arXiv subjects

Nathan Kallus

Publications and source records attributed to Nathan Kallus.

168 records · Page 10Linked to original sources

arXiv2017

The Power and Limits of Predictive Approaches to Observational-Data-Driven Optimization

While data-driven decision-making is transforming modern operations, most large-scale data is of an observational nature, such as transactional records. These data pose unique challenges in a variety of operational problems posed as stochastic optimization problems, including pricing and inventory management, where one must evaluate the effect of a decision, such as price or order quantity, on an uncertain cost/reward variable, such as demand, based on historical data where decision and outcome may be confounded. Often, the data lacks the features necessary to enable sound assessment of causal effects and/or the strong assumptions necessary may be dubious. Nonetheless, common practice is to assign a decision an objective value equal to the best prediction of cost/reward given the observation of the decision in the data. While in general settings this identification is spurious, for optimization purposes it is only the objective value of the final decision that matters, rather than the validity of any model used to arrive at it. In this paper, we formalize this statement in the case of observational-data-driven optimization and study both the power and limits of predictive approaches to observational-data-driven optimization with a particular focus on pricing. We provide rigorous bounds on optimality gaps of such approaches even when optimal decisions cannot be identified from data. To study potential limits of predictive approaches in real datasets, we develop a new hypothesis test for causal-effect objective optimality. Applying it to interest-rate-setting data, we empirically demonstrate that predictive approaches can be powerful in practice but with some critical limitations.

math.OC↗

arXiv2017

A Framework for Optimal Matching for Causal Inference

We propose a novel framework for matching estimators for causal effect from observational data that is based on minimizing the dual norm of estimation error when expressed as an operator. We show that many popular matching estimators can be expressed as optimal in this framework, including nearest-neighbor matching, coarsened exact matching, and mean-matched sampling. This reveals their motivation and aptness as structural priors formulated by embedding the effect in a particular functional space. This also gives rise to a range of new, kernel-based matching estimators that arise when one embeds the effect in a reproducing kernel Hilbert space. Depending on the case, these estimators can be found using either quadratic optimization or integer optimization. We show that estimators based on universal kernels are universally consistent without model specification. In empirical results using both synthetic and real data, the new, kernel-based estimators outperform all standard causal estimators in estimation error.

stat.ME↗

arXiv2016

Robust Sample Average Approximation

Sample average approximation (SAA) is a widely popular approach to data-driven decision-making under uncertainty. Under mild assumptions, SAA is both tractable and enjoys strong asymptotic performance guarantees. Similar guarantees, however, do not typically hold in finite samples. In this paper, we propose a modification of SAA, which we term Robust SAA, which retains SAA's tractability and asymptotic properties and, additionally, enjoys strong finite-sample performance guarantees. The key to our method is linking SAA, distributionally robust optimization, and hypothesis testing of goodness-of-fit. Beyond Robust SAA, this connection provides a unified perspective enabling us to characterize the finite sample and asymptotic guarantees of various other data-driven procedures that are based upon distributionally robust optimization. This analysis provides insight into the practical performance of these various methods in real applications. We present examples from inventory management and portfolio allocation, and demonstrate numerically that our approach outperforms other data-driven approaches in these applications.

math.OC↗

arXiv2016

Revealed Preference at Scale: Learning Personalized Preferences from Assortment Choices

We consider the problem of learning the preferences of a heterogeneous population by observing choices from an assortment of products, ads, or other offerings. Our observation model takes a form common in assortment planning applications: each arriving customer is offered an assortment consisting of a subset of all possible offerings; we observe only the assortment and the customer's single choice. In this paper we propose a mixture choice model with a natural underlying low-dimensional structure, and show how to estimate its parameters. In our model, the preferences of each customer or segment follow a separate parametric choice model, but the underlying structure of these parameters over all the models has low dimension. We show that a nuclear-norm regularized maximum likelihood estimator can learn the preferences of all customers using a number of observations much smaller than the number of item-customer combinations. This result shows the potential for structural assumptions to speed up learning and improve revenues in assortment planning and customization. We provide a specialized factored gradient descent algorithm and study the success of the approach empirically.

stat.ML↗

arXiv2014

Data-Driven Robust Optimization

The last decade witnessed an explosion in the availability of data for operations research applications. Motivated by this growing availability, we propose a novel schema for utilizing data to design uncertainty sets for robust optimization using statistical hypothesis tests. The approach is flexible and widely applicable, and robust optimization problems built from our new sets are computationally tractable, both theoretically and practically. Furthermore, optimal solutions to these problems enjoy a strong, finite-sample probabilistic guarantee. \edit{We describe concrete procedures for choosing an appropriate set for a given application and applying our approach to multiple uncertain constraints. Computational evidence in portfolio management and queuing confirm that our data-driven sets significantly outperform traditional robust optimization techniques whenever data is available.

math.OC↗

arXiv2014

Predicting Crowd Behavior with Big Public Data

With public information becoming widely accessible and shared on today's web, greater insights are possible into crowd actions by citizens and non-state actors such as large protests and cyber activism. We present efforts to predict the occurrence, specific timeframe, and location of such actions before they occur based on public data collected from over 300,000 open content web sources in 7 languages, from all over the world, ranging from mainstream news to government publications to blogs and social media. Using natural language processing, event information is extracted from content such as type of event, what entities are involved and in what role, sentiment and tone, and the occurrence time range of the event discussed. Statements made on Twitter about a future date from the time of posting prove particularly indicative. We consider in particular the case of the 2013 Egyptian coup d'etat. The study validates and quantifies the common intuition that data on social media (beyond mainstream news sources) are able to predict major events.

cs.SI↗