CTR prediction optimization method based on differentiable accuracy and recall rate

Abstract

The invention provides a CTR prediction optimization method based on differentiable accuracy and recall rate, and the method comprises the steps: constructing a CTR prediction model, and inputting training data and training features into the model; after an output layer of the model, the difference between a predicted value and a threshold value is calculated, and the differentiable accuracy and recall rate are calculated according to the difference; and integrating differentiable accuracy and recall rate into a loss function of the model, and minimizing the loss function through an optimization algorithm to obtain a trained CTR prediction model and the like. Therefore, the scheme has high calculation efficiency and differentiability and can be directly integrated into a gradient optimization algorithm. By eliminating dependence on threshold and condition judgment and sorting operation, large-scale unbalanced data can be processed, and the performance and training efficiency of the CTR prediction model are remarkably improved. Meanwhile, the method has a wide application prospect in the field of recommendation systems, and the prediction capability and commercial value of the model can be effectively improved.

Description

Technical Field

[0001] The present application relates to the technical field of CTR prediction optimization, and in particular to a CTR prediction optimization method based on differentiable precision and recall. Background Art

[0002] In the recommendation system, click-through rate (CTR) prediction is a key task, which aims to predict the probability of a user clicking on a recommended item. Precision, recall, and F1-Score are important indicators for evaluating the performance of CTR prediction models. Precision measures the proportion of instances predicted as positive by the model that are truly positive, which reflects the accuracy of the model; recall measures the proportion of all true positive samples that are correctly predicted as positive by the model, which reflects the coverage of the model. F1-Score is the harmonic mean of precision and recall, which is used to comprehensively evaluate the performance of the model.

[0003] In traditional methods, the calculation of these indicators usually relies on threshold setting, conditional judgment, and sorting operations. For example, in order to calculate precision and recall, you first need to set a threshold based on the model's prediction probability, binarize the prediction results into positive or negative samples, then make conditional judgments based on the true labels, and finally calculate the indicator values ​​through sorting operations. Although these methods are intuitive and easy to understand, there are many problems in the optimization process.

[0004] Traditional methods for calculating precision, recall, and F1-Score are often not differentiable during the optimization process and cannot be directly used in gradient optimization algorithms, limiting further improvements in model performance. When processing large-scale data, traditional methods have low computational efficiency. In particular, when sorting operations are involved, computational complexity increases significantly, resulting in longer training time and increased resource consumption. Summary of the invention

[0005] In order to solve the problem that the above-mentioned traditional methods for calculating precision, recall and F1-Score are often not differentiable during the optimization process and cannot be directly used in the gradient optimization algorithm, which limits the further improvement of model performance, the present application provides a CTR prediction optimization method based on differentiable precision and recall, comprising the steps of:

[0006] Collecting user click behavior data, and dividing the behavior data into a training set and a test set;

[0007] Performing preprocessing operations on the training set to obtain training data, and encoding and standardizing the data features of the training set;

[0008] According to preset conditions, the features of the data after encoding and standardization are screened, and a feature engineering method is used to extract high-level features of the data to obtain training features;

[0009] Constructing a CTR prediction model, and inputting the training data and the training features into the CTR prediction model;

[0010] After the output layer of the CTR prediction model, calculating the difference between the predicted value and the threshold;

[0011] Based on the differences, calculate differentiable precision and recall;

[0012] Integrating the differentiable precision and recall into the loss function of the CTR prediction model, and minimizing the loss function through an optimization algorithm to obtain the trained CTR prediction model;

[0013] Input the test set into the trained CTR prediction model and calculate the AUC-PR index;

[0014] When the AUC-PR indicator meets the preset standard indicator, the CTR prediction model is completed and deployed.

[0015] In a feasible implementation, the behavior data includes: user feature data, item feature data and context feature data, and the preprocessing operation includes: data cleaning, data deduplication and data missing value processing.

