About

I am an Associate Professor of Biostatistics at Brown University interested in algorithms, optimization, data science, and education. My research has focused on the design and analysis of optimization algorithms underlying machine learning with recent applications to clustering, variable selection, risk models, and bike-share or other shared mobility systems. I also enjoy thinking about prescriptive analytics: how data informs our future decisions.

Research topics

• Computer Science
• Computer Security
• Embedded system
• Operations research
• Combinatorics
• Algorithm
• Mathematical analysis
• Mathematics
• Discrete mathematics
• Statistics
• Engineering
• Transport engineering
• Automotive engineering
• Mathematical optimization

Selected publications

• Data Transformations and Summaries

  2025-06-09

  book-chapter1st authorCorresponding
  PublisherDOI

• The all-pairs vitality-maximization (VIMAX) problem

  Annals of Operations Research · 2024-05-10 · 1 citations

  articleOpen access1st author

  Abstract Traditional network interdiction problems focus on removing vertices or edges from a network so as to disconnect or lengthen paths in the network; network diversion problems seek to remove vertices or edges to reroute flow through a designated critical vertex or edge. We introduce the all-pairs vitality maximization problem (VIMAX), in which vertex deletion attempts to maximize the amount of flow passing through a critical vertex, measured as the all-pairs vitality of the vertex. The assumption in this problem is that in a network for which the structure is known but the physical locations of vertices may not be known (e.g., a social network), locating a person or asset of interest might require the ability to detect a sufficient amount of flow (e.g., communications or financial transactions) passing through the corresponding vertex in the network. We formulate VIMAX as a mixed integer program, and show that it is NP-Hard. We compare the performance of the MIP and a simulated annealing heuristic on both real and simulated data sets and highlight the potential increase in vitality of key vertices that can be attained by subset removal. We also present graph theoretic results that can be used to narrow the set of vertices to consider for removal.

  PublisherOA PDFDOI

• <i>Literature search sandbox</i>: a large language model that generates search queries for systematic reviews

  JAMIA Open · 2024-07-01 · 13 citations

  articleOpen access

  Objectives: Development of search queries for systematic reviews (SRs) is time-consuming. In this work, we capitalize on recent advances in large language models (LLMs) and a relatively large dataset of natural language descriptions of reviews and corresponding Boolean searches to generate Boolean search queries from SR titles and key questions. Materials and Methods: We curated a training dataset of 10 346 SR search queries registered in PROSPERO. We used this dataset to fine-tune a set of models to generate search queries based on Mistral-Instruct-7b. We evaluated the models quantitatively using an evaluation dataset of 57 SRs and qualitatively through semi-structured interviews with 8 experienced medical librarians. Results: The model-generated search queries had median sensitivity of 85% (interquartile range [IQR] 40%-100%) and number needed to read of 1206 citations (IQR 205-5810). The interviews suggested that the models lack both the necessary sensitivity and precision to be used without scrutiny but could be useful for topic scoping or as initial queries to be refined. Discussion: Future research should focus on improving the dataset with more high-quality search queries, assessing whether fine-tuning the model on other fields, such as the population and intervention, improves performance, and exploring the addition of interactivity to the interface. Conclusions: The datasets developed for this project can be used to train and evaluate LLMs that map review descriptions to Boolean search queries. The models cannot replace thoughtful search query design but may be useful in providing suggestions for key words and the framework for the query.

  PublisherOA PDFDOI

• Estimating Censored Spatial-Temporal Demand with Applications to Shared Micromobility

  arXiv (Cornell University) · 2023-03-17

  preprintOpen access1st authorCorresponding

  In shared micromobility networks, such as bike-share and scooter-share networks, using trip data to accurately estimate demand in docked and dockless systems is critical to analyzing how the system is operating, such as identifying the number of dissatisfied users, operational costs, and equity in access, especially for city officials. However, the distribution of available bikes affects the distribution of observed trips. Users may walk from an unobserved cell location to an available bike masking the true location of user demand, and users may look for a bike and not find one, which is unobserved user demand. In collaboration with city planners from Providence, R.I., we present a flexible and interpretable framework to estimate spatial-temporal demand as a spatial non-homogeneous Poisson process that explicitly models how users choose a bike, bridging the gap between the docked and dockless methodology. Further, we present computational experiments highlighting that our method provides more accurate estimates of demand when there is incomplete availability compared to previous methods, and we comment on the results of our algorithm on data from Providence's dockless scooter-share network. Our estimation algorithm is publicly available through an efficient and user-friendly application designed for other city planners and organizations to help inform system planning.

