HaploADMIXTURE.jl

This software package is an open-source Julia implementation of HaploADMIXTURE, ancestry inference by modeling haplotypes. By modeling haplotypes, we use information between nearby SNPs, obtaining more accurate ancestry estimates.

It supports acceleartion through multithreading and graphic processing units (GPUs). By directly utilizing the data format of the PLINK BED file, the memory usage is highly efficient.

It estimates ancestry with maximum-likelihood method for a large SNP genotype datasets, where individuals are assumed to be unrelated. The input is binary PLINK 1 BED-formatted file (.bed). Also, you will need an idea of $K$, the number of ancestral populations. One possible way to figure out a good value of $K$ is through Akaike information criterion. If the number of SNPs is too large, you may choose to run on a subset of SNPs selected by their information content, using the blockwise sparse $K$-means via feature ranking (SKFR) method. When SKFR is applied, it selects given number of blocks of two nearby SNPs.

Installation

This package requires Julia v1.7 or later, which can be obtained from https://julialang.org/downloads/ or by building Julia from the sources in the https://github.com/JuliaLang/julia repository.

The package can be installed by running the following code:

using Pkg
pkg"add https://github.com/kose-y/SparseKmeansFeatureRanking.jl"
pkg"add https://github.com/OpenMendel/OpenADMIXTURE.jl"
pkg"add https://github.com/OpenMendel/HaploADMIXTURE.jl"

For running the examples below, the following are also necessary.

pkg"add SnpArrays DelimitedFiles StableRNGs"

For GPU support, an Nvidia GPU is required. Also, the following package has to be installed:

pkg"add CUDA"

Basic Usage

We first import necessary packages:

using LinearAlgebra, Random, SnpArrays, StableRNGs
using HaploADMIXTURE
using DelimitedFiles

We will use the PLINK file included in the SnpArrays package, whose path is obtained by:

filename = SnpArrays.datadir("EUR_subset.bed");

This file contains information on 54,051 single nucleotide polymorphisms (SNP)s of 379 samples. The main driver function for admixture proportion estimation is called run_admixture().

d, clusters, aims = HaploADMIXTURE.run_admixture(filename, 379, 27025, 4; T=Float64, use_gpu=false, rng=StableRNG(7856), admix_rtol=1e-5)

Using /home/kose/.julia/packages/SnpArrays/lx5Kb/src/../data/EUR_subset.bed as input.
Loading genotype data...
Loaded 379 samples and 27025 SNPs


[ Info: EM iter 1, ll: -1.4510327066059288e7
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[ Info: EM iter 3, ll: -1.3630461295722805e7
[ Info: EM iter 4, ll: -1.3583905487448066e7
[ Info: EM iter 5, ll: -1.3560929046308124e7


initial ll: -1.3560929046308124e7
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[ Info: Iteration 1: ll=-1.3442143002068464e7, reldiff = 0.008759432619551937, ll_basic=-1.3439421296893205e7, ll_qn=-1.3442143002068464e7


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[ Info: Iteration 2: ll=-1.3383453322742362e7, reldiff = 0.004366095444533735, ll_basic=-1.3388259907460274e7, ll_qn=-1.3383453322742362e7


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[ Info: Iteration 3: ll=-1.3363811617880553e7, reldiff = 0.0014676111156177924, ll_basic=-1.3367645714833554e7, ll_qn=-1.3363811617880553e7


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[ Info: Iteration 4: ll=-1.3355847390914964e7, reldiff = 0.0005959547465435272, ll_basic=-1.3355426940109456e7, ll_qn=-1.3355847390914964e7


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[ Info: Iteration 5: ll=-1.3350276186759759e7, reldiff = 0.0004171359549222248, ll_basic=-1.3349978349386934e7, ll_qn=-1.3350276186759759e7


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[ Info: Iteration 6: ll=-1.3347625577409597e7, reldiff = 0.00019854340937084056, ll_basic=-1.3348060337232983e7, ll_qn=-1.3347625577409597e7


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[ Info: Iteration 7: ll=-1.3346229272063218e7, reldiff = 0.00010461076678253966, ll_basic=-1.3346683678589227e7, ll_qn=-1.3346229272063218e7


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[ Info: Iteration 8: ll=-1.3345567893618163e7, reldiff = 4.95554535721753e-5, ll_basic=-1.3345705325338118e7, ll_qn=-1.3345567893618163e7


