Polygenic risk scores, commonly abbreviated as PRS, summarize the combined influence of thousands or millions of genetic variants on a person’s likelihood of developing a particular condition. Constructing them is a formidable statistical challenge. Modern biobanks measure hundreds of thousands of individuals at millions of genetic positions, and the number of potential predictors vastly exceeds the number of study participants. In this high-dimensional regime, ordinary regression breaks down, and researchers must rely on penalized regression methods that shrink or eliminate weak signals. The most famous of these, the Lasso introduced by Tibshirani in 1996, adds a penalty proportional to the sum of absolute coefficient values, driving the coefficients of uninformative variants all the way to zero and thereby selecting a sparse subset of predictors.

Despite its elegance, the Lasso faces difficulties when the number of variables dwarfs the number of observations, as it does in genomic data. Feature selection can be unstable: small perturbations in the data may cause the method to pick different variants, and correlated variants can compete with one another in ways that obscure the true signal. UniLasso addresses these problems with a two-stage strategy. In the first stage, the method performs simple univariate regressions, examining each genetic variant one at a time for its individual association with the trait of interest. The signs and magnitudes of these univariate coefficients are then used to guide the second stage, a multivariate penalized regression fitted on the full set of variants simultaneously. Variants with strong univariate evidence receive favorable treatment in the penalty, while those with weak or contradictory evidence are discouraged from entering the model.

The intuition behind this design is that univariate screening provides a stable, data-driven prior about which variants matter. By anchoring the multivariate fit to this prior, uniLasso stabilizes feature selection across datasets and reduces the variance of the resulting coefficient estimates. The authors emphasize that the univariate stage does not replace the multivariate fit; it merely informs it. The final model is still learned from individual-level data in the target population, which means the method can adapt to the specific ancestry, cohort composition, and phenotype definitions of the dataset at hand. This two-stage architecture also confers a computational advantage: the initial univariate screen is embarrassingly parallel and can be distributed across many processors, making the approach feasible for datasets with more than one million genetic variants measured on hundreds of thousands of people.

To test the method at true biobank scale, the team applied uniLasso to the UK Biobank, a population-based repository containing genetic, health, and lifestyle data from roughly half a million participants across the United Kingdom. The researchers adapted the algorithm to handle the sheer dimensionality of the resource, where more than a million variants must be evaluated simultaneously. They also introduced an extension called uniLasso ES, short for external scores, which incorporates summary statistics from pre-existing genome-wide association studies. These external signals, drawn from large meta-analyses that may involve millions of additional participants, guide the regression toward variants with prior evidence of association by informing penalty weights and imposing sign constraints that keep coefficient directions consistent with earlier findings.

The uniLasso ES framework is particularly significant because it bridges two traditionally separate paradigms in polygenic risk prediction. Summary-statistic methods, such as PRS-CS and lassosum2, rely exclusively on aggregated association results and linkage disequilibrium reference panels, avoiding the privacy and logistical hurdles of individual-level data but sacrificing some flexibility. Individual-level methods, by contrast, can model the full joint structure of the data but require access to raw genotypes. UniLasso ES occupies a middle ground: external summary statistics act as a soft guide, shaping the penalty landscape, while the definitive fitting happens on individual-level target data. The external evidence informs the model without dictating it, allowing the method to correct for differences between the discovery population and the target population.

The empirical results reported in the study are striking. Across a range of traits and disease outcomes in the UK Biobank, uniLasso attained predictive performance comparable to the standard Lasso while selecting substantially fewer variants. Sparser models offer tangible benefits beyond aesthetics. A risk score built from a few thousand variants rather than hundreds of thousands costs less to genotype in a clinical setting, reduces the storage and computational burden of scoring large patient cohorts, and, crucially, is easier to interrogate biologically. When a compact set of variants drives a prediction, researchers can more readily trace which genes and pathways contribute to the score, potentially generating new hypotheses about disease mechanisms.

Interpretability has been a persistent criticism of polygenic risk scores. Critics note that scores built from millions of tiny effects are statistical black boxes whose individual components rarely correspond to established biology. By producing models that are sparse by construction and whose selected variants carry coherent univariate evidence, uniLasso nudges the field toward scores that a geneticist can actually read. The method’s reliance on univariate coefficient signs also guards against a known pathology of penalized regression in the presence of correlated predictors, where a variant may enter the model with a counterintuitive sign simply because it is absorbing the effect of a nearby variant. Sign constraints informed by univariate evidence keep the fitted coefficients aligned with the marginal signal.

