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 2022
 Article
Which Explanation Should I Choose? A Function Approximation Perspective to Characterizing Post hoc Explanations
By: Tessa Han, Suraj Srinivas and Himabindu Lakkaraju
A critical problem in the field of post hoc explainability is the lack of a common foundational goal among methods. For example, some methods are motivated by function approximation, some by game theoretic notions, and some by obtaining clean visualizations. This...
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Han, Tessa, Suraj Srinivas, and Himabindu Lakkaraju. "Which Explanation Should I Choose? A Function Approximation Perspective to Characterizing Post hoc Explanations." Advances in Neural Information Processing Systems (NeurIPS) (2022). (Best Paper Award, International Conference on Machine Learning (ICML) Workshop on Interpretable ML in Healthcare.)
 August 2022
 Article
Contract Duration and the Costs of Market Transactions
By: Alexander MacKay
The optimal duration of a supply contract balances the costs of reselecting a supplier against the costs of being matched to an inefficient supplier when the contract lasts too long. I develop a structural model of contract duration that captures this tradeoff and...
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Keywords:
Supply Contracts;
Intermediate Goods;
Switching Costs;
Vertical Relationships;
Transaction Costs;
Contract Duration;
Identification;
Supply Chain;
Cost;
Contracts;
Auctions;
Mathematical Methods
MacKay, Alexander. "Contract Duration and the Costs of Market Transactions." American Economic Journal: Microeconomics 14, no. 3 (August 2022): 164–212.
 2022
 Article
Fairness via Explanation Quality: Evaluating Disparities in the Quality of Post hoc Explanations
By: Jessica Dai, Sohini Upadhyay, Ulrich Aivodji, Stephen Bach and Himabindu Lakkaraju
As post hoc explanation methods are increasingly being leveraged to explain complex models in highstakes settings, it becomes critical to ensure that the quality of the resulting explanations is consistently high across all subgroups of a population. For instance, it...
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Dai, Jessica, Sohini Upadhyay, Ulrich Aivodji, Stephen Bach, and Himabindu Lakkaraju. "Fairness via Explanation Quality: Evaluating Disparities in the Quality of Post hoc Explanations." Proceedings of the AAAI/ACM Conference on Artificial Intelligence, Ethics, and Society (2022): 203–214.
 2022
 Article
Exploring Counterfactual Explanations Through the Lens of Adversarial Examples: A Theoretical and Empirical Analysis.
By: Martin Pawelczyk, Chirag Agarwal, Shalmali Joshi, Sohini Upadhyay and Himabindu Lakkaraju
As machine learning (ML) models become more widely deployed in highstakes applications, counterfactual explanations have emerged as key tools for providing actionable model explanations in practice. Despite the growing popularity of counterfactual explanations, a...
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Keywords:
Machine Learning Models;
Counterfactual Explanations;
Adversarial Examples;
Mathematical Methods
Pawelczyk, Martin, Chirag Agarwal, Shalmali Joshi, Sohini Upadhyay, and Himabindu Lakkaraju. "Exploring Counterfactual Explanations Through the Lens of Adversarial Examples: A Theoretical and Empirical Analysis." Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS) 25th (2022).
 2022
 Working Paper
A Linear Panel Model with Heterogeneous Coefficients and Variation in Exposure
By: Jesse M. Shapiro and Liyang Sun
Linear panel models featuring unit and time fixed effects appear in many areas of empirical economics. An active literature studies the interpretation of the ordinary least squares estimator of the model, commonly called the twoway fixed effects (TWFE) estimator, in...
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Shapiro, Jesse M., and Liyang Sun. "A Linear Panel Model with Heterogeneous Coefficients and Variation in Exposure." NBER Working Paper Series, No. 29976, April 2022.
 March 2022 (Revised July 2022)
 Module 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...
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 March 2022 (Revised July 2022)
 Module 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...
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Keywords:
Data Science;
Statistics;
Mathematical Modeling;
Mathematical Methods;
Analytics and Data Science
Bojinov, Iavor I., Michael Parzen, and Paul Hamilton. "Statistical Inference." Harvard Business School Module Note 622099, March 2022. (Revised July 2022.)
 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 subset 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...
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Keywords:
Causal Inference;
Partial Interference;
Synthetic Controls;
Bayesian Structural Time Series;
Mathematical Methods
Menchetti, Fiammetta, and Iavor Bojinov. "Estimating the Effectiveness of Permanent Price Reductions for Competing Products Using Multivariate Bayesian Structural Time Series Models." Annals of Applied Statistics 16, no. 1 (March 2022): 414–435.