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[ Info: Iteration 9: ll=-1.334485185488965e7, reldiff = 5.365367245669872e-5, ll_basic=-1.334492648906096e7, ll_qn=-1.334485185488965e7


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[ Info: Iteration 10: ll=-1.3344485904661845e7, reldiff = 2.7422577019496487e-5, ll_basic=-1.334448965648377e7, ll_qn=-1.3344485904661845e7


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[ Info: Iteration 11: ll=-1.3344174847778792e7, reldiff = 2.3309768939482905e-5, ll_basic=-1.3344216738217931e7, ll_qn=-1.3344174847778792e7


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[ Info: Iteration 12: ll=-1.3344074094647754e7, reldiff = 7.550345539300909e-6, ll_basic=-1.3344002897805652e7, ll_qn=-1.3344074094647754e7





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Matrix{Int64}, Tuple{Base.Slice{Base.OneTo{Int64}}, Int64}, true}[[4, 2, 1, 3]], -1.3344174847778792e7, -1.3344074094647754e7), nothing, nothing)

The first argument is the path to the PLINK 1 .bed, and the second argument is the number of populations. The second through fourth arguments are:

• I: Number of individuals. We use first I individuals in the PLINK file for the analysis.
• J: Number of pairs of SNPs to be used for analysis. We use the first 2J SNPs in the PLINK file for the analysis.
• K: Number of populations.

After the semicolon are the keyword arguments:

• T: Precision of the estimation. Float64 or Float32. Default Float64.
• use_gpu: Whether to use GPU for estimation. Default false.
• rng: Random number generator. Default Random.GLOBAL_RNG.
• prefix: Prefix of the PLINK file only with the SNPs selected using SKFR. The output file is named $(prefix)_$(K)_$(sparsity)aims.bed.
• sparsity: Number of pairs of SNPs selected by SKFR. Default nothing and skip SKFR.
• skfr_tries: Runs SKFR this many times and choose the best clustering. Default 1.
• skfr_max_inner_iter: Runs each SKFR for up to this many iterations or until convergence. Default 50.
• admix_n_iter: Maximum number of iterations for ADMIXTURE. Default 1000.
• admix_rtol: Convergence criteria in terms of relative change in loglikelihood. Default 1e-7.
• admix_n_em_iter: Number of EM iterations to get a good initial guess for estimation. Default 5.
• Q: Number of steps to be used in quasi-Newton acceleration. Default 3.

The output are:

• d: the strucutre to store Admixture data. In particular, d.p stores the allele frequencies and d.q stores the admixture proportions.
• clusters: cluster labels of each samples, nothing if sparsity == nothing.
• aims: The index of the selected SNPs in the decreasing order of importance, nothing if sparsity == nothing.

To see the admixture proportion of each sample:

d.q

4×379 Matrix{Float64}:
 0.0659306  1.0e-5    1.0e-5    0.139574  …  0.00558938  1.0e-5   1.0e-5
 0.293154   0.395224  0.244018  0.464112     1.0e-5      1.0e-5   1.0e-5
 0.282163   1.0e-5    1.0e-5    0.396304     0.511126    0.99997  0.99997
 0.358752   0.604756  0.755962  1.0e-5       0.483274    1.0e-5   1.0e-5

Each column represent each sample, and each row represent each population.

To see the haplotype frequencies of the first alleles listed in the .bim file accompanying the .bed file:

d.p

4×108100 Matrix{Float64}:
 0.00189887  0.150532   0.0251855  …  0.0739429  1.0e-5     0.921636
 1.0e-5      0.0597565  0.0138474     0.0957969  0.0133644  0.890829
 1.0e-5      0.0797001  0.0123388     0.0198118  0.0235794  0.951543
 1.0e-5      0.119816   1.0e-5        0.0223822  1.0e-5     0.977598

Number of columns here, 108100, is 4 * 27025. Again, each row represent each population. Each contiguous four-column block represent frequency of four haplotypes, adding up to 1. For example,

d.p[1, 1:4]

4-element Vector{Float64}:
 0.0018988672076842915
 0.1505318314348172
 0.025185507235799612
 0.8223837941216988

represents haplotype frequencies for the first pair of SNPs in the PLINK file, each representing 0|0, 0|1, 1|0, and 1|1, 0 representing "allele 1" and 1 representing "allele 2".

