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  • All HBS Web  (854)
    • News  (79)
    • Research  (639)
    • Events  (14)
    • Multimedia  (4)
  • Faculty Publications  (632)
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  • 2010
  • Other Unpublished Work

Modeling Passenger Travel and Delays in the National Air Transportation System

Many of the existing methods for evaluating an airline's on-time performance are based on flight-centric measures of delay. However, recent research has demonstrated that passenger delays depend on many factors in addition to flight delays. For instance,... View Details
Keywords: Mathematical Methods; Performance Evaluation; Air Transportation Industry; United States
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Barnhart, C., D. Fearing, and V. Vaze. "Modeling Passenger Travel and Delays in the National Air Transportation System."
  • 2005
  • Chapter

A Revised Model of the Resource Allocation Process

By: J. L. Bower and Clark Gilbert
Keywords: Resource Allocation; Mathematical Methods
Citation
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Bower, J. L., and Clark Gilbert. "A Revised Model of the Resource Allocation Process." In From Resource Allocation to Strategy, edited by Joseph L. Bower and Clark Gilbert. U.K.: Oxford University Press, 2005.
  • 2005
  • Chapter

Anomaly Seeking Research: Thirty Years of Development in Resource Allocation Theory

By: Clark Gilbert and Clayton M. Christensen
Keywords: Resource Allocation; Mathematical Methods
Citation
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Gilbert, Clark, and Clayton M. Christensen. "Anomaly Seeking Research: Thirty Years of Development in Resource Allocation Theory." In From Resource Allocation to Strategy, edited by Joseph L. Bower and Clark Gilbert. U.K.: Oxford University Press, 2005.
  • 1972
  • Chapter

Random Walks and Technical Theories: Some Additional Evidence

By: George A. Benington and Michael C. Jensen
Keywords: Mathematical Methods
Citation
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Benington, George A., and Michael C. Jensen. "Random Walks and Technical Theories: Some Additional Evidence." In Security Evaluation and Portfolio Analysis, edited by E. Elton and M. Gruber. Prentice Hall, 1972. (Also published in Journal of Finance (May 1970) and Investment Management: Some Readings, J. Lorie and R. Brealey, Editors (Praeger Publishers, 1972).)
  • 1979
  • Article

An Extension and Simple Proof of a Constrained Lattice Fix-Point Theorem

By: C. Blair and A. E. Roth
Keywords: Mathematical Methods
Citation
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Blair, C., and A. E. Roth. "An Extension and Simple Proof of a Constrained Lattice Fix-Point Theorem." Algebra Universalis 9 (1979): 131–132.
  • January 1975
  • Article

A Lattice Fixed-Point Theorem with Constraints

By: A. E. Roth
Keywords: Mathematical Methods
Citation
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Roth, A. E. "A Lattice Fixed-Point Theorem with Constraints." Bulletin of the American Mathematical Society 81 (January 1975): 136–138.
  • 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.
  • 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 high-stakes applications, counterfactual explanations have emerged as key tools for providing actionable model explanations in practice. Despite the growing popularity of counterfactual explanations, a... View Details
Keywords: Machine Learning Models; Counterfactual Explanations; Adversarial Examples; Mathematical Methods
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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).
  • November 2021
  • Article

Panel Experiments and Dynamic Causal Effects: A Finite Population Perspective

By: Iavor Bojinov, Ashesh Rambachan and Neil Shephard
In panel experiments, we randomly assign units to different interventions, measuring their outcomes, and repeating the procedure in several periods. Using the potential outcomes framework, we define finite population dynamic causal effects that capture the relative... View Details
Keywords: Panel Data; Dynamic Causal Effects; Potential Outcomes; Finite Population; Nonparametric; Mathematical Methods
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Bojinov, Iavor, Ashesh Rambachan, and Neil Shephard. "Panel Experiments and Dynamic Causal Effects: A Finite Population Perspective." Quantitative Economics 12, no. 4 (November 2021): 1171–1196.
  • 2018
  • Working Paper

