Method for predicting new plant variety through local polynomial kernel regression method and evaluation method

Abstract

The invention relates to the field of new plant variety prediction, in particular to a method for predicting a new plant variety through a local polynomial kernel regression method and an evaluation method. The method comprises the following steps: estimating predicted values of a reference variety and an application variety in each year by using local polynomial kernel regression, calculating a standard error and calculating an adjustment standard deviation; and calculating a consistency standard threshold value. According to the method, dynamic capture of data features is realized through kernel function weighting and adaptive bandwidth adjustment, and a fitting curve can accurately reflect boundary variation and also can finely describe local trend change; the accuracy and the stability of variety certification are improved on the application level, and reliable statistical support is provided for accurate decision making in modern breeding.

Description

Technical Field

[0001] The present invention relates to the field of predicting new plant varieties, and in particular to a method for predicting new plant varieties using a local polynomial kernel regression method and an evaluation method. Background Art

[0002] In recent years, the number of applications and authorizations for new plant varieties has skyrocketed, and varieties have become seriously homogenized, affecting the driving force of breeding innovation. There is an urgent need to improve the DUS review standards.

[0003] The research team used R language to develop implementation programs of COYU's moving-average correction method and cubic smoothing splines correction method, and applied them to the example data in the TGP / 8 file and the 2020-2021 tomato variety DUS test data of the New Plant Variety Testing (Beijing) Branch of the Ministry of Agriculture and Rural Affairs. It was found that the correlation coefficients of the prediction results of the two methods for many quantitative traits were very low, and they were not ideal models. In addition, the confidence interval of the consistency judgment threshold of the moving average correction method is fixed in different mean ranges, and the confidence interval of the consistency judgment threshold of the cubic smoothing splines correction method is related to the number of varieties in the segment in different mean ranges. The more varieties there are, the smaller the confidence interval. This algorithm and variety testing do not fully take into account the benchmark role of early varieties in subsequent judgments and the decisive role of the main types of varieties on the results. Summary of the Invention

[0004] In response to the shortcomings of the existing technology, the present invention proposes a local polynomial kernel regression method for predicting new plant varieties (Local polynomial kernel regression method) and an evaluation method to better capture local nonlinear relationships, improve the fitting effect and enhance the adaptability and accuracy of the testing process.

[0005] The technical solution of the present invention is: a method for predicting new plant varieties using a local polynomial kernel regression method, characterized in that it includes the following steps:

[0006] (1) Collect the mean value x of the i-th variety in the j-th year ij , standard deviation SD ij ;

[0007] (2) Transform the standard deviation of each year: y ij =log(SD ij +1);

[0008] (3) Divide the data into two parts: reference variety data and application variety data;

[0009] (4) The predicted values of reference varieties and application varieties for each year are estimated using local polynomial kernel regression:

[0010]

[0011] Among them, K h Weighted kernel function, x is the mean of the variety to be predicted, and R is the number of reference varieties;

[0012] (5) Calculate standard error

[0013]

[0014] e1=(1,0,...,0) T ,

[0015]

[0016] Where k is the year number;

[0017] (6) Calculate the adjusted standard deviation

[0018] Adjlog(SD ij +1)=y ij -T ij +mean(y ij_c )

[0019] Adjlog(SD c +1)=y ij -T c +mean(y ij_c )

[0020] T ij Log(SD r +1), T c For the application variety Log(SD c +1) predicted value, SD c SD is the standard deviation of the applied variety; r is the standard deviation of the reference variety;

[0021] (7) The average value x of reference varieties and application varieties each year ij With Adjlog(SD ij +1) to get the average across years:

[0022]

[0023] For reference varieties across years Average The average of the cross-year adjusted standard deviations of the i-th reference variety;

[0024] (8) Calculate the consistency standard threshold:

[0025]

[0026] t α，df is the t-value at the significance level a and the model degrees of freedom df.

[0027] The method for predicting new plant varieties according to the local polynomial kernel regression method is characterized by:

[0028] The adjusted standard deviation of the applied variety is compared with the sex standard threshold UC i Compare values:

[0029] The variety passes the consistency test;

[0030] The variety does not pass the consistency test.

[0031] The method for predicting new plant varieties according to the local polynomial kernel regression method as described above is characterized in that: in step (5),

[0032]

[0033] x1 is the mean of the first reference variety, x n is the mean of the nth reference variety.

[0034] The method for predicting new plant varieties according to the local polynomial kernel regression method as described above is characterized in that: in step (5),

[0035]

[0036] x1 is the mean of the first reference variety, x n is the mean of the nth reference variety.