The following shows the final loglikelihood of the parameters.

d.ll_new

-1.3344074094647754e7

The following is an example with sparsity defined. This example uses 10000 pairs of SNPs, i.e., 20000 SNPs.

d, clusters, aims = HaploADMIXTURE.run_admixture(filename, 379, 1000, 4; T=Float64, use_gpu=false, rng=StableRNG(7856), sparsity=10000, admix_rtol=1e-5, prefix="./EUR_subset")

Using /home/kose/.julia/packages/SnpArrays/lx5Kb/src/../data/EUR_subset.bed as input.
cnt of sparse1:6
./EUR_subset_4_20000aims
Loading genotype data...
Loaded 379 samples and 1000 SNPs


[ Info: EM iter 1, ll: -547316.804613733
[ Info: EM iter 2, ll: -521503.5735092382
[ Info: EM iter 3, ll: -514347.542491849
[ Info: EM iter 4, ll: -512517.7818873565


initial ll: -511610.08923740947
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[ Info: EM iter 5, ll: -511610.08923740947



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[ Info: Iteration 1: ll=-501966.53702516266, reldiff = 0.01884941758404569, ll_basic=-501947.13329052314, ll_qn=-501966.53702516266


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[ Info: Iteration 2: ll=-498620.4953091312, reldiff = 0.006665866087132633, ll_basic=-498910.54886802484, ll_qn=-498620.4953091312


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[ Info: Iteration 3: ll=-497445.32079180575, reldiff = 0.0023568516103552833, ll_basic=-497607.99433348124, ll_qn=-497445.32079180575


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[ Info: Iteration 4: ll=-497020.8517256676, reldiff = 0.0008532979372737897, ll_basic=-496775.8041321521, ll_qn=-497020.8517256676


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[ Info: Iteration 5: ll=-496286.4337403602, reldiff = 0.0014776401890534093, ll_basic=-496197.0181752268, ll_qn=-496286.4337403602


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[ Info: Iteration 6: ll=-495895.1891810066, reldiff = 0.0007883442559671306, ll_basic=-495950.7511739665, ll_qn=-495895.1891810066


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[ Info: Iteration 7: ll=-495723.9311009382, reldiff = 0.00034535136416877547, ll_basic=-495711.0044130232, ll_qn=-495723.9311009382


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[ Info: Iteration 10: ll=-495434.2317792011, reldiff = 9.043144036009807e-5, ll_basic=-495450.64330562693, ll_qn=-495434.2317792011


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[ Info: Iteration 18: ll=-495212.7616815196, reldiff = 5.194170969036113e-6, ll_basic=-495211.77728309284, ll_qn=-495212.7616815196





