Training-Free Correction of Gene Expression Predictions Using Cancer-Specific and Spatial Priors

Technical Summary: Training-Free Correction of Gene Expression Predictions Using Cancer-Specific and Spatial Priors

Problem Statement
Predicting spot-level gene expression from haematoxylin-eosin (H&E) histology images aims to extend spatially resolved molecular profiling to routine pathology archives without additional wet-lab sequencing. While recent image-to-Spatial Transcriptomics (ST) predictors have improved through better image representations and multimodal modeling, they typically optimize an image-conditional likelihood, $p_\theta(y | x)$. This focus leaves two critical structural properties of the training expression data underutilized:

1. Cancer-specific gene co-expression: Highly variable genes (HVGs) exhibit structured covariance patterns reflecting tissue composition and microenvironmental programs (e.g., immune, stromal, epithelial modules). Predictors optimized for per-gene accuracy often fail to enforce these joint expression constraints.
2. Slide-level spatial smoothness: Adjacent tissue spots share microenvironmental contexts. While some architectures incorporate spatial information via graph layers or attention, explicit coordinate-based smoothness often remains partially unexploited, particularly in models producing spot-wise outputs.

Current methods often address these issues by redesigning architectures or training losses. However, substantial residual error in state-of-the-art (SOTA) predictors suggests that biological structure present in the training data is not being fully encoded by existing models.

Methodology: Multi-Prior Posterior Guidance
The authors introduce multi-prior posterior guidance, a training-free, model-agnostic correction applied at inference time. This method refines the initial output of any spot-level gene predictor ($\hat{y}_{model}$) by projecting it toward two structural priors estimated solely from the training data. The correction is a single, closed-form Tikhonov-regularized step:

$$\hat{y}_{MP} = \hat{y}_{model} - \lambda_{bio} (\hat{y}_{model} - \mu_c) \Sigma_c^{-1} - \lambda_{sp} (\hat{y}_{model} - \bar{y}_{N})$$

Where:

• Bio Prior (Cancer-Specific Gaussian): Encodes gene co-expression structure. For a specific cancer type $c$, the prior is defined as $N(\mu_c, \Sigma_c)$, where $\mu_c$ is the empirical mean and $\Sigma_c$ is the covariance matrix of HVGs in the training set. The precision matrix $\Sigma_c^{-1}$ captures partial correlations, enforcing that co-regulated genes move together.
• Spatial Prior (Gaussian Markov Random Field): Enforces local smoothness over a $k$-nearest-neighbor (k-NN) graph constructed from spot coordinates. The term $(\hat{y}_{model} - \bar{y}_{N})$ represents the deviation of a spot's prediction from the mean of its spatial neighbors.
• Hyperparameters: $\lambda_{bio}$ and $\lambda_{sp}$ are weights tuned on validation folds but fixed across baselines. The method is applied post-hoc for non-iterative predictors and as sampling-time guidance for iterative flow-matching models.

Key Contributions

1. Inference-Time Correction: A general, plug-and-play technique that improves diverse architectures (linear, CNN, GNN, Transformer, Flow-Matching) without retraining or architectural modification.
2. Exploitation of Unutilized Structure: Demonstrates that residual error in current predictors largely reflects biological co-expression and spatial organization that the training data exposes but models fail to encode.
3. Cross-Cohort Transfer: Shows that a prior estimated on a full-coverage source cohort (HEST-bench) transfers effectively to a partial-coverage target cohort (STimage-1K4M) without retraining, circumventing issues caused by missing gene modalities in the target data.
4. Mechanistic Insight: Identifies that the performance gain is driven specifically by the off-diagonal structure of the precision matrix (partial correlations), not merely by shrinking predictions toward the mean.

Results
The method was evaluated across seven architecturally distinct baselines (Ridge, ST-Net, GCN, SEPAL, HisToGene, STPath, STFlow) on two Visium cohorts:

• HEST-bench: 10 cancer types, 72 slides.
• STimage-1K4M: 8 cancer types, 186 slides (cross-cohort transfer).

Performance Metrics:

• Uniform Improvement: The correction yielded a positive Pearson correlation coefficient (PCC) gain ($\Delta$) in all 14 (baseline, cohort) pairs.
• Statistical Significance: 11 of the 14 pairs reached Bonferroni-corrected significance ($p < 0.05$).
• Magnitude: Gains ranged from $+0.0024$ (SEPAL on STimage) to $+0.0326$ (GCN on HEST-bench).
• Baseline Dependency:
  • Baselines lacking explicit spatial inductive bias (e.g., Ridge, ST-Net) gained significantly from the spatial prior.
  • Baselines already encoding spatial structure (e.g., GCN, SEPAL, STFlow) showed smaller spatial gains but still benefited from the bio prior.
  • The bio prior was the primary contributor to gains in 12 of 14 pairs.
• Transferability: A prior trained on HEST-bench outperformed a prior trained specifically on the STimage cohort (which suffered from truncated HVG coverage and zero-padding artifacts), confirming that cancer-mode co-expression structures are conserved across cohorts.

Significance and Claims
The paper claims that a meaningful portion of the gap between current image-to-ST predictors and ground-truth measurements can be recovered cheaply at inference time. The authors argue that:

• Residual Error is Structural: The remaining error in SOTA models is not just noise but reflects unmodeled biological co-expression and spatial tissue organization.
• Explicit Modeling is Necessary: Future models should explicitly model joint biological co-expression and spatial organization rather than relying on marginal per-gene prediction losses to implicitly recover them.
• Interpretability: The injected structure is interpretable; the top partial correlations in the precision matrix recover known cell-type co-expression programs (e.g., endothelial, T-cell, keratinocyte markers) with 10–40% overlap with curated marker lists.
• Practical Utility: The method provides a practical, universal calibration tool that improves the current public state of the art across diverse model families, requiring only precomputed statistics from training data.

The authors remain modest regarding limitations, noting that the method requires a pre-classified cancer type, is currently limited to 50 HVG panels, and has not yet been tested on platforms other than Visium (e.g., Stereo-seq, Slide-seq v2). They also acknowledge that statistical power was limited for specific baseline/cohort combinations (STPath and STFlow on STimage), where results were positive but not statistically significant after correction.