[0037] The method for predicting new plant varieties according to the local polynomial kernel regression method is characterized by further comprising a step of evaluating the mean of squared differences, wherein the mean of squared differences is calculated using the following formula:

[0038]

[0039] n is the predicted number, f orig (x) is the predicted value of x using the original data, f out (x) is the predicted value of x after removing extreme values.

[0040] The method for predicting new plant varieties according to the local polynomial kernel regression method is characterized by further comprising the step of evaluating the standard deviation of the prediction difference, wherein the standard deviation of the prediction difference is calculated as follows:

[0041]

[0042] Diff = f out (x)-f orig (x)

[0043] Among them, f orig (x) is the predicted value of x using the original data, f out (x) is the predicted value of x after removing extreme values.

[0044] The method for predicting new plant varieties according to the local polynomial kernel regression method is characterized by further comprising a step of evaluating the median absolute error, wherein the median absolute error is calculated using the following formula:

[0045]

[0046] y i is the true value of the i-th sample, is the model prediction value of the i-th sample.

[0047] The present invention also provides an evaluation index for the stability of a method for predicting new plant varieties, which is characterized by comprising the following steps:

[0048] Step 1: The formula for calculating the mean of squared differences is as follows:

[0049]

[0050] n is the predicted number;

[0051] Step 2: The standard deviation of the predicted difference is calculated as follows:

[0052]

[0053] Diff = f out (x)-f orig (x)

[0054] Among them, f orig (x) is the predicted value of x using the original data, f out (x) is the predicted value of x after removing extreme values;

[0055] Step 3: The median absolute error calculation formula is as follows:

[0056]

[0057] yi is the true value of the i-th sample, is the model prediction value of the i-th sample. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 It is the consistency threshold of α=0.002 in the moving average correction method of Example 1.

[0059] Figure 2 It is the consistency threshold of α=0.002 in the cubic smoothing spline correction method of Example 1.

[0060] Figure 3 is the consistency threshold of α=0.002 in the local polynomial kernel regression method of Example 1.

[0061] Figure 4 It is the consistency threshold of α=0.002 in the moving average correction method of Example 2.

[0062] Figure 5 It is the consistency threshold of α=0.002 in the cubic smoothing spline correction method of Example 2.

[0063] Figure 6 It is the consistency threshold of α=0.002 in the local polynomial kernel regression method of Example 2.

[0064] Figure 7 It is the consistency threshold of α=0.002 in the moving average correction method of Example 3.

[0065] Figure 8 It is the consistency threshold of α=0.002 in the cubic smoothing spline correction method of Example 3.

[0066] Figure 9 It is the consistency threshold of α=0.002 in the local polynomial kernel regression method of Example 3. DETAILED DESCRIPTION

[0067] The technical solution of the present invention is further described below with reference to the accompanying drawings.

[0068] A method for predicting new plant varieties using a local polynomial kernel regression method of the present invention comprises the following steps:

[0069] (1) Collect the mean value x of the i-th variety in the j-th year ij , standard deviation SD ij .

[0070] (2) Transform the standard deviation of each year: y ij =log(SD ij +1).

[0071] (3) Divide the data into two parts: reference varieties and application varieties (x ij_r ,y ij_r )(x ij_c ,y ij_c ).

[0072] Trend calculation

[0073] (4) The predicted values of reference varieties and application varieties for each year are estimated using local polynomial kernel regression:

[0074]

[0075] in, h is the bandwidth, K(x) is the kernel function, and the kernel function used in this paper is

[0076] Among them, K is the kernel function, h is the bandwidth, and x is the mean of the variety to be predicted.

[0077] In the present invention, the kernel function is used to improve the accuracy of the predicted value, so that it can capture dynamic characteristics and accurately reflect boundary variations. The present invention adopts the Local Polynomial Kernel Regression (LPKR) method, which has achieved breakthrough improvements in the field of variety approval and significantly improved the scientific nature and reliability of the approval standards. By comparing the experimental data, it can be clearly seen that the moving average method uses a fixed window smoothing process, which leads to the problem of random omissions in the screening results; the cubic spline rule, due to its global smoothing characteristics, keeps all varieties passed at all significance levels, showing an obvious tendency of over-inclusion. In contrast, the local polynomial kernel regression shows excellent screening stability, strictly controls the number of varieties passed within a certain range, and realizes a more scientific and strict variety approval standard.

