Isotonic single-index model for high-dimensional database marketing

While database marketers collect vast amounts of customer transaction data, its utilization to improve marketing decisions presents problems. Marketers seek to extract relevant information from large databases by identifying signi6cant variables and prospective customers. In small databases, they could calibrate logistic regression models via maximum-likelihood methods to determine signi6cant variables and assess customer’s response probability. For large databases, however, this approach becomes computationally too intensive to implement in real-time, and so marketers prefer estimation methods that are scalable to high-dimensional databases. In addition, database marketing is practiced in diverse product-markets, and so marketers prefer probability models that are #exible rather than restrict to speci6c distributions (e.g., logistic). To incorporate scalability and 9exibility, we propose isotonic single-index models for database marketing. It furnishes the 6rst projective approximation to a general p-variate function. Its link function is order-preserving (i.e., isotonic), thus encompassing all proper distribution functions. We develop a direct approach for its estimation: we 6rst estimate the orientation of high-dimensional parameter vector without specifying the link function (via sliced inverse regression), and then estimate the non-decreasing link function (via isotonic regression). We illustrate its practical use by analyzing a high-dimensional customer transaction database. This approach yields dimension reduction both column- and row-wise; that is, we not only discover signi6cant variables in a large transaction database, but also prioritize customers into a few distinct groups based on estimated response probability (to enable direct mailing of catalogs). c 2003 Elsevier B.V. All rights reserved.