[0016] In a feasible implementation, the step of calculating the differentiable precision and recall according to the difference includes:

[0017] Calculate the difference between the predicted value and the threshold value, take the absolute value of the difference and perform normalization processing, and adjust the range of the difference after the normalization processing to obtain a first variable score1;

[0018] Calculate the product of the first variable score1 and the true label, retain the predicted samples whose true labels are positive samples, and obtain the second variable score2;

[0019] Sum the second variable score2 to obtain the number of samples score3 where all the predicted samples are positive samples and the true labels are positive samples;

[0020] Sum the first variable score1 to obtain the number score4 of all the predicted samples that are positive samples;

[0021] Sum the true labels to obtain the number of all true labels that are positive samples score5;

[0022] The differentiable precision and the recall are calculated based on the number of samples with the true label as positive samples (score3), the number of predicted samples as positive samples (score4), and the number of samples with the true label as positive samples (score5).

[0023] In a feasible implementation, the formula for calculating the differentiable precision and the recall rate according to the number of samples with the true label as positive samples score3, the number of predicted samples as positive samples score4 and the number of samples with the true label as positive samples score5 is as follows:

[0024] Precision=score3 / (score4+ε);

[0025] Recall=score3 / (score5+ε);

[0026] Where: ε is the preset minimum value, Precision is the precision rate, and Recall is the recall rate.

[0027] In a feasible implementation, the step of adjusting the range of the difference after normalization includes:

[0028] The normalized difference is added with 1 and then multiplied by 0.5 to obtain the first variable score1.

[0029] In a feasible implementation, the optimization algorithm minimization includes: gradient descent method, stochastic gradient descent method and dynamic learning rate adjustment algorithm.

[0030] In a feasible implementation, the step of integrating the differentiable precision and recall into the loss function of the CTR prediction model further includes:

[0031] Use Keras backend function to calculate cross entropy loss;

[0032] The cross entropy loss, the differentiable precision and recall are combined according to a given weight coefficient to form the loss function.

[0033] From the above content, it can be seen that the present application provides a CTR prediction optimization method based on differentiable precision and recall. This method approximates the precision and recall through mathematical expressions, eliminates the dependence on thresholds, conditional judgments and sorting, can be directly used in the gradient optimization process, and has efficient computing performance. This method can be integrated into the loss function of the CTR prediction model to improve the prediction ability and computing efficiency of the model in an unbalanced data environment. At the same time, this method can also be used to calculate the area under the PR curve (AUC-PR) to further improve the accuracy of model evaluation. The present application integrates the differentiable precision and recall into the loss function, and minimizes the loss function through an optimization algorithm, which can make the model training process more efficient and stable. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] The accompanying drawings herein are incorporated into and constitute a part of the specification, illustrate embodiments consistent with the implementation of the present invention, and together with the specification are used to explain the principles of the embodiments of the present invention. Obviously, the accompanying drawings described below are only some embodiments of the implementation of the present invention, and for ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without creative work.

[0035] Figure 1 A flowchart of a CTR prediction optimization method based on differentiable precision and recall is shown as an exemplary embodiment of the present application. DETAILED DESCRIPTION

[0036] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that the embodiments of the present invention will be more comprehensive and complete and fully convey the concepts of the example embodiments to those skilled in the art. The described features, mechanisms, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, many specific details are provided to provide a full understanding of the implementation of the embodiments of the present invention.

[0037] In the recommendation system, click-through rate (CTR) prediction is a key task, which aims to predict the probability of a user clicking on a recommended item. Precision, recall and F1-Score are important indicators for evaluating the performance of CTR prediction models. However, the traditional methods for calculating these indicators rely on threshold setting, conditional judgment and sorting operations, which are often not differentiable during the optimization process and difficult to be directly used in gradient optimization algorithms. In addition, traditional methods have low computational efficiency when processing large-scale data, especially when sorting is involved, the computational complexity increases significantly. Therefore, there is an urgent need for a differentiable and computationally efficient method to calculate these performance indicators to optimize the performance of the CTR prediction model.

[0038] To solve the above problems, this application provides a CTR prediction optimization method based on differentiable precision and recall. Figure 1 As shown, the steps include:

[0039] S100: Collect user click behavior data and divide the behavior data into a training set and a test set.

[0040] In some embodiments, the behavior data includes: user feature data, item feature data, and context feature data, wherein the training set is used for training and optimizing the model, and the test set is used for evaluating the performance of the model.

[0041] Collecting behavioral data can provide sufficient data support for the model, ensuring that the model can learn the laws and patterns of user behavior. By dividing the model into training sets and test sets, the generalization ability of the model can be objectively evaluated.

