ES 201: Decision Theory
Offered: 2019, 2018, 2017
Statistics can be described as the science of making decisions under uncertainty. Given a model of outcomes of games in a league, odds from bookies and a starting capital, how does one maximize return on investment while mitigating the underlying randomness? This course will teach the mathematical foundations of decision making under uncertainty. ES 201 is a course in statistical inference and estimation from a signal processing perspective. The emphasis of the course will be on the entire pipeline from writing a model, estimating its parameters and performing inference. The focus will be on generative models, and on proving certain results (e.g. when/why does $\ell_1$ regularization work? study of the convergence properties of popular optimization methods used to solve learning problems). The course will teach students how to develop new learning models, as well as to come up with learning algorithms and understand their properties. Topics include linear regression, logistic regression, maximum likelihood and kernel methods, compressive sampling and sparsity, Gaussian scale mixtures and hierarchical models, iterative re-weighted least-squares, EM and MM algorithms, state-space models, Bayesian regression, generative models of deep networks. An important component of the course will be a final project that will apply the course topics to data from Yelp, the NBA, and many other exciting sources.
ES 157: Biological Signal Processing
Offered: 2020, 2019, 2018, 2017, 2016
This is the first course on Biological Signal Processing, the science of collection, representation, manipulation, transformation, storing of biological signals, and the use of modern scientific computing tools (Python, Jupyter notebooks) to interpret biological signals and tell engaging and informative stories using biological data. We will use EEG, EKG, temperature data, neural spiking data, and data from Covid-19 as examples. Our focus will be on foundational signal processing concepts that can be applied in a variety of biological applications. Examples include the Fourier Transform, Principal Component Analysis, Clustering, etc. Applications include those to patient monitoring, diagnostics, patient prognostics, online monitoring, and the computation of wellness measures. We will introduce you to a powerful suite of mathematical and scientific computing tools will enable you to evaluate and make decisions based on evidence and data.