Global optimization method for solving missing observation value in nonlinear regulation and control network

Abstract

The invention relates to the technical field of biological information, and discloses a global optimization method for solving missing observation values in a nonlinear regulation and control network, which can be used for a pharmacological network, a physiological network, a toxicological network and a pathological network, and comprises the following steps: acquiring an experimental data set; constructing a nonlinear regulation and control network model based on a deep learning model according to the target nonlinear regulation and control network; inputting the experimental data set into the network model, and initializing the weight and deviation by adopting a default initialization method; performing non-constraint training on the initialized network model, and taking a mean value to obtain a constraint value; inputting the constraint value into a parameter updating method, and performing constraint training on the initialized network model by adopting the parameter updating method and a parameter constraint method to obtain a globally optimized network model parameter; determining quantitative regulation and control information of the target nonlinear regulation and control network according to the globally optimized network model parameters; according to the method, the training precision of two orders of magnitude can be improved, the prediction error is effectively reduced, and a globally optimized numerical solution is realized.

Description

Technical Field

[0001] This invention relates to the field of bioinformatics, specifically to a global optimization method for solving missing observations in a nonlinear control network. Background Technology

[0002] In existing technologies, the construction of nonlinear regulatory networks is typically based on metabolic pathway diagrams and their corresponding structured files. These networks include pharmacological, physiological, pathological, and toxicological networks, describing the regulatory relationships between molecular entities through nodes and edges. However, in some regulatory structures, nodes, although labeled in the pathway diagram, may not have their edge relationships with upstream and downstream nodes recorded in the structured file. Such nodes are often omitted in the network model or replaced by direct connections between upstream and downstream nodes. These nodes include aspects of the nonlinear regulatory network such as cell type, biological function, and biological anatomical tissue where observational data is unavailable.

[0003] In the published Chinese invention patent application CN202310852405.7, when the aforementioned nodes are introduced into a nonlinear control network model, their node values ​​typically rely on empirical settings or manual rules, lacking a unified determination method. Furthermore, it is difficult to guarantee the rationality and consistency under different network structures and parameter scales, and it is challenging to obtain the global optimal solution. Meanwhile, existing deep learning-based network modeling methods generally assume that nodes possess explicit supervisory information. For nodes that play a mediating role in the network but lack direct observations, effective constraints and stable training are difficult. Therefore, the interpretability of model parameters in existing technologies is insufficient, and the reliability of network modeling results is limited. Summary of the Invention

[0004] The purpose of this invention is to provide a global optimization method for solving missing observations in nonlinear control networks, which can improve training accuracy by two orders of magnitude, effectively reduce prediction errors, and achieve a globally optimal numerical solution.

[0005] This invention is implemented as follows:

[0006] A global optimization method for solving missing observations in a nonlinear control network includes the following steps:

[0007] Obtain the experimental dataset, which includes: biological components and their expression levels; biological components include: active pharmaceutical ingredients, target proteins, biomarkers, and genes;

[0008] Construct a nonlinear control network model based on a deep learning model based on the target nonlinear control network;

[0009] The nonlinear control network model includes: an input layer, several hidden layers, and an output layer;

[0010] Each network node in the input layer, hidden layer, and output layer represents a biological component; the value of each network node represents the expression level of the biological component; and the network links between each network node represent the interactions between the biological components.

[0011] The experimental dataset was input into the nonlinear control network model, and the weights and biases were initialized using the default initialization method.

[0012] The initialized nonlinear control network model is trained without constraints, and the mean value is taken to obtain the constraint value, thereby achieving global optimization.

[0013] The constraint values ​​are input into the parameter update method. The parameter update method and the parameter constraint method are used to perform constraint training on the initialized nonlinear control network model to obtain the globally optimized network model parameters.

[0014] The quantitative regulation information of the target nonlinear regulation network is determined based on the parameters of the globally optimized network model; the quantitative regulation information is used to predict the regulation result based on the given drug input.

[0015] Furthermore, methods for obtaining experimental datasets include:

[0016] Raw data of the nonlinear control network were extracted from experimental data in the literature;

[0017] The original data of the nonlinear control network is expanded using methods based on normal or uniform distribution to generate an experimental dataset.

[0018] Furthermore, a nonlinear control network model based on a deep learning model is constructed according to the target nonlinear control network, specifically including:

[0019] The input layer, several hidden layers, and the output layer are determined based on the order of action of each biological component in the target nonlinear regulatory network.

[0020] The input layer represents the drug input to the target nonlinear regulatory network, the hidden layer represents the intermediate regulatory part of the target nonlinear regulatory network, and the output layer represents the regulatory result of the target nonlinear regulatory network.

[0021] Based on the target nonlinear control network, determine whether there is a direct interaction between network nodes in non-adjacent layers, and fill in blank nodes when there is a direct interaction between network nodes in non-adjacent layers.

[0022] By adding network links between network nodes in the input layer, hidden layer, and output layer, and setting activation functions, loss functions, and optimizers, a nonlinear control network model is obtained.

