Nathan Kallus

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.

The Power of Optimization Over Randomization in Designing Experiments Involving Small Samples

Random assignment, typically seen as the standard in controlled trials, aims to make experimental groups statistically equivalent before treatment. However, with a small sample, which is a practical reality in many disciplines, randomized groups are often too dissimilar to be useful. We propose an approach based on discrete linear optimization to create groups whose discrepancy in their means and variances is several orders of magnitude smaller than with randomization. We provide theoretical and computational evidence that groups created by optimization have exponentially lower discrepancy than those created by randomization and that this allows for more powerful statistical inference.

Scheduling, revenue management, and fairness in an academic-hospital radiology division.

RATIONALE AND OBJECTIVES Physician staff of academic hospitals today practice in several geographic locations including their main hospital. This is referred to as the extended campus. With extended campuses expanding, the growing complexity of a single divisions schedule means that a naive approach to scheduling compromises revenue. Moreover, it may provide an unfair allocation of individual revenue, desirable or burdensome assignments, and the extent to which the preferences of each individual are met. This has adverse consequences on incentivization and employee satisfaction and is simply against business policy. MATERIALS AND METHODS We identify the daily scheduling of physicians in this context as an operational problem that incorporates scheduling, revenue management, and fairness. Noting previous success of operations research and optimization in each of these disciplines, we propose a simple unified optimization formulation of this scheduling problem using mixed-integer optimization. RESULTS Through a study of implementing the approach at the Division of Angiography and Interventional Radiology at the Brigham and Womens Hospital, which is directed by one of the authors, we exemplify the flexibility of the model to adapt to specific applications, the tractability of solving the model in practical settings, and the significant impact of the approach, most notably in increasing revenue by 8.2% over previous operating revenue while adhering strictly to a codified fairness and objectivity. CONCLUSIONS We found that the investment in implementing such a system is far outweighed by the large potential revenue increase and the other benefits outlined.

Personalized Diabetes Management Using Electronic Medical Records.

OBJECTIVE Current clinical guidelines for managing type 2 diabetes do not differentiate based on patient-specific factors. We present a data-driven algorithm for personalized diabetes management that improves health outcomes relative to the standard of care. RESEARCH DESIGN AND METHODS We modeled outcomes under 13 pharmacological therapies based on electronic medical records from 1999 to 2014 for 10,806 patients with type 2 diabetes from Boston Medical Center. For each patient visit, we analyzed the range of outcomes under alternative care using a k-nearest neighbor approach. The neighbors were chosen to maximize similarity on individual patient characteristics and medical history that were most predictive of health outcomes. The recommendation algorithm prescribes the regimen with best predicted outcome if the expected improvement from switching regimens exceeds a threshold. We evaluated the effect of recommendations on matched patient outcomes from unseen data. RESULTS Among the 48,140 patient visits in the test set, the algorithm’s recommendation mirrored the observed standard of care in 68.2% of visits. For patient visits in which the algorithmic recommendation differed from the standard of care, the mean posttreatment glycated hemoglobin A1c (HbA1c) under the algorithm was lower than standard of care by 0.44 ± 0.03% (4.8 ± 0.3 mmol/mol) (P < 0.001), from 8.37% under the standard of care to 7.93% under our algorithm (68.0 to 63.2 mmol/mol). CONCLUSIONS A personalized approach to diabetes management yielded substantial improvements in HbA1c outcomes relative to the standard of care. Our prototyped dashboard visualizing the recommendation algorithm can be used by providers to inform diabetes care and improve outcomes.

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 customers 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.

On the Predictive Power of Web Intelligence and Social Media

With more information becoming widely accessible and new content created every day on todays web, more are turning to harvesting such data and analyzing it to extract insights. But the relevance of such data to see beyond the present is not clear. We present efforts to predict future events based on web intelligence - data harvested from the web - with specific emphasis on social media data and on timed event mentions, thereby quantifying the predictive power of such data. We focus on predicting crowd actions such as large protests and coordinated acts of cyber activism - predicting their occurrence, specific timeframe, and location. Using natural language processing, statements about events are extracted from content collected from hundred of thousands of open content web sources. Attributes extracted include event type, entities involved and their role, sentiment and tone, and - most crucially - the reported timeframe for the occurrence of the event discussed - whether it be in the past, present, or future. Tweets (Twitter posts) that mention an event to occur reportedly in the future prove to be important predictors. These signals are enhanced by cross referencing with the fragility of the situation as inferred from more traditional media, allowing us to sift out the social media trends that fizzle out before materializing as crowds on the ground.

On the predictive power of web intelligence and social media the best way to predict the future is to tweet it

With more information becoming widely accessible and new content created every day on todays web, more are turning to harvesting such data and analyzing it to extract insights. But the relevance of such data to see beyond the present is not clear. We present efforts to predict future events based on web intelligence - data harvested from the web - with specific emphasis on social media data and on timed event mentions, thereby quantifying the predictive power of such data. We focus on predicting crowd actions such as large protests and coordinated acts of cyber activism - predicting their occurrence, specific timeframe, and location. Using natural language processing, statements about events are extracted from content collected from hundred of thousands of open content web sources. Attributes extracted include event type, entities involved and their role, sentiment and tone, and - most crucially - the reported timeframe for the occurrence of the event discussed - whether it be in the past, present, or future. Tweets (Twitter posts) that mention an event to occur reportedly in the future prove to be important predictors. These signals are enhanced by cross referencing with the fragility of the situation as inferred from more traditional media, allowing us to sift out the social media trends that fizzle out before materializing as crowds on the ground.