Statistical Learning and Inverse Problems: An Stochastic Gradient Approach

Inverse problems are paramount in Science and Engineering. In this paper, we consider the setup of Statistical Inverse Problem (SIP) and demonstrate how Stochastic Gradient Descent (SGD) algorithms can be used in the linear SIP setting. We provide consistency and finite sample bounds for the excess risk. We also propose a modification for the SGD algorithm where we leverage machine learning methods to smooth the stochastic gradients and improve empirical performance. We exemplify the algorithm in a setting of great interest nowadays: the Functional Linear Regression model. In this case we consider a synthetic data example and examples with a real data classification problem

An Investigation into Potential Differences in Measurements of Neck Proprioception between Asymptomatic Subjects and Those with Cervical Pain

A poster on the study of joint perception comparing people with and without cervical pain