A federal decision tree information quantity measurement method based on information entropy

Abstract

The present application relates to federated learning and machine learning tree model technology, in particular to a federated decision tree information measurement method based on information entropy, comprising a training process and a measurement process. In the training process, first configure the environment of federated learning, based on the configured learning environment, obtain sample data, and preprocess it; jointly build a CART tree through a joint participant and a parameter server; finally, a plurality of CART trees are combined to form a federated decision tree forest. When jointly building the CART tree, the calculation rate is improved by introducing a screening of inferior participants. In the measurement process, for a single decision tree, first divide the nodes of the tree according to the participant number; then, calculate the probability of all flow routes and the entropy value of the tree; the information content of the tree is obtained by the difference between the entropy value of the tree and the empty tree. The information content of the decision tree in the federated decision tree forest is quantified, and the purpose of optimizing the interest distribution of the federated decision tree participants is achieved.

Description

Technical Field

[0001] This invention relates to federated learning and machine learning tree model technology, specifically to a method for measuring the information content of a federated decision tree based on information entropy. Background Technology

[0002] With the continuous development of the internet and the rise of e-commerce and short videos, the research on recommendation algorithms has become increasingly in-depth, and their applications are becoming more and more widespread. Due to its good interpretability, the decision tree algorithm is often used to implement recommendation algorithms. Traditional decision tree algorithms often require centralized collection and processing of user data, and then training a global model based on this data; however, this method carries the risk of data privacy leakage.

[0003] Federated decision trees enable collaboration and data sharing among platforms while protecting data privacy, improving the accuracy and robustness of recommendation models. Federated Forest, proposed by Liu et al. in 2019, is an implementation of the federated decision tree method. In a federated forest, each participant, such as different platforms, retains its own data. Using federated learning, the model is trained on each participant, and these models are ultimately integrated to obtain a global model. Because each participant only retains its own data, data privacy issues are avoided. Federated forests can utilize integrated user data and behavior from various platforms to train a more accurate recommendation model. Taking e-commerce platforms as an example, federated forests can use users' search and browsing history across different platforms to recommend more suitable online shopping products.

[0004] Because federated decision trees require collaboration among various platforms, and all information is contained within the decision tree, there is a lack of effective allocation methods for the final distribution of benefits. Therefore, providing an effective method for measuring decision tree information is a significant challenge in solving the application of federated decision trees. Summary of the Invention

[0005] The purpose of this invention is to provide a method for measuring the information content of a federated decision tree based on information entropy, so as to solve the problem that the existing technology cannot quantify the distribution of benefits among participants in a federated decision tree.

[0006] To achieve the above objectives, the present invention addresses the following technical problem:

[0007] A method for measuring the information content of a federated decision tree based on information entropy includes the following training and measurement processes:

[0008] The training process includes:

[0009] S1. Configure the federated learning environment and prepare data.

[0010] The federated learning environment configuration includes configuring a parameter server and connecting N participants and the parameter server to a private network;

[0011] The data preparation includes sample data acquisition and preprocessing, and the sample data acquisition and preprocessing process is as follows:

[0012] Each participant obtains their own sample data. With data label F i and sample data With data label F i Uploaded to the parameter server; sample data Includes sample ID, product ID, category, browsing time, browsing duration, etc. F represents the sample data of the i-th participant. i This represents the data label for the i-th participant. This embodiment obtains sample data by collecting user product browsing behavior data and the labels of items added to the shopping cart. With data label F i .

[0013] The parameter server merges the sample IDs uploaded by each participant to obtain the sample ID set D, and merges the tags uploaded by each participant to obtain the tag set F;

[0014] S2, Joint participants and parameter server jointly construct CART tree

[0015] S2.1 The parameter server creates a decision tree T and an empty root node node on T to initialize the decision tree construction;

[0016] S2.2 The parameter server distributes the structure of the decision tree T to each participant and marks the newly added empty nodes.

[0017] S2.3 After updating their local decision tree structure based on the structure provided in S2.2, participants calculate the splitting parameters of the current node and feed the results back to the parameter server. The node splitting parameters include: the local optimal Gini index. i Optimal segmentation label j i Optimal segmentation value s i and the probability of flow p i ;

[0018] S2.4 The parameter server calculates global node segmentation parameters to determine the candidate participants for this communication round and screen out inferior participants to terminate the subsequent training process.

[0019] S2.5. Based on the candidate participants for this communication round determined by the parameter server in S2.4, the participants choose to delete or save node information and send the deleted or saved node information to the parameter server.

[0020] S2.6. Repeat S2.2 to S2.6 to update the decision tree structure T until the federated decision tree is completed;

[0021] S3. Combine multiple CART trees to form a federated decision tree forest.

