Thursday, 3 May 2018, 15:00 - 16:30
Aula Expo, via Alfonso Corti 12, Milano, Italy
Bayesian Modeling of Non Gaussian Multivariate Time Series
(Refik Soyer, School of Business, George Washington University)
Deep Learning: a Bayesian Perspective
(Nicholas Polson, Booth School of Business, University of Chicago)
Refik Soyer, School of Business, George Washington University
BAYESIAN MODELING OF NON GAUSSIAN MULTIVARIATE TIME SERIES
Modeling of multivariate non Gaussian time series of correlated observations is considered. In so doing, we focus on time series from multivariate counts and durations.
Dependence among series arises as a result of sharing a common dynamic environment. We discuss characteristics of the resulting multivariate time series models and develop Bayesian inference for them using particle filtering and Markov chain Monte Carlo methods.
We illustrate application of the proposed approach using conditionally multivariate Poisson and gamma time series.
Joint work with Tevfik Aktekin, University of New Hampshire and Nicholas Polson, University of Chicago
Nicholas Polson, Booth School of Business, University of Chicago
DEEP LEARNING: A BAYESIAN PERSPECTIVE
Deep learning is a form of machine learning for nonlinear high dimensional pattern matching and prediction. By taking a Bayesian probabilistic perspective, we provide a number of insights into more efficient algorithms for optimisation and hyper-parameter tuning. Traditional high-dimensional data reduction techniques, such as principal component analysis (PCA), partial least squares (PLS), reduced rank regression (RRR), projection pursuit regression (PPR) are all shown to be shallow learners. Their deep learning counterparts exploit multiple deep layers of data reduction which provide predictive performance gains. Stochastic gradient descent (SGD) training optimisation and Dropout (DO) regularization provide estimation and variable selection. Bayesian regularization is central to finding weights and connections in networks to optimize the predictive bias-variance trade-off.
To illustrate our methodology, we provide an analysis of international bookings on Airbnb. Finally, we conclude with directions for future research.
Joint work with Vladimir Sokolov, Sistems Engineering and Operations Research, George Mason University