stable, additive and infinitely divisible distributions

Mean-covariance framework

• Introduction: mean-covariance

• Mean-covariance classes

• Visualization

• Affine transformations

• Uncorrelation

• Linear Projection

• Partial uncorrelation

Estimation - mean-covariance

• Estimation techniques

• Flexible probabilities

• Historical

• Maximum likelihood

• Bayesian

• Shrinkage

Linear factor models - supervised

• Linear factor models

• Definitions

• Regression

• Cross-section

Linear factor models - unsupervised

• Principal component

• Factor-analysis

Estimation - regression loadings

• Estimation: regression loadings

• Historical

• Maximum likelihood

• Bayesian

• Regularization and factor selection