BLUP model solving method and system capable of obviating genetic relationship matrix inversion, device and medium

Abstract

The present invention relates to the technical field of animal breeding. Disclosed are a BLUP model solving method and system capable of obviating genetic relationship matrix inversion, a device and a medium. The method comprises: constructing an original BLUP model, wherein the original BLUP model comprises a genetic relationship matrix and a matrix containing a fixed effect; and multiplying both sides of a matrix equation in the original BLUP model by a set intermediate matrix, constructing a unit matrix of a G matrix and a G-1 matrix in the original BLUP model, and performing model solving on the basis of obviating genetic relationship matrix inversion to obtain a breeding value. The present invention can directly obviate genetic relationship matrix version, thereby halving the calculation amount in the BLUP model solving process, significantly increasing the calculation speed of BLUP model solving, and maintaining the accuracy of breeding value estimation without loss.

Description

BLUP model solving method, system, device and medium for avoiding inverse of kinship matrix TECHNICAL FIELD

[0001] The present application relates to the field of animal breeding technology, in particular to a BLUP model solving method, system, device and medium for avoiding inverse of kinship matrix. BACKGROUND

[0002] Animal breeding emphasizes improvement and promotion from genetic structure. The scientific theory of modern breeding can be traced back to the rediscovery of Mendel's law of inheritance in 1900. Breeding work can only be carried out according to scientific genetic laws. Systematic breeding of domestic animals has made great progress after World War II. C. R. Henderson, an American statistician, developed BLUP (Best Linear Unbiased Prediction) in the 1960s of last century, which made a decisive contribution to the calculation technology. BLUP model optimizes breeding selection by estimating empirical best prediction value (EBV). Using BLUP to evaluate the genetic potential of animals is a standard method commonly used by countries around the world.

[0003] With the reduction of sequencing technology cost, the amount of data obtained by gene chip sequencing is increasing, and the application of GBLUP model in animal breeding becomes more widespread. However, this increasing amount of data also brings new challenges: when the number of animals becomes extremely large, the traditional calculation method faces huge calculation pressure and resource limitation. Processing large-scale data sets requires a large amount of computing resources, especially when complex genetic evaluation and large matrix operations are involved. Therefore, how to improve the calculation efficiency of BLUP model on large-scale data sets while maintaining its accuracy has become an urgent problem to be solved.

[0004] The traditional BLUP model has the problem of low calculation efficiency when solving EBV on large-scale data sets, mainly because it involves two matrix inversion operations, one of which is the inverse of the kinship matrix, and the other is the inverse of a larger matrix containing fixed effects. Matrix inversion operation is a step with extremely high computational consumption, so optimizing this process is crucial to improve the solving efficiency of BLUP model.

[0005] In ABLUP, the first matrix inversion is the inversion of A matrix. In 1975, Henderson proposed a simple method to construct A -1 directly from pedigree. Iterative method directly constructs A -1Avoid the first matrix inversion, to a certain extent, improve the operation efficiency of ABLUP. In GBLUP, Apy algorithm proposes to divide the population into core group (c) and non-core group (n), which can directly construct G -1 , there is an inverse of the core group matrix in the construction process. Reducing the number of core groups, the accuracy of the breeding value estimation is reduced, and in large-scale population, the inverse of the core matrix is still difficult. The existing Apy algorithm and ssGBLUP algorithm cannot avoid the inverse of the large matrix, and the accuracy of the breeding value estimation is lost.

[0006] SUMMARY

[0007] The purpose of the present application is to provide a BLUP model solving method, system, device and medium which avoids the inverse of the kinship matrix, can directly avoid the inverse of the kinship matrix, reduce the calculation amount in the BLUP model solving process by half, significantly improve the calculation speed of the BLUP model solving, and maintain the lossless accuracy of the breeding value estimation.

[0008] To achieve the above purpose, the present application provides the following scheme:

[0009] A BLUP model solving method which avoids the inverse of the kinship matrix, comprising:

[0010] Constructing an original BLUP model; the original BLUP model includes a kinship matrix and a matrix containing fixed effects;

[0011] Multiplying the matrix equation in the original BLUP model by a set intermediate matrix on both sides, and solving the model on the basis of avoiding the inverse of the kinship matrix by constructing the unit matrix of the G matrix and the G -1 matrix in the original BLUP model, to obtain the breeding value.

[0012] Optionally, the original BLUP model is expressed as:

[0013] Wherein, X is a fixed effect matrix; X' is the transpose of X; Z is a random effect matrix, and Z' is the transpose of Z; y is an observation value matrix; G is a kinship matrix with a size of n*n; n is the number of animal individuals; G -1 is the inverse matrix of G; k represents the heritability of the phenotype, which is a constant; is the fixed effect value to be solved, is the random effect value to be solved.

