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Show Results For
- All HBS Web
(840)
- News (79)
- Research (641)
- Events (14)
- Multimedia (4)
- Faculty Publications (635)
- 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.
- 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
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. View Details
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. View Details
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.)
- 1985
- Chapter
The Role of Contingent Claims Analysis in Corporate Finance
By: Scott P. Mason and Robert C. Merton
- 1999
- Chapter
Interest Rate Rules in an Estimated Sticky Price Model
By: Julio J. Rotemberg and Michael Woodford
Rotemberg, Julio J., and Michael Woodford. "Interest Rate Rules in an Estimated Sticky Price Model." In Monetary Policy Rules, edited by John B. Taylor. Chicago: University of Chicago Press, 1999.
- August 2018
- Article
Extrapolation and Bubbles
By: Nicholas Barberis, Robin Greenwood, Lawrence Jin and Andrei Shleifer
We present an extrapolative model of bubbles. In the model, many investors form their demand for a risky asset by weighing two signals: an average of the asset’s past price changes and the asset’s degree of overvaluation. The two signals are in conflict, and investors... View Details
Barberis, Nicholas, Robin Greenwood, Lawrence Jin, and Andrei Shleifer. "Extrapolation and Bubbles." Journal of Financial Economics 129, no. 2 (August 2018): 203–227.
- 2016
- Working Paper
Algorithmic Foundations for Business Strategy
By: Mihnea Moldoveanu
I introduce algorithmic and meta-algorithmic models for the study of strategic problem solving, aimed at illuminating the processes and procedures by which strategic managers and firms deal with complex problems. These models allow us to explore the relationship... View Details
Moldoveanu, Mihnea. "Algorithmic Foundations for Business Strategy." Harvard Business School Working Paper, No. 17-036, October 2016.
- 1995
- Book
Introduction to Statistical Decision Theory
By: John W. Pratt, Howard Raiffa and Robert Schlaifer
Pratt, John W., Howard Raiffa, and Robert Schlaifer. Introduction to Statistical Decision Theory. MIT Press, 1995.
- 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.)
- Web
Prelude - Option Pricing in Theory & Practice: The Nobel Prize Research of Robert C. Merton - Exhibits - Historical Collections
economics through his working relationship with Paul Samuelson. Perhaps more than any other economist to date, Paul Samuelson is credited with ushering in the modern era of mathematical economic analysis incorporating formal probability... View Details