Optimal Subsampling Methods for Statistical Models

Balancing computational and statistical efficiency, subsampling techniques offer a practical solution for handling large-scale data analysis. Subsampling methods enhance statistical modeling for massive datasets by efficiently drawing representative subsamples from full dataset based on tailored sampling probabilities. These probabilities are optimized for specific goals, such as minimizing the variance of coefficient estimates or reducing prediction error. Based on specified modeling assumptions and subsampling techniques, the package provides functions to draw subsamples from the full data, fit the model on the subsamples, and perform statistical inference.

subsampling

A major challenge in big data statistical analysis is the demand for computing resources. For example, when fitting a logistic regression model to binary response variable with $N \times d$ dimensional covariates, the computational complexity of estimating the coefficients using the IRLS algorithm is $O(\zeta N d^2)$, where $\zeta$ is the number of iteration. When $N$ is large, the cost can be prohibitive, especially if high performance computing resources are unavailable. Subsampling has become a widely used technique to balance the trade-off between computational efficiency and statistical efficiency.

The R package subsampling provides optimal subsampling methods for various statistical models such as generalized linear models (GLMs), softmax (multinomial) regression, rare event logistic regression, quantile regression model and GLMs with rare features. Specialized subsampling techniques are provided to address specific challenges across different models and datasets. With specified model assumptions and subsampling techniques, it draws subsample from the full data, fits model on the subsample and perform statistical inferences.

Installation

You can install the package by

# Install from CRAN
install.packages("subsampling")

# Or install the development version from GitHub
# install.packages("devtools")
devtools::install_github("dqksnow/subsampling")

Getting Started

The Online document provides a guidance for quick start.

Example

This is an example of subsampling method on logistic regression:

library(subsampling)
set.seed(1)
N <- 1e4
beta0 <- rep(-0.5, 7)
d <- length(beta0) - 1
corr <- 0.5
sigmax  <- matrix(corr, d, d) + diag(1-corr, d)
X <- MASS::mvrnorm(N, rep(0, d), sigmax)
colnames(X) <- paste("V", 1:ncol(X), sep = "")
P <- 1 - 1 / (1 + exp(beta0[1] + X %*% beta0[-1]))
Y <- rbinom(N, 1, P)
data <- as.data.frame(cbind(Y, X))
formula <- Y ~ .
n.plt <- 200
n.ssp <- 600
ssp.results <- ssp.glm(formula = formula,
                       data = data,
                       n.plt = n.plt,
                       n.ssp = n.ssp,
                       family = "quasibinomial",
                       criterion = "optL",
                       sampling.method = "poisson",
                       likelihood = "weighted"
                       )
summary(ssp.results)
#> Model Summary
#> 
#> Call:
#> 
#> ssp.glm(formula = formula, data = data, n.plt = n.plt, n.ssp = n.ssp, 
#>     family = "quasibinomial", criterion = "optL", sampling.method = "poisson", 
#>     likelihood = "weighted")
#> 
#> Subsample Size:
#>                                
#> 1       Total Sample Size 10000
#> 2 Expected Subsample Size   600
#> 3   Actual Subsample Size   635
#> 4   Unique Subsample Size   635
#> 5  Expected Subample Rate    6%
#> 6    Actual Subample Rate 6.35%
#> 7    Unique Subample Rate 6.35%
#> 
#> Coefficients:
#> 
#>           Estimate Std. Error z value Pr(>|z|)
#> Intercept  -0.4149     0.0924 -4.4920  <0.0001
#> V1         -0.5874     0.1084 -5.4191  <0.0001
#> V2         -0.4723     0.1283 -3.6812   0.0002
#> V3         -0.5492     0.1163 -4.7205  <0.0001
#> V4         -0.4044     0.1173 -3.4471   0.0006
#> V5         -0.3725     0.1234 -3.0177   0.0025
#> V6         -0.6703     0.1138 -5.8929  <0.0001