Bundling Incentives in (Many-to-Many) Matching with Contracts

By: Jonathan Ma and Scott Duke Kominers
In many-to-many matching with contracts, the way in which contracts are specified can affect the set of stable equilibrium outcomes. Consequently, agents may be incentivized to modify the set of contracts upfront. We consider one simple way in which agents may do so:... View Details
Keywords: Matching With Contracts; Contract Design; Bundling-proofness; Substitutability; Mathematical Methods
Citation
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Ma, Jonathan, and Scott Duke Kominers. "Bundling Incentives in (Many-to-Many) Matching with Contracts." Harvard Business School Working Paper, No. 19-011, August 2018.
  • 2011
  • Chapter

Fundamental Data Anomalies

By: Ian D. Gow
Keywords: Mathematical Methods; Data and Data Sets
Citation
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Gow, Ian D. "Fundamental Data Anomalies." Chap. 5 in The Handbook of Equity Market Anomalies: Translating Market Inefficiencies into Effective Investment Strategies, edited by Len Zacks, 117–128. John Wiley & Sons, 2011.
  • November 1990 (Revised November 1992)
  • Background Note

Note on Linear Programming

Gives an elementary introduction to formulating linear programming models and interpreting linear programmings output. Other aspects of linear programming are discussed briefly. View Details
Keywords: Mathematical Methods
Citation
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Eckstein, Jonathan. "Note on Linear Programming." Harvard Business School Background Note 191-085, November 1990. (Revised November 1992.)
  • August 2005 (Revised April 2008)
  • Teaching Note

GuestFirst Hotel (A): Statistics Review with Data Desk (TN)

By: Frances X. Frei
Presents an overview of the statistical analysis covered in the case discussion. View Details
Keywords: Mathematical Methods
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Frei, Frances X. "GuestFirst Hotel (A): Statistics Review with Data Desk (TN)." Harvard Business School Teaching Note 606-038, August 2005. (Revised April 2008.)
  • 2001
  • Other Teaching and Training Material

Interaction Terms in Regression

By: William B. Simpson and Kimball Lewis
Keywords: Mathematical Methods
Citation
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Simpson, William B., and Kimball Lewis. "Interaction Terms in Regression." 2001. Electronic.
  • May 1983
  • Article

The Fragility of Econometric Reporting

By: Edward Leamer and Dutch Leonard
Keywords: Mathematical Methods
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Leamer, Edward, and Dutch Leonard. "The Fragility of Econometric Reporting." Review of Economics and Statistics 65, no. 2 (May 1983).
  • 2004
  • Other Unpublished Work

Long-Horizon Mean-Variance Analysis: A User Guide

By: Luis M. Viceira and John Y. Campbell
Keywords: Mathematical Methods
Citation
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Viceira, Luis M., and John Y. Campbell. "Long-Horizon Mean-Variance Analysis: A User Guide." September 2004.
  • April 1966
  • Article

A Two-Stage Forecasting Model: Exponential Smoothing and Multiple Regression

By: D. B. Crane and James R. Crotty
Keywords: Mathematical Methods
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Crane, D. B., and James R. Crotty. "A Two-Stage Forecasting Model: Exponential Smoothing and Multiple Regression." Management Science 13, no. 8 (April 1966).
  • November 1977 (Revised February 1979)
  • Background Note

Growth Analysis

By: David F. Hawkins
Keywords: Mathematical Methods
Citation
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Hawkins, David F. "Growth Analysis." Harvard Business School Background Note 178-113, November 1977. (Revised February 1979.)
  • 2022
  • Article

Probing GNN Explainers: A Rigorous Theoretical and Empirical Analysis of GNN Explanation Methods.

By: Chirag Agarwal, Marinka Zitnik and Himabindu Lakkaraju
As Graph Neural Networks (GNNs) are increasingly employed in real-world applications, it becomes critical to ensure that the stakeholders understand the rationale behind their predictions. While several GNN explanation methods have been proposed recently, there has... View Details
Keywords: Graph Neural Networks; Explanation Methods; Mathematical Methods; Framework; Theory; Analysis
Citation
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Agarwal, Chirag, Marinka Zitnik, and Himabindu Lakkaraju. "Probing GNN Explainers: A Rigorous Theoretical and Empirical Analysis of GNN Explanation Methods." Proceedings of the International Conference on Artificial Intelligence and Statistics (AISTATS) 25th (2022).
  • 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
Keywords: Predictive Models; Decision Making; Framework; Mathematical Methods
Citation
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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).
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