---
title: "Interpretable models"
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  %\VignetteEngine{knitr::rmarkdown}
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  - figures/logo.svg
  - figures/logo-dark.svg
---

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```{r setup, include=FALSE}
library(hypermodR)
knitr::opts_chunk$set(collapse = TRUE, comment = "#>", error = FALSE)
```
The task is synthetic continuous regression; subjects are independent units.
Band coefficients describe the fitted coordinate system, not causal tissue
properties. Scaling and all learned transformations use training rows only.

```{r workflow}
data <- hm_example(seed = 42L)
if (!isTRUE(all(
  methods::validObject(data), nrow(data@observations) == 96L,
  identical(data@bands$wavelength, seq(500, 850, length.out = 8L))
))) {
  cli::cli_abort("Example assertion failed.", class = "hm_example_error")
}
task <- hm_task("response", "regression", "spectrum", "subject_id")
splits <- hm_split(data, task, folds = 3L, inner_folds = 2L, seed = 7L)
fold <- splits$folds[[1L]]
if (!isTRUE(all(!length(intersect(
  data@observations$subject_id[fold$train],
  data@observations$subject_id[fold$test]
))))) {
  cli::cli_abort("Example assertion failed.", class = "hm_example_error")
}
workflow <- hm_workflow(
  task, hm_recipe(list(list(type = "scale"))),
  hm_model_spec("lm", task)
)
fit <- hm_fit(workflow, data, fold)
heldout <- hm_spectra(data, list(
  observation_id = data@observations$observation_id[fold$test]
))
prediction <- hm_predict(fit, heldout)
evaluation <- hm_evaluate(prediction, heldout$observations)
errors <- prediction$values - heldout$observations$response
expected_rmse <- sqrt(mean(errors^2))
if (!isTRUE(all(isTRUE(all.equal(unname(evaluation$metrics["rmse"]),
                                 expected_rmse))))) {
  cli::cli_abort("Example assertion failed.", class = "hm_example_error")
}
evaluation
uncertainty <- hm_bootstrap(evaluation, unit = "subject_id", draws = 20L,
                            seed = 9L)
if (!isTRUE(all(uncertainty$invalid_draws == 0L))) {
  cli::cli_abort("Example assertion failed.", class = "hm_example_error")
}
uncertainty$conditioning
run <- tempfile("hypermodR-run-")
hm_save_run(list(
  fit = fit, prediction = prediction, evaluation = evaluation,
  uncertainty = uncertainty
), run)
restored <- hm_read_run(run)
if (!isTRUE(all(identical(restored$prediction, prediction)))) {
  cli::cli_abort("Example assertion failed.", class = "hm_example_error")
}
unlink(run, recursive = TRUE)
```

```{r coefficients}
coef(fit)
summary(fit)
```

Canonical statistical IDs include `lm`, `glm`, `glmnet`, `gam`, `mixed`, `pls`,
`pcr`, `bayes_conjugate` and optional `brms`. Chemometric/physiological IDs are
`pca`, `ica`, `nmf`, `mcr_als`, `fcls` and `beer_lambert`. Use
`hm_spectral_library()` to declare wavelength, units, source and license for
endmembers. Nonnegative abundances or a Beer–Lambert fit do not prove biological
identifiability. Baselines, scattering, endmember ambiguity, priors, random
effects and reference calibration need task-specific justification. Unsupported
coefficient retrieval raises a typed error rather than inventing uncertainty.

## Supplied physical and residual models

`hm_physics_kernel()` declares an explicit forward/inverse pair. The
`physics_inverse` engine applies that inverse; `physics_hybrid` learns a residual
model only on training rows. A declaration records code/constants and units; it
is not physiological validation. Do not scale physical inputs unless the kernel
is defined in that scaled coordinate system.

```{r physical-declaration}
kernel <- hm_physics_kernel(
  forward = function(concentration, parameters) {
    concentration * parameters$gain
  },
  inverse = function(spectra, parameters) spectra[, 1L] / parameters$gain,
  parameters = list(gain = 2), source = "synthetic linear law",
  units = c(input = "arbitrary absorbance",
            output = "arbitrary concentration")
)
if (!isTRUE(all(identical(
  kernel$inverse(matrix(c(2, 4), 2, 1), kernel$parameters),
  c(1, 2)
)))) {
  cli::cli_abort("Example assertion failed.", class = "hm_example_error")
}
hm_model_spec(
  "physics_hybrid", task,
  list(kernel = kernel, residual_model = "lm")
)$model_id
```

This deliberately simple law illustrates an interface, not radiative transport,
validated tissue chromophores or independently calibrated concentrations.