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REVIEW 4 major objections 6 minor 56 references

Training Flexible Models of Genetic Variant Effects from Functional Annotations using Accelerated Linear Algebra

T0 review · 4 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read DeepWAS trains large neural-network priors for variant effects by maximizing the full likelihood, and shows that bigger models improve held-out predictions only under this objective.

desk verdict Solid computational contribution held back by an overclaimed headline result that its own Figure 5 does not support. read the letter →

arxiv 2506.19598 v2 pith:MA2R2VNP submitted 2025-06-24 cs.LG q-bio.PE

Alan N. Amin , Andres Potapczynski , Andrew Gordon Wilson This is my paper · ORCID
classification cs.LGq-bio.PE
keywords varianteffectpredictionfulllikelihoodlinkagedisequilibriumfunctionalannotationsGWASsummarystatisticsiterativelinearalgebraneuralnetworkpriorsheritability
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

DeepWAS is a method for training flexible neural-network priors that predict how strongly each genetic variant affects a trait from genomic features. The paper's thesis is that such models have failed to benefit from extra capacity because they are trained by fitting summary statistics rather than by maximizing the full likelihood of observed associations. DeepWAS makes full-likelihood training feasible by splitting the genome into one-megabase windows, treating the linkage disequilibrium (correlation) matrix as approximately banded, and rewriting the likelihood with the Woodbury identity so that only a well-conditioned matrix must be inverted with fast iterative solvers. In experiments on large public biobank data for BMI, height, and asthma, larger transformer-based priors improve held-out prediction when trained with DeepWAS but not when trained by LD score regression. The paper concludes that the bottleneck for flexible variant-effect models was optimization, not data.

What carries the argument

Two mechanisms carry the argument. First, the genome is divided into roughly 2700 windows of one million base pairs, and the linkage disequilibrium matrix $R$ is treated as banded, so associations in different windows are approximately independent and each window becomes a mini-batch for stochastic gradient descent. Second, the Woodbury identity and the matrix determinant lemma convert the expensive inverse and log-determinant of $A^{(i)}_\theta = R^{(i),(i)+}F_\theta R^{(i)+,(i)} + \sigma_N^2 R^{(i),(i)}$ into operations on the strictly positive definite and well-conditioned matrix $B^{(i)}_\theta = I + \sigma_N^{-2} F_\theta^{(i)1/2} W^{(i)} F_\theta^{(i)1/2}$, with $W^{(i)}$ and related factors precomputed before training because they do not depend on $\theta$. The paper then uses conjugate gradients for solves and stochastic Lanczos quadrature for log-determinants, both of which converge quickly for well-conditioned matrices, and this is what makes a 52-million-parameter model trainable in about 15 to 20 hours on a single GPU.

What would settle it

Train DeepWAS on the same trait twice, once with the standard one-megabase window and once with the window doubled in size; if the held-out likelihood keeps rising and the ranking of model sizes changes, the banded window-independence assumption is doing the work and should be checked against full-LD training on a genomic region known to have long-range correlation.

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Extended reading notes

Core claim

DeepWAS trains a model $f_\theta$ that maps functional annotations around a variant to its prior variance $f_{\theta,m}$, embedded in the hierarchical model $y \sim \mathcal{N}(0, X^\top F X + \sigma^2 I)$, or in public statistics $\hat\beta \sim \mathcal{N}(0, R F R + \sigma_N^2 R)$. The central finding is that larger models only improve performance when $\theta$ is learned by maximizing this marginal likelihood; when the same capacity is trained by fitting LD score regression summary statistics, larger models perform no better than small ones, and worse for BMI. On held-out chromosomes 6 through 8, the 52-million-parameter transformer prior trained with DeepWAS yields larger likelihood increases per person than constant or linear priors for all three traits, and ablations confirm that larger LD windows, more features, and more parameters each help. In semi-synthetic data with a known ground-truth prior, the full-likelihood objective recovers the true $f$ closely.

Load-bearing premise

The argument rests on the assumption that associations in different one-megabase windows are statistically independent, which holds only if variants separated by more than about a million base pairs have negligible correlation.

