Data Science
Principal lecturer: Dr Damon Wischik
Taken by: Part IB CST 50%, Part IB CST 75%
Hours: 16 (12 lectures + 4 practicals)
Suggested hours of supervisions: 4
Prerequisites: Mathematics for Natural Sciences
This course is a prerequisite for: Computer Systems Modelling, Data Science: principles and practice, Data Science: principles and practice, Machine Learning and Bayesian Inference, Natural Language Processing, Quantum Computing
Past exam questions
Aims
This course introduces fundamental tools for describing and reasoning about data. There are two themes: describing the behaviour of random systems; and making inferences based on data generated by such systems. The course will survey a wide range of models and tools, and it will emphasize how to design a model and what sorts of questions one might ask about it.
Lectures
- Likelihood. Random variables. Random samples. Maximum likelihood estimation, likelihood profile.
- Random variables. Rules for expectation and variance. Generating random variables. Empirical distribution. Monte Carlo estimation; law of large numbers. Central limit theorem.
- Inference. Estimation, confidence intervals, hypothesis testing, prediction. Bootstrap. Bayesianism. Logistic regression, natural parameters.
- Feature spaces. Vector spaces, bases, inner products, projection. Model fitting as projection. Linear modeling. Choice of features.
- Random processes. Markov chains. Stationarity and convergence. Drift models. Examples, including estimation and memory.
- Probabilistic modelling. Independence; joint distributions. Descriptive, discriminative, and causal models. Latent variable models. Random fields.
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
- be able to use expectation and conditional expectation, limit theorems, equilibrium distributions
- 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 model representation
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.