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    • All HBS Web  (1,968)
      • Faculty Publications  (556)

      Qualitative Research MethodsRemove Qualitative Research Methods →

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      • 2024
      • Article

      A Universal In-Place Reconfiguration Algorithm for Sliding Cube-Shaped Robots in Quadratic Time

      By: Zachary Abel, Hugo A. Akitaya, Scott Duke Kominers, Matias Korman and Frederick Stock
      In the modular robot reconfiguration problem we are given n cube-shaped modules (or "robots") as well as two configurations, i.e., placements of the n modules so that their union is face-connected. The goal is to find a sequence of moves that reconfigures the modules... View Details
      Keywords: Robots; Mathematical Methods
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      Abel, Zachary, Hugo A. Akitaya, Scott Duke Kominers, Matias Korman, and Frederick Stock. "A Universal In-Place Reconfiguration Algorithm for Sliding Cube-Shaped Robots in Quadratic Time." Proceedings of the International Symposium on Computational Geometry (SoCG) 40th (2024): 1:1–1:14.
      • June 2024
      • Article

      Redistributive Allocation Mechanisms

      By: Mohammad Akbarpour, Piotr Dworczak and Scott Duke Kominers
      Many scarce public resources are allocated at below-market-clearing prices, and sometimes for free. Such "non-market" mechanisms sacrifice some surplus, yet they can potentially improve equity. We develop a model of mechanism design with redistributive concerns. Agents... View Details
      Keywords: Equality and Inequality; Welfare; Mathematical Methods; Market Design; Cost vs Benefits
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      Akbarpour, Mohammad, Piotr Dworczak, and Scott Duke Kominers. "Redistributive Allocation Mechanisms." Journal of Political Economy 132, no. 6 (June 2024): 1831–1875. (Authors' names are in certified random order.)
      • 2024
      • Working Paper

      What Is Newsworthy? Theory and Evidence

      By: Luis Armona, Matthew Gentzkow, Emir Kamenica and Jesse M. Shapiro
      We study newsworthiness in theory and practice. We focus on situations in which a news outlet observes the realization of a state of the world and must decide whether to report the realization to a consumer who pays an opportunity cost to consume the report. The... View Details
      Keywords: News; Mathematical Methods; Prejudice and Bias; Media and Broadcasting Industry
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      Armona, Luis, Matthew Gentzkow, Emir Kamenica, and Jesse M. Shapiro. "What Is Newsworthy? Theory and Evidence." NBER Working Paper Series, No. 32512, May 2024.
      • 2025
      • Working Paper

      Greenlighting Innovative Projects: How Evaluation Format Shapes the Perceived Feasibility of Early-Stage Ideas

      By: Jacqueline N. Lane, Simon Friis, Tianxi Cai, Michael Menietti, Griffin Weber and Eva C. Guinan
      The evaluation of innovative early-stage projects is essential for allocating limited resources. We investigate how the evaluation format affects the identification of feasibility issues through a field experiment at a leading research university. Experts were... View Details
      Keywords: Innovation Evaluation; Evaluation Criteria; Feasibility Assessment; Attention Allocation; Cognitive Mechanisms; Field Experiment; Research; Performance Evaluation; Innovation and Invention; Prejudice and Bias
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      Lane, Jacqueline N., Simon Friis, Tianxi Cai, Michael Menietti, Griffin Weber, and Eva C. Guinan. "Greenlighting Innovative Projects: How Evaluation Format Shapes the Perceived Feasibility of Early-Stage Ideas." Harvard Business School Working Paper, No. 24-064, March 2024. (Revised May 2025.)
      • 2023
      • Working Paper

      An Experimental Design for Anytime-Valid Causal Inference on Multi-Armed Bandits

      By: Biyonka Liang and Iavor I. Bojinov
      Typically, multi-armed bandit (MAB) experiments are analyzed at the end of the study and thus require the analyst to specify a fixed sample size in advance. However, in many online learning applications, it is advantageous to continuously produce inference on the... View Details
      Keywords: Analytics and Data Science; AI and Machine Learning; Mathematical Methods
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      Liang, Biyonka, and Iavor I. Bojinov. "An Experimental Design for Anytime-Valid Causal Inference on Multi-Armed Bandits." Harvard Business School Working Paper, No. 24-057, March 2024.
      • 2024
      • Working Paper

      Anytime-Valid Inference in Linear Models and Regression-Adjusted Causal Inference

