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      Mathematical MethodsRemove Mathematical Methods →

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      • 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... View Details
      Keywords: Machine Learning; Transfer Theorem; Mathematical Methods
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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.
      • March 2020
      • Article

      Diagnosing Missing Always at Random in Multivariate Data

      By: Iavor I. Bojinov, Natesh S. Pillai and Donald B. Rubin
      Models for analyzing multivariate data sets with missing values require strong, often assessable, assumptions. The most common of these is that the mechanism that created the missing data is ignorable—a twofold assumption dependent on the mode of inference. The first... View Details
      Keywords: Missing Data; Diagnostic Tools; Sensitivity Analysis; Hypothesis Testing; Missing At Random; Row Exchangeability; Analytics and Data Science; Mathematical Methods
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      Bojinov, Iavor I., Natesh S. Pillai, and Donald B. Rubin. "Diagnosing Missing Always at Random in Multivariate Data." Biometrika 107, no. 1 (March 2020): 246–253.
      • 2021
      • Working Paper

      Impact Investing: A Theory of Financing Social Enterprises

      By: Benjamin N. Roth
      I present a model of financing social enterprises to delineate the role of impact investors relative to “pure” philanthropists. I characterize the optimal scale and structure of a social enterprise when financed by grants, and when financed by investments. Impact... View Details
      Keywords: Impact Investing; Social Entrepreneurship; Finance; Investment; Mathematical Methods
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      Roth, Benjamin N. "Impact Investing: A Theory of Financing Social Enterprises." Harvard Business School Working Paper, No. 20-078, February 2020. (Revised June 2021.)
      • Article

      Detecting Adversarial Attacks via Subset Scanning of Autoencoder Activations and Reconstruction Error

      By: Celia Cintas, Skyler Speakman, Victor Akinwande, William Ogallo, Komminist Weldemariam, Srihari Sridharan and Edward McFowland III
      Reliably detecting attacks in a given set of inputs is of high practical relevance because of the vulnerability of neural networks to adversarial examples. These altered inputs create a security risk in applications with real-world consequences, such as self-driving... View Details
      Keywords: Autoencoder Networks; Pattern Detection; Subset Scanning; Computer Vision; Statistical Methods And Machine Learning; Machine Learning; Deep Learning; Data Mining; Big Data; Large-scale Systems; Mathematical Methods; Analytics and Data Science
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      Cintas, Celia, Skyler Speakman, Victor Akinwande, William Ogallo, Komminist Weldemariam, Srihari Sridharan, and Edward McFowland III. "Detecting Adversarial Attacks via Subset Scanning of Autoencoder Activations and Reconstruction Error." Proceedings of the International Joint Conference on Artificial Intelligence 29th (2020).
      • 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
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      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).
      • May 2020
      • Article

      Scalable Holistic Linear Regression

      By: Dimitris Bertsimas and Michael Lingzhi Li
      We propose a new scalable algorithm for holistic linear regression building on Bertsimas & King (2016). Specifically, we develop new theory to model significance and multicollinearity as lazy constraints rather than checking the conditions iteratively. The resulting... View Details
      Keywords: Mathematical Methods; Analytics and Data Science
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      Bertsimas, Dimitris, and Michael Lingzhi Li. "Scalable Holistic Linear Regression." Operations Research Letters 48, no. 3 (May 2020): 203–208.
      • December 2019
      • Technical Note

      Technical Note on Bayesian Statistics and Frequentist Power Calculations

      By: Amitabh Chandra and Ariel Dora Stern
      This Technical Note provides an introduction to Bayes’ Rule and the statistical intuition that stems from it. In this note, we review the concepts that underlie Bayesian statistics, and we offer several simple mathematical examples to illustrate applications of Bayes’... View Details
      Keywords: Bayesian Statistics; Mathematical Methods
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      Chandra, Amitabh, and Ariel Dora Stern. "Technical Note on Bayesian Statistics and Frequentist Power Calculations." Harvard Business School Technical Note 620-032, December 2019.
      • 2019
      • Article

      Configurations of Extremal Type II Codes via Harmonic Weight Enumerators

      By: Noam D. Elkies and Scott Duke Kominers
      We prove configuration results for extremal Type II codes, analogous to the configuration results of Ozeki and of the second author for extremal Type II lattices. Specifically, we show that for n ∈{8,24,32,48,56,72,96} every extremal Type II code of length n is... View Details
      Keywords: Mathematical Methods
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      Elkies, Noam D., and Scott Duke Kominers. "Configurations of Extremal Type II Codes via Harmonic Weight Enumerators." Journal de Théorie des Nombres de Bordeaux 31, no. 3 (2019): 679–688.
      • December 2019
      • Article

      Costly Concessions: An Empirical Framework for Matching with Imperfectly Transferable Utility

