Streaming predictions need not reread history: ReMAQ turns model-averaging updates into one quadratic program per batch
Synopsis
In real-time prediction over streaming data, an investigator often holds several generalized linear models at once, while model averaging is typically a convex optimization over all historical data. ReMAQ replaces that procedure with a quadratic approximation, so when a new batch arrives the averaged prediction is updated sequentially by solving one quadratic program, without accessing the entire history. Under regularity conditions its weights are asymptotically equivalent to oracle model averaging built on the inaccessible full data, which establishes asymptotic optimality; simulation studies and an application to the Airline On-Time Performance Dataset assess the method.
Interpretation
With data arriving continuously, a model-averaged prediction can be updated batch by batch instead of being recomputed over the whole history each time. Model averaging for generalized linear models is typically a convex optimization problem whose solution previously took all historical data as input. Under regularity conditions the updated weights are asymptotically equivalent to those of oracle model averaging based on the inaccessible full data, and asymptotic optimality follows.
The procedure replaces the model-averaging step for generalized linear models with a quadratic optimization form, so each update involves only a quadratic programming problem. The method is named ReMAQ, renewable model averaging through quadratic approximation, and targets generalized linear models for streaming data. It is assessed through simulation studies and applied to the Airline On-Time Performance Dataset, where the results demonstrate its superiority in practical situations.
Perspective
The demonstrated scope is model averaging for generalized linear models on streaming data: asymptotic equivalence to oracle model averaging under regularity conditions, assessed through simulation studies and an application to the Airline On-Time Performance Dataset.
Asymptotic equivalence and asymptotic optimality hold under certain regularity conditions rather than unconditionally; practical performance is reported from simulation studies and the application to the Airline On-Time Performance Dataset.