(HaploADMIXTURE.AdmixData2{Float64, Float64}(379, 1000, 4, 3, [0.19148587979679502 0.44089456617600614 … 1.0e-5 0.9999699999999999; 1.0000000000083268e-5 0.09064853934975588 … 1.0e-5 0.9999699999999999; 0.5444656511551741 1.0e-5 … 1.0e-5 1.0e-5; 0.2640384690480307 0.4684468944742379 … 1.0e-5 0.9999699999999999], [0.19204916717925596 0.4419499763464079 … 1.0e-5 0.9999699999999999; 1.0e-5 0.07860189915065856 … 1.0e-5 0.9999699999999999; 0.5481446219156164 1.0e-5 … 1.0e-5 1.0e-5; 0.25979621090512767 0.47943812450293344 … 1.0e-5 0.9999699999999999], [0.19205385045603865 0.44222078722642627 … 1.0e-5 0.9999699999999999; 1.0e-5 0.08010309906324803 … 1.0e-5 0.9999699999999999; 0.5481027316667246 1.0e-5 … 1.0e-5 1.0e-5; 0.2598334178772366 0.4776661137103257 … 1.0e-5 0.9999699999999999], [0.19148587979679502 0.44089456617600614 … 1.0e-5 0.9999699999999999; 1.0000000000083268e-5 0.09064853934975588 … 1.0e-5 0.9999699999999999; 0.5444656511551741 1.0e-5 … 1.0e-5 1.0e-5; 0.2640384690480307 0.4684468944742379 … 1.0e-5 0.9999699999999999], [0.19148587979679502, 1.0000000000083268e-5, 0.5444656511551741, 0.2640384690480307, 0.44089456617600614, 0.09064853934975588, 1.0e-5, 0.4684468944742379, 0.5265130429702344, 1.0e-5  …  1.0e-5, 1.0e-5, 1.0e-5, 1.0e-5, 1.0e-5, 1.0e-5, 0.9999699999999999, 0.9999699999999999, 1.0e-5, 0.9999699999999999], [0.19204916717925596, 1.0e-5, 0.5481446219156164, 0.25979621090512767, 0.4419499763464079, 0.07860189915065856, 1.0e-5, 0.47943812450293344, 0.5258242818476563, 1.0e-5  …  1.0e-5, 1.0e-5, 1.0e-5, 1.0e-5, 1.0e-5, 1.0e-5, 0.9999699999999999, 0.9999699999999999, 1.0e-5, 0.9999699999999999], [0.19205385045603865, 1.0e-5, 0.5481027316667246, 0.2598334178772366, 0.44222078722642627, 0.08010309906324803, 1.0e-5, 0.4776661137103257, 0.5259409566596593, 1.0e-5  …  1.0e-5, 1.0e-5, 1.0e-5, 1.0e-5, 1.0e-5, 1.0e-5, 0.9999699999999999, 0.9999699999999999, 1.0e-5, 0.9999699999999999], [0.19148587979679502, 1.0000000000083268e-5, 0.5444656511551741, 0.2640384690480307, 0.44089456617600614, 0.09064853934975588, 1.0e-5, 0.4684468944742379, 0.5265130429702344, 1.0e-5  …  1.0e-5, 1.0e-5, 1.0e-5, 1.0e-5, 1.0e-5, 1.0e-5, 0.9999699999999999, 0.9999699999999999, 1.0e-5, 0.9999699999999999], [2.50486e-319, 1.325524e-318, 6.8995953889201e-310, 1.00286188e-315, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0  …  5.163e-321, 8.08e-321, 7.8003e-320, 0.0, 0.0, 8.3206e-320, 0.0, 0.0, 0.0, 2.16213e-319], [6.89959538901813e-310, 6.89959538901813e-310, 1.006423183e-315, 1.006423183e-315, 0.0, 0.0, 0.0, 6.89959461016475e-310, 5.0e-324, 1.0e-323  …  1.3631e-319, 1.36313e-319, 1.3632e-319, 1.36323e-319, 1.36367e-319, 1.3637e-319, 1.36407e-319, 1.3641e-319, 1.36426e-319, 1.3643e-319], [0.0 0.0 … 0.0 0.0], [0.19148587979679502 0.44089456617600614 … 1.0e-5 1.0e-5; 1.0000000000083268e-5 0.09064853934975588 … 0.31555137081498785 0.2863315643504618; 0.5444656511551741 1.0e-5 … 0.6844286291850121 0.7136484356495382; 0.2640384690480307 0.4684468944742379 … 1.0e-5 1.0e-5], 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6.8992469432701e-310, 6.8992469432859e-310, 6.8992469433096e-310, 6.8992469433017e-310, 6.8992469433254e-310, 6.89924694320684e-310, 6.89958441251503e-310, 6.89924694334913e-310, 5.1e-322]], SubArray{Float64, 1, Matrix{Float64}, Tuple{Base.Slice{Base.OneTo{Int64}}, Int64}, true}[[6.89924727700866e-310, 6.89924727701103e-310, 6.8992472770134e-310, 6.8992472770158e-310, 6.89924727701815e-310, 6.8992472770205e-310, 6.8992472770229e-310, 6.89924727702526e-310, 6.89924727702763e-310, 6.89924727703e-310  …  6.89924727703475e-310, 6.8992472770371e-310, 6.8992472770395e-310, 6.89924727704186e-310, 6.8992472770466e-310, 6.89924727705846e-310, 6.89924727706083e-310, 6.8992472770632e-310, 6.8992472770656e-310, 5.1e-322]], SubArray{Float64, 2, Array{Float64, 3}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}[[6.8986079087876e-310 6.8986109990504e-310 … 6.8986110040045e-310 6.8986110040211e-310; 6.8986087332606e-310 6.8986109990528e-310 … 6.89861100400688e-310 6.89861100402585e-310; … ; 6.89861099904567e-310 6.89861099906227e-310 … 6.89861100401636e-310 6.8986110040377e-310; 6.89861099904804e-310 6.8986109990694e-310 … 6.89861100401873e-310 6.8986110040709e-310]], SubArray{Float64, 2, Array{Float64, 3}, Tuple{Base.Slice{Base.OneTo{Int64}}, Base.Slice{Base.OneTo{Int64}}, Int64}, true}[[6.2167845e-317 2.00995441320324e-310 … 6.89957362919754e-310 6.8995940698838e-310; 5.432371392717e-312 2.06427750545196e-310 … 6.89957362919754e-310 6.8994571147446e-310; … ; 1.9013082287058e-310 3.0420931659296e-310 … 6.89957362919754e-310 NaN; 1.95563132095453e-310 3.0964162581783e-310 … 6.2582252e-316 7.6592171e-316]], SubArray{Bool, 1, Matrix{Bool}, Tuple{Base.Slice{Base.OneTo{Int64}}, Int64}, true}[[1, 1, 1, 1]], SubArray{Bool, 1, Matrix{Bool}, Tuple{Base.Slice{Base.OneTo{Int64}}, Int64}, true}[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1]], [3; 2; 4; 1;;], SubArray{Int64, 1, Matrix{Int64}, Tuple{Base.Slice{Base.OneTo{Int64}}, Int64}, true}[[3, 2, 4, 1]], [4; 3; 1; 2;;], SubArray{Int64, 1, Matrix{Int64}, Tuple{Base.Slice{Base.OneTo{Int64}}, Int64}, true}[[4, 3, 1, 2]], -495215.33391463046, -495212.7616815196), [1, 2, 1, 4, 2, 1, 2, 3, 2, 1  …  1, 4, 1, 2, 4, 4, 1, 4, 4, 4], [5717, 5718, 43817, 43818, 43821, 43822, 51813, 51814, 5835, 5836  …  35113, 35114, 44757, 44758, 2073, 2074, 26917, 26918, 6533, 6534])

