Data Science

Aims

This course introduces fundamental tools for describing and reasoning about data. There are two themes: designing probability models to describe systems; and drawing conclusions based on data generated by such systems.

Lectures

• Specifying and fitting probability models. Random variables. Maximum likelihood estimation. Generative and supervised models. Goodness of fit.
• Feature spaces. Vector spaces, bases, inner products, projection. Linear models. Model fitting as projection. Design of features.
• Handling probability models. Handling pdf and cdf. Bayes’s rule. Monte Carlo estimation. Empirical distribution.
• Inference. Bayesianism. Frequentist confidence intervals, hypothesis testing. Bootstrap resampling.
• Random processes. Markov chains. Stationarity, and drift analysis. Processes with memory. Learning a random process.

Objectives

At the end of the course students should

• be able to formulate basic probabilistic models, including discrete time Markov chains and linear models
• be familiar with common random variables and their uses, and with the use of empirical distributions rather than formulae
• understand different types of inference about noisy data, including model fitting, hypothesis testing, and making predictions
• understand the fundamental properties of inner product spaces and orthonormal systems, and their application to modelling

Recommended reading

* F.M. Dekking, C. Kraaikamp, H.P. Lopuhaä, L.E. Meester (2005). A modern introduction to probability and statistics: understanding why and how. Springer.

S.M. Ross (2002). Probability models for computer science. Harcourt / Academic Press.

M. Mitzenmacher and E. Upfal (2005). Probability and computing: randomized algorithms and probabilistic analysis. Cambridge University Press.