[0023] Activation functions include at least one of the following: Sigmoid function, Tanh function, ReLU function, LeakyReLU function, and Softplus function;

[0024] The loss function is the mean squared error loss function; the optimizer is the Adam optimizer.

[0025] Furthermore, a parameter initialization method is used to adjust the sign of the weights in the nonlinear regulatory network model so that the weights satisfy the interaction relationship between biological components. The interaction relationship includes activation relationship and inhibition relationship. When the weight is positive, the interaction relationship between biological components is an activation relationship, and when the weight is negative, the interaction relationship between biological components is an inhibition relationship.

[0026] Furthermore, the initialized nonlinear control network model is trained without constraints using randomly selected values, and the mean value is taken to obtain the constraint value, thereby achieving global optimization. Specifically, this includes:

[0027] Random values ​​are used to train the initialized nonlinear control network model, and the prediction results of each node in the output layer are calculated respectively.

[0028] Remove outliers from the prediction results of each node in the output layer;

[0029] The arithmetic mean of the prediction results of each node in the output layer after removing outliers is calculated to obtain the constraint value, thereby achieving global optimization.

[0030] Furthermore, outliers in the prediction results of each node in the output layer are removed. Specifically, this includes: based on the quartile structure defined by the box plot, calculating the mean of the predicted values ​​located between the first and third quartiles, i.e., within the interquartile range, to characterize the central tendency of the main distribution interval.

[0031] According to the criteria for determining extreme values ​​in the box plot, predicted values ​​located outside the main distribution range are removed.

[0032] Furthermore, a parameter update method is adopted to assign the weights of network links in adjacent layers that do not interact with each other to 0, assign the weights of network links with blank input nodes to constraint values, and assign the deviations corresponding to blank nodes to 0.

[0033] Using a parameter constraint method, a network node is randomly selected from the hidden layer of the nonlinear control network model. The target ratio is determined based on the model calculation value and the original data value of the network node. The deviation of the network node is then updated according to the target ratio, so that the ratio of the model calculation value and the original data value of each network node in the hidden layer is unified to the target ratio.

[0034] The loss value is determined based on the model calculation value and the original data value of the network node in the output layer. When the loss value is less than the set threshold, the weights and biases of the nonlinear control network model are extracted as network model parameters for global optimization.

[0035] The deviation of network nodes is updated based on the target ratio, using the following formula:

[0036] ;

[0037] in, This represents the post-update deviation of network nodes. This represents the current deviation of the network node. These are the raw data values ​​of the network nodes. Calculate values ​​for the network node model. The target ratio.

[0038] A global optimization system for solving missing observations in a nonlinear control network includes:

[0039] The data acquisition module is used to acquire experimental datasets; the experimental datasets include: biological components and their expression levels; the biological components include: active pharmaceutical ingredients, target proteins, biomarkers, and genes;

[0040] The model building module is used to construct a nonlinear regulation network model based on a deep learning model according to the target nonlinear regulation network. The nonlinear regulation network model includes an input layer, several hidden layers, and an output layer. Each network node in the input layer, the hidden layers, and the output layer represents the biological component, the value of each network node represents the expression level of the biological component, and the network links between each network node represent the interaction between the biological components.

[0041] The model training module is used to input the experimental dataset into the nonlinear control network model and initialize the weights and biases using the default initialization method.

[0042] Random values ​​are randomly selected to perform unconstrained training on the initialized nonlinear control network model. The mean value is then taken to obtain the constraint value, thereby achieving global optimization.

[0043] The constraint values ​​are input into the parameter update method. The parameter update method and the parameter constraint method are used to perform constraint training on the initialized nonlinear control network model to obtain the globally optimized network model parameters.

[0044] The information determination module is used to determine the quantitative regulation information of the target nonlinear regulation network based on the network model parameters; the quantitative regulation information is used to predict the regulation result based on the given drug input.

[0045] An electronic device includes a memory and a processor, the memory storing a computer program, and the processor running the computer program to enable the electronic device to perform the global optimization method for solving missing observations in a nonlinear control network as described above.

[0046] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the global optimization method for solving missing observations in a nonlinear control network as described above.

[0047] Compared with the prior art, the beneficial effects of the present invention are:

[0048] This invention combines constrained and unconstrained training, performs statistical analysis and back-substitution verification on the prediction results of the output layer, and thus determines the optimal target value setting method for the weights of network links in the input blank nodes. This method can improve training accuracy by two orders of magnitude, effectively reduce prediction errors, and achieve a globally optimized numerical solution. Attached Figure Description

[0049] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained from these drawings without creative effort.

