QUASAR

Placeholder. The QUASAR interface is not yet exported. This page describes the method and the planned interface; it will be replaced with a worked example on release.

Motivation

Most deconvolution methods return a single number per cell type per sample. That number carries no indication of how much to trust it, which matters because two very different situations produce identical point estimates: a confident prediction from a well-matched reference, and a guess from a reference that does not represent the target tissue or condition.

QUASAR returns intervals alongside the point estimate, and separates two kinds of uncertainty that answer different questions.

Aleatoric uncertainty

Each predicted composition is represented by a Dirichlet distribution rather than a point on the simplex. The mean gives the predicted proportions; the dispersion gives a sample-specific measure of aleatoric uncertainty — the irreducible variability around a predicted composition, inherent to the observed sample.

Each network predicts one compositional logit per cell type plus a single evidence value. The logits pass through a softmax to give the mean composition, the evidence through a softplus to give a non-negative concentration. The Dirichlet expectation then corresponds exactly to the predicted proportion, while the concentration controls how tightly the distribution sits around it.

Parameters are learned from the known pseudo-bulk proportions using the negative Dirichlet log-likelihood, with an evidential regulariser that penalises high evidence when the predicted mean disagrees with the known proportions. The regularisation weight is annealed from zero over an initial fraction of training, so the model learns the proportions before it is asked to be confident about them.

Epistemic uncertainty

Epistemic uncertainty is the reducible uncertainty in the estimated prediction function, and QUASAR captures it in two parts.

Multiple independently initialised networks quantify variability arising from stochastic optimisation — a standard deep ensemble. But because every member trains on the same targets, an ensemble alone cannot express uncertainty in the pseudo-bulk training targets themselves.

QUASAR therefore adds parametric-bootstrap retraining. During the initial fit, network and optimizer states are checkpointed before training completes. Each member is then applied to the pseudo-bulk expression profiles to obtain its Dirichlet distributions, alternative proportion vectors are sampled from those distributions, and the remaining training is repeated from the checkpoint using the resampled targets. Restarting from a late checkpoint rather than from scratch isolates the effect of the target variation from the noise of a full retrain.

The total epistemic variance combines the bootstrap contribution with the ensemble variance of the mean.

Confidence and prediction intervals

The two components support different intervals, and the distinction is not cosmetic:

Confidence intervals use epistemic uncertainty alone. They describe uncertainty in the estimated mean proportion — how much the answer would move if you refit the model.
Prediction intervals additionally propagate the Dirichlet dispersion. They describe the broader range of plausible compositions for an individual sample.

Prediction intervals are constructed by first perturbing the ensemble mean according to its epistemic uncertainty, then sampling a composition from a Dirichlet built around each perturbed mean. Limits come from the empirical quantiles of those draws and are restricted to [0, 1].

Planned interface

# fit <- quasar(
#   sc_data      = sc_ref,
#   bulk         = bulk,
#   celltype_col = "cell_type",
#   n_models     = 5,
#   device       = "auto"
# )
#
# fit$proportions          # ensemble-mean cell-type proportions
# fit$confidence_interval  # epistemic only
# fit$prediction_interval  # epistemic + aleatoric
# fit$uncertainty          # per-sample, per-cell-type variance components

In the meantime

The four ported deep-learning methods are fully available and documented under Deep learning methods. They return point estimates only, but quasar_prop_metrics() (see Utilities) scores any of them against known ground truth.

Reference

Ruff, S., Tam, W., Bullerjahn, C., Beineke, A., Altenbuchinger, M., & Jung, K. (YEAR). Uncertainty aware deep learning for cell type deconvolution with confidence and prediction interval estimation. Journal, volume(issue), pages.

Sergej Ruff