[0022] S3. Add the federated decision tree to the federated decision tree forest, and determine the size of the forest as needed. If the forest is not large enough, repeat S2.

[0023] The measurement process includes:

[0024] S4. Calculate the information content of each tree; taking participant i as an example, the calculation process for the information content of each tree is as follows:

[0025] S4.1. Divide the tree nodes according to the participant number. The node division rule is: retain the node information where the candidate participant number in the communication round is the same as the participant i number, and set the remaining nodes as empty nodes.

[0026] S4.2 Find the node flow path combination, which includes finding all node flow paths and calculating the flow probability; the flow path is found using the decision tree sample prediction principle, and the flow path probability is obtained by a preset calculation rule;

[0027] S4.3 Summarize all flow route combinations and construct a flow route probability distribution table;

[0028] S4.4 Calculate the entropy value CH of each flow path using formula (1), as shown in formula (1) below:

[0029] CH=-∑p(x j )*log2(p(x j ))#(1)

[0030] Where p(x) j ) represents the xth j The probability distribution of the leaves;

[0031] S4.5 Calculate the flow probability for each flow route;

[0032] S4.6 Calculate the entropy value TH of decision tree T using formula (2), as shown below:

[0033] T=∑p k *CH#(2)

[0034] Where, p k This represents the probability of the k-th flow route.

[0035] S4.7 Set all nodes to empty nodes and calculate the entropy value TH′ of the empty decision tree T;

[0036] S4.8. Based on the entropy value TH of decision tree T and the entropy value TH′ of empty tree, the information content T of decision tree T is calculated using formula (3). info Formula (3) is shown below;

[0037] T info =TH′-TH.

[0038] Furthermore, the specific operation method for the parameter server to distribute the structure of decision tree T to each participant in S2.2 is as follows:

[0039] S2.2.1 The parameter server randomly samples from D with an 80% probability to obtain the global sample ID sample set D′, and randomly samples from F with an 80% probability to obtain the global data label sample set F′.

[0040] S2.2.2 Perform the following operation on all i∈N:

[0041] Connect D′ and D i Find the intersection to obtain the sample set D′ of participant i's sample IDs. i , with F' and D i Find the intersection to obtain the sample set F′ of the data labels of participant i. i Then distribute D′ to the i-th participant. i With F′ i .

[0042] Furthermore, the specific operation method for calculating the segmentation parameters of the current node in S2.3 is as follows:

[0043] S2.3.1, Receive D′ i With F′ i , D′ i and The intersection of sample IDs yields the sample set of data for participant i.

[0044] S2.3.3 Calculation based on the principle of constructing a CART tree The local optimal Gini index i Optimal segmentation label j i With the optimal segmentation value s i ;

[0045] Calculate the probability of flow direction These represent the percentage of samples flowing to the left child node and the percentage of samples flowing to the right child node after segmentation according to the optimal segmentation label and the optimal segmentation value, respectively.

[0046] Furthermore, the specific operation method of step S2.4 is as follows:

[0047] The parameter server aggregates the local optimal Gini index, optimal split label, optimal split value, and flow probability p of all participants. i The participant with the highest local Gini index will be selected as the candidate participant for this communication round.

[0048] If the candidate participants in this communication round are the same as those in the previous round, then the participant with the second highest local Gini index will be selected as the candidate participant for this communication round; the candidate participant for this communication round will be notified to save the node information, i.e., send a sign. i =Save, notify other participants to delete node information, i.e., send a sign i =Delete;

[0049] If a participant is not selected as a candidate participant in any of the N*|F|*2 communication rounds, then that participant is considered a poor participant, and their subsequent training process ends. It should be noted that poor participants can retain the generated tree model, but cannot participate in any subsequent processes.

[0050] Furthermore, the specific operation method of S2.5 is as follows:

[0051] S2.5.1, Signal for receiving parameter server to save and delete node information. i and perform the following operations:

[0052] If sign i =Delete, then delete Gini i Optimal segmentation label j i Optimal segmentation value s i With the probability of flow direction p i At the same time, it does not screen for inferior participants;

[0053] If sign i =Save, then store Gini in the current empty node. i Optimal segmentation label j i Optimal segmentation value s i With the probability of flow direction p i ;

[0054] S2.5.2, Based on the optimal segmentation label j i With the optimal segmentation value s i segmentation The subset of data samples flowing to the left child node under participant i. The subset of data samples flowing to the right child node under participant i.

[0055] S2.5.3, Extraction and The data labels are used to obtain the subset of sample IDs flowing to the left child node under participant i. The subset of sample IDs flowing to the right child node under participant i.