[0014] Optionally, the specific process of the model solving is:

[0015] Multiplying the expression of the original BLUP model by After multiplying the formula by G matrix and G Wherein, I represents a unit matrix;

[0016] Construct B matrix: let The entire formula is transformed into:

[0017] Construct G matrix and G -1 Unit matrix of the matrix:

[0018] Let the transformed B matrix formula multiply G matrix and G -1 Unit matrix of the matrix, get:

[0019] Construct A matrix: let The entire formula is transformed into:

[0020] Let the matrix multiplication in the formula, in turn get:

[0021] The formula after multiplication accords with the form of linear equation group Ax=b, let A matrix multiply the unit matrix of G matrix, get And simplify to get

[0022] The application also provides a BLUP model solving system for avoiding inverse of kinship matrix, comprising:

[0023] A model construction module is configured to construct an original BLUP model, wherein the original BLUP model comprises a kinship matrix and a matrix containing fixed effects;

[0024] A model solving module is configured to multiply the matrix equation in the original BLUP model by a set intermediate matrix on both sides, and to solve the model on the basis of avoiding inverse of the kinship matrix by constructing a unit matrix of G matrix and G -1 Matrix in the original BLUP model, so as to obtain breeding values.

[0025] The application also provides an electronic device comprising a memory and a processor, wherein the memory is configured to store a computer program, and the processor is configured to run the computer program to enable the electronic device to perform the BLUP model solving method for avoiding inverse of kinship matrix.

[0026] The application also provides a computer readable storage medium storing a computer program, wherein the computer program is configured to be executed by a processor to implement the BLUP model solving method for avoiding inverse of kinship matrix.

[0027] According to the specific embodiments of the present application, the following technical effects are disclosed:

[0028] The application discloses a BLUP model solving method and system for avoiding inverse of a kinship matrix, a device and a medium. -1 The application can directly avoid inverse of the kinship matrix, halve the calculation amount in the BLUP model solving process, significantly improve the calculation speed of the BLUP model solving, and keep the estimation accuracy of the breeding value. BRIEF DESCRIPTION OF DRAWINGS

[0029] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed in the embodiments will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0030] Fig. 1 is a flowchart of the BLUP model solving method for avoiding inverse of a kinship matrix according to the present application. DETAILED DESCRIPTION

[0031] The technical solutions in the embodiments of the present application will be described clearly and completely with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some embodiments of the present application, not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0032] The present application aims to provide a BLUP model solving method and system for avoiding inverse of a kinship matrix, which can directly avoid inverse of the kinship matrix, halve the calculation amount in the BLUP model solving process, significantly improve the calculation speed of the BLUP model solving, and keep the estimation accuracy of the breeding value.

[0033] In order to make the above-mentioned purposes, features and advantages of the present application more apparent and easy to understand, the present application will be further described in detail with reference to the drawings and specific embodiments.

[0034] As shown in Fig. 1, the present application provides a BLUP model solving method for avoiding inverse of a kinship matrix, which comprises:

[0035] Step 100: constructing an original BLUP model; the original BLUP model includes a kinship matrix and a matrix containing fixed effects;

[0036] Step 200: multiplying both sides of the matrix equation in the original BLUP model by a set intermediate matrix, and solving the model by constructing a unit matrix of the G matrix and the G -1 matrix in the original BLUP model, on the basis of avoiding inversion of the kinship matrix, to obtain breeding values.

[0037] Based on the above technical solution, the following embodiments are provided.

[0038] Taking GBLUP as an example, when constructing a BLUP model, the G -1 matrix needs to be calculated by inversion to obtain G

[0039] The embodiment provides a BLUP model optimization idea in a mathematical aspect, and the mathematical principle is as follows:

[0040] On the basis of the original formula, the left and right sides are multiplied by

[0041] After multiplication, the formula is:

[0042] Construct B: let

[0043] The entire formula is transformed into:

[0044] Construct a unit matrix of G and G -1 :

[0045] The left and right sides are multiplied by the unit matrix of G and G -1 :

[0046] Construct A: let

[0047] The entire formula is transformed into:

[0048] Matrix multiplication obtains:

[0049] Matrix multiplication again obtains:

[0050] The constructed formula conforms to the form of a linear equation group Ax=b, and the linear equation group can be solved by a Krylov subspace set method A.

[0051] Solving A brings A back to the original formula:

[0052] Multiply the unit matrix on both sides by G:

[0053] Simplify:

[0054] That is, without solving the inverse, the fixed effects and random effects (breeding values) are obtained.