The following shows the clustering result of the samples:

clusters

379-element Vector{Int64}:
 1
 2
 1
 4
 2
 1
 2
 3
 2
 1
 1
 1
 1
 ⋮
 1
 4
 1
 4
 1
 2
 4
 4
 1
 4
 4
 4

And the following shows the SNPs selected.

aims

20000-element Vector{Int64}:
  5717
  5718
 43817
 43818
 43821
 43822
 51813
 51814
  5835
  5836
  5651
  5652
  5813
     ⋮
 14511
 14512
 35113
 35114
 44757
 44758
  2073
  2074
 26917
 26918
  6533
  6534

The allele frequencies can be shown as in:

d.p

4×40000 Matrix{Float64}:
 0.201256   0.0740125  0.0199012  0.70483   …  1.0e-5  0.283447  0.601149
 0.0827117  0.0387316  0.0107814  0.867775     1.0e-5  0.309742  0.340943
 0.153377   0.0370591  1.0e-5     0.809554     1.0e-5  0.261117  0.563059
 0.180305   0.0516882  1.0e-5     0.767997     1.0e-5  0.31928   0.518856

!!! The order of alleles is in the order of index (as in sort(aim)). This can be verified by checking the .bim file generated along with the newly filtered .bed file.

The admixture proportions can be viewed by:

d.q

4×379 Matrix{Float64}:
 1.0e-5     0.333264  0.276992  0.215578  …  0.934272   1.0e-5   1.0e-5
 0.0728986  0.133901  0.151148  0.116068     0.0259248  1.0e-5   1.0e-5
 0.495104   0.532825  0.57185   0.142498     0.0397931  1.0e-5   1.0e-5
 0.431987   1.0e-5    1.0e-5    0.525857     1.0e-5     0.99997  0.99997

d.ll_new

-5.046319427299974e6

Multithreading

If you have multiple CPU cores available, it is recommended to launch Julia with multiple threads, for example, by using -t option from the terminal:

julia -t 8

You may also set up a multithreaded Jupyter kernel following the instruction given here.

GPU support

GPU is enabled by setting the keyword argument use_gpu to true. The parts computing gradients and Hessians of the loglikelihood is moved to GPU.