Trevor Hastie - US grants

Proposal: DMS 9504495 PI: Trevor Hastie Institution: Stanford University Title: Flexible Regression and Classification Abstract: The research concerns several research directions with a common theme: to push widely accepted but limited statistical tools in more adventurous directions, while retaining some of their attractive features, such as model interpretability. Specifically, the research involves the development of: a) nonparametric extensions of logistic regression for multiclass responses, including additive, projection pursuit and basis expansion techniques, as well as rank reduced models similar to Fisher's LDA; b) a new adaptive algorithm for basis selection, similar to Friedman's MARS model, which uses a natural penalized criterion to simultaneously select variables and shrinks their coefficients; c) a technique for locally adapting the nearest neighbor distance metric to combat the curse of dimensionality. Many important problems in data analysis and modeling focus on prediction. Some important examples include computer assisted diagnosis of disease (e.g. reading digital mammograms), heart disease risk assessment, automatic reading of handwritten digits (e.g. zip-codes on envelopes), speech recognition, to name a few. This research is about enriching the current toolbox of well established statistical models in a natural way to address some of these more complex scenarios. Often new exotic techniques, such as neural networks, are ``black boxes'' that appear to produce good results, but do not provide the analyst with an interpretable model, diagnostics or similar feedback to give them confidence that the box has produced sensible results. Statistics can play an active role in these important prediction and data analysis problems through the development competitive and defensible models. This research does just that by creating a blend between the well understood classical techniques and the new techniques that allow for model exploration.

Proposal ID: DMS-0204612
PI: Trevor Hastie
Title: Flexible statistical modeling

Abstract

The investigator and his students will study the popular support vector machines from the viewpoint of the traditional logistic regression model (with regularization). While the latter exhibits very similar generalization performance to the SVM, it has several advantages: it estimates class probabilities, and generalizes to multiclass problems seamlessly. This and several other even simpler approaches will be developed for the classification of gene expression arrays.

This proposal will thus develop useful models for making class predictions in a variety of high-dimensional situations, in particular for gene expression arrays. While the science journals abound with exotic statistical and computational algorithms for use in this fashionable domain, this investigator and his colleagues firmly believe that some very simple modifications of classical approaches perform as well or better, and are easier to understand.

ABSTRACT Over 500,000 Americans suffer from peripheral nerve injury (PNI), and despite surgical interventions, most suffer permanent loss of motor function and sensation. Current clinical options for long nerve gap PNI include naturally- derived grafts, which provide native matrix cues to regenerate neurons but suffer from very limited supply and batch-to-batch variability, or synthetic nerve guidance conduits (NGCs), which are easy to manufacture but often fail due to lack of regenerative cues. The main challenge with using any NGC for treatment of PNI is the immense trade-off between providing the complex matrix cues necessary for optimal nerve regeneration while providing a conduit that is readily available, reproducible, and easily fabricated. To overcome this challenge, we propose an entirely new type of biomaterial: a computationally optimized, protein-engineered recombinant NGC (rNGC). This rNGC combines the reliability of synthetic NGCs with the presentation of multiple regenerative matrix cues of natural NGCs. Because current understanding of cell-matrix interactions is insufficient to enable to direct design of a fully functional rNGC, we hypothesize that the use of machine learning, computational optimization methods will allow identification of an rNGC that promotes nerve regeneration similar to the current gold standard autograft. We utilize a family of protein-engineered, elastin-like proteins (ELPs) that are reproducible, with predictable, consistent material properties, and fully chemically defined for streamlined FDA approval. Due to ELPs? modular design, they have biomechanical (i.e. matrix stiffness) and biochemical (i.e. cell-adhesive ligand) properties that are independently tunable over a broad range. While numerous studies detail the effects of individual biomechanical or biochemical matrix cues on neurite outgrowth using single-variable approaches, their combinatorial effects have been largely unexplored as insufficient knowledge exists to make accurate predictions of their interactions a priori. This fundamentally prohibits the direct design of combinatorial matrix cues. We hypothesize that optimized presentation of biomechanical and biochemical cues will create a microenvironment that better mimics the native ECM milieu, resulting in synergistic ligand cross-talk to improve nerve regeneration. In Aim 1, we use computational optimization methods to identify the combination of ligand identities, ligand concentrations, and matrix stiffness that best enhances neurite outgrowth. We will develop and characterize a library of ELP variants with distinct cell-adhesive ligands derived from native ECM, and assess their ability to support neurite outgrowth from rat dorsal root ganglia (DRG). In Aim 2, we will validate our in vitro optimization results in a preclinical, rat sciatic nerve injury model. A core-shell, ELP-based rNGC with an inner core matrix of the optimized ELP formulation from Aim 1 will be fabricated and evaluated for its ability to enhance therapeutic outcome. Controls include reversed nerve autograft, hollow silicone conduit, and non-optimized ELP- based rNGC. This study would represent the first use of computational optimization methods to design a reproducible, reliable, recombinant biomaterial with multiple regenerative matrix cues.