Quasi-newton methods for stochastic optimization and proximity-based methods for disparate information fusion

The difficulty of modeling and analyzing complicated data sets and data generating processes poses many difficult computational challenges in machine learning and statistics. We investigate two particular topics in this dissertation: methods for stochastic optimization and methods exploiting disparate data.We propose a class of quasi-Newton methods for stochastic optimization, i.e., optimization of a function given noisy function evaluations. In particular, we focus attention on the optimization of analytically intractable functions that we estimate pointwise by simulation. These methods adapt ideas from response surface methodology and stochastic approximation and integrate tools from numerical optimization, in particular, secant updates and trust regions. We develop a convergence theory and evaluate performance on simulated and real-world problems.Massive datasets consisting of disparate representations of objects are ubiquitous. An example of such data is a set of captioned images, that is to say, paired text and images. We propose methodology for statistical inference, classification, and visualization given data from disparate data types. In this work, we use pairwise proximities as a common representation of the data.