[0050] Figure 1 This is a flowchart of the method of the present invention;

[0051] Figure 2 This is a schematic diagram of the method for obtaining raw data of the nonlinear control network of the present invention;

[0052] Figure 3 This is a schematic diagram of the target nonlinear control network of the present invention;

[0053] Figure 4 This is a structural diagram of the nonlinear control network model of the present invention;

[0054] Figure 5 This is a structural diagram of the fully connected network model of the present invention. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to represent selected embodiments of the invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] Please see Figure 1 A global optimization method for solving missing observations in a nonlinear control network includes the following steps:

[0057] Obtain the experimental dataset, which includes: biological components and their expression levels; biological components include: active pharmaceutical ingredients, target proteins, biomarkers, and genes;

[0058] The original data of the nonlinear control network was extracted from the experimental data in the literature; the original data of the nonlinear control network was expanded using a method based on normal distribution or uniform distribution to obtain the experimental dataset.

[0059] Taking the paper "Activation of RAW264.7 cells by PCp-I, a polysaccharide from Psoralea corylifolia L, through the NF-κB / MAPK signaling pathway" (see: https: / / journals.sagepub.com / doi / full / 10.1177 / 20587384211010058) as an example, this paper uses a deep learning model to simulate a nonlinear modulation network. Since there is no publicly available data based on this paper, experimental data from the paper needs to be retrieved to support the subsequent process. Due to some error during the retrieval process, the average of multiple retrievals is used as the original data for the nonlinear modulation network. Figure 2 As shown, the original data comes from charts in the literature.

[0060] In one implementation, Origin plotting and data analysis software can be used to import literature figures and extract the figure data. Nodes in the original data (i.e., PCp-1, TLR4, etc.) represent the names of genes or proteins, and the corresponding values ​​represent the expression levels of genes or proteins.

[0061] The raw data obtained above is clearly too little for training deep learning models. Methods are needed to expand the data to a scale suitable for training.

[0062] In one implementation, a method based on a normal (Gaussian) distribution is used to augment the data, specifically using the following formula:

[0063] Among them, y 原始 Represents the original data, y 扩充 This represents the expanded data. This is the expression for the normal distribution, where μ is the mean of the normal distribution and σ is the standard deviation. Therefore, for a random x, this expression yields a value that conforms to a normal distribution. Comparing this value with y... 原始 Adding them together gives y 扩充 .

[0064] In another implementation, a method based on uniform distribution is used to augment the data, specifically using the formula: y 扩充 =y 原始 +a'+p(b'-a')

[0065] Where a' and b' represent the boundaries of the uniform distribution, p is the probability value of the uniform distribution, and a'+p(b'-a') is the inverse of the cumulative distribution function of the uniform distribution. This formula yields a value within the interval (a', b'). This value is then compared with y... 原始 Adding them together gives y 扩充 .

[0066] The above methods can be configured with different parameters to expand the dataset, which is then divided into training, validation, and test sets in a 90:5:5 ratio for subsequent training, validation, and testing of nonlinear control networks based on deep learning models.

[0067] Construct a nonlinear control network model based on a deep learning model based on the target nonlinear control network;

[0068] The nonlinear regulatory network model includes an input layer, several hidden layers, and an output layer; each network node in the input layer, the hidden layers, and the output layer represents the biological component, the value of each network node represents the expression level of the biological component, and the network links between the network nodes represent the interactions between the biological components.

[0069] The construction of a nonlinear regulation network model based on a deep learning model, according to the target nonlinear regulation network, includes: determining the input layer, several hidden layers, and the output layer based on the order of action of each biological component in the target nonlinear regulation network; the input layer represents the drug input to the target nonlinear regulation network, the hidden layer represents the intermediate regulation part of the target nonlinear regulation network, and the output layer represents the regulation result of the target nonlinear regulation network; determining whether there is a direct interaction between network nodes in non-adjacent layers based on the target nonlinear regulation network, and filling blank nodes when there is a direct interaction between network nodes in non-adjacent layers; adding network links between network nodes in the input layer, hidden layer, and output layer, and setting activation functions, loss functions, and optimizers to obtain the nonlinear regulation network model.

[0070] Specifically, the target nonlinear regulatory network can be constructed by extracting data from literature, experiments, gene chip expression data, biological pathways, and other scenarios. The constructed nonlinear regulatory network consists of three parts: an input end (i.e., drug input), an intermediate regulatory part, and an output end (i.e., the regulatory result). The data type is integer or floating-point (i.e., real number).

[0071] The construction of nonlinear regulatory networks can be derived from relevant literature, experiments, biochip data, biological pathways, and combinations thereof, or obtained from any of the network databases in KEGG, Reactome, and WikiPathways. In the literature "Activation of RAW264.7 cells by PCp-I, apolysaccharide from Psoraleacorylifolia L, through NF-κB / MAPK signaling pathway," the nonlinear regulatory network is as follows: Figure 4 As shown, PCp-I acts as the input, and after passing through the intermediate regulation section, it ultimately increases the levels of NO, IL-6, and TNF-α at the output.

