This course is an introduction to machine learning with specialization in methods for financial time series. The course is divided into two parts and will be jointly taught by Professors Megha Patnaik (Part 1) and Marta Catalano (Part 2). The programming language for the course will be R.

In the first part, we will cover linear and polynomial regression, logistic regression and linear discriminant analysis; cross-validation and the bootstrap, subset selection and model regularization methods (ridge and lasso); tree-based methods, random forests and boosting. The focus is on the important elements of modern data analysis and its applications. The computing language is the R programming language. In the second part of the course you will learn how to include prior information into your analysis and how to quantify the uncertainty in your estimates, both for static quantities and for quantities that evolve in time. Real world applications include, e.g., forecasting the returns of a set of assets in a portfolio or predicting the growth of the Gross Domestic Product of a country. We will cover Bayesian methods for unsupervised learning and time series analysis with a particular focus on parametric density estimation, conjugate priors, and dynamic linear models, a wide class of models that includes, e.g, polynomial and cyclical trends, ARMA, and VAR models. We will describe how to make forecasting and inference on these time series through the Kalman filter and discuss their implementation using the R software.

In the first part, we will cover linear and polynomial regression, logistic regression and linear discriminant analysis; cross-validation and the bootstrap, subset selection and model regularization methods (ridge and lasso); tree-based methods, random forests and boosting. The focus is on the important elements of modern data analysis and its applications. The computing language is the R programming language. In the second part of the course you will learn how to include prior information into your analysis and how to quantify the uncertainty in your estimates, both for static quantities and for quantities that evolve in time. Real world applications include, e.g., forecasting the returns of a set of assets in a portfolio or predicting the growth of the Gross Domestic Product of a country. We will cover Bayesian methods for unsupervised learning and time series analysis with a particular focus on parametric density estimation, conjugate priors, and dynamic linear models, a wide class of models that includes, e.g, polynomial and cyclical trends, ARMA, and VAR models. We will describe how to make forecasting and inference on these time series through the Kalman filter and discuss their implementation using the R software.

- 2nd edition of Introduction to Statistical Learning by Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani. (pdf available at https://hastie.su.domains/ISLR2/ISLRv2_website.pdf) - Dynamic Linear Models with R, P. Campagnoli, S. Petrone, G. Petris ,Springer New York, NY. (pdf available at https://www.researchgate.net/publication/226410454_Dynamic_Linear_M odels_with_R) - Bayesian Data Analysis, A. Gelman, J. Carlin, H. Stern, D. Dunson, A. Vehtari, and D. Rubin, 3rd Ed. Chapman & Hall. (pdf available at http://www.stat.columbia.edu/~gelman/book/ ) - Bayesian Forecasting and Dynamic Models, M. West, J. Harrison, 2nd Ed.

The course consists of lectures complemented by exercise sessions.

Evaluation will be based on a combination of homeworks and the final exam.

An interview to verify understanding and motivation.