💻 bioinformatics

GPSNorm: Gaussian Process Spatial Normalization for Spatial Transcriptomics

GPSNorm is a novel Bayesian spatial normalization framework that jointly models technical variation, spatial structure, and biological signal using a hierarchical Gaussian process approach to propagate normalization uncertainty into downstream differential expression analysis, thereby improving the robustness and interpretability of spatial transcriptomics data.

Original authors: Taychameekiatchai, A., Zhan, X., Xiao, G., Ruan, P.

Published 2026-07-27

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CC BY 4.0

Original authors: Taychameekiatchai, A., Zhan, X., Xiao, G., Ruan, P.

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ⚕️ This is an AI-generated explanation of a preprint that has not been peer-reviewed. It is not medical advice. Do not make health decisions based on this content. Read full disclaimer

Imagine you are a detective trying to solve a mystery inside a bustling, crowded city. This city is a piece of living tissue, and every building (cell) is shouting out a list of its favorite songs (genes). In the past, scientists could only listen to a giant, mixed-up recording of the whole city, losing track of which building was singing what. But now, we have a super-powerful new technology called spatial transcriptomics. It's like giving every building a microphone that not only records its song but also tags it with its exact street address. This lets us see how the city's neighborhoods are organized and how different areas talk to each other.

However, there's a catch. These microphones are finicky. Sometimes a building sounds louder just because its microphone has a bigger battery (library size), or because the wind is blowing harder on that side of the street (spatial artifacts), or because the whole block is having a bad day (slide effects). If you don't fix these technical glitches, you might think a building is singing a new song when it's just shouting louder due to a broken mic. The big question for scientists is: How do we clean up the noise without accidentally deleting the real, interesting songs? Usually, scientists try to clean the noise first and then listen to the music, but this paper argues that doing it in two separate steps is like trying to fix a car while driving it—you might miss the real problem or make the ride bumpy.

Enter GPSNorm, a new tool created by researchers Art Taychameekiatchai, Xiaowei Zhan, Guanghua Xiao, and Peifeng Ruan. Think of GPSNorm not as a simple filter, but as a smart, all-in-one detective who listens to the music and fixes the microphones at the exact same time. Instead of treating the "cleaned" data as a fixed, perfect fact, GPSNorm admits, "I'm pretty sure this is the real song, but I'm also keeping track of how uncertain I am about the noise."

The paper suggests that by using a fancy statistical method called a Bayesian hierarchical model (which is like a super-organized team of detectives sharing clues), GPSNorm can separate the "technical noise" from the "biological signal" much better than old methods. In their tests, they simulated messy city data and found that GPSNorm could accurately map out where the noise was coming from and still hear the true songs clearly. When they applied this to real-world data—like looking at the human brain, lung damage from COVID-19, and kidney tissue—they found that GPSNorm was better at spotting important biological patterns that other methods missed. For example, in the brain data, it clearly showed which areas were rich in specific cell types, even when the raw data was messy. In the lung study, where there were very few samples to work with, GPSNorm was the only method that could confidently identify genes associated with severe damage, whereas other methods were too unsure to say anything.

The researchers also showed that this "uncertainty-aware" approach is crucial. When the noise and the real signal look similar (like a loud song that happens to be in a windy neighborhood), old methods often get confused and give false answers. GPSNorm, by keeping track of its own uncertainty, avoids these traps. It suggests that treating normalization as a guessing game with a scorecard (probabilities) is better than pretending the guess is a perfect fact. While the method is computationally heavy, the team showed that they can group neighborhoods together to make it run faster without losing much accuracy. Ultimately, the paper suggests that GPSNorm makes spatial transcriptomics more reliable, helping scientists trust their maps of the biological city a little more.

Technical Summary of GPSNorm: Gaussian Process Spatial Normalization for Spatial Transcriptomics

Problem Statement

Spatial transcriptomics (ST) technologies, such as 10x Genomics Visium and NanoString GeoMx, enable genome-wide gene expression measurement while preserving tissue architecture. However, ST data is heavily confounded by technical variability, including library size differences, slide-level batch effects, and spatial artifacts (e.g., staining variations or tissue thickness). Unlike bulk or single-cell RNA sequencing, these technical components in ST are often spatially structured, making them difficult to distinguish from biologically meaningful spatial signals.

Current normalization approaches typically treat normalization as a sequential preprocessing step: counts are adjusted using global or spatially informed scaling factors, and downstream analyses (e.g., differential expression) are performed on these adjusted values as fixed inputs. This two-stage workflow ignores the uncertainty introduced during normalization. When technical and biological spatial components are partially separable, treating normalized values as fixed can lead to biased effect size estimates and anti-conservative inference in downstream statistical analyses.

Methodology: The GPSNorm Framework

The authors propose GPSNorm (Gaussian Process Spatial Normalization), a Bayesian hierarchical modeling framework that jointly estimates technical variation, spatial structure, and biological signals within a unified model.

1. Hierarchical Model Specification:

Data Model: Observed transcript counts ( $y_{gi}$ ) for gene $g$ and spatial unit $i$ are modeled using a Negative Binomial distribution with a log link.
Linear Predictor: The log-mean is decomposed into:
- Offset: Known library size/sequencing depth ( $L_i$ ).
- Biological Effects: Gene-specific baseline ( $\alpha_g$ ) and regression coefficients ( $\beta_g$ ) for covariates of interest (e.g., disease status).
- Technical Effects: Slide-level effects ( $\gamma_s$ ) and slide-specific spatial effects ( $f_{i,s}$ ).
Control Genes: The model utilizes negative control genes (NEG) and housekeeping genes (HK). For negative controls, gene-specific biological parameters are constrained to zero, allowing these features to anchor the estimation of shared technical variation and dispersion without biological signal interference.