[0072] by Figure 3 Taking a nonlinear modulation network as an example, the nonlinear modulation network model based on a deep learning model (hereinafter referred to as the network model) is constructed as follows: PCp-I is used as the input node, and this layer is the input layer of the network model; TLR4 and ROS are used as the first hidden layer of the network model; p38, ERK, JNK and MyD88 are used as the second hidden layer of the network model; there are two AP-1, which are simplified to one and IKK are used as the third hidden layer of the network model; there are three P50 and P65, which are simplified to one and used as the fourth hidden layer of the network model; TNF-α, IL-6 and iNOS are used as the fifth hidden layer of the network model; NO is used as the output layer of the network model. Figure 3In the network model, ROS points to P50P65, but when constructing the network model, the nodes in the first hidden layer need to point to the nodes in the fourth hidden layer, requiring two layers of blank nodes to be added in between. Similarly, when AP-1, as a node in the third hidden layer, is connected to the nodes TNF-α, IL-6, and iNOS in the fifth hidden layer, a layer of blank nodes also needs to be added. Since NO, IL-6, and TNF-α are to be the final output of the network model, a layer of blank nodes needs to be added after the nodes TNF-α and IL-6 in the fifth hidden layer. The final constructed network model is as follows. Figure 4 As shown.

[0073] from Figure 4 As can be seen, this network model differs from typical fully connected deep learning models. A typical fully connected deep learning model is like... Figure 5 As shown, each node in layer k is connected to every node in layer k+1, which is a fully connected layer. And... Figure 5 In the middle, some connections are broken, and the nodes in layer k are only connected to some nodes in layer k+1. This requires some changes to the original deep learning model.

[0074] This invention assigns a weight of 0 to connections that need to be broken, so that the input for those unnecessary connections is not calculated. Furthermore, blank nodes also require processing. Figure 3 The network does not currently have such nodes. This invention adds these blank nodes to ensure consistent path depth, making it more suitable for fully connected networks. The added blank nodes must meet the following requirements: First, the addition of a blank node should not affect the forward propagation of the network model; that is, the input value should not change after passing through the blank node, as if the node did not exist. Second, the issue of blank nodes must be considered during gradient updates. After gradient updates, blank nodes must still meet the requirement of not affecting forward propagation. This requires that the weights and biases connected to the blank node not be changed during gradient updates, or that the weights and biases connected to the blank node be reassigned after the gradient update. Figure 4 As can be seen, in order for blank nodes to meet the above requirements, the weight of the input edge of each blank node must be assigned a value of 1, and the bias corresponding to the blank node must also be assigned a value of 0.

[0075] In the network model, the input and output of each node satisfy the following relationship:

[0076]

[0077] Where y is the output, x i It is the input, w i Here, b is the weight for each input, b is the bias, and n is the number of inputs.

[0078] by Figure 4 Taking node AP-1 in the third hidden layer as an example, its output can be expressed as follows:

[0079] y AP-1 =w p38 x p38 +w ERK x ERK +w JNK x JNK +b

[0080] In this context, the subscripts AP-1, p38, ERK, and JNK all represent the corresponding nodes.

[0081] The above expression provides a good understanding of the input and output relationship of a single node. In fact, during the forward propagation of a network model, matrix operations are performed on a layer-by-layer basis. Therefore, the input weights and biases between layers can be expressed as follows:

[0082] The weights w from the input layer to the first hidden layer 2 and bias b 2 :

[0083]

[0084] The weight w from the first hidden layer to the second hidden layer 3 and bias b 3 :

[0085]

[0086] The weights w from the second hidden layer to the third hidden layer 4 and bias b 4 :

[0087]

[0088] The weights w from the third hidden layer to the fourth hidden layer 5 and bias b 5 :

[0089]

[0090] The weight w from the fourth hidden layer to the fifth hidden layer 6 and bias b 6 :

[0091]

[0092] The weight w from the fifth hidden layer to the output layer 7 and bias b 7 :

[0093]

[0094] in, The subscript indicates the relationship between the second node of the first hidden layer and the first node of the input layer. The subscript of a node indicates the second node in the first hidden layer, and their superscripts indicate the first hidden layer (the second layer in the network), and so on.

[0095] Having determined the structure of the network model, activation functions are still needed to achieve the nonlinear solution of the nonlinear control network. This invention uses the following activation functions:

[0096] Sigmoid function:

[0097] Tanh function:

[0098] ReLU function:

[0099] Leaky ReLU function:

[0100] Softplus function: f(x) softplus =log(1+e x )

[0101] Therefore, from the perspective of the entire network, the input layer to the output layer satisfies the following equation:

[0102]

[0103] The above formula illustrates the forward propagation process of the model. To ensure the model converges to the required range, the backpropagation algorithm is needed to continuously update the gradient. In this model, the mean squared error is used as the loss function as shown in the following formula, Adam is used as the optimizer, and an appropriate learning rate is employed:

[0104]

[0105] in, Let N represent the total number of samples, and y represent the original data values ​​of the network nodes in the output layer. This represents the model-calculated value of the network node in the output layer.

[0106] The nonlinear control network model was trained using an experimental dataset to obtain the network model parameters, which include the weights and biases of signal transmission between network nodes in the input, hidden, and output layers.

