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- February 2005 (Revised March 2005)
- Background Note
Simple Regression Mathematics
By: Frances X. Frei and Dennis Campbell
Describes the underlying mathematics of regression. View Details
Keywords: Mathematical Methods
Frei, Frances X., and Dennis Campbell. "Simple Regression Mathematics." Harvard Business School Background Note 605-061, February 2005. (Revised March 2005.)
- 1977
- Book
Applied Mathematical Programming
By: Stephen P. Bradley, Arnoldo C. Hax and Thomas L. Magnanti
Keywords: Mathematical Methods
Bradley, Stephen P., Arnoldo C. Hax, and Thomas L. Magnanti. Applied Mathematical Programming. Reading, MA: Addison-Wesley Publishing Company, 1977.
- 24 Apr 2014
- News
Creating a mathematical method to understand consumer behavior in a digital world
homophily—the “birds-of-a-feather” tendencies of like-minded people? Only by understanding the relative impacts of these factors can companies develop effective marketing strategies. Studying the adoption of a mobile app in Japan, Gupta and colleagues devised a View Details
- Article
Overhead Allocation via Mathematical Programming Models
By: Robert S. Kaplan and Gerald Thompson
Keywords: Mathematical Methods
Kaplan, Robert S., and Gerald Thompson. "Overhead Allocation via Mathematical Programming Models." Accounting Review 46, no. 2 (April 1971): 352–364.
- 2019
- Chapter
Quantitative and Qualitative Methods in Organizational Research
By: Amy C. Edmondson and Tiona Zuzul
Selecting the appropriate method for a given research question is an essential skill for organizational researchers. High-quality research involves a good fit between the methods used and the nature of the contribution to the literature. This article describes a... View Details
Edmondson, Amy C., and Tiona Zuzul. "Quantitative and Qualitative Methods in Organizational Research." In The Palgrave Encyclopedia of Strategic Management. Continuously updated edition, edited by Mie Augier and David J. Teece. Palgrave Macmillan, 2017. Electronic. (Pre-published, October 2013.)
- 2022
- Article
Data Poisoning Attacks on Off-Policy Evaluation Methods
By: Elita Lobo, Harvineet Singh, Marek Petrik, Cynthia Rudin and Himabindu Lakkaraju
Off-policy Evaluation (OPE) methods are a crucial tool for evaluating policies in high-stakes domains such as healthcare, where exploration is often infeasible, unethical, or expensive. However, the extent to which such methods can be trusted under adversarial threats... View Details
Lobo, Elita, Harvineet Singh, Marek Petrik, Cynthia Rudin, and Himabindu Lakkaraju. "Data Poisoning Attacks on Off-Policy Evaluation Methods." Proceedings of the Conference on Uncertainty in Artificial Intelligence (UAI) 38th (2022): 1264–1274.
- June 1994
- Article
Influence of Mathematical Models in Finance on Practice: Past, Present and Future
By: Robert C. Merton
Merton, Robert C. "Influence of Mathematical Models in Finance on Practice: Past, Present and Future." Series A. Philosophical Transactions of the Royal Society of London, Series A, Physical Sciences and Engineering 347 (June 1994): 451–463. (Reprinted in Financial Practice and Education, spring 1995.)
- 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.
- December 1981 (Revised September 1986)
- Background Note
Research Methods in Marketing: Survey Research
By: Robert J. Dolan
Presents basic issues in survey research, covering both measurement and sampling error. The intention is to consider each element of the survey process: problem statement, questionnaire design, sampling, and data analysis. View Details
Dolan, Robert J. "Research Methods in Marketing: Survey Research." Harvard Business School Background Note 582-055, December 1981. (Revised September 1986.)
- 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.
- March 2022 (Revised January 2025)
- Technical Note
Linear Regression
This note provides an overview of linear regression for an introductory data science course. It begins with a discussion of correlation, and explains why correlation does not necessarily imply causation. The note then describes the method of least squares, and how to... View Details
Keywords: Data Science; Linear Regression; Mathematical Modeling; Mathematical Methods; Analytics and Data Science
Bojinov, Iavor I., Michael Parzen, and Paul Hamilton. "Linear Regression." Harvard Business School Technical Note 622-100, March 2022. (Revised January 2025.)
- 1981
- Chapter
A Degeneracy Exploiting LU Factorization for the Simplex Method
By: André Perold
Keywords: Mathematical Methods
- 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).
- March 2022 (Revised January 2025)
- Technical Note
Statistical Inference
This note provides an overview of statistical inference for an introductory data science course. First, the note discusses samples and populations. Next the note describes how to calculate confidence intervals for means and proportions. Then it walks through the logic... View Details
Keywords: Data Science; Statistics; Mathematical Modeling; Mathematical Methods; Analytics and Data Science
Bojinov, Iavor I., Michael Parzen, and Paul Hamilton. "Statistical Inference." Harvard Business School Technical Note 622-099, March 2022. (Revised January 2025.)
- 1979
- Chapter
Research Methods and Data Analysis: The Challenge of Knowing How to Do What About Why
By: T. M. Amabile and W. DeJong
- 2024
- Working Paper
Empirical Guidance: Data Processing and Analysis with Applications in Stata, R, and Python
By: Melissa Ouellet and Michael W. Toffel
This paper describes a range of best practices to compile and analyze datasets, and includes some examples in Stata, R, and Python. It is meant to serve as a reference for those getting started in econometrics, and especially those seeking to conduct data analyses in... View Details
Keywords: Empirical Methods; Empirical Operations; Statistical Methods And Machine Learning; Statistical Interferences; Research Analysts; Analytics and Data Science; Mathematical Methods
Ouellet, Melissa, and Michael W. Toffel. "Empirical Guidance: Data Processing and Analysis with Applications in Stata, R, and Python." Harvard Business School Working Paper, No. 25-010, August 2024.
- August 2020 (Revised September 2020)
- Technical Note
Assessing Prediction Accuracy of Machine Learning Models
The note introduces a variety of methods to assess the accuracy of machine learning prediction models. The note begins by briefly introducing machine learning, overfitting, training versus test datasets, and cross validation. The following accuracy metrics and tools... View Details
Keywords: Machine Learning; Statistics; Econometric Analyses; Experimental Methods; Data Analysis; Data Analytics; Forecasting and Prediction; Analytics and Data Science; Analysis; Mathematical Methods
Toffel, Michael W., Natalie Epstein, Kris Ferreira, and Yael Grushka-Cockayne. "Assessing Prediction Accuracy of Machine Learning Models." Harvard Business School Technical Note 621-045, August 2020. (Revised September 2020.)