[0042] S200: performing preprocessing operations on the training set to obtain training data, and encoding and standardizing data features of the training set.

[0043] In some embodiments, the preprocessing operation includes: data cleaning, data deduplication and data missing value processing. The data features of the training set are encoded and standardized, such as one-hot encoding, label encoding, normalization, standardization, etc. The preprocessing operation can improve the data quality and reduce the impact of noise on model training.

[0044] Furthermore, encoding and standardization processes make the features have a unified dimension and distribution, which is conducive to model training and optimization.

[0045] S300: According to preset conditions, the features of the data after encoding and standardization processing are screened, and the features of high-level data are extracted using feature engineering methods to obtain training features.

[0046] Among them, feature engineering methods include principal component analysis (PCA) and linear discriminant analysis (LDA), which can remove redundant and irrelevant features, reduce the complexity of the model, and improve training efficiency. At the same time, extracting high-level features can better capture the laws and patterns of user behavior and improve the prediction performance of the model.

[0047] S400: construct a CTR prediction model, and input the training data and training features into the CTR prediction model.

[0048] CTR prediction models include logistic regression models, support vector machine models, deep learning models, etc. This application does not impose specific restrictions. This step builds a model framework for predicting user click behavior, and then inputs the processed data into CTR prediction to provide data support for CTR prediction training and optimization.

[0049] S500: After the output layer of the CTR prediction model, the difference between the predicted value and the threshold is calculated, and based on the difference, the differentiable precision and recall are calculated.

[0050] The predicted value here refers to the output of the CTR prediction model, and the threshold is a preset value used to determine whether the predicted value meets a certain condition (such as whether it belongs to a certain category). Calculating the difference between the predicted value and the threshold is to calculate the difference between these two values. This difference can be used to evaluate the reliability or accuracy of the prediction result.

[0051] Specifically, based on the difference, the differentiable precision and recall are calculated. The differentiable precision and recall can be used as part of the loss function to guide the training and optimization of the model, and then the prediction performance of the model is evaluated and used as the optimization target.

[0052] S600: Integrate the differentiable precision and recall into the loss function of the CTR prediction model, and minimize the loss function through an optimization algorithm to obtain a trained CTR prediction model;

[0053] The loss function is used to optimize the model. In machine learning and deep learning, the loss function (or cost function) is a function that measures the difference between the model's prediction results and the actual results. The purpose of constructing a loss function is to find an optimal set of model parameters during the model training process so that the model's prediction results are as close to the actual results as possible. The loss function integrates differentiable precision and recall rates, as well as traditional loss functions, such as the cross entropy loss function. The purpose of this is to not only consider the model's CTR prediction ability when optimizing the model, but also optimize the two important performance indicators of precision and recall.

[0054] In the model training phase, the model is trained using the training data set and the loss function is minimized through an optimization algorithm. For example, the gradient descent algorithm. The gradient descent algorithm calculates the gradient of the loss function with respect to the model parameters and updates the model parameters based on the gradient information to gradually reduce the value of the loss function. Through continuous iteration of the training process, the model parameters will gradually converge to an optimal solution (or a near-optimal solution), at which point the model's prediction results will be as close to the actual results as possible, and the precision, recall, and CTR prediction capabilities will be optimized.

[0055] S700: Input the test set into the trained CTR prediction model and calculate the AUC-PR index; AUC-PR is one of the important indicators for evaluating the performance of the CTR prediction model, which takes into account the balance between precision and recall. By calculating the AUC-PR index, the prediction performance of the model can be objectively evaluated and compared with the preset standard index.

[0056] S800: When the AUC-PR indicator meets the preset standard indicator, the CTR prediction model is completed and deployed. When the AUC-PR indicator meets the preset standard indicator, the model is considered to have been trained and has achieved the expected prediction performance. The trained CTR prediction model is deployed in the actual production environment to predict the user's click behavior. Specifically, in actual applications, the method of the present application can be used to calculate the area under the PR curve (AUC-PR), further improving the accuracy of model evaluation.