[0107] This step specifically includes: inputting the experimental dataset into the nonlinear regulatory network model and initializing the weights and biases using the default initialization method; adjusting the sign of the weights in the nonlinear regulatory network model using the parameter initialization method so that the weights satisfy the interaction relationships between biological components; the interaction relationships include: activation relationships and inhibition relationships. When the weight is positive, the interaction relationship between biological components is an activation relationship, and when the weight is negative, the interaction relationship between biological components is an inhibition relationship.

[0108] Unconstrained training is performed on the initialized nonlinear control network model, and the prediction results of each node in the output layer are calculated respectively.

[0109] Remove outliers from the prediction results of each node in the output layer;

[0110] The constraint value is obtained by taking the arithmetic mean of the prediction results of each node in the output layer after removing outliers.

[0111] The constraint values ​​are input into the parameter update method. The parameter update method and the parameter constraint method are used to perform constraint training on the initialized nonlinear control network model to obtain the globally optimized network model parameters.

[0112] The parameter update method is adopted to assign the weights of network links in adjacent layers that do not interact with each other to 0, assign the weights of network links with blank input nodes to the constraint values, and assign the deviations corresponding to blank nodes to 0.

[0113] A parameter constraint method is adopted to select a network node from the hidden layer of the nonlinear control network model. The target ratio is determined based on the model calculation value and the original data value of the network node. The deviation of the network node is updated according to the target ratio to unify the ratio of the model calculation value and the original data value of each network node in the hidden layer to the target ratio. The loss value is determined based on the model calculation value and the original data value of the network node in the output layer. When the loss value is less than a set threshold, the weights and deviations of the nonlinear control network model are extracted as network model parameters.

[0114] Specifically, the nonlinear control network model based on deep learning, constructed through the above steps, needs to be trained to achieve convergence and stability, yielding the final network model parameters. The network model training is implemented using the PyTorch framework, where the model's weights and biases have a default initialization, as shown in the following formula:

[0115]

[0116] Where w represents the model weights and b represents the model bias. Indicates the boundary as The uniform distribution of the input, k is a parameter determined by the dimension of the input, and in_features is the dimension of the input, which is 1 in this embodiment.

[0117] To ensure that the completed network model meets the requirements of the construction process, it is necessary to design some methods to participate in the training process of the network model.

[0118] This invention designs a parameter update method, the main content of which is:

[0119] The initialized nonlinear control network model is trained without constraints. After deep learning training, the prediction results of the output layer are calculated. Based on the quartile structure defined by the box plot, the mean of the predicted values ​​located between the first quartile (Q1) and the third quartile (Q3), i.e., the interquartile range (IQR), is calculated to characterize the central tendency of the main distribution interval. According to the criteria for judging extreme values ​​in the box plot, predicted values ​​outside the interval [Q1−1.5×IQR,Q3+1.5×IQR] are removed. Only the mean of the prediction results of the remaining non-extreme output layer is calculated, and this arithmetic mean is used as the constraint value to obtain a robust statistical estimate that is insensitive to abnormal fluctuations. In addition to removing predicted values ​​outside the main distribution interval, any one of the following methods can be used to remove outliers from the prediction results of the output layer: Z-score, modified Z-score, isolated forest, density-based LOF, single-class support vector machine anomaly detection, and density-based DBSCAN.

[0120] After obtaining the constraint values, the weights of the connections that need to be broken are assigned to 0. Next, the weights of the input edges of the blank nodes are assigned the constraint values, and then the deviations corresponding to the blank nodes are assigned to 0. To ensure that the above requirements are still met after the gradient update, the parameter update method is called after the gradient update.

[0121] Taking the transition from the first hidden layer to the second hidden layer as an example, the requirement is... =0, For constraint values, =0,

[0122] As shown in the following formula:

[0123]

[0124] In addition, from Figure 3 As can be seen, all edges controlled by the nonlinear control network are solid arrows, indicating that their relationships are activation rather than inhibition. This requires the corresponding... Figure 4The connection weights between nodes in the model are positive. To address this issue, this invention designs a parameter initialization method, which is called during model initialization to ensure that the final model parameters meet the requirements. Figure 3 The activation relationship shown is manifested in Figure 4 In this context, the weights of all connections between non-empty nodes are positive. However, in the PyTorch framework, after default initialization, the weights can be both positive and negative, so the parameter initialization method of this invention must be used. Taking the connection from the first hidden layer to the second hidden layer as an example, all weights must be greater than 0, as shown in the following formula:

[0125]

[0126] To ensure that the ratio of the calculated node values ​​in the model to the original data values ​​at that node is consistent, it is necessary to introduce other values ​​from the original data besides the input and output into the model and constrain their ratio during training. Since the weights have already been constrained in the previous parameter initialization and update methods, this invention designs a parameter constraint method that focuses on the bias. Each time a node is selected, the ratio r of the model's calculated value to the original data value is calculated. This ratio r is then generalized to all hidden layer nodes of the model. The specific operation is shown in the following formula:

[0127]

[0128] Among them, b new Let be the updated deviation of the network node, b be the current deviation of the network node, and y be the deviation of the network node. 原始 These are the raw data values ​​of the network nodes. is the model calculated value for network nodes, and r is the target proportion.

