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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)
- Article
Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions
By: Daniel M. Kane and Scott Duke Kominers
For relatively prime positive integers and r, we consider the least common multiple L_n:=\mathop{\textrm{lcm}}(u_0,u_1,\dots, u_n) of the finite arithmetic progression \{u_k:=u_0+kr\}_{k=0}^n. We derive new lower bounds on L_n that improve upon those obtained...
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Keywords:
Mathematical Methods
Kane, Daniel M., and Scott Duke Kominers. "Asymptotic Improvements of Lower Bounds for the Least Common Multiples of Arithmetic Progressions." Canadian Mathematical Bulletin 57, no. 3 (September 2014): 551–561.
- 1987
- Chapter
Continuous-Time Stochastic Models
By: Robert C. Merton
Keywords:
Mathematical Methods
Merton, Robert C. "Continuous-Time Stochastic Models." In The New Palgrave: A Dictionary of Economic Theory and Doctrine, edited by John Eatwell, Murray Milgate, and Peter Newman. London: Macmillan Press, 1987. (Revised in The New Palgrave Dictionary of Money and Finance, London: MacMillan Press, Ltd., 1992.)
- February 1996
- Exercise
Problems in Variance Analysis
By: William J. Bruns Jr.
Keywords:
Mathematical Methods
Bruns, William J., Jr. "Problems in Variance Analysis." Harvard Business School Exercise 196-120, February 1996.
- May 1983
- Article
Optimality Conditions and Strong Duality in Abstract and Continuous Time Linear Programming
By: André Perold and R. Meidan
Keywords:
Mathematical Methods
Perold, André, and R. Meidan. "Optimality Conditions and Strong Duality in Abstract and Continuous Time Linear Programming." Journal of Optimization Theory and Applications 40, no. 1 (May 1983): 61–76.
- February 2005 (Revised November 2006)
- Background Note
Using Data Desk for Statistical Analysis
By: Frances X. Frei and Dennis Campbell
Describes how to use the Data Desk software package to perform statistical analysis.
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Keywords:
Mathematical Methods
Frei, Frances X., and Dennis Campbell. "Using Data Desk for Statistical Analysis." Harvard Business School Background Note 605-060, February 2005. (Revised November 2006.)
- March 2004
- Tutorial
Variance Analysis Tutorial
By: David F. Hawkins and Jacob Cohen
An interactive tutorial on variance analysis, flexible budgets, and overhead allocation.
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Keywords:
Mathematical Methods
- 1977
- Article
On the Joint Distribution of Left- and Right-sided Outliner Statistics
By: André Perold and D. M. Hawkins
Keywords:
Mathematical Methods
Perold, André, and D. M. Hawkins. "On the Joint Distribution of Left- and Right-sided Outliner Statistics." Utilitas mathematica 12 (1977): 129–143.
- 01 Oct 1998
- News
Merton Named University Professor
mathematics from Columbia University in 1966, Merton studied applied mathematics at the California Institute of Technology and earned an MS in 1967. In 1970 he completed a Ph.D. in economics at MIT and...
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- Career Coach
Wendi Zhang
development policies and analysis in the public sector. Wendi attended the Massachusetts Institute of Technology, where she received Bachelor of Science degrees in both Mathematics and Management Science, along with minors in Economics...
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- 16 Oct 2019
- News
The Road to Impact
increasing the organization’s visibility. “We may have discovered a better way to teach young kids mathematics or to teach non-English speakers how to read English in third grade, or how to better inhibit suicidal patients from taking...
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- April 1990
- Case
Clark Material Handling Group-Overseas: Brazilian Product Strategy (A&B) (Condensed)
By: Robert J. Dolan
Assumes some knowledge of conjoint analysis. Permits analysis of basic results and dynamic market simulations in one class session.
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Dolan, Robert J. "Clark Material Handling Group-Overseas: Brazilian Product Strategy (A&B) (Condensed)." Harvard Business School Case 590-081, April 1990.
- 01 Mar 2016
- News
Research Brief: The Benefits of Bias
specialized expertise to the process—which some worry might create subject-area bias in the decision-making process and affect the quality of research. Assistant Professor Danielle Li takes a mathematical approach to examining this issue...
