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(837)
- News (79)
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- Faculty Publications (632)
Show Results For
- All HBS Web
(837)
- News (79)
- Research (639)
- Events (12)
- Multimedia (4)
- Faculty Publications (632)
- 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.)
- Alumni WDYDWYD
Margaret Regan
education was definitely emphasized by my dad as a vehicle to growth and expanding my horizons. I got a BS in Mathematics and then worked in computer programming before managing the computer facility at a major company. That sounds like... View Details
- May 2017
- Article
Stable and Strategy-Proof Matching with Flexible Allotments
By: John William Hatfield, Scott Duke Kominers and Alexander Westkamp
We introduce a framework of matching with flexible allotments that can be used to model firms with cross-division hiring restrictions. Our framework also allows us to nest some prior models of matching with distributional constraints. Building upon our recent work on... View Details
Hatfield, John William, Scott Duke Kominers, and Alexander Westkamp. "Stable and Strategy-Proof Matching with Flexible Allotments." American Economic Review 107, no. 5 (May 2017): 214–219.
- July 1999
- Background Note
Note on Statistical Tests for a Randomized Matched Pair Experimental Design, A
By: Alvin J. Silk
Concerns understanding the conditions under which an experimental design that employs matching and randomization may result in gains in precision as compared to a design that utilizes randomization and independent samples--i.e., no matching. An empirical example is... View Details
- 1981
- Chapter
Sparsity and Piecewise Linearity in Large Portfolio Optimization Problems
By: André Perold and Harry M. Markowitz
- Forthcoming
- Article
Branch-and-Price for Prescriptive Contagion Analytics
By: Alexandre Jacquillat, Michael Lingzhi Li, Martin Ramé and Kai Wang
Contagion models are ubiquitous in epidemiology, social sciences, engineering, and management. This paper formulates a prescriptive contagion analytics model where a decision maker allocates shared resources across multiple segments of a population, each governed by... View Details
Jacquillat, Alexandre, Michael Lingzhi Li, Martin Ramé, and Kai Wang. "Branch-and-Price for Prescriptive Contagion Analytics." Operations Research (forthcoming). (Pre-published online March 13, 2024.)
- 2020
- Article
Fast Exact Matrix Completion: A Unified Optimization Framework for Matrix Completion
By: Dimitris Bertsimas and Michael Lingzhi Li
We formulate the problem of matrix completion with and without side information as a non-convex optimization problem. We design fastImpute based on non-convex gradient descent and show it converges to a global minimum that is guaranteed to recover closely the... View Details
Keywords: Mathematical Methods
Bertsimas, Dimitris, and Michael Lingzhi Li. "Fast Exact Matrix Completion: A Unified Optimization Framework for Matrix Completion." Journal of Machine Learning Research 21, no. 1 (2020).
- Article
How Much Should We Trust Staggered Difference-In-Differences Estimates?
By: Andrew C. Baker, David F. Larcker and Charles C.Y. Wang
We explain when and how staggered difference-in-differences regression estimators, commonly applied to assess the impact of policy changes, are biased. These biases are likely to be relevant for a large portion of research settings in finance, accounting, and law that... View Details
Keywords: Difference In Differences; Staggered Difference-in-differences Designs; Generalized Difference-in-differences; Dynamic Treatment Effects; Mathematical Methods
Baker, Andrew C., David F. Larcker, and Charles C.Y. Wang. "How Much Should We Trust Staggered Difference-In-Differences Estimates?" Journal of Financial Economics 144, no. 2 (May 2022): 370–395. (Editor's Choice, May 2022; Jensen Prize, First Place, June 2023.)
- Mar 2021
- Conference Presentation
Descent-to-Delete: Gradient-Based Methods for Machine Unlearning
By: Seth Neel, Aaron Leon Roth and Saeed Sharifi-Malvajerdi
We study the data deletion problem for convex models. By leveraging techniques from convex optimization and reservoir sampling, we give the first data deletion algorithms that are able to handle an arbitrarily long sequence of adversarial updates while promising both... View Details
Neel, Seth, Aaron Leon Roth, and Saeed Sharifi-Malvajerdi. "Descent-to-Delete: Gradient-Based Methods for Machine Unlearning." Paper presented at the 32nd Algorithmic Learning Theory Conference, March 2021.
- Article
Oracle Efficient Private Non-Convex Optimization
By: Seth Neel, Aaron Leon Roth, Giuseppe Vietri and Zhiwei Steven Wu
One of the most effective algorithms for differentially private learning and optimization is objective perturbation. This technique augments a given optimization problem (e.g. deriving from an ERM problem) with a random linear term, and then exactly solves it.... View Details
Neel, Seth, Aaron Leon Roth, Giuseppe Vietri, and Zhiwei Steven Wu. "Oracle Efficient Private Non-Convex Optimization." Proceedings of the International Conference on Machine Learning (ICML) 37th (2020).
- Article
Aztec Castles and the dP3 Quiver
By: Megan Leoni, Gregg Musiker, Seth Neel and Paxton Turner
Bipartite, periodic, planar graphs known as brane tilings can be associated to a large class of quivers. This paper will explore new algebraic properties of the well-studied del Pezzo 3 (dP3) quiver and geometric properties of its corresponding brane tiling. In... View Details
Leoni, Megan, Gregg Musiker, Seth Neel, and Paxton Turner. "Aztec Castles and the dP3 Quiver." Journal of Physics A: Mathematical and Theoretical 47, no. 47 (November 28, 2014).