 March 2022
 Article
Sensitivity Analysis of Agentbased Models: A New Protocol
By: Emanuele Borgonovo, Marco Pangallo, Jan Rivkin, Leonardo Rizzo and Nicolaj Siggelkow
Agentbased 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...
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Keywords:
Agentbased Modeling;
Sensitivity Analysis;
Design Of Experiments;
Total Order Sensitivity Indices;
Organizations;
Behavior;
Decision Making;
Mathematical Methods
Borgonovo, Emanuele, Marco Pangallo, Jan Rivkin, Leonardo Rizzo, and Nicolaj Siggelkow. "Sensitivity Analysis of Agentbased Models: A New Protocol." Computational and Mathematical Organization Theory 28, no. 1 (March 2022): 52–94.
 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 highstakes 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...
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Krishna, Satyapriya, Tessa Han, Alex Gu, Javin Pombra, Shahin Jabbari, Steven Wu, and Himabindu Lakkaraju. "The Disagreement Problem in Explainable Machine Learning: A Practitioner's Perspective." Working Paper, 2022.
 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 wellknown mechanisms: learning from prices and...
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Bordalo, Pedro, Nicola Gennaioli, Spencer Yongwook Kwon, and Andrei Shleifer. "Diagnostic Bubbles." Journal of Financial Economics 141, no. 3 (September 2021).
 Article
Learning Models for Actionable Recourse
By: Alexis Ross, Himabindu Lakkaraju and Osbert Bastani
As machine learning models are increasingly deployed in highstakes domains such as legal and financial decisionmaking, there has been growing interest in posthoc methods for generating counterfactual explanations. Such explanations provide individuals adversely...
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Ross, Alexis, Himabindu Lakkaraju, and Osbert Bastani. "Learning Models for Actionable Recourse." Advances in Neural Information Processing Systems (NeurIPS) 34 (2021).
 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...
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 April 2021
 Article
A Model of MultiPass Search: Price Search Across Stores and Time
By: Navid Mojir and K. Sudhir
In retail settings with price promotions, consumers often search across stores and time. However, the search literature typically only models one pass search across stores, ignoring revisits to stores; the choice literature using scanner data has modeled search across...
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Keywords:
Consumer Search;
Multipass Search;
Price Search;
Store Search;
Spatial Search;
Temporal Search;
Spatiotemporal Search;
Dynamic Structural Models;
MPEC;
Price Promotions;
Store Loyalty;
Consumer Behavior;
Price;
Spending;
Marketing;
Mathematical Methods
Mojir, Navid, and K. Sudhir. "A Model of MultiPass Search: Price Search Across Stores and Time." Management Science 67, no. 4 (April 2021): 2126–2150.
 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...
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 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...
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Keywords:
Commitment;
Multiple Borrowing;
Common Agency;
Misallocation;
Microfinance;
Investment;
Mathematical Methods
Green, Daniel, and Ernest Liu. "A Dynamic Theory of Multiple Borrowing." Journal of Financial Economics 139, no. 2 (February 2021): 389–404.
 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...
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Joseph, Matthew, Michael J Kearns, Jamie Morgenstern, Seth Neel, and Aaron Leon Roth. "Fair Algorithms for Infinite and Contextual Bandits." Proceedings of the AAAI/ACM Conference on Artificial Intelligence, Ethics, and Society 4th (2021).
 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...
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Keywords:
Model Persuasion;
Analytics and Data Science;
Forecasting and Prediction;
Mathematical Methods;
Framework
Schwartzstein, Joshua, and Adi Sunderam. "Using Models to Persuade." American Economic Review 111, no. 1 (January 2021): 276–323.
 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 highstakes decisionmaking, 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...
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Rawal, Kaivalya, and Himabindu Lakkaraju. "Beyond Individualized Recourse: Interpretable and Interactive Summaries of Actionable Recourses." Advances in Neural Information Processing Systems (NeurIPS) 33 (2020).
 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...
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Keywords:
Machine Learning;
Statistics;
Econometric Analyses;
Experimental Methods;
Data Analysis;
Data Analytics;
Forecasting and Prediction;
Analytics and Data Science;
Analysis;
Mathematical Methods
Toffel, Michael W., Natalie Epstein, Kris Ferreira, and Yael GrushkaCockayne. "Assessing Prediction Accuracy of Machine Learning Models." Harvard Business School Technical Note 621045, August 2020. (Revised September 2020.)