Editorial extensions

If this is right

  • Full-likelihood training is what lets larger capacity help: under summary-statistic fitting, bigger models overfit and predict no better than small ones.
  • Held-out chromosome likelihoods for BMI, height, and asthma all improve when the LD window, feature window, and hidden dimension are enlarged, so further scaling of each should continue to improve variant-effect prediction.
  • In semi-synthetic experiments, the full-likelihood objective recovers a known ground-truth variant-effect function, indicating that the trained prior is identifiable and not merely a better fit to noise.
  • Because the trained prior is a drop-in component, it can replace the priors used in existing fine-mapping, causal-variant, and gene-prioritization pipelines.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An implication the paper leaves implicit: LD score regression is the window-size-one extreme of the DeepWAS objective, so comparing the two across intermediate window sizes would isolate how much of the gain comes from modelling correlation rather than from the network architecture.
  • The same Woodbury-style reformulation should transfer to other Bayesian regression models with diagonal priors, including mixture or non-normal priors, so the acceleration likely outlives the specific normal-linear model tested.
  • A stress test the authors do not run: train DeepWAS in an admixed or multi-ancestry cohort, where LD decays differently and the banded approximation is less safe; the current results use only a single European-ancestry cohort.
  • If the banded assumption holds at larger scales, one testable consequence is that a model trained on many traits simultaneously with full likelihood should outperform per-trait training, since the prior would share functional signal across traits.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper introduces DeepWAS, a method for training large and flexible neural network priors over genetic variant effects by maximizing the marginal likelihood of GWAS summary statistics. The key algorithmic contributions are (i) a banded/block-diagonal approximation of the LD matrix that turns genomic windows into minibatches, (ii) a Woodbury/pseudo-inverse reformulation that replaces the near-singular LD-block inverse with an iterative solve on a well-conditioned matrix, and (iii) the use of GPU-accelerated conjugate gradients and stochastic Lanczos quadrature via the CoLA library. The empirical sections include a semi-synthetic recovery experiment, held-out chromosome likelihood evaluations for BMI, height, and asthma in UK Biobank, and ablations on window size, feature set, and model size. The central claim is that larger models improve prediction only when trained with the full likelihood, not when trained with LDSR summary-statistic fitting.

Significance. If the central empirical claim held, this would be a substantive methodological advance: it removes a major computational bottleneck in fitting flexible functionally informed priors and demonstrates that a statistically efficient objective can be optimized at scale. The paper ships code, uses public data, and provides derivations in Appendix C that are largely plausible. The connection between LDSR and the window-size-one limit of the proposed objective is also a nice conceptual point. However, the headline claim is currently not supported by the paper's own reported point estimates and the empirical evaluation lacks uncertainty quantification, so the significance of the real-data contribution remains unestablished.

major comments (4)
  1. [Abstract; Sec. 6.2; Fig. 5] The central claim that "larger models only improve performance when using our full likelihood approach" is not supported by the paper's own point estimates. In Fig. 5, under any natural reading of the row groups, the LDSR transformer value exceeds the LDSR linear value for all three traits: height 9.47 vs 9.39, BMI 2.33 vs 2.28, and asthma 0.296 vs 0.226. The body text softens this to "does not significantly increase," but no error bars, confidence intervals, repeated-seed variation, or significance tests are reported, so the claim is untestable. Please add uncertainty quantification and a statistical comparison, or revise the abstract and Section 6.2 to state accurately what the point estimates show.
  2. [Sec. 4.1; Eq. (5)] The factorization of the likelihood into independent windows assumes that R is approximately block diagonal and that correlations between variants more than one megabase apart are negligible. This is a structural modeling assumption, not an algorithmic detail, and the paper does not quantify the resulting bias. Indeed, App. D.1 explicitly removes known long-range LD regions, suggesting that long-range LD is a real concern. Please provide a sensitivity analysis (e.g., varying the window size or comparing against an exact full-LD solve on a subset of variants) or carefully scope the claims to the banded approximation.
  3. [Sec. 6.1; Fig. 4; App. B.1] The semi-synthetic recovery experiment draws the ground-truth f from a randomly initialized Enformer model, which is the same architecture class as the flexible model being evaluated. This demonstrates within-class identifiability but does not establish that the full-likelihood objective is necessary for the real-data improvements claimed in Fig. 5. The misspecified ground truth in App. B.1 is a step in the right direction, but the load-bearing real-data comparison still lacks statistical support, as detailed in the first major comment.
  4. [Sec. 6.2; Fig. 6; Table 1] The ablation results are presented as single point estimates without error bars or repeated runs. Several differences are very small (e.g., BMI full model 3.02 vs 2.68, 2.64, and 3.01 across the ablations), so it is not possible to determine whether "ablating the number of variants, model size, or feature set often harms model performance" reflects real effects or noise. Please report variability across seeds or bootstraps for these comparisons.
minor comments (6)
  1. [App. C.1] The displayed determinant identity has typographical plus signs where products of determinants are intended; as printed, "|A(i)_theta| = |sigma^2_N R(i),(i)| + |F(i)_theta| ..." is not a valid equality.
  2. [Sec. 6.2; Fig. 5] The figure caption and legend do not clearly specify whether the two row groups are LDSR followed by DeepWAS or vice versa; please state this explicitly, since the interpretation of the central comparison depends on it.
  3. [Abstract; throughout] The name "DeepW AS" appears with an unwanted space in several places; please fix the formatting.
  4. [Sec. 2.1; Sec. 6.2] There are typos "heritibility" and "phentotype" that should be corrected to "heritability" and "phenotype."
  5. [Sec. 4.2.2] The claim that "sigma^{-2}_N times F_theta is approximately N/M < 1" is stated without derivation; given that F_theta is a learned function, please justify this bound or soften the statement.
  6. [App. D.3] The feature curation selects "a random 20 tissues" and "a randomly chosen annotation" or replicate; please clarify whether these choices were made before the experiments and whether the reported results are robust to this randomness.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the likelihood reformulation and held-out evaluation are derived from standard matrix identities and external fitted constants, with no prediction reducing to its input.

