Srikanth Jagabathula

A Nonparametric Approach to Modeling Choice with Limited Data

Choice models today are ubiquitous across a range of applications in operations and marketing. Real-world implementations of many of these models face the formidable stumbling block of simply identifying the “right” model of choice to use. Because models of choice are inherently high-dimensional objects, the typical approach to dealing with this problem is positing, a priori, a parametric model that one believes adequately captures choice behavior. This approach can be substantially suboptimal in scenarios where one cares about using the choice model learned to make fine-grained predictions; one must contend with the risks of mis-specification and overfitting/underfitting. Thus motivated, we visit the following problem: For a “generic” model of consumer choice namely, distributions over preference lists and a limited amount of data on how consumers actually make decisions such as marginal information about these distributions, how may one predict revenues from offering a particular assortment of choices? An outcome of our investigation is a nonparametric approach in which the data automatically select the right choice model for revenue predictions. The approach is practical. Using a data set consisting of automobile sales transaction data from a major U.S. automaker, our method demonstrates a 20% improvement in prediction accuracy over state-of-the-art benchmark models; this improvement can translate into a 10% increase in revenues from optimizing the offer set. We also address a number of theoretical issues, among them a qualitative examination of the choice models implicitly learned by the approach. We believe that this paper takes a step toward “automating” the crucial task of choice model selection. This paper was accepted by Yossi Aviv, operations management.

Inferring Rankings Using Constrained Sensing

We consider the problem of recovering a function over the space of permutations (or, the symmetric group) over n elements from given partial information; the partial information we consider is related to the group theoretic Fourier Transform of the function. This problem naturally arises in several settings such as ranked elections, multi-object tracking, ranking systems, and recommendation systems. Inspired by the work of Donoho and Stark in the context of discrete-time functions, we focus on non-negative functions with a sparse support (support size <;<; domain size). Our recovery method is based on finding the sparsest solution (through l0 optimization) that is consistent with the available information. As the main result, we derive sufficient conditions for functions that can be recovered exactly from partial information through l0 optimization. Under a natural random model for the generation of functions, we quantify the recoverability conditions by deriving bounds on the sparsity (support size) for which the function satisfies the sufficient conditions with a high probability as n → ∞. ℓ0 optimization is computationally hard. Therefore, the popular compressive sensing literature considers solving the convex relaxation, ℓ1 optimization, to find the sparsest solution. However, we show that ℓ1 optimization fails to recover a function (even with constant sparsity) generated using the random model with a high probability as n → ∞. In order to overcome this problem, we propose a novel iterative algorithm for the recovery of functions that satisfy the sufficient conditions. Finally, using an Information Theoretic framework, we study necessary conditions for exact recovery to be possible.

On High Spatial Reuse Link Scheduling in STDMA Wireless Ad Hoc Networks

We consider the point-to-point link scheduling problem in Spatial Time Division Multiple Access (STDMA) wireless ad hoc networks, motivate the use of spatial reuse as performance metric and provide an explicit characterization of spatial reuse. We assume uniform transmission power at all nodes and propose an algorithm based on a graph model of the network as well as Signal to Interference and Noise Ratio (SINR) computations. Our algorithm achieves higher spatial reuse than existing algorithms, without compromising on computational complexity.

Assortment Optimization Under General Choice

We consider the key operational problem of optimizing the mix of offered products to maximize revenues when product prices are exogenously set and product demand follows a general discrete choice model. The key challenge in making this decision is the computational difficulty of finding the best subset, which often requires exhaustive search. Existing approaches address the challenge by either deriving efficient algorithms for specific parametric structures or studying the performance of general-purpose heuristics. The former approach results in algorithms that lack portability to other structures; whereas the latter approach has resulted in algorithms with poor performance. We study a portable and easy-to-implement local search heuristic. We show that it efficiently finds the global optimum for the multinomial logit (MNL) model and derive performance guarantees for general choice structures. Empirically, it is better than prevailing heuristics when no efficient algorithms exist, and it is within 0.02% of optimality otherwise.

A Nonparametric Joint Assortment and Price Choice Model

The selection of products and prices offered by a firm significantly impacts its profits. Existing approaches do not provide flexible models that capture the joint effect of assortment and price. We propose a nonparametric framework in which each customer is represented by a particular price threshold and a particular preference list over the alternatives. The customers follow a two-stage choice process; they consider the set of products with prices less than the threshold and choose the most preferred product from the set considered. We develop a tractable nonparametric expectation maximization (EM) algorithm to fit the model to the aggregate transaction data and design an efficient algorithm to determine the profit-maximizing combination of offer set and price. We also identify classes of pricing structures of increasing complexity, which determine the computational complexity of the estimation and decision problems. Our pricing structures are naturally expressed as business constraints, allowing a mana...

