lwpls implements locally-weighted partial least squares (LW-PLS) for the tidymodels ecosystem.
LW-PLS is a just-in-time learning method used in chemometrics and process monitoring (soft sensors). Instead of fitting a single global model, it builds a dedicated weighted PLS model around each new sample, where every training sample is weighted by its similarity to that sample. A linear method can therefore capture nonlinear and time-varying relationships.
lwpls(): a parsnip model for
regression (one or more outcomes) and
classification (LW-PLS-DA).similarity = "covariance").set_engine("lwpls", robust = TRUE)), and
sparse local models that select their own predictors
(sparsity), with the trimmed_rmse() metric to
tune robust models on contaminated data.localization() and similarity() are tuning
parameters, and all values of num_comp are evaluated from a
single fit (the “submodel trick”).lwpls_fit(): a standalone hardhat modeling function with
matrix, data frame, formula and recipe interfaces.lwpls_local()) with publication-ready ggplot2 plots:
reliability of each prediction (applicability domain), local regression
vectors along the spectrum, robust weights that point to wrong reference
values, and wavelengths selected by sparse models.Install a prebuilt binary from r-universe, which needs no compiler:
install.packages(
"lwpls",
repos = c("https://christiangoueguel.r-universe.dev", "https://cloud.r-project.org")
)Or build the development version from GitHub with:
# install.packages("pak")
pak::pak("ChristianGoueguel/lwpls")Building from source compiles C++ code, so it needs the R compiler tools. On macOS, that includes gfortran from https://mac.r-project.org/tools/.
Predict the water content of meat samples from their near-infrared spectra and tune both hyperparameters with cross-validation:
library(tidymodels)
library(lwpls)
data(meats, package = "modeldata")
meats <- meats |> select(-fat, -protein)set.seed(123)
meats_split <- initial_split(meats, prop = 0.75)
meats_folds <- vfold_cv(training(meats_split), v = 5)
lwpls_wflow <- workflow(
water ~ .,
lwpls(
num_comp = tune(),
localization = tune()
) |>
set_mode("regression")
)
lwpls_grid <- grid_regular(
num_comp(c(1, 15)),
localization(),
levels = c(num_comp = 15, localization = 8)
)
lwpls_res <- tune_grid(lwpls_wflow, meats_folds, grid = lwpls_grid)show_best(lwpls_res, metric = "rmse", n = 3)
#> # A tibble: 3 × 8
#> num_comp localization .metric .estimator mean n std_err .config
#> <int> <dbl> <chr> <chr> <dbl> <int> <dbl> <chr>
#> 1 10 0.5 rmse standard 1.66 5 0.156 pre0_mod077_post0
#> 2 13 0.5 rmse standard 1.68 5 0.198 pre0_mod101_post0
#> 3 9 0.5 rmse standard 1.70 5 0.174 pre0_mod069_post0The 120 candidate models are evaluated with only 8 fits per resample. Their cross-validated RMSE forms a surface over the two hyperparameters, with a valley between very local models and global PLS (the best model is the orange point):
rmse_grid <- lwpls_res |>
collect_metrics() |>
filter(.metric == "rmse") |>
select(num_comp, localization, rmse = mean)
best <- slice_min(rmse_grid, rmse)# color each facet by its mean RMSE
rmse_mat <- with(rmse_grid, tapply(rmse, list(num_comp, log2(localization)), mean))
n <- dim(rmse_mat)
facets <- (rmse_mat[-1, -1] + rmse_mat[-1, -n[2]] + rmse_mat[-n[1], -1] + rmse_mat[-n[1], -n[2]]) / 4
blues <- colorRampPalette(c("#cde2fb", "#3987e5", "#0d366b"))(50)
par(mar = c(1, 0, 0, 0))
view <- persp(
x = as.numeric(rownames(rmse_mat)),
y = as.numeric(colnames(rmse_mat)),
z = rmse_mat,
theta = 140,
phi = 25,
expand = 0.7,
ticktype = "detailed",
col = blues[cut(facets, 50)],
border = "white",
lwd = 0.5,
xlab = "num_comp",
ylab = "log2(localization)",
zlab = "RMSE", cex.axis = 0.7
)
points(
trans3d(best$num_comp, log2(best$localization), best$rmse, view),
pch = 21,
bg = "#eb6834",
col = "white",
cex = 1.6
)
The final model is evaluated on the test set:
lwpls_wflow |>
finalize_workflow(select_best(lwpls_res, metric = "rmse")) |>
last_fit(meats_split) |>
collect_metrics()
#> # A tibble: 2 × 4
#> .metric .estimator .estimate .config
#> <chr> <chr> <dbl> <chr>
#> 1 rmse standard 1.38 pre0_mod0_post0
#> 2 rsq standard 0.978 pre0_mod0_post0Each prediction comes from its own local model.
lwpls_local() returns these models with their diagnostics;
for example, their regression vectors along the spectrum (100 channels
between 850 and 1050 nm) show how the bands used change with the water
content:
final_fit <- lwpls_wflow |>
finalize_workflow(select_best(lwpls_res, metric = "rmse")) |>
fit(training(meats_split))
final_fit |>
lwpls_local(testing(meats_split), wavelength = seq(850, 1050, length.out = 100)) |>
plot_coefficients(axis_label = "Wavelength (nm)")
See vignette("lwpls") for more details, including the
comparison with global PLS and classification,
vignette("robust-sparse") for robust and sparse local
models, and vignette("diagnostics") for the diagnostic
plots.
For a query sample \(x_q\), each training sample \(x_i\) receives the weight
\[\omega_i = \exp\left(-\frac{\lVert x_i - x_q \rVert}{\sigma_d \varphi}\right)\]
where \(\sigma_d\) is the standard
deviation of the distances and \(\varphi\) is the localization
parameter. A PLS model with num_comp components is then
fitted with these weights, and the query is projected onto it. Small
values of \(\varphi\) give very local
models; large values give global PLS.