      By: Alfred Galichon, Scott Duke Kominers and Simon Weber
      We introduce an empirical framework for models of matching with imperfectly transferable utility and unobserved heterogeneity in tastes. Our framework allows us to characterize matching equilibrium in a flexible way that includes as special cases the classic fully- and... View Details
      Keywords: Sorting; Matching; Marriage Market; Intrahousehold Allocation; Imperfectly Transferable Utility; Marketplace Matching; Mathematical Methods
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      Galichon, Alfred, Scott Duke Kominers, and Simon Weber. "Costly Concessions: An Empirical Framework for Matching with Imperfectly Transferable Utility." Journal of Political Economy 127, no. 6 (December 2019): 2875–2925.
      • 2019
      • Article

      Time Series Experiments and Causal Estimands: Exact Randomization Tests and Trading

      By: Iavor I Bojinov and Neil Shephard
      We define causal estimands for experiments on single time series, extending the potential outcome framework to dealing with temporal data. Our approach allows the estimation of a broad class of these estimands and exact randomization based p-values for testing causal... View Details
      Keywords: Causality; Nonparametric; Potential Outcomes; Trading Costs; Mathematical Methods
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      Bojinov, Iavor I., and Neil Shephard. "Time Series Experiments and Causal Estimands: Exact Randomization Tests and Trading." Journal of the American Statistical Association 114, no. 528 (2019): 1665–1682.
      • November 2019
      • Article

      Full Substitutability

      By: John William Hatfield, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky and Alexander Westkamp
      Various forms of substitutability are essential for establishing the existence of equilibria and other useful properties in diverse settings such as matching, auctions, and exchange economies with indivisible goods. We extend earlier models’ definitions of... View Details
      Keywords: Substitutability; Mathematical Methods; Auctions; Market Design
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      Hatfield, John William, Scott Duke Kominers, Alexandru Nichifor, Michael Ostrovsky, and Alexander Westkamp. "Full Substitutability." Theoretical Economics 14, no. 4 (November 2019): 1535–1590.
      • September 2019
      • Article

      Optimizing Reserves in School Choice: A Dynamic Programming Approach

      By: Franklyn Wang, Ravi Jagadeesan and Scott Duke Kominers
      We introduce a new model of school choice with reserves in which a social planner is constrained by a limited supply of reserve seats and tries to find an optimal matching according to a social welfare function. We construct the optimal distribution of reserves via a... View Details
      Keywords: Matching; Reserves; Dynamic Programming; Marketplace Matching; Mathematical Methods
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      Wang, Franklyn, Ravi Jagadeesan, and Scott Duke Kominers. "Optimizing Reserves in School Choice: A Dynamic Programming Approach." Operations Research Letters 47, no. 5 (September 2019): 438–446.
      • August 2019
      • Article

      When and How to Diversify—A Multicategory Utility Model for Personalized Content Recommendation

      By: Yicheng Song, Nachiketa Sahoo and Elie Ofek
      Sometimes we desire change, a break from the same or an opportunity to fulfill different aspects of our needs. Noting that consumers seek variety, several approaches have been developed to diversify items recommended by personalized recommender systems. However,... View Details
      Keywords: Recommender Systems; Personalization; Recommendation Diversity; Variety Seeking; Collaborative Filtering; Consumer Utility Models; Digital Media; Clickstream Analysis; Learning-to-rank; Consumer Behavior; Media; Customization and Personalization; Strategy; Mathematical Methods
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      Song, Yicheng, Nachiketa Sahoo, and Elie Ofek. "When and How to Diversify—A Multicategory Utility Model for Personalized Content Recommendation." Management Science 65, no. 8 (August 2019): 3737–3757.
      • July 2019
      • Article

      Optimal Capital Structure and Bankruptcy Choice: Dynamic Bargaining vs Liquidation

      By: Samuel Antill and Steven R. Grenadier
      We model a firm’s optimal capital structure decision in a framework in which it may later choose to enter either Chapter 11 reorganization or Chapter 7 liquidation. Creditors anticipate equityholders’ ex-post reorganization incentives and price them into the ex-ante... View Details
      Keywords: Default; Dynamic Bargaining; Capital Structure; Insolvency and Bankruptcy; Mathematical Methods
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      Antill, Samuel, and Steven R. Grenadier. "Optimal Capital Structure and Bankruptcy Choice: Dynamic Bargaining vs Liquidation." Journal of Financial Economics 133, no. 1 (July 2019): 198–224.
      • 2019
      • Article