[0057] From the above content, it can be seen that the CTR prediction optimization method based on differentiable precision and recall provided by this application can significantly improve the prediction performance of the CTR prediction model by introducing differentiable precision and recall as part of the loss function and continuously optimizing the model parameters; by dividing the training set and the test set, and using evaluation indicators such as AUC-PR, the generalization ability of the model can be objectively evaluated to ensure the stability and reliability of the model in practical applications; through steps such as feature screening and extraction, redundant and irrelevant features can be removed, and high-level features can be extracted, thereby improving the training efficiency and prediction performance of the model. The trained CTR prediction model can be used to predict the user's click behavior in real time, provide strong support for personalized recommendations, and improve user experience and satisfaction.

[0058] In some embodiments of the present application, the step of calculating the differentiable precision and recall according to the difference includes:

[0059] S510: Calculate the difference between the predicted value and the threshold value, take the absolute value of the difference and perform normalization processing, and adjust the range of the difference after the normalization processing to obtain the first variable score1.

[0060] Specifically, the difference between the predicted value of the CTR prediction model and the preset threshold is calculated. The absolute value of the difference is taken to ensure that the difference value is a positive number for subsequent processing. The difference is normalized and the difference value is scaled to an appropriate range (such as between 0 and 1) to eliminate the influence of different feature dimensions. Adjusting the range of the difference value after normalization may involve further scaling or translation operations to meet the needs of subsequent calculations. The first variable score1 obtained reflects the relative difference between the predicted value and the threshold, which is the basis for the subsequent calculation of precision and recall. At the same time, the normalization process ensures that all features are compared on the same scale, which improves the stability and robustness of the model.

[0061] S520: Calculate the product of the first variable score1 and the true label, retain the predicted samples whose true labels are positive samples, and obtain the second variable score2.

[0062] Multiply the first variable score1 by the true label (0 or 1). Keep the predicted samples whose true label is positive (i.e. 1), which are the key to the subsequent calculation of precision and recall. The second variable score2 obtained only contains the scores of the predicted samples whose true label is positive. Through this step, samples that contribute to the calculation of precision and recall can be screened out, reducing the complexity of subsequent calculations.

[0063] S530: Sum the second variable score2 to obtain the number of samples score3 where all predicted samples are positive samples and the true labels are positive samples.

[0064] Sum all the values ​​in the second variable score2. This sum represents the number of samples that are predicted to be positive and are actually positive (i.e., True Positives, TP). The number of samples with the actual label of positive samples (score3) is one of the bases for calculating the precision rate. The sum operation simplifies the calculation process and directly obtains the required statistics.

[0065] S540: summing the first variable score1 to obtain the number score4 of all predicted samples as positive samples; the number score4 of predicted samples as positive samples is another basis for calculating the precision and recall rate. Through this step, the total number of predicted positive samples can be obtained for subsequent calculation of the precision rate.

[0066] S550: Sum the true labels to obtain the number score5 of all true labels as positive samples.

[0067] S560: Calculate the differentiable precision and recall rate according to the number of samples with true labels as positive samples (score3), the number of predicted samples as positive samples (score4), and the number of samples with true labels as positive samples (score5).

[0068] Conventional precision and recall are usually calculated based on discrete values ​​(i.e., classification results of 0 or 1), but in the embodiments of the present application, calculations are performed using continuous values, thereby achieving differentiable precision and recall. This allows precision and recall to be used as part of the loss function for optimization operations such as gradient descent. By integrating differentiable precision and recall into the loss function, the model can directly optimize these two indicators during training, thereby improving optimization efficiency.

[0069] In some embodiments of the present application, the formula for calculating the differentiable precision and recall is as follows based on the number of samples with true labels as positive samples score3, the number of predicted samples as positive samples score4, and the number of true labels as positive samples score5:

[0070] Precision = score3 / (score4+ε); where ε is a preset minimum value and Precision is the accuracy rate.

[0071] Specifically, we get the ratio of samples predicted by the model to samples that are actually positive. The higher this ratio is, the more accurate the model's prediction is.

[0072] Recall = score3 / (score5+ε); where ε is a preset minimum value and Recall is the recall rate.

[0073] The proportion of samples predicted by the model as positive samples to all real positive samples. The higher this proportion is, the more real positive samples the model covers.

[0074] Specifically, ε is a preset very small value used to prevent division by zero errors caused by a zero denominator. This improves the robustness of the formula. At the same time, the value of ε is usually very small, so the impact on the calculation results of precision and recall can be ignored.