full rationale

The derivation chain is self-contained. The likelihood objective (Eqn. 3) is the standard marginal likelihood for the public summary statistics beta-hat (Eqn. 2), rewritten via the Woodbury identity and the matrix-determinant lemma (Appendix C.1); no fitted constants are introduced as predictions. The banded/window approximation (Sec. 4.1) is a stated modeling assumption justified by external LD-decay references, not by the paper's own results. The frequency-scaling exponent alpha is fixed at 0.7 after observing convergence, and sigma is taken from BOLT-LMM; neither is fitted to the held-out likelihoods reported as predictions. Held-out chromosomes 6-8 are not used to train theta, and Appendix C.2 derives the equivalence between individual-level and summary-statistic held-out likelihoods rather than assuming it. The semi-synthetic ground truth is generated from a random Enformer network, but this is a recoverability test and Appendix B.1 repeats it with a misspecified ground truth; it does not build the real-data conclusion. The only self-citations (CoLA, the GPyTorch lineage) are software/algorithmic implementations that are independently runnable and are not invoked as evidence for the empirical claims. The apparent contradiction between the abstract's 'only improve' phrasing and the Fig. 5 point estimates (LDSR transformer exceeds LDSR linear for BMI, height, and asthma) is an internal consistency and correctness concern, not a reduction of the claim to its inputs.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

The method introduces no new biological entities or forces. The load-bearing assumptions are the generative model for GWAS summary statistics, the banded/block-diagonal approximation of LD, and the conditioning of the reformulated matrix. The only hand-chosen numeric parameters are alpha and sigma, both taken from prior fits or heuristics rather than derived from the likelihood.

free parameters (2)
  • alpha (allele frequency scaling exponent) = 0.7
    In Eq. 6, the paper states alpha converged between 0.6 and 0.7 and was fixed at 0.7 for all experiments to simplify comparisons.
  • sigma (residual noise variance) = from BOLT-LMM
    Sec. A.3: 'For all models we use sigma calculated using BOLT-LMM'. The model treats sigma as known rather than fitting it from the likelihood.
assumptions (6)
  • domain assumption Infinitesimal linear model: y = X^T beta + epsilon with beta_m ~ N(0, f_m) independently across variants.
    Sec. 2.1, Eq. 1. The entire likelihood and the functional prior are built on this generative model.
  • domain assumption Public association statistics follow \hat\beta ~ N(0, R F R + sigma^2_N R).
    Eq. 2. This ignores uncertainty in the estimated LD matrix and treats summary statistics as exact. It is load-bearing for the training objective.
  • domain assumption R is approximately block diagonal with zero correlation beyond one million base pairs.
    Sec. 4.1 justifies independent windows and the banded approximation. Long-range LD would make the windowed likelihood misspecified.
  • domain assumption B(i)_theta is well-conditioned because sigma^{-2} F approx N/M < 1.
    Sec. 4.2.1. If typical effect sizes are larger or sigma is smaller, the conditioning argument weakens and the iterative methods may need many more iterations.
  • domain assumption Population stratification is adequately controlled by using BOLT-LMM-adjusted summary statistics.
    Sec. 7 acknowledges this as a limitation and future work item.
  • standard math Woodbury matrix identity and matrix determinant lemma.
    Sec. C.1. Standard identities used to rewrite the loss in terms of a well-conditioned matrix.