[0129] Taking the change from the first hidden layer to the second hidden layer as an example, the specific formula for updating the deviation is:

[0130]

[0131] It is important to note that during training, the parameter initialization method should be called during model initialization. Before calling the parameter update method and parameter constraint method, unconstrained model training with random values ​​is required first. After the model training stabilizes, constraint values ​​are obtained. Then, the parameter update method is obtained based on the constraint values. The parameter update method and parameter constraint method should be called after the model updates the gradient. The model is then trained with constraints again. After the model training stabilizes, given a drug input, its regulatory effect can be predicted, and global optimization can be obtained.

[0132] By combining constrained and unconstrained training, statistical analysis and back-substitution verification are performed on the prediction results of the output layer, thereby determining the optimal target value setting method for the weights of network links in the input blank nodes.

[0133] The quantitative regulation information of the target nonlinear regulation network is determined based on the network model parameters; the quantitative regulation information is used to predict the regulation result based on the given drug input.

[0134] After training, the original data from the literature is input, and the results at each node will be proportional to the data of each node in the literature's nonlinear regulation network. The root mean square error between the output of the network model and the final regulation result of the literature's nonlinear regulation network will be controlled below 0.01. In addition, the activation / inhibition relationship between nodes fully meets the requirements of the target nonlinear regulation network in the literature.

[0135] Once the network model is stable and accurate, its parameters, namely weights and biases, are extracted. These parameters form the nonlinear quantitative regulatory information of the nonlinear regulatory network (the weights and biases after the nonlinear regulatory network model is trained represent the regulatory information of the nonlinear regulatory network, where weights represent the activation / inhibition relationship between two nodes, and biases represent the threshold at that node). With all weights and biases obtained, the regulatory outcome can be predicted for a given drug input, thus achieving global optimization of the missing observations in the nonlinear regulatory network. This invention combines constrained and unconstrained training, performs statistical analysis and back-substitution verification on the prediction results of the output layer, and determines the optimal target value setting method for the weights of network links to input blank nodes. This achieves two orders of magnitude of training accuracy, effectively reduces prediction errors, and realizes a globally optimized numerical solution.

[0136] To further illustrate the technical effects of the method for solving the quantization control information of nonlinear control networks provided by the present invention, a set of specific embodiments and comparative examples are provided below.

[0137] Example:

[0138] Experimental conditions: The dataset was divided into training and test sets in an 8:2 ratio. Nonlinear control network models with an input dimension of 2 and an output dimension of 3 were constructed using PyTorch. The hyperparameters for training were as follows: optimizer: Adam; learning rate: 0.01; loss function: mean squared error function; training epochs: 1000; training iterations: 300.

[0139] When the interaction relationship is activation: the weights of the network links at the input blank nodes in the nonlinear control network model are assigned values ​​of 0.01, 0.1, 1, 10, and 100, respectively, with losses of 2.010742188, 2.068115234, 0.746788201, 0.027478388, and 313.4483324, respectively. The calculated predicted values ​​of the output layer are... The mean and variance of the difference between the optimal solution and the objective value are: -0.277485915, 0.265621268; -0.270890196, 0.266878957; -0.154424212, 0.139228154; -0.000966536, 0.00065216; -0.000972254, 0.001033539.

[0140] With the addition of suppression in the interaction relationship: the weights of the network links in the nonlinear control network model with blank input nodes are assigned values ​​of 0.01, 0.1, 1, 10, and 100 respectively, and the losses are 2.310786881, 2.071931085, 0.744453262, 0.026185739, and 1109.243243 respectively. The calculated output layer pre- The mean and variance of the difference between the optimal solution and the target value are as follows: -0.267191984, 0.265604443; -0.233836043, 0.209249293; -0.147887718, 0.134040316; -0.001220733, 0.001067847; 0.001201436, 0.007151529.

[0141] The experimental results provide a preliminary conclusion: when the weight of the network link with the input blank node is 10, the best results are obtained for different interaction relationships. This indicates that the high-precision value of the weight of the network link with the input blank node is around 10, but the exact value is still unknown.

[0142] Comparative example:

[0143] first step:

[0144] In the embodiment, five orders of magnitude values ​​were artificially set to find the approximate range of weights for network links with blank input nodes. After processing the results, it was found that the best performance was achieved when the weight of the network link with a blank input node was 10, indicating that the optimal value of the weight of the network link with a blank input node is around 10, but there is no precise value. Therefore, in order to explore a high-precision value for the weight of the network link with a blank input node, a set of experiments was set up for the nonlinear control network model under two experimental conditions. The experimental conditions were: one was a constrained condition, i.e., the experimental conditions in the embodiment; the other was an unconstrained condition, i.e., removing the constraints on edges and nodes in the network model, that is, only calculating the output layer when calculating the loss, allowing the weights of the network links with blank input nodes in the hidden layer to be free, and no longer allowing the value of that layer to fit the target value.