[0078] This technological breakthrough is primarily reflected in the following aspects: First, LPKR leverages the locally weighted nature of the kernel function to accurately identify subtle differences in varietal traits. Second, through an adaptive bandwidth adjustment mechanism, the method dynamically adjusts screening criteria based on the distribution characteristics of different varietal traits, ensuring both rigorous screening and reproducible results. This rigorous screening criteria is not a simple "one-size-fits-all" approach, but rather is based on scientific statistical modeling and data analysis, resulting in a higher degree of stability and consistency in the field performance of selected varieties.

[0079] This technological innovation, which reduces the approval rate for varieties, effectively achieves a "fewer, better" screening effect, providing a more reliable basis for decision-making in modern breeding. By raising approval standards, this not only reduces unnecessary waste of subsequent breeding resources but also ensures that approved varieties demonstrate superior agronomic traits and more stable yields in actual production, thus providing agricultural production with truly valuable, high-quality varieties.

[0080] (5) Calculate standard error

[0081]

[0082] e1=(1,0,...,0) T ,

[0083]

[0084] Where R is the number of reference varieties and k is the number of years.

[0085]

[0086] x1 is the mean of the first reference variety, x n is the mean of the nth reference variety;

[0087] (6) Calculate the adjusted standard deviation

[0088] Adjlog(SD ij +1)=y ij -T ij +mean(y ij_c )

[0089] Adjlog(SD c +1)=y ij -T c +mean(y ij_c )

[0090] T ij Log(SD) r +1), T c For the application variety Log(SD c +1) predicted value, SD c SD is the standard deviation of the applied variety; r is the standard deviation of the reference variety.

[0091] Cross-year average

[0092] (7) The average value x of reference varieties and application varieties each year ij With Adjlog(SD ij +1) to get the average across years

[0093]

[0094] For reference varieties across years Average R is the number of reference varieties, is the average of the cross-year adjusted standard deviations of the i-th reference variety;

[0095] (8) Calculate the consistency standard threshold:

[0096]

[0097] dr represents the model error degrees of freedom, a is the significance level, t α，df The t value is the value at the significance level a and the model degree of freedom df. Using the sex standard threshold of the present invention to predict the application variety can achieve a dual improvement in the accuracy and stability of variety approval.

[0098] The present invention may further comprise the step of comparing the results:

[0099] The adjusted standard deviation of the applied variety is compared with the UC i Compare values:

[0100] The variety passes the consistency test.

[0101] The variety does not pass the consistency test.

[0102] The present invention also discloses an evaluation index for the stability of a method for predicting new plant varieties, comprising the following steps:

[0103] Step 1: Mean Squared Difference (MSD)

[0104] The calculation formula is as follows:

[0105]

[0106] n is the number of predictions, and the mean of squared errors measures the degree of fluctuation in model predictions. The smaller the value, the higher the stability of the model to extreme values and the more reliable the judgment results.

[0107] Step 2: Predict the standard deviation of differences (SDD)

[0108] The calculation formula is as follows:

[0109]

[0110] Diff = f out(x)-f orig (x)

[0111] Among them, f orig (x) is the predicted value of x using the original data (including extreme values), f out (x) is the predicted value of x after removing extreme values. The standard deviation of the prediction difference measures the stability of the model when making repeated predictions.

[0112] Step 3: Median Absolute Error (MedAE)

[0113] The calculation formula is as follows:

[0114]

[0115] y i is the true value of the i-th sample, is the model prediction value of the i-th sample. The smaller the value, the higher the model prediction accuracy and the more stable the model.

[0116] First: Analysis of sample data stability results

[0117] As shown in Table 1, the local polynomial kernel regression method performed best in both mean squared deviation (MSD) (0.00078) and standard deviation of prediction errors (SDD) (0.0117), outperforming the other methods. The cubic spline method achieved the highest MSD (0.0061) and SDD (0.0421), indicating its greatest sensitivity to data perturbations. While the moving average method achieved a similar MSD (0.00079) to the local polynomial kernel, its SDD (0.0188) was approximately 60% higher, indicating greater volatility in the prediction results. These results demonstrate that local polynomial regression offers the greatest robustness and reliability, making it the optimal choice for stable predictions.

[0118] Table 1 Comparison of stability index results of sample data in the first year

[0119]

[0120] As can be seen in Table 2, local polynomial regression demonstrated the best stability across all three years of data. In the first year, the three methods performed similarly, but the local polynomial maintained the lowest error. In the second year, where data fluctuated the most, the cubic spline method achieved a MedAE 13.9% higher than the local polynomial. In the third year, the local polynomial performed similarly to the cubic spline method but significantly outperformed the moving average, demonstrating its robust predictive performance.