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Cite this review

Pith. "Pith review of Training Flexible Models of Genetic Variant Effects from Functional Annotations using Accelerated Linear Algebra." pith.science (2026). https://pith.science/paper/MA2R2VNP

@misc{pith2026250619598,
  author       = {Pith},
  title        = {Pith review of: Training Flexible Models of Genetic Variant Effects from Functional Annotations using Accelerated Linear Algebra},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MA2R2VNP}},
  note         = {Machine review of arXiv:2506.19598}
}
read the original abstract

To understand how genetic variants in human genomes manifest in phenotypes -- traits like height or diseases like asthma -- geneticists have sequenced and measured hundreds of thousands of individuals. Geneticists use this data to build models that predict how a genetic variant impacts phenotype given genomic features of the variant, like DNA accessibility or the presence of nearby DNA-bound proteins. As more data and features become available, one might expect predictive models to improve. Unfortunately, training these models is bottlenecked by the need to solve expensive linear algebra problems because variants in the genome are correlated with nearby variants, requiring inversion of large matrices. Previous methods have therefore been restricted to fitting small models, and fitting simplified summary statistics, rather than the full likelihood of the statistical model. In this paper, we leverage modern fast linear algebra techniques to develop DeepWAS (Deep genome Wide Association Studies), a method to train large and flexible neural network predictive models to optimize likelihood. Notably, we find that larger models only improve performance when using our full likelihood approach; when trained by fitting traditional summary statistics, larger models perform no better than small ones. We find larger models trained on more features make better predictions, potentially improving disease predictions and therapeutic target identification.

Figures

Figures reproduced from arXiv: 2506.19598 by the authors.

Figure 1
Figure 1. DeepWAS enables training large models to predict the effect of variants from genomic features by leveraging fast linear algebra. Top: We want to train a model, fθ, to predict the effect of a variant in our genome from a large set of curated genomic features in a window around the variant. Bottom: We train fθ to maximize the likelihood of observed associations be￾tween variants and traits. We efficiently compute the … view at source ↗
Figure 2
Figure 2. DeepWAS efficiently computes the loss and its gradi￾ent. We measure the time it takes to compute our loss Eqn. 3 as well as its gradients with respect to θ. We do this for 20 mini-batches of real UKBB data and display the mean runtime as barplots. Chol stands for Cholesky decomposition. Iter stands for the iterative algorithms SLQ and CG. Nys stands for the itera￾tive algorithms with Nystrom preconditioning. We set … view at source ↗
Figure 4
Figure 4. DeepWAS using a transformer model best recovers the true f. The bars represent the RMSE difference between the learnt fθ and the ground truth f in the log space evaluated over a set of validation functional annotations. do not have access to real f in real data. We therefor turn to semi-synthetic simulations, which are a staple of statistical genetics literature (ex. Candes et al. ` (2016) or O’Connor et al. (2019))… view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: More flexible models trained with DeepWAS better explain phenotype using held-out chromosomes. We try to predict the phenotype y of individuals in UK Biobank using only variants in held out chromosomes 6, 7, 8 as in Eqn. 1. We report how much the marginal likelihoods i…
Figure 6
Figure 6. Figure 6: Ablations show that larger models with more features better explain genetic associations. We ablate the number of vari￾ants in an LD window ((i) +), the feature set (w and the presence of conservation features) and the model size of our transformer-based model. We repo…
Figure 7
Figure 7. Figure 7: DeepWAS using a transformer model best recovers the true f even in a challenging setting. The bars represent the RMSE difference between the learnt fθ and the ground truth f in the log space evaluated over a set of validation functional annotations. B.2. Ablation resul…

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Reference graph

Works this paper leans on

56 extracted references · 54 canonical work pages

  1. [1]

    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION format.date year duplicate empty "emp...

  2. [2]

    R., Grabska-Barwinska, A., Taylor, K

    Avsec, Z., Agarwal, V., Visentin, D., Ledsam, J. R., Grabska-Barwinska, A., Taylor, K. R., Assael, Y., Jumper, J., Kohli, P., and Kelley, D. R. Effective gene expression prediction from sequence by integrating long-range interactions. bioRxiv, pp.\ 2021.04.07.438649, 2021

    work page 2021

  3. [3]

    H., Etheridge, A

    Barton, N. H., Etheridge, A. M., and Véber, A. The infinitesimal model. bioRxiv, February 2016

    work page 2016

  4. [4]

    and Pickrell, J

    Berisa, T. and Pickrell, J. K. Approximately independent linkage disequilibrium blocks in human populations. Bioinformatics, 32 0 (2): 0 283--285, January 2016

    work page 2016

  5. [5]

    A., Li, Y

    Boyle, E. A., Li, Y. I., and Pritchard, J. K. An expanded view of complex traits: From polygenic to omnigenic. Cell, 169 0 (7): 0 1177--1186, June 2017

    work page 2017

  6. [6]