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Keywords:
Erin Peterson
- 01 Dec 1997
- News
"Economists are puzzle solvers..."
(I've always been a car buff!) when I was ten. I can remember going with my dad to the stockbroker's and sitting there watching the NYSE and AMEX tapes, learning all the companies' symbols. And when I was in graduate school in applied View Details
- Forthcoming
- Article
A Universal In-Place Reconfiguration Algorithm for Sliding Cube-Shaped Robots in Quadratic Time
By: Zachary Abel, Hugo A. Akitaya, Scott Duke Kominers, Matias Korman and Frederick Stock
In the modular robot reconfiguration problem we are given n cube-shaped modules (or "robots") as well as two configurations, i.e., placements of the n modules so that their union is face-connected. The goal is to find a sequence of moves that reconfigures the modules...
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- 2023
- Working Paper
Causal Interpretation of Structural IV Estimands
By: Isaiah Andrews, Nano Barahona, Matthew Gentzkow, Ashesh Rambachan and Jesse M. Shapiro
We study the causal interpretation of instrumental variables (IV) estimands of nonlinear, multivariate structural models with respect to rich forms of model misspecification. We focus on guaranteeing that the researcher's estimator is sharp zero consistent, meaning...
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Keywords:
Mathematical Methods
Andrews, Isaiah, Nano Barahona, Matthew Gentzkow, Ashesh Rambachan, and Jesse M. Shapiro. "Causal Interpretation of Structural IV Estimands." NBER Working Paper Series, No. 31799, October 2023.
- 2022
- Working Paper
Slowly Varying Regression under Sparsity
By: Dimitris Bertsimas, Vassilis Digalakis Jr, Michael Lingzhi Li and Omar Skali Lami
We consider the problem of parameter estimation in slowly varying regression models with sparsity constraints. We formulate the problem as a mixed integer optimization problem and demonstrate that it can be reformulated exactly as a binary convex optimization problem...
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Keywords:
Mathematical Methods
Bertsimas, Dimitris, Vassilis Digalakis Jr, Michael Lingzhi Li, and Omar Skali Lami. "Slowly Varying Regression under Sparsity." Working Paper, September 2022.
- Article
Learning Models for Actionable Recourse
By: Alexis Ross, Himabindu Lakkaraju and Osbert Bastani
As machine learning models are increasingly deployed in high-stakes domains such as legal and financial decision-making, there has been growing interest in post-hoc methods for generating counterfactual explanations. Such explanations provide individuals adversely...
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Ross, Alexis, Himabindu Lakkaraju, and Osbert Bastani. "Learning Models for Actionable Recourse." Advances in Neural Information Processing Systems (NeurIPS) 34 (2021).
- Mar 2020
- Conference Presentation
A New Analysis of Differential Privacy's Generalization Guarantees
By: Christopher Jung, Katrina Ligett, Seth Neel, Aaron Roth, Saeed Sharifi-Malvajerdi and Moshe Shenfeld
We give a new proof of the "transfer theorem" underlying adaptive data analysis: that any mechanism for answering adaptively chosen statistical queries that is differentially private and sample-accurate is also accurate out-of-sample. Our new proof is elementary and...
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Jung, Christopher, Katrina Ligett, Seth Neel, Aaron Roth, Saeed Sharifi-Malvajerdi, and Moshe Shenfeld. "A New Analysis of Differential Privacy's Generalization Guarantees." Paper presented at the 11th Innovations in Theoretical Computer Science Conference, Seattle, March 2020.
- Article
Active World Model Learning with Progress Curiosity
By: Kuno Kim, Megumi Sano, Julian De Freitas, Nick Haber and Daniel Yamins
World models are self-supervised predictive models of how the world evolves. Humans learn world models by curiously exploring their environment, in the process acquiring compact abstractions of high bandwidth sensory inputs, the ability to plan across long temporal...
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Kim, Kuno, Megumi Sano, Julian De Freitas, Nick Haber, and Daniel Yamins. "Active World Model Learning with Progress Curiosity." Proceedings of the International Conference on Machine Learning (ICML) 37th (2020).