      By: Michael Lindon, Dae Woong Ham, Martin Tingley and Iavor I. Bojinov
      Linear regression adjustment is commonly used to analyze randomized controlled experiments due to its efficiency and robustness against model misspecification. Current testing and interval estimation procedures leverage the asymptotic distribution of such estimators to... View Details
      Keywords: Mathematical Methods; Analytics and Data Science
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      Lindon, Michael, Dae Woong Ham, Martin Tingley, and Iavor I. Bojinov. "Anytime-Valid Inference in Linear Models and Regression-Adjusted Causal Inference." Harvard Business School Working Paper, No. 24-060, March 2024.
      • 2023
      • Working Paper

      Design-Based Inference for Multi-arm Bandits

      By: Dae Woong Ham, Iavor I. Bojinov, Michael Lindon and Martin Tingley
      Multi-arm bandits are gaining popularity as they enable real-world sequential decision-making across application areas, including clinical trials, recommender systems, and online decision-making. Consequently, there is an increased desire to use the available... View Details
      Keywords: Analytics and Data Science; Mathematical Methods
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      Ham, Dae Woong, Iavor I. Bojinov, Michael Lindon, and Martin Tingley. "Design-Based Inference for Multi-arm Bandits." Harvard Business School Working Paper, No. 24-056, March 2024.
      • February 2024
      • Article

      Fifty Shades of QE: Robust Evidence

      By: Brian Fabo, Marina Jančoková, Elisabeth Kempf and Ľuboš Pástor
      Fabo et al. (2021) show that papers written by central bank researchers find quantitative easing (QE) to be more effective than papers written by academics. Weale and Wieladek (2022) show that a subset of these results lose statistical significance when OLS regressions... View Details
      Keywords: Quantitative Easing; Research; Mathematical Methods; Perception; Banks and Banking; Body of Literature
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      Fabo, Brian, Marina Jančoková, Elisabeth Kempf, and Ľuboš Pástor. "Fifty Shades of QE: Robust Evidence." Art. 107065. Journal of Banking & Finance 159 (February 2024).
      • 2024
      • Working Paper

      Bootstrap Diagnostics for Irregular Estimators

      By: Isaiah Andrews and Jesse M. Shapiro
      Empirical researchers frequently rely on normal approximations in order to summarize and communicate uncertainty about their findings to their scientific audience. When such approximations are unreliable, they can lead the audience to make misguided decisions. We... View Details
      Keywords: Mathematical Methods; Decision Choices and Conditions
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      Andrews, Isaiah, and Jesse M. Shapiro. "Bootstrap Diagnostics for Irregular Estimators." NBER Working Paper Series, No. 32038, January 2024.
      • January 2024
      • Article

      Subset Scanning for Multi-Trait Analysis Using GWAS Summary Statistics

      By: Rui Cao, Evan Olawsky, Edward McFowland III, Erin Marcotte, Logan Spector and Tianzhong Yang
      Multi-trait analysis has been shown to have greater statistical power than single-trait analysis. Most of the existing multi-trait analysis methods only work with a limited number of traits and usually prioritize high statistical power over identifying relevant traits,... View Details
      Keywords: Mathematical Methods; Health Disorders
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      Cao, Rui, Evan Olawsky, Edward McFowland III, Erin Marcotte, Logan Spector, and Tianzhong Yang. "Subset Scanning for Multi-Trait Analysis Using GWAS Summary Statistics." Bioinformatics 40, no. 1 (January 2024).
      • 2023
      • Article

      Balancing Risk and Reward: An Automated Phased Release Strategy

      By: Yufan Li, Jialiang Mao and Iavor Bojinov
      Phased releases are a common strategy in the technology industry for gradually releasing new products or updates through a sequence of A/B tests in which the number of treated units gradually grows until full deployment or deprecation. Performing phased releases in a... View Details
      Keywords: Product Launch; Mathematical Methods; Product Development
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      Li, Yufan, Jialiang Mao, and Iavor Bojinov. "Balancing Risk and Reward: An Automated Phased Release Strategy." Advances in Neural Information Processing Systems (NeurIPS) (2023).
      • 2023
      • Article

      Post Hoc Explanations of Language Models Can Improve Language Models

      By: Satyapriya Krishna, Jiaqi Ma, Dylan Slack, Asma Ghandeharioun, Sameer Singh and Himabindu Lakkaraju
      Large Language Models (LLMs) have demonstrated remarkable capabilities in performing complex tasks. Moreover, recent research has shown that incorporating human-annotated rationales (e.g., Chain-of-Thought prompting) during in-context learning can significantly enhance... View Details
      Keywords: AI and Machine Learning; Performance Effectiveness
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      Krishna, Satyapriya, Jiaqi Ma, Dylan Slack, Asma Ghandeharioun, Sameer Singh, and Himabindu Lakkaraju. "Post Hoc Explanations of Language Models Can Improve Language Models." Advances in Neural Information Processing Systems (NeurIPS) (2023).
      • 2023
      • Other Article