2. Spatial Modeling:

Spatial dependence within each slide is modeled using an Intrinsic Conditional Autoregressive (ICAR) prior. This serves as a sparse discrete approximation to a smooth Gaussian Process (via the stochastic partial differential equation link).
The spatial field is represented as a Gaussian Markov Random Field (GMRF), defined by a graph Laplacian derived from the neighborhood structure of spatial units. This ensures computational scalability compared to dense Gaussian process covariance matrices.

3. Inference:

The model belongs to the class of Latent Gaussian Models (LGMs).
Integrated Nested Laplace Approximation (INLA) is used for efficient approximate Bayesian inference. INLA avoids the computational cost of Markov Chain Monte Carlo (MCMC) by exploiting the sparse precision matrix structure of the ICAR prior and performing deterministic integration over hyperparameters.
Uncertainty Propagation: Unlike two-stage methods, GPSNorm integrates over the uncertainty of latent normalization components ( $u$ ) when estimating differential expression parameters ( $\beta$ ). This results in wider, more calibrated credible intervals when normalization and biological signals are confounded.

4. Normalized Output:
The framework provides two methods to project posterior estimates back to the count scale:

Posterior-Median Projection: Computes the median of the negative binomial distribution using the biological component of the linear predictor.
Percentile-Adjusted Counts (PAC): Transforms observed counts to preserve rank and dispersion while adjusting the mean structure to remove technical effects.

Key Contributions

Joint Modeling: GPSNorm reframes normalization not as a preprocessing step but as a joint estimation problem within a hierarchical Bayesian framework, explicitly propagating normalization uncertainty into downstream inference.
Spatial Technical Modeling: It introduces a slide-specific ICAR prior to capture smooth, spatially structured technical artifacts that are often confounded with biological gradients.
Scalability: By utilizing INLA and the sparse structure of GMRFs, the method enables efficient inference on large spatial graphs without the cubic complexity associated with dense Gaussian process inversion.
Control Integration: The framework formally incorporates negative control and housekeeping genes to anchor technical variation estimation, reducing confounding between technical and biological components.

Results

The authors evaluated GPSNorm through simulation studies anchored to empirical data distributions and applications to three real-world datasets.

1. Simulation Studies:

Technical Recovery: GPSNorm accurately recovered simulated spatial technical fields (correlation > 0.92) even under strong biological confounding (70% overlap between differential expression and spatial signals).
Differential Expression (DE) Performance: Compared to existing methods (e.g., scran, Giotto, SpaNorm, sct), GPSNorm demonstrated:
- Minimal bias in log-fold change estimation.
- Reduced Root Mean Squared Error (RMSE).
- Improved ranking performance (AUC) for DE genes, particularly in scenarios with high technical complexity.
Uncertainty Calibration: In reduced simulations where the true DE effect was zero, joint estimation maintained nominal 95% credible interval coverage even under strong spatial confounding, whereas two-stage approaches produced anti-conservative intervals (coverage approaching 0%).

2. Real Data Applications:

10x Visium Human DLPFC: GPSNorm successfully recovered the expected enrichment of the oligodendrocyte marker MOBP within white matter regions, a pattern obscured by library size heterogeneity in raw data and partially missed by non-spatial methods. It provided posterior uncertainty estimates for these spatial patterns.
NanoString GeoMx COVID-19 Lung Damage: In a small-sample study (46 AOIs), GPSNorm identified biologically relevant chemokines (CCL18, CXCL10, CCL2) associated with severe damage and SCGB1A1 with mild damage. Other methods failed to identify significant genes, likely due to the inability to propagate normalization uncertainty in small cohorts.
GeoMx Spatial Organ Atlas Kidney: GPSNorm maintained high prioritization of curated marker genes for both glomerular and proximal tubule compartments, outperforming other methods in preserving expected transcriptional contrasts between anatomical regions.

3. Computational Scaling:
The authors demonstrated that aggregating Areas of Interest (AOIs) into clusters prior to model fitting significantly reduced runtime (up to 5-fold speedup) while preserving the ranking of high-signal genes and effect size magnitudes.

Significance and Claims

The paper claims that treating normalization as a latent statistical inference problem, rather than a deterministic preprocessing step, substantially improves the robustness and interpretability of spatial transcriptomics analyses.

Robustness: By jointly modeling technical and biological effects, GPSNorm reduces the risk of absorbing biologically meaningful variation during normalization and prevents the underestimation of uncertainty in downstream differential expression.
Interpretability: The framework allows researchers to quantify the uncertainty of spatial expression surfaces and normalization adjustments, providing a more complete picture of experimental variability.
Applicability: The method is particularly advantageous in settings where technical and biological spatial structures are intertwined, or where sample sizes are small (e.g., targeted spatial platforms like GeoMx), as the hierarchical structure allows for information sharing across genes and spatial units.

The authors note limitations, including the computational cost for extremely large datasets (mitigated by AOI clustering) and the assumption of smooth spatial priors for technical effects. They suggest future work could extend the framework to jointly model spatially variable gene detection and integrate single-cell reference data.