  PublisherOA PDFDOI

• The All-Pairs Vitality-Maximization (VIMAX) Problem

  arXiv (Cornell University) · 2023-02-02

  preprintOpen access1st authorCorresponding

  Traditional network interdiction problems focus on removing vertices or edges from a network so as to disconnect or lengthen paths in the network; network diversion problems seek to remove vertices or edges to reroute flow through a designated critical vertex or edge. We introduce the all-pairs vitality maximization problem (VIMAX), in which vertex deletion attempts to maximize the amount of flow passing through a critical vertex, measured as the all-pairs vitality of the vertex. The assumption in this problem is that in a network for which the structure is known but the physical locations of vertices may not be known (e.g. a social network), locating a person or asset of interest might require the ability to detect a sufficient amount of flow (e.g., communications or financial transactions) passing through the corresponding vertex in the network. We formulate VIMAX as a mixed integer program, and show that it is NP-Hard. We compare the performance of the MIP and a simulated annealing heuristic on both real and simulated data sets and highlight the potential increase in vitality of key vertices that can be attained by subset removal. We also present graph theoretic results that can be used to narrow the set of vertices to consider for removal.

  PublisherOA PDFDOI

• Erratum to “Budgeted Prize-Collecting Traveling Salesman and Minimum Spanning Tree Problems”

  Mathematics of Operations Research · 2022-12-12 · 3 citations

  erratum1st authorCorresponding

  There is an error in our paper [Paul A, Freund D, Ferber A, Shmoys DB, Williamson DP (2020) Budgeted prize-collecting traveling salesman and minimum spanning tree problems. Math. Oper. Res. 45(2):576–590]. In that paper, we consider constrained versions of the prize-collecting traveling salesman and the prize-collecting minimum spanning tree problems. The goal is to maximize the number of vertices in the returned tour/tree subject to a bound on the tour/tree cost. Rooted variants of the problems have the additional constraint that a given vertex, the root, must be contained in the tour/tree. In our previous paper, we present a 2-approximation algorithm for the rooted and unrooted versions of both the tree and tour variants using a parameterized primal–dual approach. Here, we illustrate an error in the proof of a lemma for the rooted version of the algorithm and show that the algorithm has no finite approximation guarantee for the rooted version of the problem. We also show that the lemma and the approximation guarantee of 2 continue to hold true for the unrooted version. This leaves the best-known approximations for the rooted tour an established [Formula: see text]-approximation algorithm and for the tree variant a previously published poly-log approximation algorithm.

  PublisherDOI

• Iterated linear optimization

  Quarterly of Applied Mathematics · 2021-05-06 · 1 citations

  preprintOpen accessSenior author

  We introduce a fixed point iteration process built on optimization of a linear function over a compact domain. We prove the process always converges to a fixed point and explore the set of fixed points in various convex sets. In particular, we consider elliptopes and derive an algebraic characterization of their fixed points. We show that the attractive fixed points of an elliptope are exactly its vertices. Finally, we discuss how fixed point iteration can be used for rounding the solution of a semidefinite programming relaxation.

  PublisherOA PDFDOI

• Operations Research

  2020-08-18

  book-chapter1st authorCorresponding

  This chapter provides an overview of the field and its connection to data science, articulating the fundamental trade-off in mathematical modeling between model efficiency and model complexity. It provides a brief overview of the commercial and open-source software available for operations research methods. The chapter describes four ways in which operations research connects to data science. It describes the key probability principles on which simulation relies and fundamental techniques for generating random variables. The chapter focuses on the role of simulation techniques in statistical and machine learning. Without high-speed computers to analyze data and solve optimization problems, early operations researchers embraced the craft of trading off model complexity for model efficiency.

  PublisherDOI

• Clustering with Iterated Linear Optimization.

  arXiv (Cornell University) · 2020-12-16

  preprintOpen accessSenior author

  We introduce a novel method for clustering using a semidefinite programming (SDP) relaxation of the Max k-Cut problem. The approach is based on a new methodology for rounding the solution of an SDP using iterated linear optimization. We show the vertices of the Max k-Cut SDP relaxation correspond to partitions of the data into at most k sets. We also show the vertices are attractive fixed points of iterated linear optimization. We interpret the process of fixed point iteration with linear optimization as repeated relaxations of the closest vertex problem. Our experiments show that using fixed point iteration for rounding the Max k-Cut SDP relaxation leads to significantly better results when compared to randomized rounding.

  Publisher

• Easy capacitated facility location problems, with connections to lot-sizing

  Operations Research Letters · 2020-01-05 · 1 citations

  articleOpen access1st author
  PublisherOA PDFDOI

Frequent coauthors

• David P. Williamson

  29 shared

• David B. Shmoys

  Cornell University

  28 shared

• Aaron Ferber

  26 shared

• Daniel Freund

  Massachusetts Institute of Technology

  23 shared

• Pedro F. Felzenszwalb

  11 shared

• Caroline J. Klivans

  11 shared

• Jacob Feldman

  10 shared

• Amariah Becker

  7 shared

Education

• Ph.D., Operations Research and Information Engineering

  Cornell University

• B.S., Mathematics

  Harvey Mudd College