In BenBarnard/slidR: Heteroscedastic Linear Dimension Reduction

This document will serve as a "flow of thought" for how Ben and I decided to restructure the slidR package. This work is from a brainstorming session on 8 September, 2017, due to the fact that I had a few days off from work at UM because of Irma.

Purpose of the slidR Package

Subject matter experts in machine learning often look to reduce the complexity of their classification or attribution problems through linear dimension reduction (LDR). This package seeks to wrap up a few different LDR methods for classification, regression, and survival analysis. Currently, the lion's share of functional support is for classification, but we are adding other analysis patterns as time progresses.

Data Analysis Workflow with slidR

We would like to establish a data analysis workflow for this package:

1. Center and scale the data.
   • The predictors should be both centered and scaled, while the response vector need only be centered.
   • For classification and other methods which require completely partitioned testing and training data sets, save the centering vector and scaling matrix from the training data externally.
   • We assume that the data passed to this workflow is appropriately centered and scaled by an external process.
2. Reduce the dimension of the predictor matrix. Arguments are data, reductMethod, and projectionRoutine.
   • The data argument can take in the following:
     • response and predictor (both as data frames or matrices).
     • list of data frames or matrices
     • formula and data (data as a data frame or matrix)
     • resample or permute objects (from the modelR package)
     • grouped_df
     • tibble
   • This function will employ UseMethod functionality to account for the data being in different classes. Classes we support are:
     • data.frame
     • resample
     • matrix
     • tibble (in progress)
     • grouped_df
   • This function will wrangle the data from its current class into a list of matrices.
     • The chosen reductMethod will govern how the function assumes the inputs should be discussed.
     • For example, if reductMethod = LD, then we assume the user is trying to classify observations and that the response is a grouping variable.
     • If response is an $n \times 2$ matrix, then survival analysis is the assumed technique and the response is assumed to be a survival pair of event times and censoring indicator (in that order).
     • If response is a factor, then classification is the assumed technique.
     • Otherwise, regression is assumed. The list will have only one matrix.
   • Given an appropriate list of matrices, call the chosen reductionMethod. These are different estimators of the data sufficiency (or M) matrix. These methods all return a projection matrix.
     • Loog and Duin (2004), called LD
     • Ounpreseuth et al (2015), called SY
     • Odom et al (in prep), called SYS
     • SIR from Li (1992)
     • SAVE from Cook and Weisberg (1992)
     • PCA (our version of the eigen function from base R); use the sample covariance matrix as the M matrix estimate
     • identity (use the data itself as its M matrix)
   • Given the SVD of our estimate of M, M_hat choose the appropriate columns of M_hat according to the function specified as the argument of projectRoutine. These can be functions like
     • Choose the first $k$ columns of the projection matrix
     • Choose the $q$ columns which preserve a specified proportion of the variance (relative sums of egienvalues)
     • Some Principal Component ordering scheme (like Canonical Variates Analysis)
   • Multiply the list of matrices by the projection matrix to create a list of reduced data matrices
   • Return a list of:
     • The list reduced matrices
     • The list of unreduced matrices
     • The complete projection matrix U
     • Additional (optional) information from the projection routine
3. Perform analysis. These options must match the type of response variable.
   • Classification and Prediction
   • Logistic Regression and Attribution
   • Regression (Least Squares) and Prediction
   • Regression (Least Squares) and Attribution
   • Survival (Cox PH) and Attribution

BenBarnard/slidR documentation built on May 5, 2019, 2:40 p.m.