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(835)
- News (77)
- Research (638)
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- Faculty Publications (633)
Show Results For
-
All HBS Web
(835)
- News (77)
- Research (638)
- Events (11)
- Multimedia (4)
- Faculty Publications (633)
- 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...
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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...
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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).
- 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...
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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.
- 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:...
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Keywords:
Matching With Contracts;
Contract Design;
Bundling-proofness;
Substitutability;
Mathematical Methods
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
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.
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Keywords:
Mathematical Methods
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.
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Keywords:
Mathematical Methods
- 2001
- Other Teaching and Training Material
Interaction Terms in Regression
By: William B. Simpson and Kimball Lewis
Keywords:
Mathematical Methods
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
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
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
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
Hawkins, David F. "Growth Analysis." Harvard Business School Background Note 178-113, November 1977. (Revised February 1979.)
- 1969
- Other Unpublished Work
An Empirical Investigation of the Samuelson Rational Warrant Pricing Theory
By: Robert C. Merton
- 03 Aug 2015
- Research & Ideas
Why Fierce Competitors Apple and Amazon Became ’Frenemies’ Over eReaders
researchers use a complex mathematical model to get to the bottom of just why enemies might decide to share a locker. It boils down to a difference in how they make their money. "Even though both [companies] make money from hardware and...
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- Web
Bibliography - Option Pricing in Theory & Practice: The Nobel Prize Research of Robert C. Merton - Exhibits - Historical Collections
the American Mathematical Society , no. 4. New York, N.Y.: American Mathematical Society, 1951. * Samuelson, Paul A. Foundations of Economic Analysis . Cambridge, Mass.: Harvard University Press, 1947. *...
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- July 2023
- Article
Design and Analysis of Switchback Experiments
By: Iavor I Bojinov, David Simchi-Levi and Jinglong Zhao
In switchback experiments, a firm sequentially exposes an experimental unit to a random treatment, measures its response, and repeats the procedure for several periods to determine which treatment leads to the best outcome. Although practitioners have widely adopted...
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Bojinov, Iavor I., David Simchi-Levi, and Jinglong Zhao. "Design and Analysis of Switchback Experiments." Management Science 69, no. 7 (July 2023): 3759–3777.
- January 1997
- Background Note
Simulation as a Decision Aid
By: Roy D. Shapiro
A brief introduction to simulation--what it is, why it's used, etc. Meant to set context for a first class on simulation. A rewritten version of an earlier note.
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Shapiro, Roy D. "Simulation as a Decision Aid." Harvard Business School Background Note 697-062, January 1997.
- 1982
- Chapter
Informal Covariation Assessment: Data-based vs. Theory-based Judgements
By: D. Jennings, T. M. Amabile and L. D. Ross
Keywords:
Mathematical Methods