[0056] S2.5.4, will and Send to the parameter server.

[0057] Furthermore, the specific operation method of S2.6 is as follows:

[0058] S2.6.1 Store in the newly added node the candidate participant number for this communication round, as well as the participant's local optimal Gini index, optimal split label, optimal split value, and flow probability; receive data from the candidate participants for this communication round. and Set it to D′ left With D′ right If D′ left The length is less than 5% of D or D′ right If the length of is less than 5% of D, then stop this communication round and do not execute the remaining steps.

[0059] S2.6.2, Create the left and right child nodes of the node;

[0060] S2.6.3 For the left child node, create a new communication round. Let the left child node be node, and let D′ be... left Let D′ be the node, and recursively execute S2.3 to S2.6; for the right child node, create a new communication round, let the right child node be node, and let D′ be the node. right Let D′ be the value, and recursively execute S2.3 to S2.6.

[0061] After adopting the above technical solution, the present invention has the following beneficial effects:

[0062] (1) In the training process, this invention improves the computation speed by introducing a screening method to identify inferior participants. Moreover, this method only requires participants to upload one additional parameter, thus maximizing the protection of participant privacy.

[0063] (2) The present invention decomposes the flow probability of the decision tree, thereby quantifying the information content of the decision tree in the federated decision tree forest and achieving the goal of optimizing the distribution of benefits among the participants in the federated decision tree. Attached Figure Description

[0064] Figure 1 This is a flowchart of the training process in an embodiment of the present invention;

[0065] Figure 2 This is a flowchart of the measurement process in an embodiment of the present invention;

[0066] Figure 3 This is an example diagram of the probability distribution table of flow routes in an embodiment of the present invention. Detailed Implementation

[0067] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0068] This embodiment uses e-commerce product recommendation as an application background and provides a federated decision tree information content measurement method based on information entropy, comprising two parts: a training process and a measurement process. In the training process, the federated learning environment is first configured, including additional configuration of parameter servers and access participants. The participants are servers used by the e-commerce platform to collect shopping cart information; they generally do not belong to the same business unit. Next, the participants acquire sample data and preprocess it. Then, the participants and parameter servers jointly construct a CART tree for predicting user product preferences. Finally, multiple CART trees are aggregated to form a federated decision tree forest. In the measurement process, for a single decision tree, the tree nodes are first divided according to the participant number. Then, the probability of all flow routes is calculated, and the entropy value of the tree is calculated. Finally, the information content of the tree is obtained by the difference between the entropy value of the tree and that of an empty tree. This invention quantifies the contribution of each participant in the prediction process, providing a basis for the e-commerce platform to settle revenue for different business units. Detailed descriptions of each part are as follows:

[0069] See Figure 1 The training process includes the following steps:

[0070] S1. Configure the federated learning environment and prepare data, including:

[0071] The federated learning environment configuration includes configuring a parameter server and connecting N participants and the parameter server to a private network;

[0072] The data preparation includes sample data acquisition and preprocessing. The sample data acquisition and preprocessing process is as follows:

[0073] Participants in each business unit obtain product sample data for their respective businesses. With product data label F i and sample data With data label F i Uploaded to the parameter server; sample data Includes sample ID, product ID, category, browsing time, browsing duration, order status, etc. F represents the sample data of the i-th participant. iThis represents the data label for the i-th participant. This embodiment obtains sample data by collecting user product browsing behavior data and the labels of items added to the shopping cart. With data label F i .

[0074] The parameter server merges the sample IDs uploaded by each participant to obtain the sample ID set D, and merges the tags uploaded by each participant to obtain the tag set F;

[0075] S2, Joint participants and parameter server jointly construct CART tree

[0076] S2.1 The parameter server creates a decision tree T and an empty root node node on T to initialize the decision tree construction;

[0077] S2.2 The parameter server distributes the structure of decision tree T to each participant and marks the newly added empty nodes; the specific operation of distributing the structure of decision tree T is as follows:

[0078] S2.2.1 The parameter server randomly samples from D with an 80% probability to obtain the global sample ID sample set D', and randomly samples from F with an 80% probability to obtain the global sample ID sample set F'.

[0079] S2.2.2 Perform the following operation on all i∈N:

[0080] Connect D′ and D i Find the intersection to obtain D′ i , with F' and D i Find the intersection to obtain F′ i Then distribute D′ to the i-th participant. i With F′ i .

[0081] S2.3 After updating their local decision tree structure based on the structure provided in S2.2, participants calculate the node splitting parameters for the current node and feed the results back to the parameter server. The node splitting parameters include: the local optimal Gini index. i Optimal segmentation label j i Optimal segmentation value s i and the probability of flow p i ;

[0082] The steps for calculating the node segmentation parameters are as follows;

[0083] S2.3.1, Receive D′ i With F′ i D ′i and Find the intersection of the sample IDs to obtain...