[0075] In this application, precision and recall are two indicators that directly reflect the performance of the model. The higher the precision, the more accurate the model's prediction; the higher the recall, the more real positive samples the model covers. After calculating the precision and recall, it can be used as one of the goals of model optimization. By adjusting model parameters or feature selection, the precision and recall can be improved, thereby improving the performance of the model.

[0076] In some embodiments of the present application, the step of adjusting the range of the normalized difference includes: adding 1 to the normalized difference and then multiplying it by 0.5 to obtain a first variable score1.

[0077] Specifically, adding 1 to the difference ensures that all difference values ​​are positive. The normalized difference values ​​may contain negative numbers or zeros, and the addition operation can convert them all to positive numbers for subsequent processing. At the same time, the range of the difference values ​​is adjusted. The addition operation actually performs a translation transformation on the difference values, changing their range.

[0078] The multiplication by 0.5 actually performs a scaling transformation on the difference value, reducing its range by half. This is convenient for subsequent calculations. By adjusting the range of the difference value, it can be more suitable for subsequent calculations and comparisons.

[0079] In some embodiments of the present application, the optimization algorithm minimization includes: gradient descent method, stochastic gradient descent method and dynamic learning rate adjustment algorithm.

[0080] Among them, the gradient descent method is a commonly used numerical optimization algorithm for finding the minimum or local minimum of a function. It finds the optimal solution by iteratively adjusting the parameters and gradually reducing the objective function value in the opposite direction of the function gradient. The stochastic gradient descent method is a variant of the gradient descent algorithm and is widely used in the optimization process of machine learning models. The main feature of SGD is that each iteration does not use the entire data set to calculate the gradient, but randomly selects a sample (or a small batch of samples) to calculate the gradient and update the model parameters. The dynamic learning rate adjustment algorithm is a strategy that adjusts the learning rate according to the situation during the training process to improve model performance and training efficiency. The learning rate is a key parameter in the optimization algorithm, which controls the step size of the model parameter update. Dynamically adjusting the learning rate can dynamically adjust the learning rate according to different training stages and model performance, thereby optimizing the training process.

[0081] Gradient descent method, stochastic gradient descent method and dynamic learning rate adjustment algorithm are all commonly used optimization algorithms, and they have their own advantages and applicability in different application scenarios. In practical applications, the performance and training efficiency of the model can be improved by selecting a suitable optimization algorithm according to the characteristics of the specific problem and data set. In the embodiments of the present application, there is no specific restriction on the optimization algorithm actually selected.

[0082] In some embodiments of the present application, the step of integrating the differentiable precision and recall rate into the loss function of the CTR prediction model also includes: calculating the cross entropy loss using the Keras backend function; combining the cross entropy loss, the differentiable precision and recall rate according to a given weight coefficient to form a loss function.

[0083] Cross entropy loss is a common method to measure the difference between two probability distributions. In CTR prediction, it is used to measure the difference between the CTR predicted by the model and the actual click behavior. By minimizing the cross entropy loss, the prediction accuracy of the model can be improved. Using the backend functions provided by the Keras framework, the cross entropy loss between the probability distribution output by the model and the actual label can be easily calculated.

[0084] Specifically, in this embodiment, the backend function provided by the Keras framework is used to calculate the cross entropy loss between the CTR predicted by the model and the actual click behavior. The cross entropy loss, the differentiable precision rate and the recall rate are linearly combined according to the preset weight coefficients to form the final loss function. This loss function takes into account both the prediction accuracy of the model (reflected by the cross entropy loss) and the classification performance of the model (reflected by the precision rate and the recall rate).

[0085] In this application, the code (based on Keras and TensorFlow) that can integrate differentiable precision and recall into the loss function of the CTR prediction model is also provided as follows:

[0086]

[0087]

[0088] From the above content, it can be seen that the present application provides a CTR prediction optimization method based on differentiable precision and recall, including the steps of: constructing a CTR prediction model, inputting training data and training features into the CTR prediction model; after the output layer of the CTR prediction model, calculating the difference between the predicted value and the threshold, and calculating the differentiable precision and recall based on the difference; integrating the differentiable precision and recall into the loss function of the CTR prediction model, and minimizing the loss function through an optimization algorithm to obtain a trained CTR prediction model, etc. The scheme has high computational efficiency and differentiability, and can be directly integrated into the gradient optimization algorithm. By eliminating the dependence on thresholds, conditional judgments, and sorting operations, the present application can handle large-scale unbalanced data and significantly improve the performance and training efficiency of the CTR prediction model. At the same time, it has broad application prospects in the field of recommendation systems and can effectively improve the prediction ability and commercial value of the model.