    K., Loh, P.-R., Finucane, H

    Bulik-Sullivan, B. K., Loh, P.-R., Finucane, H. K., Ripke, S., Yang, J., Schizophrenia Working Group of the Psychiatric Genomics Consortium , Patterson, N., Daly, M. J., Price, A. L., and Neale, B. M. LD score regression distinguishes confounding from polygenicity in genome-wide association studies. Nat. Genet., 47 0 (3): 0 291--295, March 2015

    work page 2015

  7. [7]

    Panning for gold: ‘model‐x’ knockoffs for high dimensional controlled variable selection

    Candès, E., Fan, Y., Janson, L., and Lv, J. Panning for gold: ‘model‐x’ knockoffs for high dimensional controlled variable selection. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 80, October 2016

    work page 2016

  8. [8]

    M., DenAdel, A., and Crawford, L

    Conard, A. M., DenAdel, A., and Crawford, L. A spectrum of explainable and interpretable machine learning approaches for genomic studies. Wiley Interdiscip. Rev. Comput. Stat., May 2023

    work page 2023

Show all 56 references
  1. [9]

    M., Stone, E

    Cooper, G. M., Stone, E. A., Asimenos, G., NISC Comparative Sequencing Program , Green, E. D., Batzoglou, S., and Sidow, A. Distribution and intensity of constraint in mammalian genomic sequence. Genome Res., 15 0 (7): 0 901--913, July 2005

    2005

  2. [10]

    M., Carranza, N

    Dalla-Torre, H., Gonzalez, L., Revilla, J. M., Carranza, N. L., Grzywaczewski, A. H., Oteri, F., Dallago, C., Trop, E., Sirelkhatim, H., Richard, G., Skwark, M., Beguir, K., Lopez, M., and Pierrot, T. The nucleotide transformer: Building and evaluating robust foundation models...

    2023

  3. [11]

    An integrated encyclopedia of DNA elements in the human genome

    ENCODE Project Consortium . An integrated encyclopedia of DNA elements in the human genome. Nature, 489 0 (7414): 0 57--74, September 2012

    2012

  4. [12]

    S., Moore, J

    Fabiha, T., Evergreen, I., Kundu, S., Pampari, A., Abramov, S., Boytsov, A., Strouse, K., Dura, K., Fang, W., Kerner, G., Butts, J., Ali, T., Gschwind, A., Mualim, K. S., Moore, J. E., Weng, Z., Ulirsch, J., Ji, H. E., Vierstra, J., Reddy, T. E., Montgomery, S. B., Engreitz, J...

    2024

  5. [13]

    K., Bulik-Sullivan, B., Gusev, A., Trynka, G., Reshef, Y., Loh, P.-R., Anttila, V., Xu, H., Zang, C., Farh, K., Ripke, S., Day, F

    Finucane, H. K., Bulik-Sullivan, B., Gusev, A., Trynka, G., Reshef, Y., Loh, P.-R., Anttila, V., Xu, H., Zang, C., Farh, K., Ripke, S., Day, F. R., ReproGen Consortium , Schizophrenia Working Group of the Psychiatric Genomics Consortium , RACI Consortium , Purcell, S., Stahl, ...

    2015

  6. [14]

    A., and Udell, M

    Frangella, Z., Tropp, J. A., and Udell, M. Randomized Nystr\" o m Preconditioning . arXiv 2110.02820v2, 2021

    2021 arXiv

  7. [15]

    R., Pleiss, G., Bindel, D., Weinberger, K

    Gardner, J. R., Pleiss, G., Bindel, D., Weinberger, K. Q., and Wilson, A. G. GPyTorch : blackbox matrix-matrix gaussian process inference with GPU acceleration. In Proceedings of the 32nd International Conference on Neural Information Processing Systems, NIPS'18, pp.\ 7587--75...

    2018

  8. [16]

    K., Furlotte, N

    Gazal, S., Finucane, H. K., Furlotte, N. A., Loh, P.-R., Palamara, P. F., Liu, X., Schoech, A., Bulik-Sullivan, B., Neale, B. M., Gusev, A., and Price, A. L. Linkage disequilibrium-dependent architecture of human complex traits shows action of negative selection. Nat. Genet., ...

    2017

  9. [17]

    Golub, G. H. and Loan, C. F. V. Matrix Computations . The Johns Hopkins University Press, 2018. Fourth Edition

    2018

  10. [18]

    H., Trynka, G., Finucane, H., Vilhjálmsson, B

    Gusev, A., Lee, S. H., Trynka, G., Finucane, H., Vilhjálmsson, B. J., Xu, H., Zang, C., Ripke, S., Bulik-Sullivan, B., Stahl, E., Schizophrenia Working Group of the Psychiatric Genomics Consortium , SWE-SCZ Consortium , Kähler, A. K., Hultman, C. M., Purcell, S. M., McCarroll,...