[0145] When the interaction relationship is active: the loss of the nonlinear control network model is reduced to 0.01084874. The mean and variance of the difference between the predicted value and the target value of the output layer calculated in the model with the minimum loss are: -0.000328872 and 0.000236221, respectively. In the embodiment, when the weight of the network link of the input blank node is 10 and the model with the minimum loss is used, the mean and variance of the difference between the predicted value and the target value of the output layer calculated in the nonlinear control network model are: -0.000966536 and 0.00065216, respectively.

[0146] With the addition of suppression in the interaction relationship: the loss of the nonlinear control network model decreased to 0.047741858. The mean and variance of the difference between the predicted and target values ​​of the output layer calculated in the model with the minimum loss were -0.001200778 and 0.001042504, respectively. In the embodiment, with the weight of the network link at the input blank node = 10, the mean and variance of the difference between the predicted and target values ​​of the output layer calculated in the model with the minimum loss were -0.001220733 and 0.001067847, respectively.

[0147] From the above, we can draw an additional conclusion: the nonlinear control network model trained under unconstrained conditions yields model parameters with the minimum loss that are better than those trained under constrained conditions.

[0148] Step Two:

[0149] To find the precise optimal value for the weights of the network links to the blank input node, a set of experiments was conducted on the nonlinear control network model. The weights of the network links to the blank input node were set as follows: 1. Calculate the arithmetic mean of the predicted values ​​of all output layers; 2. Calculate the mean of the predicted values ​​of all output layers within the interquartile range (IQR) between the first quartile (Q1) and the third quartile (Q3) according to the quartile structure defined by the box plot; 3. According to the criteria for judging extreme values ​​in the box plot, remove the predicted values ​​of all output layers that are outside the interval [Q1−1.5×IQR,Q3+1.5×IQR], and calculate the mean only for the remaining non-extreme predicted values. The mean values ​​obtained in these three cases were used as the weights of the network links to the blank input node. The nonlinear control network model was trained under the experimental conditions (constraints) of the embodiment, and the results are shown in Tables 1 and 2.

[0150] Table 1. Comparison of the three mean values ​​for activated edges

[0151] Table 2. Comparison of the three mean values ​​for adding suppression edges

[0152] The analysis of the results leads to the conclusion that, under the condition that the interaction relationship is activated, the best performance is achieved by using the mean (9.73280922676356) of all non-extreme values ​​of the predicted values ​​of the output layer of the unconstrained nonlinear control network model as the high-precision value for the weights of the network links to the input blank nodes. The mean and variance of the obtained global optimal solution relative to the target value are -0.000466744 and 0.000334824, respectively. Compared to the mean and variance of the global optimal solution relative to the target value obtained when the weights of the network links to the input blank nodes are =1 (-0.154424212 and 0.139228154), the prediction error is reduced by approximately 3%. The prediction error was reduced by 30 times. Under the condition of suppression in the interaction relationship, the mean value of all predicted values ​​of the output layer of the unconstrained nonlinear control network model in the Q1-Q3 interval (8.04976418177287) was used as the optimal value for the weights of the network links to the input blank nodes. This yielded the best results, with the mean and variance of the global optimal solution relative to the target value being -0.000882625 and 0.000440521, respectively. Compared to the mean and variance of the global optimal solution relative to the target value when the weight of the network link to the input blank node was 1 (-0.1478877180.134040316), the prediction error was reduced by approximately 167 times. This demonstrates a method for calculating high-precision values ​​of the weights of the network links to the input blank nodes to find the globally optimal numerical solution under different edge types.

[0153] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A global optimization method for solving missing observations in a nonlinear control network, characterized in that: Includes the following steps: Obtain the experimental dataset, which includes: biological components and their expression levels; biological components include: active pharmaceutical ingredients, target proteins, biomarkers, and genes; Construct a nonlinear control network model based on a deep learning model based on the target nonlinear control network; The nonlinear control network model includes: an input layer, several hidden layers, and an output layer; Each network node in the input layer, hidden layer, and output layer represents a biological component; the value of each network node represents the expression level of the biological component; and the network links between each network node represent the interactions between the biological components. The experimental dataset was input into the nonlinear control network model, and the weights and biases were initialized using the default initialization method. The initialized nonlinear control network model is trained without constraints, and the mean value is taken to obtain the constraint value, thereby achieving global optimization. The constraint values ​​are input into the parameter update method. The parameter update method and the parameter constraint method are used to perform constraint training on the initialized nonlinear control network model to obtain the globally optimized network model parameters. The quantitative regulation information of the target nonlinear regulation network is determined based on the parameters of the globally optimized network model; the quantitative regulation information is used to predict the regulation result based on the given drug input.

2. The global optimization method for solving missing observations in a nonlinear control network according to claim 1, characterized in that, Methods for obtaining experimental datasets include: Raw data of the nonlinear control network were extracted from experimental data in the literature; The original data of the nonlinear control network is expanded using methods based on normal or uniform distribution to generate an experimental dataset.