[0121] Table 2 Comparison of three-year sample data stability

[0122]

[0123] Secondly: Confidence interval analysis results of sample data

[0124] The confidence interval results of the moving mean method and cubic spline method obtained by the self-developed algorithm are consistent with the example results (see Table 3). Figures 1 to 3 It can be seen that the consistency threshold of the moving mean method exhibits static characteristics, and the error value remains constant at different mean levels. In contrast, the threshold determination of the cubic spline method and the local polynomial method has dynamic characteristics and can adaptively adjust the error value according to the change of the mean, showing better theoretical rationality.

[0125] The confidence intervals for the cubic spline method were larger when the number of similar varieties was small and were significantly influenced by the local variety with the worst consistency. Conversely, the confidence intervals for the local regression method were smaller when the number of similar varieties was small and were less influenced by the local variety with the worst consistency. This phenomenon suggests that the local polynomial regression method is more consistent with the principle of similar comparison when evaluating the consistency of the tested varieties.

[0126] Table 3 Results of three methods at different significance level judgment thresholds (UC) in the sample data

[0127]

[0128] Analysis Example 1: The analysis is performed using the goodness of fit analysis of tomato data as an example, as follows.

[0129] From Table 4, it can be concluded that the local polynomial shows better fitting performance in both 2022 and 2023. 2 The indicator increased from 0.0805 of the cubic spline to 0.1024, an increase of 27.2%, while the MSE decreased from 0.0399 to 0.0390, a decrease of 2.3%; R in 2023 2 The performance increased from 0.1007 to 0.1532, an increase of 52.1%, and the MSE decreased from 0.0376 to 0.0354, a decrease of 5.8%.

[0130] From Table 5, it can be concluded that the local polynomial kernel regression shows a significant statistical advantage over the cubic spline in the cross-year test. In the Year 1 (2022) test, the coefficient of determination (R 2 =0.1239) is better than the cubic spline (R 2 =0.0655) increased by 89.2%; the R 2 The results show that the proposed method has a 52.1% improvement from 0.0157 to 0.0409. Meanwhile, the mean square error (MSE) of this method is lower than that of the cubic spline MSE.

[0131] Table 4 Fitting results of tomato trait 5

[0132]

[0133]

[0134] Table 5 Fitting results of tomato traits 8

[0135]

[0136] Analysis Example 2: Analysis of confidence interval results of different methods and different significance levels for tomato data

[0137] We selected traits 5 and 8 from tomato data, which included 53 similar tomato varieties and 207 proposed varieties. Using different significance levels and a one-sided t-test, we compared the number of proposed varieties passing the consistency test using different methods. If a proposed variety falls below the upper confidence interval, it passes the consistency test.

[0138] 1. Characteristics 5

[0139] This paper compared the consistency of 207 tomato trait 5 varieties under different methods. The results in Table 6 show that at different significance levels, the cubic spline method showed the most relaxed screening criteria, with all the applied varieties passing; the moving average method was second; and the local polynomial kernel regression had the least number of passes and was the most stable. This difference was confirmed by Figures 4 to 6 The confidence intervals in the paper are explained. The moving average method produces static equal-bandwidth confidence intervals, which cannot adapt to the local characteristics of the data. Although the cubic spline can generate dynamic confidence intervals, its global smoothness leads to a large interval width, which reduces the screening stringency. In contrast, the local polynomial kernel regression uses kernel function weighted estimation to maintain the dynamic adaptability of the confidence interval while controlling the interval width within the optimal range, significantly reducing the approval rate of the applied varieties.

[0140] Table 6 Number of tomato varieties with different significance levels that passed the consistency test

[0141]

[0142] Table 7 Consistency qualification rate of applied varieties with different significance levels for tomato traits 5

[0143]

[0144] 2. Characteristics 8

[0145] In the variety screening of tomato compound leaf length, the smaller the significance level, the smaller the rejection region, the higher the variety pass rate, and the more relaxed the review standards.

[0146] The number of tomato compound leaf length application varieties that passed in Table 8 was analyzed. The moving average method showed a certain screening gradient, with the number of passes decreasing from 205 to 188. The cubic spline method maintained 207 varieties passing at all significance levels. Due to global smoothness, the screening criteria were loose and it was impossible to effectively distinguish variety differences. The local polynomial kernel regression showed strict screening stability, with the least number of passes and a stable range of 143-157. Therefore, when determining variety consistency, the local polynomial kernel regression method was selected to avoid the over-inclusion of the cubic spline method and prevent the random omission of the moving average method. Figures 7 to 9 .