    2014

  11. [19]

    V., Eggertsson, H

    Halldorsson, B. V., Eggertsson, H. P., Moore, K. H. S., Hauswedell, H., Eiriksson, O., Ulfarsson, M. O., Palsson, G., Hardarson, M. T., Oddsson, A., Jensson, B. O., Kristmundsdottir, S., Sigurpalsdottir, B. D., Stefansson, O. A., Beyter, D., Holley, G., Tragante, V., Gylfason,...

    2021

  12. [20]

    Handbook of Linear Algebra

    Hogben, L. Handbook of Linear Algebra . Chapman and Hall/CRC, 2013

    2013

  13. [21]

    Y., Pasaniuc, B., and Eskin, E

    Hormozdiari, F., Kostem, E., Kang, E. Y., Pasaniuc, B., and Eskin, E. Identifying causal variants at loci with multiple signals of association. Genetics, 198 0 (2): 0 497--508, October 2014

    2014

  14. [22]

    S., Majumdar, A., Shi, H., Mancuso, N., Wu, Y., Sankararaman, S., and Pasaniuc, B

    Hou, K., Burch, K. S., Majumdar, A., Shi, H., Mancuso, N., Wu, Y., Sankararaman, S., and Pasaniuc, B. Accurate estimation of SNP -heritability from biobank-scale data irrespective of genetic architecture. Nat. Genet., 51 0 (8): 0 1244--1251, August 2019

    2019

  15. [23]

    G., Cortes, A., Aiello, K., Branson, K., Pfenning, A., Engreitz, J

    Huang, K., Zeng, T., Koc, S., Pettet, A., Zhou, J., Jain, M., Sun, D., Ruiz, C., Ren, H., Howe, L., Richardson, T. G., Cortes, A., Aiello, K., Branson, K., Pfenning, A., Engreitz, J. M., Zhang, M. J., and Leskovec, J. Small-cohort GWAS discovery with AI over massive functional...

    2024

  16. [24]

    J., Pollard, K

    Hubisz, M. J., Pollard, K. S., and Siepel, A. PHAST and RPHAST : phylogenetic analysis with space/time models. Brief. Bioinform., 12 0 (1): 0 41--51, January 2011

    2011

  17. [25]

    K., Schoech, A., Pasaniuc, B., and Price, A

    Kichaev, G., Bhatia, G., Loh, P.-R., Gazal, S., Burch, K., Freund, M. K., Schoech, A., Pasaniuc, B., and Price, A. L. Leveraging polygenic functional enrichment to improve GWAS power. Am. J. Hum. Genet., 104 0 (1): 0 65--75, January 2019

    2019

  18. [26]

    R., Boehnke, M., and Lin, X

    Lee, S., Abecasis, G. R., Boehnke, M., and Lin, X. Rare-variant association analysis: study designs and statistical tests. Am. J. Hum. Genet., 95 0 (1): 0 5--23, July 2014

    2014

  19. [27]

    Improved heritability partitioning and enrichment analyses using summary statistics with graphREML

    Li, H., Kamath, T., Mazumder, R., Lin, X., and O'Connor, L. Improved heritability partitioning and enrichment analyses using summary statistics with graphREML . Genetic and Genomic Medicine, 0 (medrxiv;2024.11.04.24316716v1), November 2024

    2024

  20. [28]

    M., Liu, Y., Chen, H., Sun, R., Dey, R., Arnett, D

    Li, X., Li, Z., Zhou, H., Gaynor, S. M., Liu, Y., Chen, H., Sun, R., Dey, R., Arnett, D. K., Aslibekyan, S., Ballantyne, C. M., Bielak, L. F., Blangero, J., Boerwinkle, E., Bowden, D. W., Broome, J. G., Conomos, M. P., Correa, A., Cupples, L. A., Curran, J. E., Freedman, B. I....

    2020

  21. [29]

    dbNSFP v4 : a comprehensive database of transcript-specific functional predictions and annotations for human nonsynonymous and splice-site SNVs

    Liu, X., Li, C., Mou, C., Dong, Y., and Tu, Y. dbNSFP v4 : a comprehensive database of transcript-specific functional predictions and annotations for human nonsynonymous and splice-site SNVs . Genome Med., 12 0 (1): 0 103, December 2020

    2020

  22. [30]

    J., Arner, E., Baillie, J

    Lizio, M., Harshbarger, J., Shimoji, H., Severin, J., Kasukawa, T., Sahin, S., Abugessaisa, I., Fukuda, S., Hori, F., Ishikawa-Kato, S., Mungall, C. J., Arner, E., Baillie, J. K., Bertin, N., Bono, H., de Hoon, M., Diehl, A. D., Dimont, E., Freeman, T. C., Fujieda, K., Hide, W...

