Semiparametric Statistical (Machine) Learning

背景

Background Statistical learning algorithms (SLAs) are processes that are used worldwide as modern methods for predicting results from complex relationships. SLAs learn from a set of data consisting of a response (the target for prediction) and one or more explanatory variables (the inputs). The learning consists of minimizing the lossa distance between the predictions and the observed responses across the entire data set. SLAs have features called tuning parameters that users can vary to get a better-fitting result. However, the process of finding the best values for tuning parameters is cumbersome, relying on a computationally intensive process called cross-validation where the entire learning process is repeated numerous times. Furthermore, different SLAs can provide somewhat different results on a given data set, and it is unclear in advance which one should be used. Work to be done The proposed research will generate ways to simplify the process of tuning SLAs. We will also provide new ways to combine SLAs into one ensemble predictor that makes use of the different strengths of each individual SLA. To do this, we will develop a new method for mathematically deriving an information criterion (IC) on each SLA. ICs measure the fit of a statistical model to a data set, balancing between making the loss smaller and making a model too complex. Because SLAs are not based on statistical models, we will mathematically approximate the SLA (or features of the SLA) with a statistical model, from which the IC will be developed. The model complexity component is difficult to estimate exactly, but our group has had success doing this on related problems, resulting in new statistical analysis methods with better properties than existing ones. There are hundreds of different SLAs that could be targets for this work. We will perform preliminary tests of many of these candidates to select the ones that have the best combinations of prediction quality and structurally amenable features upon which ICs can be created. These ICs can then be computed on different versions of a single SLA or on multiple SLAs to help select the best-fitting ones. The ICs can also be for model averaging, where different SLA predictions are averaged into a single prediction using weighting determined by their ICs. Outcomes and Benefits The results of this research will be new statistical methods that lead to faster and better prediction algorithms. These algorithms will be developed into software that is freely accessible to millions of users nationwide and worldwide. Users who need fast, accurate answers to important questionsfor example, forecasting consumer trends, comparing potential patient responses to different therapies, and anticipating impacts of public policieswill have better tools for performing these tasks.