Vivak Patel

Ph.D. Candidate, Statistics

The sections below contain information about my research and academic career. If you want to get in touch, email me. Thank you for visiting!


Research

In general, my research is on statisical estimation, statistical computing and numerical optimization for problems arising engineering applications. Below you will find a list of papers which are published, submitted or in the manuscript stage.

Papers

Kalman-based Stochastic Gradient Method for Generalized Linear Models. In progress. statistical estimation

Adding Memory to Randomized Iterative Methods for Solving Linear Systems. In progress. linear algebra

Maldonado, D.A., Patel, V., Anitescu, M. Bayesian Dynamic Load Modelling: Diversity and Sensitivity. In progress. statistical estimation power systems (abstract)

Patel, V. The Impact of Local Geometry and Batch Size on Convergence and Divergence of Stochastic Gradient Descent. Submitted. optimization machine learning (arxiv, abstract)

Patel, V., Anitescu, M. Identifiability of Inertia with Partial Measurements and Stochastic Inputs. Submitted. identifiability dynamical systems power systems (preprint, abstract)

Patel, V. Kalman-based Stochastic Gradient Method with Stop Condition and Insensitivity to Conditioning. SIAM Journal on Optimization 2016. optimization machine learning statistical estimation (arXiv, doi, abstract)

Proceedings

Patel, V., Maldonado, D.A., Anitescu, M. Semiparametric Estimation of Solar Generation. Submitted. statistical estimation power systems (preprint, abstract)

Maldonado, D.A., Patel, V., Anitescu, M., Flueck, A. A Statistical Approach to Dynamic Load Modelling and Identification with High Frequency Measurements. Power & Energy Society General Meeting 2017. statistical estimation power systems Best Paper Award (preprint, abstract)

Presentations

Patel, V. SGD: What drives convergence and divergence? Optimization Methods and Software Conference, December 16, 2017. optimization machine learning (pdf)

Patel, V. A Statistical Theory of the Kalman Filter. SIAM Uncertainty Quantification, April 8, 2016. statistical estimation (html, pdf)

Patel, V. Static Parameter Estimation using Kalman Filtering and Proximal Operators. Argonne National Labs, December 2, 2015. optimization statistical estimation (html, pdf)

Code

Source: kSGD.R
Documentation: Coming soon.
Description: A simple implementation of Stochastic Gradient Descent (SGD) and Kalman-based Stochastic Gradient Descent (kSGD) for the R Language on both regular and large data sets. For working with large data sets, the implementation depends on the bit and ffbase packages.
Nota bene: This is not the fastest implementation of the kSGD algorithm given that it is written entirely in R. I am working on a C version with an R interface to improve calculation speed.


Career

Education


Teaching

Lecturer. In Winter 2015, I taught a section of Statistical Models and Methods. Here are a sample of my lecture notes and slide decks (tar).

Teaching Assistant. I have assisted in teaching a number of undergraduate and graduate courses: Elementary Statistics, Numerical Linear Algebra, Sample Surveys, and Nonparametric Inference.

Service

Data Intensive Computing Reading Group. In Autumn 2015, I started a reading group around the topic of data intensive computing systems. Here is my original reading list. If you are interested in joining, subscribe here.

Student Representative. From October 2014 to September 2015, I served as the Student Representative for the Department of Statistics to the Dean's Student Advisory Committee. In this capacity, I also represented student interests to the Statistics faculty.

PSD Co-Organizer. During the 2014 to 2015 academic year, I helped start and organize a series of graduate student lectures to encourage interdisciplinary conversations between the departments in the Physical Sciences Division.

Awards

Harper Dissertation Fellowship. Awarded by the University of Chicago (2017).

Senior Consultant. Awarded by the University of Chicago, Department of Statistics (2017).

SIAM Travel Award. Awarded to travel to SIAM UQ (2016) in Lausanne, Switzerland.


Miscellaneous

Notes

These are some notes of mine from lectures, courses and books on certain topics. If you find errata, please email me. Also, there are missing sections which I plan on completing over time.

Mathematics Reading List

Here is a list of books that I highly recommend or intend to read. If you have any additional recommendations, please get in touch. Also, I really appreciate the Chicago undergraduate mathematics bibliography.