Benchmarking against competing approaches reinforced the method’s promise. The authors report that both uniLasso and uniLasso ES remained competitive with PRS-CS and lassosum2, two widely used PRS estimation methods that represent the current state of the art. Achieving parity with these established tools while producing markedly sparser models positions uniLasso as a practical alternative for research groups that need both accuracy and parsimony. The scalability of the implementation matters as much as its statistical properties; as biobanks grow toward cohorts of millions and sequencing expands the variant catalogue into the billions, methods that cannot be distributed efficiently will simply fall out of use.

The study arrives at a moment when polygenic risk scores are edging toward clinical application, with health systems beginning to explore their use in screening programs for conditions such as cardiovascular disease, diabetes, and several cancers. The promise of personalized prevention depends on scores that are accurate, portable across ancestries, and affordable to deploy. A method that delivers competitive accuracy with a fraction of the variants addresses all three concerns at once. The work also exemplifies a broader trend in statistics: the creative combination of classical ideas, in this case univariate screening and penalized regression, to meet the demands of modern data scale. As the authors and their collaborators continue to refine the framework, uniLasso may well become a standard tool in the geneticist’s arsenal, helping to convert the torrent of biobank data into models that clinicians and patients can understand and act upon.

Subject of Research: Scalable sparse regression methods for polygenic risk score computation in biobank-scale genomic data

Article Title: Univariate-guided sparse regression for Biobank-scale high-dimensional omics data

Article References: Univariate-guided sparse regression for Biobank-scale high-dimensional omics data. (n.d.). https://doi.org/10.1371/journal.pgen.1012314

Image Credits: AI Generated

DOI: 10.1371/journal.pgen.1012314

Keywords: polygenic risk scores, uniLasso, UK Biobank, sparse regression, Lasso, genome-wide association studies, high-dimensional statistics, summary statistics, predictive modeling, genomics, feature selection, PLOS Genetics

The mathematical stage for this work is the Gaussian graphical model, a workhorse of high-dimensional statistics in which each node represents a random variable and an edge indicates that two variables are conditionally dependent given all the others. In genetics, such a graph might capture regulatory relationships among thousands of genes; in neuroscience, it can summarize which brain regions coordinate their activity at rest. When researchers collect samples from two populations, say healthy individuals and patients, the natural scientific question is not whether the two graphs are different in some vague, global sense, but exactly which edges differ. This is the domain of differential network analysis, and it has been hampered by a stubborn technical constraint: nearly every existing method assumes that the base graphs themselves are sparse, meaning each node connects to only a handful of neighbors.

That sparsity assumption is often unrealistic. Biological and social networks can be densely connected, with each node linked to many others, while the true differences between two conditions remain concentrated in a small subset of edges. Methods built for sparse graphs can break down entirely in this regime, producing floods of spurious discoveries or missing genuine signals altogether. DNetEx departs from this tradition by requiring only that the differential edges, the connections that actually change between the two models, be few, while placing essentially no restrictions on the density or structure of the base graphs. According to the authors’ theoretical analysis, this makes the framework substantially more general than prior approaches.

The method’s statistical core is a guarantee of false discovery rate control, one of the most celebrated ideas in modern multiple testing. When a procedure tests thousands of hypotheses simultaneously, as happens when every possible edge in a graph is a candidate for change, some false positives are inevitable. The false discovery rate, introduced by Yoav Benjamini and Yosef Hochberg in 1995, measures the expected proportion of false positives among the declared discoveries, and keeping it below a user-chosen threshold is what separates trustworthy exploratory science from an undisciplined laundry list of findings. DNetEx is proven, under mild conditions, to control this rate asymptotically, meaning that as sample sizes grow, the fraction of reported edges that are genuine changes remains reliably high.