3. The global optimization method for solving missing observations in a nonlinear control network according to claim 1, characterized in that, Based on the target nonlinear modulation network, a nonlinear modulation network model based on a deep learning model is constructed, specifically including: The input layer, several hidden layers, and the output layer are determined based on the order of action of each biological component in the target nonlinear regulatory network. The input layer represents the drug input to the target nonlinear regulatory network, the hidden layer represents the intermediate regulatory part of the target nonlinear regulatory network, and the output layer represents the regulatory result of the target nonlinear regulatory network. Based on the target nonlinear control network, determine whether there is a direct interaction between network nodes in non-adjacent layers, and fill in blank nodes when there is a direct interaction between network nodes in non-adjacent layers. By adding network links between network nodes in the input layer, hidden layer, and output layer, and setting activation functions, loss functions, and optimizers, a nonlinear control network model is obtained. Activation functions include at least one of the following: Sigmoid function, Tanh function, ReLU function, LeakyReLU function, and Softplus function; The loss function is the mean squared error loss function; the optimizer is the Adam optimizer.

4. The global optimization method for solving missing observations in a nonlinear control network according to claim 1, characterized in that, A parameter initialization method is used to adjust the sign of the weights in the nonlinear regulatory network model so that the weights satisfy the interaction relationship between biological components. Interaction relationships include activation relationships and inhibition relationships. When the weight is positive, the interaction relationship between biological components is an activation relationship, and when the weight is negative, the interaction relationship between biological components is an inhibition relationship.

5. The global optimization method for solving missing observations in a nonlinear control network according to claim 1, characterized in that, Randomly selected values ​​are used to perform unconstrained training on the initialized nonlinear control network model. The mean value is then taken to obtain the constraint value, achieving global optimization. This process includes: Random values ​​are used to train the initialized nonlinear control network model, and the prediction results of each node in the output layer are calculated respectively. Remove outliers from the prediction results of each node in the output layer; The arithmetic mean of the prediction results of each node in the output layer after removing outliers is calculated to obtain the constraint value. The arithmetic mean is used to constrain the node output results to achieve global optimization.

6. The global optimization method for solving missing observations in a nonlinear control network according to claim 5, characterized in that, Remove outliers from the prediction results of each node in the output layer. Specifically, this includes: calculating the mean of the predicted values ​​located between the first and third quartiles, i.e., within the interquartile range, based on the quartile structure defined by the box plot, to characterize the central tendency of the main distribution interval. According to the criteria for determining extreme values ​​in the box plot, predicted values ​​located outside the main distribution range are removed.

7. The global optimization method for solving missing observations in a nonlinear control network according to claim 1, characterized in that, The parameter update method is adopted to assign the weights of network links in adjacent layers that do not interact with each other to 0, assign the weights of network links with blank input nodes to the constraint values, and assign the deviations corresponding to blank nodes to 0. Using a parameter constraint method, a network node is randomly selected from the hidden layer of the nonlinear control network model. The target ratio is determined based on the model calculation value and the original data value of the network node. The deviation of the network node is then updated according to the target ratio, so that the ratio of the model calculation value and the original data value of each network node in the hidden layer is unified to the target ratio. The loss value is determined based on the model calculation value and the original data value of the network node in the output layer. When the loss value is less than the set threshold, the weights and biases of the nonlinear control network model are extracted as network model parameters for global optimization. The deviation of network nodes is updated based on the target ratio, using the following formula: ； in, This represents the post-update deviation of network nodes. This represents the current deviation of the network node. These are the raw data values ​​of the network nodes. Calculate values ​​for the network node model. The target ratio.

8. A global optimization system for solving missing observations in a nonlinear control network, characterized in that, include: The data acquisition module is used to acquire experimental datasets; The experimental dataset includes: biological components and their expression levels; the biological components include: active pharmaceutical ingredients, target proteins, biomarkers, and genes; The model building module is used to construct a nonlinear regulation network model based on a deep learning model according to the target nonlinear regulation network. The nonlinear regulation network model includes an input layer, several hidden layers, and an output layer. Each network node in the input layer, the hidden layers, and the output layer represents the biological component, the value of each network node represents the expression level of the biological component, and the network links between each network node represent the interaction between the biological components. The model training module is used to input the experimental dataset into the nonlinear control network model and initialize the weights and biases using the default initialization method. Random values ​​are randomly selected to perform unconstrained training on the initialized nonlinear control network model. The mean value is then taken to obtain the constraint value, thereby achieving global optimization. The constraint values ​​are input into the parameter update method. The parameter update method and the parameter constraint method are used to perform constraint training on the initialized nonlinear control network model to obtain the globally optimized network model parameters. The information determination module is used to determine the quantitative regulation information of the target nonlinear regulation network based on the network model parameters; the quantitative regulation information is used to predict the regulation result based on the given drug input.

9. An electronic device, characterized in that, The device includes a memory and a processor, the memory being used to store a computer program, and the processor running the computer program to enable the electronic device to perform a global optimization method for solving missing observations in a nonlinear control network as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, It stores a computer program that, when executed by a processor, implements the global optimization method for solving missing observations in a nonlinear control network as described in any one of claims 1 to 7.

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