PRESCRIBE: Predicting Single-Cell Responses with Bayesian Estimation

TL;DR

PRESCRIBE addresses the problem of predicting single-cell responses to unseen gene perturbations by jointly modeling data and model uncertainty. It introduces a multivariate Natural Posterior Network that outputs not only post-perturbation expression statistics but also an evidence-driven uncertainty signal, operationalized via a pseudo E-distance that combines predictive entropy and posterior evidence. The approach yields well-calibrated, instance-level uncertainty estimates and improves predictive accuracy when unreliable predictions are filtered, outperforming baselines across multiple datasets. This framework enhances reliability for in silico perturbation studies and can generalize to other scientific domains where out-of-distribution predictions and inherent data stochasticity matter. Overall, PRESCRIBE offers a principled, scalable way to quantify and leverage uncertainty in complex, high-dimensional biological prediction tasks.

Abstract

In single-cell perturbation prediction, a central task is to forecast the effects of perturbing a gene unseen in the training data. The efficacy of such predictions depends on two factors: (1) the similarity of the target gene to those covered in the training data, which informs model (epistemic) uncertainty, and (2) the quality of the corresponding training data, which reflects data (aleatoric) uncertainty. Both factors are critical for determining the reliability of a prediction, particularly as gene perturbation is an inherently stochastic biochemical process. In this paper, we propose PRESCRIBE (PREdicting Single-Cell Response wIth Bayesian Estimation), a multivariate deep evidential regression framework designed to measure both sources of uncertainty jointly. Our analysis demonstrates that PRESCRIBE effectively estimates a confidence score for each prediction, which strongly correlates with its empirical accuracy. This capability enables the filtering of untrustworthy results, and in our experiments, it achieves steady accuracy improvements of over 3% compared to comparable baselines.

Figures (5)

• Figure 1: Preliminary experiments on the Norman dataset using three representative models: (a) High overall predictive accuracy does not ensure individual prediction reliability. (b) E-distance exhibits a strong correlation with prediction accuracy across these models. (c) Calibration analysis demonstrates that E-distance percentiles effectively stratify prediction accuracy.
• Figure 2: Overview of PRESCRIBE. Each perturbation $X_{i}$ under condition $c$ is first mapped onto a perturbation density space $z_{i}$ by the encoder $f_{\alpha}$. From $z_{i}$, the decoder $f_{\beta}$ derives the parameter update $\boldsymbol{\chi}_{i}^{\text{out}}$ while a normalizing flow $f_{\psi}$ yields the evidence update $\nu_{i}^{\text{out}}$. Posterior parameters $\boldsymbol{\omega}_{i}$ are obtained from a weighted combination of prior $\nu^{\text{prior}}_{i}$and updated parameters according to $\nu^{\text{out}}_{i}$.
• Figure 3: (a) The line plot depicts confidence scores from different models plotted against generalization difficulty. An accompanying bar plot displays the average E-distance for corresponding levels of generalization difficulty. (b) t-SNE visualization of the Normal-Inverse Wishart space.
• Figure 4: Calibration curves relating model-estimated confidence scores to prediction accuracy ($r_{\text{pred,truth}}$). Each row corresponds to a dataset, while columns and colors distinguish different models (in order: Ours, Ours-MLPs, GEARS-Drop, and GEARS-Ens). Text in each subplot indicates the Spearman Correlation Coefficient ($r^{s}_{\text{perf,conf}}$) between $r_{\text{pred,truth}}$ and confidence scores.
• Figure 5: Hyperparameter Search on Norman Dataset. (a) Box plots illustrating the relationship between $\lambda_2$ and the distributions of $r_{\text{pred,truth}}$, $\text{ACC}_{\text{pred,truth}}$, and $r^{s}_{\text{perf,conf}}$. (b) Line plots illustrating the relationship between the ratio $\lambda_1/\lambda_3$ and metrics $r_{\text{pred,truth}}$, $\text{ACC}_{\text{pred,truth}}$, and $r^{s}_{\text{perf,conf}}$, when $\lambda_2=0.1$.

Theorems & Definitions (14)

• Remark 1
• Proposition 1
• proof
• Proposition 2
• proof
• Proposition 3
• proof
• Proposition 4
• proof
• Theorem 1