Isotonic single-index model for high-dimensional database marketing

Abstract

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 significant variables and prospective customers. In small databases, they could calibrate logistic regression models via maximum-likelihood methods to determine significant 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 flexible rather than restrict to specific distributions (e.g., logistic). To incorporate scalability and flexibility, we propose isotonic single-index models for database marketing. It furnishes the first 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 first 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 significant 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).