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  • 2022
  • Article

Which Explanation Should I Choose? A Function Approximation Perspective to Characterizing Post hoc Explanations
By: Tessa Han, Suraj Srinivas and Himabindu Lakkaraju
A critical problem in the field of post hoc explainability is the lack of a common foundational goal among methods. For example, some methods are motivated by function approximation, some by game theoretic notions, and some by obtaining clean visualizations. This...  View Details
Keywords: Mathematical Methods; Decision Choices and Conditions; Analytics and Data Science
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  • August 2022
  • Article

Contract Duration and the Costs of Market Transactions
By: Alexander MacKay
The optimal duration of a supply contract balances the costs of reselecting a supplier against the costs of being matched to an inefficient supplier when the contract lasts too long. I develop a structural model of contract duration that captures this tradeoff and...  View Details
Keywords: Supply Contracts; Intermediate Goods; Switching Costs; Vertical Relationships; Transaction Costs; Contract Duration; Identification; Supply Chain; Cost; Contracts; Auctions; Mathematical Methods
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  • 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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  • 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
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  • 2022
  • Working Paper

A Linear Panel Model with Heterogeneous Coefficients and Variation in Exposure
By: Jesse M. Shapiro and Liyang Sun
Linear panel models featuring unit and time fixed effects appear in many areas of empirical economics. An active literature studies the interpretation of the ordinary least squares estimator of the model, commonly called the two-way fixed effects (TWFE) estimator, in...  View Details
Keywords: Econometric Models; Mathematical Methods
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  • March 2022 (Revised July 2022)
  • Module Note

Linear Regression
By: Iavor I. Bojinov, Michael Parzen and Paul Hamilton
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
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  • March 2022 (Revised July 2022)
  • Module Note

Statistical Inference
By: Iavor I. Bojinov, Michael Parzen and Paul Hamilton
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
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  • 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
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  • 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
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  • 2022
  • Working Paper

The Disagreement Problem in Explainable Machine Learning: A Practitioner's Perspective
By: Satyapriya Krishna, Tessa Han, Alex Gu, Javin Pombra, Shahin Jabbari, Steven Wu and Himabindu Lakkaraju
As various post hoc explanation methods are increasingly being leveraged to explain complex models in high-stakes settings, it becomes critical to develop a deeper understanding of if and when the explanations output by these methods disagree with each other, and how...  View Details
Keywords: AI and Machine Learning; Analytics and Data Science; Mathematical Methods
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  • September 2021
  • Article

Diagnostic Bubbles
By: Pedro Bordalo, Nicola Gennaioli, Spencer Yongwook Kwon and Andrei Shleifer
We introduce diagnostic expectations into a standard setting of price formation in which investors learn about the fundamental value of an asset and trade it. We study the interaction of diagnostic expectations with two well-known mechanisms: learning from prices and...  View Details
Keywords: Bubble; Speculation; Diagnostic Expectations; Price Bubble; Mathematical Methods
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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
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  • June 2021
  • Technical Note

Introduction to Linear Regression
By: Michael Parzen and Paul Hamilton
This technical note introduces (from an applied point of view) the theory and application of simple and multiple linear regression. The motivation for the model is introduced, as well as how to interpret the summary output with regard to prediction and statistical...  View Details
Keywords: Linear Regression; Regression; Analysis; Forecasting and Prediction; Risk and Uncertainty; Theory; Compensation and Benefits; Mathematical Methods; Analytics and Data Science
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  • April 2021
  • Article

A Model of Multi-Pass Search: Price Search Across Stores and Time
By: Navid Mojir and K. Sudhir
In retail settings with price promotions, consumers often search across stores and time. However, the search literature typically only models one pass search across stores, ignoring revisits to stores; the choice literature using scanner data has modeled search across...  View Details
Keywords: Consumer Search; Multi-pass Search; Price Search; Store Search; Spatial Search; Temporal Search; Spatiotemporal Search; Dynamic Structural Models; MPEC; Price Promotions; Store Loyalty; Consumer Behavior; Price; Spending; Marketing; Mathematical Methods
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  • February 2021
  • Tutorial

What is AI?
By: Tsedal Neeley
This video explores the elements that constitute artificial intelligence (AI). From its mathematical basis to current advances in AI, this video introduces students to data, tools, and statistical models that make a computer 'intelligent.' Through an explanation of...  View Details
Keywords: Artificial Intelligence; Digital; Technological Innovation; Leadership; AI and Machine Learning; Mathematical Methods
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  • February 2021
  • Article

A Dynamic Theory of Multiple Borrowing
By: Daniel Green and Ernest Liu
Multiple borrowing—a borrower obtains overlapping loans from multiple lenders—is a common phenomenon in many credit markets. We build a highly tractable, dynamic model of multiple borrowing and show that, because overlapping creditors may impose default externalities...  View Details
Keywords: Commitment; Multiple Borrowing; Common Agency; Misallocation; Microfinance; Investment; Mathematical Methods
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  • 2021
  • Article

Fair Algorithms for Infinite and Contextual Bandits
By: Matthew Joseph, Michael J Kearns, Jamie Morgenstern, Seth Neel and Aaron Leon Roth
We study fairness in linear bandit problems. Starting from the notion of meritocratic fairness introduced in Joseph et al. [2016], we carry out a more refined analysis of a more general problem, achieving better performance guarantees with fewer modelling assumptions...  View Details
Keywords: Algorithms; Bandit Problems; Fairness; Mathematical Methods
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  • January 2021
  • Article

Using Models to Persuade
By: Joshua Schwartzstein and Adi Sunderam
We present a framework where "model persuaders" influence receivers’ beliefs by proposing models that organize past data to make predictions. Receivers are assumed to find models more compelling when they better explain the data, fixing receivers’ prior beliefs. Model...  View Details
Keywords: Model Persuasion; Analytics and Data Science; Forecasting and Prediction; Mathematical Methods; Framework
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  • Article

Beyond Individualized Recourse: Interpretable and Interactive Summaries of Actionable Recourses
By: Kaivalya Rawal and Himabindu Lakkaraju
As predictive models are increasingly being deployed in high-stakes decision-making, there has been a lot of interest in developing algorithms which can provide recourses to affected individuals. While developing such tools is important, it is even more critical to...  View Details
Keywords: Predictive Models; Decision Making; Framework; Mathematical Methods
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  • August 2020 (Revised September 2020)
  • Technical Note

Assessing Prediction Accuracy of Machine Learning Models
By: Michael W. Toffel, Natalie Epstein, Kris Ferreira and Yael Grushka-Cockayne
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
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