## 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

I started my Ph.D. studies at the University of Chicago, Department of Statistics, in October 2013. My coursework focused on probability theory, applied mathematics and machine learning. I have been the teaching assistant for a number of courses, and taught an introductory calculus-based statistics course for undergraduates in the Winter quarter of 2015. My thesis is being advised by Mihai Anitescu.

Snr. Comp. Mathematician, ANL

Professor, University of Chicago

In June 2013, I received a masters degree from Cambridge University. My coursework in Part III of the Mathematical Tripos covered a range of fields from compressed sensing and numerical methods for PDEs to such theoretical fields as the theory of generalized functions and nonparametric statistical theory. As a member of Churchill College, my studies were supervised by James Norris.

Director of Statistics Laboratory

Professor, University of Cambridge

Between September 2008 and May 2012, I completed a Bachelors of Science at Rutgers University, majoring in both Applied Physics and Biomathematics with a minor in Inorganic Chemistry. My research was in Biomedical Engineering. Under the advisement of David Shreiber, I studied, through experimentation and computer simulations, the biomechanics of nervous system tissue.

Chair, Biomedical Engineering

Professor, Rutgers University

#### 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.

##### Statistics

#### 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.