ECE PhD Prospectus Defense- Hatice Kubra Cilingir

<P><B>Title:</B> Learning Functional Bregman Divergences and its variants for Machine Learning Application</P><P><B>Advisor:</B> Prof. Brian Kulis, ECE,SE</P><P><B>Chair:</B> Prof. Prakash Ishwar, ECE,SE</P><P><B>Committee:</B> Prof. Yannis Paschalidis, ECE, BME, SE; Prof. Kate Saenko, CS</P><P><B>Abstract:</B> Functional Bregman divergences are an important class of divergences in machine learning that generalize classical Bregman divergences. Functional Bregman divergences have the advantage of allowing one to define a notion of similarity between both sample points and distributions. This class of divergences includes many useful distance measures such as squared Euclidean, KL-divergence, relative entropy and logistic loss through a corresponding strictly convex functional. However, these functionals do not have a unifying and applicable closed form for many possible divergences, which limits their applications. As a result, in many embedding learning problems, a metric has to be manually chosen rather than being learnable.</P><P>In this thesis, we first propose a framework in which we learn and parameterize functional Bregman divergences within a deep learning formulation. Our learning framework is flexible and scalable to large datasets and problems. We extend the scope of this work to the two following directions that proceed mostly in parallel: (1) The first direction is to provide theoretical insight into the relationship between functional Bregman divergences and other metrics (f-divergences, IPMs, etc.), as well as connections to existing distance learning models. For this purpose, we show symmetric forms and their connections with MMD and Wasserstein metrics. Given that functional Bregman divergences are characterized by convex functionals, we plan to further investigate convex functional properties and representations in order to explore alternative parametrizations with deep learning. We propose to find ways to generalize beyond the current model to include f-divergences and compare architectural similarities with other deep similarity learning models. (2) The second direction is the application side, for which we obtained compelling results in GANs, semi-supervised learning, KNN classification, and few-shot learning problems, with identifying the necessary adaptations on our model and loss functions. We claim that not requiring symmetry and the triangle inequality may be useful properties for some scenarios. Further, having desirable properties such as convexity, affine invariance, and mean minimization makes this class of divergences attractive. We plan to further adapt our framework to more advanced Siamese and triplet settings and ranking problems in the light of these arguments.</P>

When 3:00 pm to 5:00 pm on Friday, June 5, 2020
Location https://bostonu.zoom.us/j/97904226385?pwd=dGtuWmVwR0VCL2xKNE96bVNXVEY2dz09