Fair Scheduling in Networks Through Packet Election

We consider the problem of designing a fair scheduling algorithm for discrete-time constrained queuing networks. Each queue has dedicated exogenous packet arrivals. There are constraints on which queues can be served simultaneously. This model effectively describes important special instances like network switches, interference in wireless networks, bandwidth sharing for congestion control and traffic scheduling in road roundabouts. Fair scheduling is required because it provides isolation to different traffic flows; isolation makes the system more robust and enables providing quality of service. Existing work on fairness for constrained networks concentrates on flow based fairness. As a main result, we describe a notion of packet based fairness by establishing an analogy with the ranked election problem: packets are voters, schedules are candidates, and each packet ranks the schedules based on its priorities. We then obtain a scheduling algorithm that achieves the described notion of fairness by drawing upon the seminal work of Goodman and Markowitz (1952). This yields the familiar Maximum Weight (MW) style algorithm. As another important result, we prove that the algorithm obtained is throughput optimal. There is no reason a priori why this should be true, and the proof requires nontraditional methods.

Shopping for products you don't know you need

Recommendation engines today suggest one product to another, e.g., an accessory to a product. However, intent to buy often precedes a users appearance in a commerce vertical: someone interested in buying a skateboard may have earlier searched for {varial heelflip}, a trick performed on a skateboard. This paper considers how a search engine can provide early warning of commercial intent. The naive algorithm of counting how often an interest precedes a commercial query is not sufficient due to the number of related ways of expressing an interest. Thus, methods are needed for finding sets of queries where all pairs are related, what we call a query community, and this is the technical contribution of the paper. We describe a random model by which we obtain relationships between search queries and then prove general conditions under which we can reconstruct query communities. We propose two complementary approaches for inferring recommendations that utilize query communities in order to magnify the recommendation signal beyond what an individual query can provide. An extensive series of experiments on real search logs shows that the query communities found by our algorithm are more interesting and unexpected than a baseline of clustering the query-click graph. Also, whereas existing query suggestion algorithms are not designed for making commercial recommendations, we show that our algorithms do succeed in forecasting commercial intent. Query communities increase both the quantity and quality of recommendations.

A Partial-Order-Based Model to Estimate Individual Preferences using Panel Data

In retail operations, customer choices may be affected by stockout and promotion events. Given panel data with the transaction history of customers, and product availability and promotion data, our goal is to predict future individual purchases. We use a general nonparametric framework in which we represent customers by partial orders of preferences. In each store visit, each customer samples a full preference list of the products consistent with her partial order, forms a consideration set, and then chooses to purchase the most preferred product among the considered ones. Our approach involves: (a)~defining behavioral models to build consideration sets as subsets of the products on offer, (b)~proposing a clustering algorithm for determining customer segments, and (c)~deriving marginal distributions for partial preferences under the multinomial logit (MNL) model. Numerical experiments on real-world panel data show that our approach allows more accurate, fine-grained predictions for individual purchase behavior compared to state-of-the-art alternative methods.

Offline Assortment Optimization in the Presence of an Online Channel

Firms are increasingly selling through both offline and online channels, allowing customers to experience the touch and feel of product attributes before purchasing those products. Consequently, the selection of products offered offline affects the demand in both channels. We address how firms should select an optimal offline assortment to maximize profits across both channels; we call this the showcase decision problem. We incorporate the impact of physical evaluation on preferences into the consumer demand model. Under this model, we show that the decision problem is NP-hard. Analytically, we derive optimal results for special cases and near-optimal approximations for general cases. Empirically, we use conjoint analysis to identify changes in consumer preferences resulting from physically evaluating products. For this application, we demonstrate gains in expected revenue of up to 40% due to accounting for the impact of offline assortment on the online sales. The online appendix is available at https://d...

Accounting for Discrepancies between Online and Offline Product Evaluations

Most preference-elicitation methods that are used to design products and predict market shares (such as conjoint analysis) ask respondents to evaluate product descriptions, mostly online. However, many of these products are then sold offline. In this paper we ask how well preference-elicitation studies conducted online perform when predicting offline consumer evaluation. To that end, we conduct two within-subject conjoint studies, one online and one with physical products offline. We find that the weights of the product attributes (partworths) are different in the online and offline studies, and that these differences might be considerable.We propose a model that captures this change in weights and derive an estimator for offline parameters based on the individual respondent’s online parameter, and for population-level parameters. We demonstrate that such augmentation of online conjoint data with offline data leads to significant improvement in both individual prediction and estimation of population-level parameters. We also ask respondents to state their uncertainty about product attributes, and we find that while respondents anticipate some of the attributes whose weights change, they completely miss others. Thus this bias might not be accurately detected through an online study.Most preference-elicitation methods that are used to design products and predict market shares (such as conjoint analysis) ask respondents to evaluate product descriptions, mostly online. However, many of these products are then sold offline. In this paper we ask how well preference-elicitation studies conducted online perform when predicting offline consumer evaluation. To that end, we conduct two within-subject conjoint studies, one online and one with physical products offline. We find that the weights of the product attributes (partworths) are different in the online and offline studies, and that these differences might be considerable.We propose a model that captures this change in weights and derive an estimator for offline parameters based on the individual respondent’s online parameter, and for population-level parameters. We demonstrate that such augmentation of online conjoint data with offline data leads to significant improvement in both individual prediction and estimation of population-level parameters. We also ask respondents to state their uncertainty about product attributes, and we find that while respondents anticipate some of the attributes whose weights change, they completely miss others. Thus this bias might not be accurately detected through an online study.