Publications
Publications
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- All HBS Web
(854)
- Faculty Publications (432)
- 2020
- Working Paper
Demystifying the Math of the Coronavirus
By: Elon Kohlberg and Abraham Neyman
We provide an elementary mathematical description of the spread of the coronavirus. We explain two fundamental relationships: How the rate of growth in new infections is determined by the “effective reproductive number” and how the effective reproductive number is... View Details
- April 2020 (Revised October 2022)
- Case
Medellín Reborn (A)
By: Jorge Tamayo, Ashish Nanda and Margaret Cross
In 2003, mathematics professor Sergio Fajardo was elected mayor of Medellín, Colombia—one of the most violent cities in the world at that time. As mayor, Fajardo faced a host of daunting challenges. Rampant gang violence had raised Medellín’s homicide rate... View Details
- Mar 2020
- Conference Presentation
A New Analysis of Differential Privacy's Generalization Guarantees
By: Christopher Jung, Katrina Ligett, Seth Neel, Aaron Roth, Saeed Sharifi-Malvajerdi and Moshe Shenfeld
We give a new proof of the "transfer theorem" underlying adaptive data analysis: that any mechanism for answering adaptively chosen statistical queries that is differentially private and sample-accurate is also accurate out-of-sample. Our new proof is elementary and... View Details
- March 2020
- Article
Diagnosing Missing Always at Random in Multivariate Data
By: Iavor I. Bojinov, Natesh S. Pillai and Donald B. Rubin
Models for analyzing multivariate data sets with missing values require strong, often assessable, assumptions. The most common of these is that the mechanism that created the missing data is ignorable—a twofold assumption dependent on the mode of inference. The first... View Details
- 2021
- Working Paper
Impact Investing: A Theory of Financing Social Enterprises
By: Benjamin N. Roth
I present a model of financing social enterprises to delineate the role of impact investors relative to “pure” philanthropists. I characterize the optimal scale and structure of a social enterprise when financed by grants, and when financed by investments. Impact... View Details
- Article
Detecting Adversarial Attacks via Subset Scanning of Autoencoder Activations and Reconstruction Error
By: Celia Cintas, Skyler Speakman, Victor Akinwande, William Ogallo, Komminist Weldemariam, Srihari Sridharan and Edward McFowland III
Reliably detecting attacks in a given set of inputs is of high practical relevance because of the vulnerability of neural networks to adversarial examples. These altered inputs create a security risk in applications with real-world consequences, such as self-driving... View Details
- 2020
- Article
Fast Exact Matrix Completion: A Unified Optimization Framework for Matrix Completion
By: Dimitris Bertsimas and Michael Lingzhi Li
We formulate the problem of matrix completion with and without side information as a non-convex optimization problem. We design fastImpute based on non-convex gradient descent and show it converges to a global minimum that is guaranteed to recover closely the... View Details
Keywords: Mathematical Methods
- May 2020
- Article
Scalable Holistic Linear Regression
By: Dimitris Bertsimas and Michael Lingzhi Li
We propose a new scalable algorithm for holistic linear regression building on Bertsimas & King (2016). Specifically, we develop new theory to model significance and multicollinearity as lazy constraints rather than checking the conditions iteratively. The resulting... View Details
- December 2019
- Technical Note
Technical Note on Bayesian Statistics and Frequentist Power Calculations
By: Amitabh Chandra and Ariel Dora Stern
This Technical Note provides an introduction to Bayes’ Rule and the statistical intuition that stems from it. In this note, we review the concepts that underlie Bayesian statistics, and we offer several simple mathematical examples to illustrate applications of Bayes’... View Details
- 2019
- Article
Configurations of Extremal Type II Codes via Harmonic Weight Enumerators
By: Noam D. Elkies and Scott Duke Kominers
We prove configuration results for extremal Type II codes, analogous to the configuration results of Ozeki and of the second author for extremal Type II lattices. Specifically, we show that for n ∈{8,24,32,48,56,72,96} every extremal Type II code of length n is... View Details
Keywords: Mathematical Methods
- December 2019
- Article
Costly Concessions: An Empirical Framework for Matching with Imperfectly Transferable Utility
