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 2023
 Article
Verifiable Feature Attributions: A Bridge between Post Hoc Explainability and Inherent Interpretability
By: Usha Bhalla, Suraj Srinivas and Himabindu Lakkaraju
With the increased deployment of machine learning models in various realworld applications, researchers and practitioners alike have emphasized the need for explanations of model behaviour. To this end, two broad strategies have been outlined in prior literature to...
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Bhalla, Usha, Suraj Srinivas, and Himabindu Lakkaraju. "Verifiable Feature Attributions: A Bridge between Post Hoc Explainability and Inherent Interpretability." Advances in Neural Information Processing Systems (NeurIPS) (2023).
 2023
 Article
Which Models Have PerceptuallyAligned Gradients? An Explanation via OffManifold Robustness
By: Suraj Srinivas, Sebastian Bordt and Himabindu Lakkaraju
One of the remarkable properties of robust computer vision models is that their inputgradients are often aligned with human perception, referred to in the literature as perceptuallyaligned gradients (PAGs). Despite only being trained for classification, PAGs cause...
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Srinivas, Suraj, Sebastian Bordt, and Himabindu Lakkaraju. "Which Models Have PerceptuallyAligned Gradients? An Explanation via OffManifold Robustness." Advances in Neural Information Processing Systems (NeurIPS) (2023).
 2023
 Working Paper
Causal Interpretation of Structural IV Estimands
By: Isaiah Andrews, Nano Barahona, Matthew Gentzkow, Ashesh Rambachan and Jesse M. Shapiro
We study the causal interpretation of instrumental variables (IV) estimands of nonlinear, multivariate structural models with respect to rich forms of model misspecification. We focus on guaranteeing that the researcher's estimator is sharp zero consistent, meaning...
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Keywords:
Mathematical Methods
Andrews, Isaiah, Nano Barahona, Matthew Gentzkow, Ashesh Rambachan, and Jesse M. Shapiro. "Causal Interpretation of Structural IV Estimands." NBER Working Paper Series, No. 31799, October 2023.
 2023
 Working Paper
Large Shocks Travel Fast
By: Alberto Cavallo, Francesco Lippi and Ken Miyahara
We leverage the inflation upswing of 2022 and various granular datasets to identify robust pricesetting patterns following a large supply shock. We show that the frequency of price changes increases dramatically after a large shock. We set up a parsimonious New...
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Keywords:
Macroeconomics;
Analytics and Data Science;
Inflation and Deflation;
Cost;
Mathematical Methods
Cavallo, Alberto, Francesco Lippi, and Ken Miyahara. "Large Shocks Travel Fast." NBER Working Paper Series, No. 31659, September 2023.
 2023
 Article
On Minimizing the Impact of Dataset Shifts on Actionable Explanations
By: Anna P. Meyer, Dan Ley, Suraj Srinivas and Himabindu Lakkaraju
The Right to Explanation is an important regulatory principle that allows individuals to request actionable explanations for algorithmic decisions. However, several technical challenges arise when providing such actionable explanations in practice. For instance, models...
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Meyer, Anna P., Dan Ley, Suraj Srinivas, and Himabindu Lakkaraju. "On Minimizing the Impact of Dataset Shifts on Actionable Explanations." Proceedings of the Conference on Uncertainty in Artificial Intelligence (UAI) 39th (2023): 1434–1444.
 2023
 Working Paper
How People Use Statistics
By: Pedro Bordalo, John J. Conlon, Nicola Gennaioli, Spencer Yongwook Kwon and Andrei Shleifer
We document two new facts about the distributions of answers in famous statistical problems: they are i) multimodal and ii) unstable with respect to irrelevant changes in the problem. We offer a model in which, when solving a problem, people represent each hypothesis...
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Bordalo, Pedro, John J. Conlon, Nicola Gennaioli, Spencer Yongwook Kwon, and Andrei Shleifer. "How People Use Statistics." NBER Working Paper Series, No. 31631, August 2023.