[0055] The embodiment has the beneficial effects as follows:

[0056] In the traditional method, the complexity of inverse calculation is the third power of n, while the present application adopts the strategy of avoiding inverse of the kinship matrix, converting the inverse operation into multiple multiplication operations, and the complexity is the square of n. With the increase of the number of animal individuals n, the efficiency of avoiding inverse calculation is better than that of the direct inverse method.

[0057] Under large-scale data sets, the present technology significantly improves the computing efficiency. In addition, this technology not only performs well in reducing the calculation time, but also greatly improves the computing efficiency when processing large-scale data sets, providing a more efficient and energy-saving solution for complex genetic evaluation and breeding value estimation. At the same time, by reducing the calculation time, this method also helps to reduce energy consumption, thereby reducing the demand for high-performance computing resources, and helps to realize more environmentally friendly and cost-effective scientific computing.

[0058] In addition, the present application also provides a BLUP model solving system for avoiding inverse of the kinship matrix, comprising:

[0059] A model construction module for constructing an original BLUP model; the original BLUP model includes a kinship matrix and a matrix containing fixed effects;

[0060] A model solving module for multiplying the matrix equation in the original BLUP model by a set intermediate matrix on both sides, and obtaining the breeding value by constructing the G matrix and G -1 matrix unit matrix, based on avoiding inverse of the kinship matrix, to solve the model and obtain the breeding value.

[0061] The present application also provides an electronic device comprising a memory and a processor, the memory being used to store a computer program, and the processor running the computer program to make the electronic device execute the BLUP model solving method for avoiding inverse of the kinship matrix according to the above.

[0062] The application further provides a computer readable storage medium, which stores a computer program, and the computer program is executed by a processor to realize the BLUP model solving method for avoiding inverse of a kinship matrix.

[0063] The various embodiments are described in a progressive manner in the specification, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the various embodiments can be mutually referred to.

[0064] The principles and implementation manners of the application are described by using specific examples in the specification, and the above description of the examples is only used to help understand the core idea of the application. Meanwhile, for the general technical personnel in the field, the specific implementation manners and application ranges can be changed according to the idea of the application. In conclusion, the content of the specification should not be understood as the limitation of the application.

Claims

1. A BLUP model solving method that circumvents inverse of a relationship matrix, characterized by, The method comprises the following steps: constructing an original BLUP model; the original BLUP model comprises a kinship matrix and a matrix containing fixed effects; The original BLUP model is multiplied by a set intermediate matrix on both sides of the matrix equation, and the original BLUP model G matrix and G -1 matrix are constructed to solve the model on the basis of avoiding the inverse of the kinship matrix, and breeding values are obtained.

2. The BLUP model solving method for circumventing inverse of a relationship matrix according to claim 1, characterized in that, The original BLUP model is represented as: wherein X is a fixed effects matrix; X' is the transpose of X; Z is a random effects matrix, Z' is the transpose of Z; y is an observation matrix; G is a kinship matrix, size n*n; n is the number of animal individuals; G -1 is the inverse matrix of G; k represents the heritability of the phenotype, which is a constant; for the fixed effect value to be solved, solving a random effect value to be solved.

3. The BLUP model solving method for circumventing inverse of a relationship matrix according to claim 2, characterized in that, The specific process of the model solving is as follows: In the expression of the original BLUP model, multiply both sides of the equation by The formula after the ride is wherein I represents a unit matrix; Constructing the B matrix: Let The entire formula translates to: Constructing the G matrix and G -1 The identity matrix of the G matrix: Let the B matrix formula after the conversion both sides of the multiplication G matrix and G -1 matrix, the unit matrix, get: Constructing the A matrix: Let The entire formula translates to: Let the matrix multiplication in the formula, in turn, get: The multiplied formula conforms to the form of linear equation set Ax = b, and the unit matrix of the G matrix is multiplied on both sides of the A matrix to obtain and simplifying to obtain 4. A BLUP model solving system that circumvents inverse of a relationship matrix, characterized by, The method comprises the following steps: a model construction module, configured to construct an original BLUP model; the original BLUP model comprises a kinship matrix and a matrix containing fixed effects; a model solving module, configured to multiply both sides of a matrix equation in the original BLUP model by a set intermediate matrix, and solve the original BLUP model by constructing a G matrix and a G -1 matrix a matrix, on the basis of avoiding inversion of the kinship matrix, the model is solved to obtain a breeding value.

5. An electronic device, comprising: The electronic device comprises a memory and a processor, the memory is used for storing a computer program, and the processor runs the computer program to enable the electronic device to perform the BLUP model solving method for avoiding inversion of the kinship matrix according to any one of claims 1-3.

6. A computer-readable storage medium, characterized in that, The computer program is stored in the memory and is executed by the processor to implement the BLUP model solving method for avoiding inversion of the kinship matrix according to any one of claims 1-3.

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