      The Harvard USPTO Patent Dataset: A Large-Scale, Well-Structured, and Multi-Purpose Corpus of Patent Applications

      By: Mirac Suzgun, Luke Melas-Kyriazi, Suproteem K. Sarkar, Scott Duke Kominers and Stuart Shieber
      Innovation is a major driver of economic and social development, and information about many kinds of innovation is embedded in semi-structured data from patents and patent applications. Though the impact and novelty of innovations expressed in patent data are difficult... View Details
      Keywords: USPTO; Natural Language Processing; Classification; Summarization; Patent Novelty; Patent Trolls; Patent Enforceability; Patents; Innovation and Invention; Intellectual Property; AI and Machine Learning; Analytics and Data Science
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      Suzgun, Mirac, Luke Melas-Kyriazi, Suproteem K. Sarkar, Scott Duke Kominers, and Stuart Shieber. "The Harvard USPTO Patent Dataset: A Large-Scale, Well-Structured, and Multi-Purpose Corpus of Patent Applications." Conference on Neural Information Processing Systems (NeurIPS), Datasets and Benchmarks Track 36 (2023).
      • 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 real-world 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... View Details
      Keywords: AI and Machine Learning; Mathematical Methods
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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 Perceptually-Aligned Gradients? An Explanation via Off-Manifold Robustness

      By: Suraj Srinivas, Sebastian Bordt and Himabindu Lakkaraju
      One of the remarkable properties of robust computer vision models is that their input-gradients are often aligned with human perception, referred to in the literature as perceptually-aligned gradients (PAGs). Despite only being trained for classification, PAGs cause... View Details
      Keywords: AI and Machine Learning; Mathematical Methods
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      Srinivas, Suraj, Sebastian Bordt, and Himabindu Lakkaraju. "Which Models Have Perceptually-Aligned Gradients? An Explanation via Off-Manifold 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... View Details
      Keywords: Mathematical Methods
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      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.
      • September 2023
      • Module Note

      Live Case Exercise for Financial Reporting

      By: Tatiana Sandino and Marshal Herrmann
      Harvard Business School employs the case method as a cornerstone of its pedagogy, providing students with opportunities to engage in discussions related to difficult or contentious decisions confronted by real-world organizations. In this “live case,” we depart from... View Details
      Keywords: Financial Reporting; Research; Corporate Disclosure
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      Sandino, Tatiana, and Marshal Herrmann. "Live Case Exercise for Financial Reporting." Harvard Business School Module Note 124-031, September 2023.
      • September–October 2023
      • Article

      Interpretable Matrix Completion: A Discrete Optimization Approach

      By: Dimitris Bertsimas and Michael Lingzhi Li
      We consider the problem of matrix completion on an n × m matrix. We introduce the problem of interpretable matrix completion that aims to provide meaningful insights for the low-rank matrix using side information. We show that the problem can be... View Details
      Keywords: Mathematical Methods
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      Bertsimas, Dimitris, and Michael Lingzhi Li. "Interpretable Matrix Completion: A Discrete Optimization Approach." INFORMS Journal on Computing 35, no. 5 (September–October 2023): 952–965.
      • 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... View Details
      Keywords: Mathematical Methods; Analytics and Data Science
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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.
      • July–August 2023
      • Article

      Demand Learning and Pricing for Varying Assortments

      By: Kris Ferreira and Emily Mower
      Problem Definition: We consider the problem of demand learning and pricing for retailers who offer assortments of substitutable products that change frequently, e.g., due to limited inventory, perishable or time-sensitive products, or the retailer’s desire to... View Details
      Keywords: Experiments; Pricing And Revenue Management; Retailing; Demand Estimation; Pricing Algorithm; Marketing; Price; Demand and Consumers; Mathematical Methods
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      Ferreira, Kris, and Emily Mower. "Demand Learning and Pricing for Varying Assortments." Manufacturing & Service Operations Management 25, no. 4 (July–August 2023): 1227–1244. (Finalist, Practice-Based Research Competition, MSOM (2021) and Finalist, Revenue Management & Pricing Section Practice Award, INFORMS (2019).)
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