\sessionHeader{Wed1D: Nectar Track}{Thomas G\"{a}rtner}{Chem, LT4}
\timeTitlePeople{10:30--11:20}{Learning Submodular Functions}{Maria-Florina Balcan and Nicholas J.A.\ Harvey} 

\abst{Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications that have been used in many areas, including combinatorial optimization, machine learning, and economics. In this work we use a learning theoretic angle for studying submodular functions. We provide algorithms for learning submodular functions, as well as lower bounds on
their learnability. In doing so, we uncover several novel structural results revealing both extremal properties
as well as regularities of submodular functions, of interest to many areas.}


\timeTitlePeople{11:20--12:10}{Modelling Input Varying Correlations between Multiple Responses}{Andrew Gordon Wilson and Zoubin Ghahramani} 

\abst{We introduced a generalised Wishart process (GWP) for modelling input dependent covariance matrices $\Sigma(x)$, allowing one to model input varying correlations and uncertainties between multiple response variables.  The GWP can naturally scale to thousands of response
variables, as opposed to competing \textit{multivariate volatility} models which are typically intractable for greater than 5 response variables.  The GWP can also naturally capture a rich class of covariance dynamics -- periodicity, Brownian motion, smoothness, \dots -- through a covariance kernel.}

\sessionend