    2015

  23. [31]

    K., Vilhjálmsson, B

    Loh, P.-R., Tucker, G., Bulik-Sullivan, B. K., Vilhjálmsson, B. J., Finucane, H. K., Salem, R. M., Chasman, D. I., Ridker, P. M., Neale, B. M., Berger, B., Patterson, N., and Price, A. L. Efficient bayesian mixed-model analysis increases association power in large cohorts. Nat...

    2015

  24. [32]

    P., and Price, A

    Loh, P.-R., Kichaev, G., Gazal, S., Schoech, A. P., and Price, A. L. Mixed-model association for biobank-scale datasets. Nat. Genet., 50 0 (7): 0 906--908, July 2018

    2018

  25. [33]

    GenoWAP : GWAS signal prioritization through integrated analysis of genomic functional annotation

    Lu, Q., Yao, X., Hu, Y., and Zhao, H. GenoWAP : GWAS signal prioritization through integrated analysis of genomic functional annotation. Bioinformatics, 32 0 (4): 0 542--548, February 2016

    2016

  26. [34]

    A., Collins, F

    Manolio, T. A., Collins, F. S., Cox, N. J., Goldstein, D. B., Hindorff, L. A., Hunter, D. J., McCarthy, M. I., Ramos, E. M., Cardon, L. R., Chakravarti, A., Cho, J. H., Guttmacher, A. E., Kong, A., Kruglyak, L., Mardis, E., Rotimi, C. N., Slatkin, M., Valle, D., Whittemore, A....

    2009

  27. [35]

    A flexible empirical bayes approach to multivariate multiple regression, and its improved accuracy in predicting multi-tissue gene expression from genotypes

    Morgante, F., Carbonetto, P., Wang, G., Zou, Y., Sarkar, A., and Stephens, M. A flexible empirical bayes approach to multivariate multiple regression, and its improved accuracy in predicting multi-tissue gene expression from genotypes. PLoS Genet., 19 0 (7): 0 e1010539, July 2023

    2023

  28. [36]

    R., and Lee, S

    Ni, G., Moser, G., Schizophrenia Working Group of the Psychiatric Genomics Consortium , Wray, N. R., and Lee, S. H. Estimation of genetic correlation via linkage disequilibrium score regression and genomic restricted maximum likelihood. Am. J. Hum. Genet., 102 0 (6): 0 1185--1...

    2018

  29. [37]

    and Wright, S

    Nocedal, J. and Wright, S. J. Numerical Optimization . Springer, 2006. Second Edition

    2006

  30. [38]

    J., Schoech, A

    O'Connor, L. J., Schoech, A. P., Hormozdiari, F., Gazal, S., Patterson, N., and Price, A. L. Extreme polygenicity of complex traits is explained by negative selection. Am. J. Hum. Genet., 105 0 (3): 0 456--476, September 2019

    2019

  31. [39]

    PyTorch : An imperative style, high-performance deep learning library

    Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., Köpf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., and Chintala, S. PyTorch : An imper...

    2019

  32. [40]

    S., Hubisz, M

    Pollard, K. S., Hubisz, M. J., Rosenbloom, K. R., and Siepel, A. Detection of nonneutral substitution rates on mammalian phylogenies. Genome Res., 20 0 (1): 0 110--121, January 2010

    2010

  33. [41]

    Potapczynski, A., Finzi, M., Pleiss, G., and Wilson, A. G. CoLA: Exploiting Compositional Structure for Automatic and Efficient Numerical Linear Algebra . Advances in Neural Information Processing Systems (NeurIPS), 2023

    2023

  34. [42]

    Iterative Methods for Sparse Linear Systems

    Saad, Y. Iterative Methods for Sparse Linear Systems . SIAM, 2003

    2003

  35. [43]

    Numerical methods for large eigenvalue problems

    Saad, Y. Numerical methods for large eigenvalue problems . SIAM, 2011

    2011

  36. [44]

    W., Ballard, J

    Salehi Nowbandegani, P., Wohns, A. W., Ballard, J. L., Lander, E. S., Bloemendal, A., Neale, B. M., and O'Connor, L. J. Extremely sparse models of linkage disequilibrium in ancestrally diverse association studies. Nat. Genet., 55 0 (9): 0 1494--1502, September 2023

    2023

  37. [45]

    E., Robinson, E

    Samocha, K. E., Robinson, E. B., Sanders, S. J., Stevens, C., Sabo, A., McGrath, L. M., Kosmicki, J. A., Rehnström, K., Mallick, S., Kirby, A., Wall, D. P., MacArthur, D. G., Gabriel, S. B., DePristo, M., Purcell, S. M., Palotie, A., Boerwinkle, E., Buxbaum, J. D., Cook, Jr, E...

