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(837)
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Show Results For
- All HBS Web
(837)
- News (79)
- Research (639)
- Events (12)
- Multimedia (4)
- Faculty Publications (632)
- January 1990 (Revised February 1990)
- Case
MSA: The Software Company--Planning the AMAPs Product Line
By: Robert J. Dolan
MSA has commissioned a major market research study to assess demand potential for a computer software system designed for aerospace and defense contractors. Students must evaluate the results of the study (including a conjoint analysis) to assess whether MSA should... View Details
Dolan, Robert J. "MSA: The Software Company--Planning the AMAPs Product Line." Harvard Business School Case 590-069, January 1990. (Revised February 1990.)
- May 1984 (Revised September 1986)
- Background Note
Basic Quantitative Analysis for Marketing
By: Robert J. Dolan
Shows how to calculate and use the break-even volume in marketing decision making. View Details
Dolan, Robert J. "Basic Quantitative Analysis for Marketing." Harvard Business School Background Note 584-149, May 1984. (Revised September 1986.)
- 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
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
Rawal, Kaivalya, and Himabindu Lakkaraju. "Beyond Individualized Recourse: Interpretable and Interactive Summaries of Actionable Recourses." Advances in Neural Information Processing Systems (NeurIPS) 33 (2020).
- October 2020
- Article
Comparative Statics for Size-Dependent Discounts in Matching Markets
By: David Delacretaz, Scott Duke Kominers and Alexandru Nichifor
We prove a natural comparative static for many-to-many matching markets in which agents’ choice functions exhibit size-dependent discounts: reducing the extent to which some agent discounts additional partners leads to improved outcomes for the agents on the other side... View Details
Keywords: Size-dependent Discounts; Path-independence; Respect For Improvements; Market Design; Mathematical Methods
Delacretaz, David, Scott Duke Kominers, and Alexandru Nichifor. "Comparative Statics for Size-Dependent Discounts in Matching Markets." Journal of Mathematical Economics 90 (October 2020): 127–131.
- September 2019
- Article
Optimizing Reserves in School Choice: A Dynamic Programming Approach
By: Franklyn Wang, Ravi Jagadeesan and Scott Duke Kominers
We introduce a new model of school choice with reserves in which a social planner is constrained by a limited supply of reserve seats and tries to find an optimal matching according to a social welfare function. We construct the optimal distribution of reserves via a... View Details
Wang, Franklyn, Ravi Jagadeesan, and Scott Duke Kominers. "Optimizing Reserves in School Choice: A Dynamic Programming Approach." Operations Research Letters 47, no. 5 (September 2019): 438–446.
- Article
Distributionally Robust Optimization and Its Tractable Approximations
By: Joel Goh and Melvyn Sim
In this paper we focus on a linear optimization problem with uncertainties, having expectations in the objective and in the set of constraints. We present a modular framework to obtain an approximate solution to the problem that is distributionally robust and more... View Details
Goh, Joel, and Melvyn Sim. "Distributionally Robust Optimization and Its Tractable Approximations." Operations Research 58, no. 4 (pt.1) (July–August 2010): 902–917.
- June 2007
- Tutorial
Congruence Model Tutorial
By: Christopher Marquis and Alison Comings
Utilizes Beer & Tushman's SMA: Microelectronic Products Division (A) case to explore O'Reilly and Tushman's congruence model. Participants learn about the model through a series of video presentations and become familar with the problems facing SMA through an... View Details
- spring 1973
- Article
A Stochastic Model for Auditing
By: Robert S. Kaplan
Kaplan, Robert S. "A Stochastic Model for Auditing." Journal of Accounting Research 11 (spring 1973): 38–46.
- September 1984
- Background Note
Marketing Research: An Overview of Research Methods
By: Robert J. Dolan
Broadly describes the scope of marketing research, and describes experiments, non-survey methods, and internal data. View Details
Dolan, Robert J. "Marketing Research: An Overview of Research Methods." Harvard Business School Background Note 585-039, September 1984.
- 2004
- Chapter
Paradoxes of Trust: Empirical and Theoretical Departures from a Traditional Model
By: J. Keith Murnighan, Deepak Malhotra and J. Mark Weber
Murnighan, J. Keith, Deepak Malhotra, and J. Mark Weber. "Paradoxes of Trust: Empirical and Theoretical Departures from a Traditional Model." In Trust and Distrust in Organizations: Dilemmas and Approaches, edited by Roderick Kramer and Karen Cook. New York: Russell Sage Foundation, 2004.
- 1972
- Chapter
Random Walks and Technical Theories: Some Additional Evidence
By: George A. Benington and Michael C. Jensen
Keywords: Mathematical Methods
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
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
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
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
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
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.