Cost-sensitive Selection of Variables by Ensemble of Model Sequences

Many applications require the collection of data on different variables or measurements overa number of system performance metrics. For example, some cyber systems rely on scanning various system metrics to detect or to predict potential cyber intrusions or threats. In the maintenance of airplanes or major factorymachinery, measurements of different system components and their usage statistics are collected to determine when a maintenance is required. In medical diagnosis, a patient may be asked to take various medical tests, such 1 as on blood pressure, cholesterol level, heart rates and so on, so that the doctor coulddetermine if the patient has a certain disease. In the development of an e-commerce product that predicts the click or purchase of a product at an e-commerce website, many data related to a user's shopping behavior will be collected, and often extra data relevant to the product or the user's shopping behavior are purchased from a third-party vendor etc. The data collected on various measures need to be combined, and if cost is a concern, a subset of measures need to be selected to satisfy the budget constraint. The problem of combining measures for a target application can be formulated as follows.