M3 4206 and Zoom (please email amgrad@uwaterloo.ca for the meeting link)

## Candidate

Esha Saha | Applied Mathematics, University of Waterloo

## Title

Expanding the Scope of Random Feature Models: Theory and Applications

## Abstract

Data, defined as facts and statistics collected together for analysis is at the core of every inference or decision made by any living organism. With the advent of technology, humans have been trying to develop methods that can learn from data and generalize well based on past information. It is important to understand the workings of these methods to be able to quantify the cause and nature of the error they can make so that informed decisions can be made using these results. One such method that particularly caught the attention of researchers recently is the random feature model (RFM), introduced for reducing the complexity and faster computation of kernel methods in large-scale machine learning algorithms. This thesis aims to explore RFMs by expanding their theory and applications in the machine-learning community. We begin our exploration by developing a fast algorithm for high dimensional additive function approximation using a random feature-based surrogate model. Extending the idea of learning functions, we build a model to learn and predict the dynamics of an epidemic from incomplete and scarce data. This model combines the idea of random feature approximation with the use of Takens' delay embedding theorem on the given input data. In our final project, motivated to work on the idea of multiple layers in an RFM, we propose an interpretable deep RFM whose architecture is inspired by diffusion models.