By: Alfred Galichon, Scott Duke Kominers and Simon Weber
We introduce an empirical framework for models of matching with imperfectly transferable utility and unobserved heterogeneity in tastes. Our framework allows us to characterize matching equilibrium in a flexible way that includes as special cases the classic fully- and... View Details
- 2019
- Article
Time Series Experiments and Causal Estimands: Exact Randomization Tests and Trading
By: Iavor I Bojinov and Neil Shephard
We define causal estimands for experiments on single time series, extending the potential outcome framework to dealing with temporal data. Our approach allows the estimation of a broad class of these estimands and exact randomization based p-values for testing causal... View Details
- November 2019
- Article
Full Substitutability
By: John William Hatfield, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky and Alexander Westkamp
Various forms of substitutability are essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, and exchange economies with indivisible goods. We extend earlier models’ definitions of... View Details
- 2019
- Working Paper
Design Rules, Volume 2: How Technology Shapes Organizations: Chapter 8 Rationalizing Flow Processes
The purpose of this chapter is to examine the value structure of flow production processes and to explain why it is necessary to rationalize flow processes using the tools of systematic management. I first explain the problems facing managers of multi-step flow... View Details
- September 2019
- Article
Optimizing Reserves in School Choice: A Dynamic Programming Approach
By: Franklyn Wang, Ravi Jagadeesan and Scott Duke Kominers
We introduce a new model of school choice with reserves in which a social planner is constrained by a limited supply of reserve seats and tries to find an optimal matching according to a social welfare function. We construct the optimal distribution of reserves via a... View Details
- August 2019
- Article
When and How to Diversify—A Multicategory Utility Model for Personalized Content Recommendation
By: Yicheng Song, Nachiketa Sahoo and Elie Ofek
Sometimes we desire change, a break from the same or an opportunity to fulfill different aspects of our needs. Noting that consumers seek variety, several approaches have been developed to diversify items recommended by personalized recommender systems. However,... View Details
- July 2019
- Article
Optimal Capital Structure and Bankruptcy Choice: Dynamic Bargaining vs Liquidation
By: Samuel Antill and Steven R. Grenadier
We model a firm’s optimal capital structure decision in a framework in which it may later choose to enter either Chapter 11 reorganization or Chapter 7 liquidation. Creditors anticipate equityholders’ ex-post reorganization incentives and price them into the ex-ante... View Details
- 2019
- Article
Ridesharing with Driver Location Preferences
By: Duncan Rheingans-Yoo, Scott Duke Kominers, Hongyao Ma and David C. Parkes
We study revenue-optimal pricing and driver compensation in ridesharing platforms when drivers have heterogeneous preferences over locations. If a platform ignores drivers' location preferences, it may make inefficient trip dispatches; moreover, drivers may strategize... View Details
- March 2019 (Revised May 2019)
- Case
Fetchr: A New Way of Last Mile Delivery
By: V.G. Narayanan and Eren Kuzucu
By mid-2016, five years of aggressive growth had transformed Fetchr from a small logistics startup to a 1,000-employee, full-fledged last-mile delivery company operating across four countries in the Middle East and North Africa (MENA). Already beneficiaries of the... View Details
Keywords: Startup; Decision; Financial Strategy; UAE; KSA; MENA; Cost Accounting; Business Model; Business Startups; Transformation; Cost Management; Strategy; Disruptive Innovation; Technological Innovation; Growth and Development Strategy; Growth Management; Logistics; Service Delivery; Supply Chain Management; Performance Evaluation; Mathematical Methods; Mobile and Wireless Technology; Transportation Networks; Middle East; United Arab Emirates; Dubai; Bahrain; Egypt; Saudi Arabia; North Africa
- 2020
- Working Paper
Overcoming the Cold Start Problem of CRM Using a Probabilistic Machine Learning Approach
By: Eva Ascarza
The success of Customer Relationship Management (CRM) programs ultimately depends on the firm's ability to understand consumers' preferences and precisely capture how these preferences may differ across customers. Only by understanding customer heterogeneity, firms can... View Details