Technically, the framework weaves together three ingredients. First, sample splitting divides the available data, with one portion used to screen and rank candidate differential edges and the remainder reserved for independent statistical validation, a strategy that avoids the circularity of testing hypotheses on the same data used to generate them. Second, a screening mechanism prunes the enormous space of possible edges down to a manageable candidate set, slashing computational cost while a tunable parameter lets practitioners balance statistical power against runtime. Third, validation relies on e-values and the e-BH procedure, a modern alternative to traditional p-values that has gained traction in fields ranging from quantum cryptography to clinical trials. The method constructs mirror statistics whose null distributions are symmetric about zero, and the proof that the resulting procedure is a valid instance of e-BH testing leans on an elegant supermartingale argument adapted from earlier work on knockoffs and data splitting.

The theoretical scaffolding is backed by theorems establishing joint asymptotic normality of the quadratic forms underlying the test statistics, derived through Taylor expansions of the sample covariance inverse, Lyapunov central limit arguments, and careful control of remainder terms using operator norm bounds and Weyl’s inequality. In extensive experiments on synthetic data, DNetEx maintained accurate false discovery rate control and strong detection power, including settings where competing approaches failed to control the rate at all. Supplementary analyses pushed the dimension to a thousand variables and confirmed that the method remains computationally tractable and statistically sound, even as the number of possible edges grows quadratically with dimension and sparse differential structure becomes ever harder to recover.

The sensitivity analyses reveal a method with tunable, well-understood knobs. Increasing the screening parameter enlarges the candidate set and initially boosts power, but beyond a moderate point the gains flatten while computational cost keeps climbing. Adjusting the sample-splitting ratio shows that starving the screening stage of data erodes the quality of candidate selection, while over-allocating samples to validation wastes information. Randomness in the split does introduce some variability in which edges get detected on any single run, an honest limitation the authors acknowledge, though average false discovery proportions remained controlled across all tested configurations, and more robust splitting strategies are flagged as a promising direction for future work.

The most striking demonstration, however, came from real brain imaging data. Applying DNetEx to resting-state functional MRI connectivity from the Autism Brain Imaging Data Exchange, the team compared neurotypical individuals with people on the autism spectrum. Where competing methods detected no differential edges whatsoever, DNetEx identified eighteen connections between regions of the Dosenbach atlas whose connectivity differed between groups. Crucially, many of these edges involve regions long implicated in autism research, including the temporoparietal junction, the ventromedial prefrontal cortex, the insula, and the precuneus, areas tied to face expression processing, theory of mind, and the sense of self. The method recovered these biologically plausible patterns without any domain-specific priors, relying purely on statistical structure.

For the autism research community, the result is more than a technical curiosity. Altered functional connectivity has been a central, and sometimes contentious, theme in neuroimaging studies of the spectrum, with reports of both hyperconnectivity and reduced connectivity across various cortical networks. A method that can rigorously certify which specific connections differ, while provably limiting false discoveries, offers a path toward more reproducible findings in a field where small samples and thousands of simultaneous tests have fueled concerns about reliability. The same logic applies directly to genomics, where differential network analysis has been proposed as a way to trace how disease rewires gene regulatory circuits, and to domains as varied as finance and anomaly detection in streaming data.

The researchers have released their source code publicly on GitHub, allowing other teams to apply the framework and reproduce every experimental result reported in the paper. As scientific datasets grow in size and complexity, tools that combine rigorous error control with genuine scalability become not just convenient but essential. DNetEx suggests that the next generation of network comparison methods can be both statistically honest and computationally practical, and that when the mathematics is done right, the tangled wiring diagrams of the brain and the cell may finally begin giving up their secrets, one verified edge at a time.

Subject of Research: FDR-controlled differential network analysis between Gaussian graphical models

Article Title: DNetEx: FDR-controlled differential network analysis for knowledge discovery from graphs

Article References: Nikahd, M., Emrani, A., & Motahari, S. A. (2026). DNetEx: FDR-controlled differential network analysis for knowledge discovery from graphs. Data Mining and Knowledge Discovery, 40(6), Article 97. https://doi.org/10.1007/s10618-026-01245-4

Image Credits: AI Generated

DOI: 10.1007/s10618-026-01245-4

Keywords: differential network analysis, Gaussian graphical models, false discovery rate, e-values, graph structure learning, brain connectivity, autism spectrum disorder, fMRI, multiple testing, high-dimensional statistics, knowledge discovery, machine learning