 July 2023 (Revised July 2023)
 Background Note
Generative AI Value Chain
By: Andy Wu and Matt Higgins
Generative AI refers to a type of artificial intelligence (AI) that can create new content (e.g., text, image, or audio) in response to a prompt from a user. ChatGPT, Bard, and Claude are examples of text generating AIs, and DALLE, Midjourney, and Stable Diffusion are...
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Keywords:
AI;
Artificial Intelligence;
Model;
Hardware;
Data Centers;
AI and Machine Learning;
Applications and Software;
Analytics and Data Science;
Value
Wu, Andy, and Matt Higgins. "Generative AI Value Chain." Harvard Business School Background Note 724355, July 2023. (Revised July 2023.)
 2023
 Article
Probabilistically Robust Recourse: Navigating the Tradeoffs between Costs and Robustness in Algorithmic Recourse
By: Martin Pawelczyk, Teresa Datta, Johannes vandenHeuvel, Gjergji Kasneci and Himabindu Lakkaraju
As machine learning models are increasingly being employed to make consequential decisions in realworld settings, it becomes critical to ensure that individuals who are adversely impacted (e.g., loan denied) by the predictions of these models are provided with a means...
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Pawelczyk, Martin, Teresa Datta, Johannes vandenHeuvel, Gjergji Kasneci, and Himabindu Lakkaraju. "Probabilistically Robust Recourse: Navigating the Tradeoffs between Costs and Robustness in Algorithmic Recourse." Proceedings of the International Conference on Learning Representations (ICLR) (2023).
 2023
 Working Paper
Distributionally Robust Causal Inference with Observational Data
By: Dimitris Bertsimas, Kosuke Imai and Michael Lingzhi Li
We consider the estimation of average treatment effects in observational studies and propose a new framework of robust causal inference with unobserved confounders. Our approach is based on distributionally robust optimization and proceeds in two steps. We first...
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Bertsimas, Dimitris, Kosuke Imai, and Michael Lingzhi Li. "Distributionally Robust Causal Inference with Observational Data." Working Paper, February 2023.
 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.)
 2022
 Working Paper
Slowly Varying Regression under Sparsity
By: Dimitris Bertsimas, Vassilis Digalakis Jr, Michael Lingzhi Li and Omar Skali Lami
We consider the problem of parameter estimation in slowly varying regression models with sparsity constraints. We formulate the problem as a mixed integer optimization problem and demonstrate that it can be reformulated exactly as a binary convex optimization problem...
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Keywords:
Mathematical Methods
Bertsimas, Dimitris, Vassilis Digalakis Jr, Michael Lingzhi Li, and Omar Skali Lami. "Slowly Varying Regression under Sparsity." Working Paper, September 2022.
 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).
 April 12, 2022
 Article
Evaluation of Individual and Ensemble Probabilistic Forecasts of COVID19 Mortality in the United States
By: Estee Y. Cramer, Evan L. Ray, Velma K. Lopez, Johannes Bracher, Andrea Brennen, Alvaro J. Castro Rivadeneira, Michael Lingzhi Li and et al.
Shortterm probabilistic forecasts of the trajectory of the COVID19 pandemic in the United States have served as a visible and important communication channel between the scientific modeling community and both the general public and decisionmakers. Forecasting models...
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Keywords:
COVID19;
Forecasting and Prediction;
Health Pandemics;
Mathematical Methods;
Partners and Partnerships
Cramer, Estee Y., Evan L. Ray, Velma K. Lopez, Johannes Bracher, Andrea Brennen, Alvaro J. Castro Rivadeneira, Michael Lingzhi Li, and et al. "Evaluation of Individual and Ensemble Probabilistic Forecasts of COVID19 Mortality in the United States." e2113561119. Proceedings of the National Academy of Sciences 119, no. 15 (April 12, 2022). (See full author list here.)
 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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Keywords:
Data Science;
Linear Regression;
Mathematical Modeling;
Mathematical Methods;
Analytics and Data Science
Bojinov, Iavor I., Michael Parzen, and Paul Hamilton. "Linear Regression." Harvard Business School Module Note 622100, March 2022. (Revised July 2022.)
 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.