[0147] Table 8 Number of approved varieties with different significance levels for trait 8

[0148]

[0149] This paper systematically compares the fitting performance and variety consistency determination results of different methods, demonstrating the advantages of local polynomial kernel regression in variety certification. From the perspective of fitting performance, the moving average method uses the mean prediction of adjacent points, resulting in a non-smooth fitting curve and an inability to predict boundary points. While the cubic spline improves boundary prediction capabilities through node settings, its global smoothness leads to insufficient sensitivity to local data trends, affecting the interpretability of the model. In contrast, local polynomial kernel regression achieves dynamic capture of data features through kernel function weighting and adaptive bandwidth adjustment. The fitting curve can accurately reflect boundary variation and finely depict local trend changes.

[0150] In terms of variety consistency assessment, this method effectively overcomes the bias caused by the fixed threshold of the traditional COYU moving average method by establishing a dynamic threshold determination mechanism. Example data results show that the variety approval rate of the local polynomial kernel regression is significantly lower than that of the moving average method and the cubic spline method. This more stringent variety approval standard achieves a dual improvement in the accuracy and stability of variety approval at the application level, providing reliable statistical support for precise decision-making in modern breeding.

Claims

1. A method for predicting new plant varieties using a local polynomial kernel regression method, characterized by: The following steps are involved: (1) Collect the mean value x of the i-th variety in the j-th year ij , standard deviation SD ij ; (2) Transform the standard deviation of each year: y ij =log(SD ij +1); (3) Divide the data into two parts: reference variety data and application variety data; (4) The predicted values of reference varieties and application varieties for each year are estimated using local polynomial kernel regression: Among them, K(x) is the kernel function, x is the mean of the variety to be predicted, and R is the number of reference varieties; (5) Calculate standard error e1＝(1，0，...，0) T ， Where k is the year number; (6) Calculate the adjusted standard deviation Adjlog(SD ij +1)=y ij -T ij +mean(y ij_c ) Adjlog(SD c +1)=y ij -T c +mean(y ij_c ) T ij Log(SD) r +1), T c For the application variety Log(SD c +1) predicted value, SD c SD is the standard deviation of the applied variety; r is the standard deviation of the reference variety; (7) The average value x of reference varieties and application varieties each year ij With Adjlog(SD ij +1) to get the average across years: For reference varieties across years Average is the average of the cross-year adjusted standard deviations of the i-th reference variety; (8) Calculate the consistency standard threshold: t α , df is the t value under the significance level a and the model degrees of freedom df.

2. The method for predicting new plant varieties using the local polynomial kernel regression method according to claim 1, characterized in that: The adjusted standard deviation of the applied variety is compared with the sex standard threshold UC i Compare values: The variety passes the consistency test; The variety does not pass the consistency test.

3. The method for predicting new plant varieties using the local polynomial kernel regression method according to claim 1 or 2, characterized in that: In step (5), x1 is the mean of the first reference variety, x n is the mean of the nth reference variety.

4. The method for predicting new plant varieties using the local polynomial kernel regression method according to claim 1 or 2, characterized in that: In step (5), x1 is the mean of the first reference variety, x n is the mean of the nth reference variety.

5. The method for predicting new plant varieties using the local polynomial kernel regression method according to claim 1 or 2, characterized in that: It also includes the step of evaluating the mean of squared differences. The formula for calculating the mean of squared differences is as follows: n is the predicted number, f orig (x) is the predicted value of x using the original data, f out (x) is the predicted value of x after removing extreme values.

6. The method for predicting new plant varieties using the local polynomial kernel regression method according to claim 1 or 2, characterized in that: It also includes the step of evaluating the standard deviation of the prediction difference. The standard deviation of the prediction difference is calculated as follows: Diff=f out (x)-f orig (x) Among them, f orig (x) is the predicted value of x using the original data, f out (x) is the predicted value of x after removing extreme values.

7. The method for predicting new plant varieties using the local polynomial kernel regression method according to claim 1 or 2, characterized in that: It also includes the step of evaluating the median absolute error. The formula for calculating the median absolute error is as follows: y i is the true value of the i-th sample, is the model prediction value of the i-th sample.

8. The method for predicting new plant varieties using the local polynomial kernel regression method according to claim 1 or 2, characterized in that: In step (4), 9. An evaluation index for the stability of a method for predicting new plant varieties, characterized by: The following steps are involved: Step 1: The formula for calculating the mean of squared differences is as follows: n is the predicted number; Step 2: The standard deviation of the predicted difference is calculated as follows: Diff=f out (x)-f orig (x) Among them, f orig (x) is the predicted value of x using the original data, f out (x) is the predicted value of x after removing extreme values; Step 3: The median absolute error calculation formula is as follows: y i is the true value of the i-th sample, is the model prediction value of the i-th sample.

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