      Ridesharing with Driver Location Preferences

      By: Duncan Rheingans-Yoo, Scott Duke Kominers, Hongyao Ma and David C. Parkes
      We study revenue-optimal pricing and driver compensation in ridesharing platforms when drivers have heterogeneous preferences over locations. If a platform ignores drivers' location preferences, it may make inefficient trip dispatches; moreover, drivers may strategize... View Details
      Keywords: Ridesharing; Pricing; Compensation and Benefits; Geographic Location; Market Design; Mathematical Methods
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      Rheingans-Yoo, Duncan, Scott Duke Kominers, Hongyao Ma, and David C. Parkes. "Ridesharing with Driver Location Preferences." Proceedings of the International Joint Conference on Artificial Intelligence (2019): 557–564.
      • March 2019 (Revised May 2019)
      • Case

      Fetchr: A New Way of Last Mile Delivery

      By: V.G. Narayanan and Eren Kuzucu
      By mid-2016, five years of aggressive growth had transformed Fetchr from a small logistics startup to a 1,000-employee, full-fledged last-mile delivery company operating across four countries in the Middle East and North Africa (MENA). Already beneficiaries of the... View Details
      Keywords: Startup; Decision; Financial Strategy; UAE; KSA; MENA; Cost Accounting; Business Model; Business Startups; Transformation; Cost Management; Strategy; Disruptive Innovation; Technological Innovation; Growth and Development Strategy; Growth Management; Logistics; Service Delivery; Supply Chain Management; Performance Evaluation; Mathematical Methods; Mobile and Wireless Technology; Transportation Networks; Middle East; United Arab Emirates; Dubai; Bahrain; Egypt; Saudi Arabia; North Africa
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      Narayanan, V.G., and Eren Kuzucu. "Fetchr: A New Way of Last Mile Delivery." Harvard Business School Case 119-018, March 2019. (Revised May 2019.)
      • 2020
      • Working Paper

      Overcoming the Cold Start Problem of CRM Using a Probabilistic Machine Learning Approach

      By: Eva Ascarza
      The success of Customer Relationship Management (CRM) programs ultimately depends on the firm's ability to understand consumers' preferences and precisely capture how these preferences may differ across customers. Only by understanding customer heterogeneity, firms can... View Details
      Keywords: Customer Management; Targeting; Deep Exponential Families; Probabilistic Machine Learning; Cold Start Problem; Customer Relationship Management; Customer Value and Value Chain; Consumer Behavior; Analytics and Data Science; Mathematical Methods; Retail Industry
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      Padilla, Nicolas, and Eva Ascarza. "Overcoming the Cold Start Problem of CRM Using a Probabilistic Machine Learning Approach." Harvard Business School Working Paper, No. 19-091, February 2019. (Revised May 2020. Accepted at the Journal of Marketing Research.)
      • 2018
      • Working Paper

      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: Bubbles; Price Bubble; Mathematical Methods
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      Bordalo, Pedro, Nicola Gennaioli, Spencer Yongwook Kwon, and Andrei Shleifer. "Diagnostic Bubbles." NBER Working Paper Series, No. 25399, December 2018.
      • November–December 2018
      • Article

      Online Network Revenue Management Using Thompson Sampling

      By: Kris J. Ferreira, David Simchi-Levi and He Wang
      We consider a network revenue management problem where an online retailer aims to maximize revenue from multiple products with limited inventory constraints. As common in practice, the retailer does not know the consumer's purchase probability at each price and must... View Details
      Keywords: Online Marketing; Revenue Management; Revenue; Management; Marketing; Internet and the Web; Price; Mathematical Methods
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      Ferreira, Kris J., David Simchi-Levi, and He Wang. "Online Network Revenue Management Using Thompson Sampling." Operations Research 66, no. 6 (November–December 2018): 1586–1602.
      • November 2018
      • Case

      Sportradar (A): From Data to Storytelling

      By: Ramon Casadesus-Masanell, Karen Elterman and Oliver Gassmann
      In 2013, the Swiss sports data company Sportradar debated whether to expand from its core business of data provision to bookmakers into sports media products. Sports data was becoming a commodity, and in the future, sports leagues might reduce their dependence on... View Details
      Keywords: Sports Data; Data; Sport; Sportradar; Football; Soccer; Gambling; Betting; Betting Markets; Statistics; Odds; Live Data; Bookmakers; Betradar; Visualization; Integrity; Monitoring; Gaming; Streaming; 2013; St.Gallen; Algorithm; Mathematical Modeling; Carsten Koerl; Betandwin; Bwin; Wagering; Probability; Sports; Analytics and Data Science; Mathematical Methods; Games, Gaming, and Gambling; Transition; Strategy; Media; Sports Industry; Technology Industry; Information Technology Industry; Media and Broadcasting Industry; Europe; Switzerland; Asia; Austria; Germany; England
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      Casadesus-Masanell, Ramon, Karen Elterman, and Oliver Gassmann. "Sportradar (A): From Data to Storytelling." Harvard Business School Case 719-429, November 2018.
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