    2014

  38. [46]

    Contrasting the genetic architecture of 30 complex traits from summary association data

    Shi, H., Kichaev, G., and Pasaniuc, B. Contrasting the genetic architecture of 30 complex traits from summary association data. Am. J. Hum. Genet., 99 0 (1): 0 139--153, July 2016

    2016

  39. [47]

    R., Nejentsev, S., and Balding, D

    Speed, D., Cai, N., UCLEB Consortium , Johnson, M. R., Nejentsev, S., and Balding, D. J. Reevaluation of SNP heritability in complex human traits. Nat. Genet., 49 0 (7): 0 986--992, July 2017

    2017

  40. [48]

    P., Sinnott-Armstrong, N., Assimes, T

    Spence, J. P., Sinnott-Armstrong, N., Assimes, T. L., and Pritchard, J. K. A flexible modeling and inference framework for estimating variant effect sizes from GWAS summary statistics. bioRxiv, April 2022

    2022

  41. [49]

    V., Xiao, L., Chopra, A., Chaffin, M

    Theodoris, C. V., Xiao, L., Chopra, A., Chaffin, M. D., Al Sayed, Z. R., Hill, M. C., Mantineo, H., Brydon, E. M., Zeng, Z., Liu, X. S., and Ellinor, P. T. Transfer learning enables predictions in network biology. Nature, 618 0 (7965): 0 616--624, May 2023

    2023

  42. [50]

    For high-dimensional hierarchical models, consider exchangeability of effects across covariates instead of across datasets

    Trippe, B., Finucane, H., and Broderick, T. For high-dimensional hierarchical models, consider exchangeability of effects across covariates instead of across datasets. In Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P. S., and Vaughan, J. W. (eds.), Advances in Neural Inf...

    2021

  43. [51]

    M., Wray, N

    Visscher, P. M., Wray, N. R., Zhang, Q., Sklar, P., McCarthy, M. I., Brown, M. A., and Yang, J. 10 years of GWAS discovery: Biology, function, and translation. Am. J. Hum. Genet., 101 0 (1): 0 5--22, July 2017

    2017

  44. [52]

    M., Ulirsch, J

    Weeks, E. M., Ulirsch, J. C., Cheng, N. Y., Trippe, B. L., Fine, R. S., Miao, J., Patwardhan, T. A., Kanai, M., Nasser, J., Fulco, C. P., Tashman, K. C., Aguet, F., Li, T., Ordovas-Montanes, J., Smillie, C. S., Biton, M., Shalek, A. K., Ananthakrishnan, A. N., Xavier, R. J., R...

    2020

  45. [53]

    P., van de Geijn, B., Reshef, Y., Márquez-Luna, C., O'Connor, L., Pirinen, M., Finucane, H

    Weissbrod, O., Hormozdiari, F., Benner, C., Cui, R., Ulirsch, J., Gazal, S., Schoech, A. P., van de Geijn, B., Reshef, Y., Márquez-Luna, C., O'Connor, L., Pirinen, M., Finucane, H. K., and Price, A. L. Functionally informed fine-mapping and polygenic localization of complex tr...

    2020

  46. [54]

    P., Gordon, S., Henders, A

    Yang, J., Benyamin, B., McEvoy, B. P., Gordon, S., Henders, A. K., Nyholt, D. R., Madden, P. A., Heath, A. C., Martin, N. G., Montgomery, G. W., Goddard, M. E., and Visscher, P. M. Common SNPs explain a large proportion of the heritability for human height. Nat. Genet., 42 0 (...

    2010

  47. [55]

    Improved genetic prediction of complex traits from individual-level data or summary statistics

    Zhang, Q., Privé, F., Vilhjálmsson, B., and Speed, D. Improved genetic prediction of complex traits from individual-level data or summary statistics. Nat. Commun., 12 0 (1): 0 4192, July 2021

    2021

  48. [56]

    M., Snieder, H., LifeLines Cohort Study , Yang, J., Wray, N

    Zheng, Z., Liu, S., Sidorenko, J., Wang, Y., Lin, T., Yengo, L., Turley, P., Ani, A., Wang, R., Nolte, I. M., Snieder, H., LifeLines Cohort Study , Yang, J., Wray, N. R., Goddard, M. E., Visscher, P. M., and Zeng, J. Leveraging functional genomic annotations and genome coverag...

    2024

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.