[0089] Those skilled in the art will readily appreciate other embodiments of the present disclosure after considering the disclosure of the specification and the examples. This application is intended to cover any variations, uses or adaptations of the present disclosure, which follow the general principles of the present disclosure and include common knowledge or customary techniques in the art that are not disclosed in the present disclosure. The specification and the examples are intended to be exemplary only, and the true scope and spirit of the present disclosure are indicated by the following claims.

Claims

1. A CTR prediction optimization method based on differentiable precision and recall, characterized in that: Includes steps: Collecting user click behavior data, and dividing the behavior data into a training set and a test set; Performing preprocessing operations on the training set to obtain training data, and encoding and standardizing the data features of the training set; According to preset conditions, the features of the data after encoding and standardization are screened, and a feature engineering method is used to extract high-level features of the data to obtain training features; Constructing a CTR prediction model, and inputting the training data and the training features into the CTR prediction model; After the output layer of the CTR prediction model, the difference between the predicted value and the threshold is calculated, and based on the difference, the differentiable precision and recall are calculated; Integrating the differentiable precision and recall into the loss function of the CTR prediction model, and minimizing the loss function through an optimization algorithm to obtain the trained CTR prediction model; Input the test set into the trained CTR prediction model and calculate the AUC-PR index; When the AUC-PR indicator meets the preset standard indicator, the CTR prediction model is completed and deployed.

2. The CTR prediction optimization method based on differentiable precision and recall according to claim 1, characterized in that: The behavior data includes: user feature data, item feature data and context feature data, and the preprocessing operations include: data cleaning, data deduplication and data missing value processing.

3. The CTR prediction optimization method based on differentiable precision and recall according to claim 1, characterized in that: The step of calculating the differentiable precision and recall according to the difference comprises: Calculate the difference between the predicted value and the threshold value, take the absolute value of the difference and perform normalization processing, and adjust the range of the difference after the normalization processing to obtain a first variable score1; Calculate the product of the first variable score1 and the true label, retain the predicted samples whose true labels are positive samples, and obtain the second variable score2; Sum the second variable score2 to obtain the number of samples score3 where all the predicted samples are positive samples and the true labels are positive samples; Sum the first variable score1 to obtain the number score4 of all the predicted samples that are positive samples; Sum the true labels to obtain the number of all true labels that are positive samples score5; The differentiable precision and the recall are calculated based on the number of samples with the true label as positive samples (score3), the number of predicted samples as positive samples (score4), and the number of samples with the true label as positive samples (score5).

4. The CTR prediction optimization method based on differentiable precision and recall according to claim 3, characterized in that: The formula for calculating the differentiable precision and recall rate according to the number of samples with the true label as positive samples score3, the number of predicted samples as positive samples score4 and the number of samples with the true label as positive samples score5 is as follows: Precision=score3 / (score4+ε); Recall=score3 / (score5+ε); Where: ε is the preset minimum value, Precision is the precision rate, and Recall is the recall rate.

5. The CTR prediction optimization method based on differentiable precision and recall according to claim 3, characterized in that: The step of adjusting the range of the difference after normalization processing comprises: The normalized difference is added with 1 and then multiplied by 0.5 to obtain the first variable score1.

6. The CTR prediction optimization method based on differentiable precision and recall according to claim 1, characterized in that: The optimization algorithm minimization includes: gradient descent method, stochastic gradient descent method and dynamic learning rate adjustment algorithm.

7. The CTR prediction optimization method based on differentiable precision and recall according to claim 1, characterized in that: The step of integrating the differentiable precision and recall into the loss function of the CTR prediction model further includes: Use Keras backend function to calculate cross entropy loss; The cross entropy loss, the differentiable precision and recall are combined according to a given weight coefficient to form the loss function.

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