Publications
Publications
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- All HBS Web
(308)
- Faculty Publications (156)
- March 2022 (Revised January 2025)
- Technical Note
Linear Regression
This note provides an overview of linear regression for an introductory data science course. It begins with a discussion of correlation, and explains why correlation does not necessarily imply causation. The note then describes the method of least squares, and how to... View Details
- March 2022 (Revised January 2025)
- Technical Note
Statistical Inference
This note provides an overview of statistical inference for an introductory data science course. First, the note discusses samples and populations. Next the note describes how to calculate confidence intervals for means and proportions. Then it walks through the logic... View Details
- March 2022
- Article
Estimating the Effectiveness of Permanent Price Reductions for Competing Products Using Multivariate Bayesian Structural Time Series Models
By: Fiammetta Menchetti and Iavor Bojinov
Researchers regularly use synthetic control methods for estimating causal effects when a sub-set of units receive a single persistent treatment, and the rest are unaffected by the change. In many applications, however, units not assigned to treatment are nevertheless... View Details
- March 2022
- Article
Sensitivity Analysis of Agent-based Models: A New Protocol
By: Emanuele Borgonovo, Marco Pangallo, Jan Rivkin, Leonardo Rizzo and Nicolaj Siggelkow
Agent-based models (ABMs) are increasingly used in the management sciences. Though useful, ABMs are often critiqued: it is hard to discern why they produce the results they do and whether other assumptions would yield similar results. To help researchers address such... View Details
- March 2022
- Article
Where to Locate COVID-19 Mass Vaccination Facilities?
By: Dimitris Bertsimas, Vassilis Digalakis Jr, Alexander Jacquillat, Michael Lingzhi Li and Alessandro Previero
The outbreak of COVID-19 led to a record-breaking race to develop a vaccine. However, the limited vaccine capacity creates another massive challenge: how to distribute vaccines to mitigate the near-end impact of the pandemic? In the United States in particular, the new... View Details
- 2022
- Working Paper
The Disagreement Problem in Explainable Machine Learning: A Practitioner's Perspective
By: Satyapriya Krishna, Tessa Han, Alex Gu, Javin Pombra, Shahin Jabbari, Steven Wu and Himabindu Lakkaraju
As various post hoc explanation methods are increasingly being leveraged to explain complex models in high-stakes settings, it becomes critical to develop a deeper understanding of if and when the explanations output by these methods disagree with each other, and how... View Details
- October 1, 2021
- Article
An Evaluation of Cross-efficiency Methods: With an Application to Warehouse Performance.
By: B.M. Balk, M.R. De Koster, Christian Kaps and J.L. Zofio
Cross-efficiency measurement is an extension of Data Envelopment Analysis that allows for tie-breaking ranking of the Decision Making Units (DMUs) using all the peer evaluations. In this article we examine the theory of cross-efficiency measurement by comparing a... View Details
- September 2021
- Article
Diagnostic Bubbles
By: Pedro Bordalo, Nicola Gennaioli, Spencer Yongwook Kwon and Andrei Shleifer
We introduce diagnostic expectations into a standard setting of price formation in which investors learn about the fundamental value of an asset and trade it. We study the interaction of diagnostic expectations with two well-known mechanisms: learning from prices and... View Details
- Article
Learning Models for Actionable Recourse
By: Alexis Ross, Himabindu Lakkaraju and Osbert Bastani
As machine learning models are increasingly deployed in high-stakes domains such as legal and financial decision-making, there has been growing interest in post-hoc methods for generating counterfactual explanations. Such explanations provide individuals adversely... View Details
- June 2021
- Technical Note
Introduction to Linear Regression
By: Michael Parzen and Paul Hamilton
This technical note introduces (from an applied point of view) the theory and application of simple and multiple linear regression. The motivation for the model is introduced, as well as how to interpret the summary output with regard to prediction and statistical... View Details
- February 2021
- Tutorial
What is AI?
By: Tsedal Neeley
This video explores the elements that constitute artificial intelligence (AI). From its mathematical basis to current advances in AI, this video introduces students to data, tools, and statistical models that make a computer 'intelligent.' Through an explanation of... View Details
- February 2021
- Article
A Dynamic Theory of Multiple Borrowing
By: Daniel Green and Ernest Liu
Multiple borrowing—a borrower obtains overlapping loans from multiple lenders—is a common phenomenon in many credit markets. We build a highly tractable, dynamic model of multiple borrowing and show that, because overlapping creditors may impose default externalities... View Details
- 2021
- Article
Fair Algorithms for Infinite and Contextual Bandits
By: Matthew Joseph, Michael J Kearns, Jamie Morgenstern, Seth Neel and Aaron Leon Roth
We study fairness in linear bandit problems. Starting from the notion of meritocratic fairness introduced in Joseph et al. [2016], we carry out a more refined analysis of a more general problem, achieving better performance guarantees with fewer modelling assumptions... View Details
- January 2021
- Article
Using Models to Persuade
By: Joshua Schwartzstein and Adi Sunderam
We present a framework where "model persuaders" influence receivers’ beliefs by proposing models that organize past data to make predictions. Receivers are assumed to find models more compelling when they better explain the data, fixing receivers’ prior beliefs. Model... View Details
- Article
Beyond Individualized Recourse: Interpretable and Interactive Summaries of Actionable Recourses
By: Kaivalya Rawal and Himabindu Lakkaraju
As predictive models are increasingly being deployed in high-stakes decision-making, there has been a lot of interest in developing algorithms which can provide recourses to affected individuals. While developing such tools is important, it is even more critical to... View Details
- August 2020 (Revised September 2020)
- Technical Note
Assessing Prediction Accuracy of Machine Learning Models
The note introduces a variety of methods to assess the accuracy of machine learning prediction models. The note begins by briefly introducing machine learning, overfitting, training versus test datasets, and cross validation. The following accuracy metrics and tools... View Details
- Article
Matching in Networks with Bilateral Contracts: Corrigendum
By: John William Hatfield, Ravi Jagadeesan and Scott Duke Kominers
Hatfield and Kominers (2012) introduced a model of matching in networks with bilateral contracts and showed that stable outcomes exist in supply chains when firms' preferences over contracts are fully substitutable. Hatfield and Kominers (2012) also asserted that in... View Details
- Article
Active World Model Learning with Progress Curiosity
By: Kuno Kim, Megumi Sano, Julian De Freitas, Nick Haber and Daniel Yamins
World models are self-supervised predictive models of how the world evolves. Humans learn world models by curiously exploring their environment, in the process acquiring compact abstractions of high bandwidth sensory inputs, the ability to plan across long temporal... View Details
- 2021
- Conference Presentation
An Algorithmic Framework for Fairness Elicitation
By: Christopher Jung, Michael J. Kearns, Seth Neel, Aaron Leon Roth, Logan Stapleton and Zhiwei Steven Wu
We consider settings in which the right notion of fairness is not captured by simple mathematical definitions (such as equality of error rates across groups), but might be more complex and nuanced and thus require elicitation from individual or collective stakeholders.... View Details
- May 2020
- Article
Identifying Sources of Inefficiency in Health Care
By: Amitabh Chandra and Douglas O. Staiger
In medicine, the reasons for variation in treatment rates across hospitals serving similar patients are not well understood. Some interpret this variation as unwarranted and push standardization of care as a way of reducing allocative inefficiency. However, an... View Details