Publications

2022
Article

Fairness via Explanation Quality: Evaluating Disparities in the Quality of Post hoc Explanations

By: Jessica Dai, Sohini Upadhyay, Ulrich Aivodji, Stephen Bach and Himabindu Lakkaraju

As post hoc explanation methods are increasingly being leveraged to explain complex models in high-stakes settings, it becomes critical to ensure that the quality of the resulting explanations is consistently high across all subgroups of a population. For instance, it... View Details

Keywords: Prejudice and Bias; Mathematical Methods; Research; Analytics and Data Science

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2023
Article

Verifiable Feature Attributions: A Bridge between Post Hoc Explainability and Inherent Interpretability

By: Usha Bhalla, Suraj Srinivas and Himabindu Lakkaraju

With the increased deployment of machine learning models in various real-world applications, researchers and practitioners alike have emphasized the need for explanations of model behaviour. To this end, two broad strategies have been outlined in prior literature to... View Details

Keywords: AI and Machine Learning; Mathematical Methods

October 2020
Article

Comparative Statics for Size-Dependent Discounts in Matching Markets

By: David Delacretaz, Scott Duke Kominers and Alexandru Nichifor

We prove a natural comparative static for many-to-many matching markets in which agents’ choice functions exhibit size-dependent discounts: reducing the extent to which some agent discounts additional partners leads to improved outcomes for the agents on the other side... View Details

Keywords: Size-dependent Discounts; Path-independence; Respect For Improvements; Market Design; Mathematical Methods

Professor Bradley is the William Ziegler Professor of Business Administration Emeritus at the Harvard Business School. In addition to teaching Management and Strategy in the Owner President Management Program and leading an... View Details

Keywords: e-commerce industry; financial services; health care; high technology; internet; pharmaceuticals; telecommunications

March 2022
Article

Estimating the Effectiveness of Permanent Price Reductions for Competing Products Using Multivariate Bayesian Structural Time Series Models

By: Fiammetta Menchetti and Iavor Bojinov

Researchers regularly use synthetic control methods for estimating causal effects when a sub-set of units receive a single persistent treatment, and the rest are unaffected by the change. In many applications, however, units not assigned to treatment are nevertheless... View Details

Keywords: Causal Inference; Partial Interference; Synthetic Controls; Bayesian Structural Time Series; Mathematical Methods

2020
Working Paper

Design Rules, Volume 2: How Technology Shapes Organizations: Chapter 6 The Value Structure of Technologies, Part 1: Mapping Functional Relationships

By: Carliss Y. Baldwin

Organizations are formed in a free economy because an individual or group perceives value in carrying out a technical recipe that is beyond the capacity of a single person. Technology specifies what must be done, what resources must be assembled, what actions taken in... View Details

Keywords: Modularity; Information Technology; Organizations; Value Creation

SSRN

November 2007
Background Note

Asset Allocation I

By: Joshua D. Coval, Erik Stafford, Rodrigo Osmo, John Jernigan, Zack Page and Paulo Passoni

The goal of these simulations is to understand the mathematics of mean-variance optimization and the equilibrium pricing of risk if all investors use this rule with common information sets. Simulation A focuses on five to 10 years of monthly sector returns that are... View Details

Keywords: Asset Pricing; Capital; Investment Return; Risk Management; Mathematical Methods

Educators

March 2016 (Revised January 2020)
Teaching Note

Behavioural Insights Team (A) and (B)

By: Michael Luca and Patrick Rooney

The Behavioural Insights Team case introduces students to the concept of choice architecture and the value of experimental methods (sometimes called A/B testing) within organizational contexts. The exercise provides an opportunity for students to apply these principles... View Details

Keywords: Behavioral Economics; Experiments; Choice Architecture; Public Entrepreneurship; Decision Choices and Conditions; Mathematical Methods; United Kingdom

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2021
Conference Presentation

An Algorithmic Framework for Fairness Elicitation

By: Christopher Jung, Michael J. Kearns, Seth Neel, Aaron Leon Roth, Logan Stapleton and Zhiwei Steven Wu

We consider settings in which the right notion of fairness is not captured by simple mathematical definitions (such as equality of error rates across groups), but might be more complex and nuanced and thus require elicitation from individual or collective stakeholders.... View Details

Keywords: Algorithmic Fairness; Machine Learning; Fairness; Framework; Mathematical Methods

May–June 2018
Article

Data Uncertainty in Markov Chains: Application to Cost-Effectiveness Analyses of Medical Innovations

By: Joel Goh, Mohsen Bayati, Stefanos A. Zenios, Sundeep Singh and David Moore

Cost-effectiveness studies of medical innovations often suffer from data inadequacy. When Markov chains are used as a modeling framework for such studies, this data inadequacy can manifest itself as imprecision in the elements of the transition matrix. In this paper,... View Details

Keywords: Markov Chains; Cost Effectiveness; Medical Innovations; Colorectal Cancer; Health Care and Treatment; Cost vs Benefits; Innovation and Invention; Mathematical Methods; Health Industry

Article

Assent-maximizing Social Choice

By: Katherine A. Baldiga and Jerry R. Green

We take a decision theoretic approach to the classic social choice problem, using data on the frequency of choice problems to compute social choice functions. We define a family of social choice rules that depend on the population's preferences and on the probability... View Details

Keywords: Decision Choices and Conditions; Theory; Measurement and Metrics; Mathematical Methods; Society

September 1974 (Revised April 1975)
Case

Ocean Spray Cranberries, Inc. (A)

At the conclusion of a small-scale pilot survey, management must decide whether to invest in a larger survey or terminate the project. The objective of the study is to use psychographic measurement techniques to study the alternative positions of cranberry sauce.... View Details

Keywords: Surveys; Product Positioning; Mathematical Methods; Agriculture and Agribusiness Industry; Food and Beverage Industry

Educators

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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... View Details

Keywords: Machine Learning Models; Recourse; Algorithm; Mathematical Methods

November 2007
Article

Measuring Consumer and Competitive Impact with Elasticity Decompositions

Marketing investments are designed to change consumer behavior in ways that help goods compete in the marketplace. Previous research has focused on using elasticity decompositions to measure how these investments affect either consumer decision making or competing... View Details

Keywords: Decision Choices and Conditions; Investment Return; Marketing Strategy; Consumer Behavior; Measurement and Metrics; Mathematical Methods; Competitive Advantage

March 2022
Article

Sensitivity Analysis of Agent-based Models: A New Protocol

By: Emanuele Borgonovo, Marco Pangallo, Jan Rivkin, Leonardo Rizzo and Nicolaj Siggelkow

Agent-based models (ABMs) are increasingly used in the management sciences. Though useful, ABMs are often critiqued: it is hard to discern why they produce the results they do and whether other assumptions would yield similar results. To help researchers address such... View Details

Keywords: Agent-based Modeling; Sensitivity Analysis; Design Of Experiments; Total Order Sensitivity Indices; Organizations; Behavior; Decision Making; Mathematical Methods

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

2008
Working Paper

Allocating Marketing Resources

By: Sunil Gupta and Thomas J. Steenburgh

Marketing is essential for the organic growth of a company. Not surprisingly, firms spend billions of dollars on marketing. Given these large investments, marketing managers have the responsibility to optimally allocate these resources and demonstrate that these... View Details

Keywords: Investment Return; Resource Allocation; Marketing; Demand and Consumers; Mathematical Methods