[0084] S2.3.3 Calculation based on the principle of constructing a CART tree The local optimal Gini index i Optimal segmentation label j i With the optimal segmentation value s i ;

[0085] Calculate the probability of flow direction These represent the percentage of samples flowing to the left child node and the percentage of samples flowing to the right child node after segmentation according to the optimal segmentation label and the optimal segmentation value, respectively.

[0086] S2.4 The parameter server calculates the global node segmentation parameters, determines the candidate participants for this communication round, and filters out inferior participants to terminate the subsequent training process.

[0087] The parameter server aggregates the local optimal Gini index, optimal split label, optimal split value, and flow probability p of all participants. i The participant with the highest local Gini index will be selected as the candidate participant for this communication round.

[0088] If the candidate participants in this communication round are the same as those in the previous round, then the participant with the second highest local Gini index will be selected as the candidate participant for this communication round; the candidate participant for this communication round will be notified to save the node information, i.e., send a sign. i =Save, notify other participants to delete node information, i.e., send a sign i =Delete.

[0089] If a participant is not selected as a candidate participant in any of the N*|F|*2 communication rounds, then that participant is considered a poor participant, and their subsequent training process ends. It should be noted that poor participants can retain the generated tree model, but cannot participate in any subsequent processes.

[0090] S2.5. Based on the candidate participants for this communication round determined by the server in parameter S2.4, participants choose to delete or retain node information, thus completing the child node construction. The detailed process is as follows:

[0091] S2.5.1, Signal for receiving parameter server to save and delete node information. i and perform the following operations:

[0092] If sign i =Delete, then delete Gini i Optimal segmentation label j i Optimal segmentation value s i With the probability of flow direction p i At the same time, it does not screen for inferior participants;

[0093] If sign i =Save, then store Gini in the current empty node. i Optimal segmentation label j i Optimal segmentation value s i With the probability of flow direction p i ;

[0094] S2.5.2, Based on the optimal segmentation label j i With the optimal segmentation value s i segmentation get and

[0095] S2.5.3, Extraction and Data labels obtained and

[0096] S2.5.4, will and Send to the parameter server.

[0097] S2.6, The parameter server updates the tree model;

[0098] S2.6.1 Store in the node the candidate participant number for this communication round, as well as the participant's local optimal Gini index, optimal split label, optimal split value, and flow probability; receive data from the candidate participants for this communication round. and Set it to D′ left With D′ right If D′ left The length is less than 5% of D or D′ right If the length of is less than 5% of D, then stop this communication round and do not execute the remaining steps.

[0099] S2.6.2, Create the left and right child nodes of the node;

[0100] S2.6.3 For the left child node, create a new communication round. Let the left child node be node, and let D′ be... left Let D′ be the node, and recursively execute S2.3 to S2.6; for the right child node, create a new communication round, let the right child node be node, and let D′ be the node. right Let D′ be the value, and recursively execute S2.3 to S2.6;

[0101] S3. Add the federated decision tree T to the federated decision tree forest, and determine the size of the forest as needed. If the forest is not large enough, repeat S2.

[0102] See Figure 2 The measurement process includes the following steps:

[0103] S4. Calculate the information content of each tree. The calculation process is described below using participant i as an example:

[0104] S4.1. Divide the tree nodes according to the participant number. The node division rule is: retain the node information where the candidate participant number in the communication round is the same as the participant i number, and set the remaining nodes as empty nodes.

[0105] S4.2 Find the node flow path combinations, which includes finding all node flow paths and calculating the probability of flow paths.

[0106] This embodiment utilizes the decision tree sample prediction principle to identify all retained node information flow paths. Specifically: samples flow from the root node to the leaf nodes. If a non-leaf node is encountered during this process, the samples flowing to that node are split according to the splitting information, causing the split samples to flow to the left and right child nodes respectively. If an empty non-leaf node is encountered, the samples will flow to both the left and right child nodes simultaneously; that is, an empty non-leaf node will create a new flow path.

[0107] This embodiment calculates the probability of a flow path according to preset rules. The probability of a flow path represents the probability that a hypothetical sample will flow to a leaf node. The rules for calculating the probability of a flow path are as follows: if a sample can only flow to a certain leaf node on the flow path, then the probability of that leaf node in the probability distribution is 1, and the probability of the other leaf nodes is 0; if a sample passes through an empty non-leaf node on the flow path, then the probability that the sample will flow to a leaf node will be reduced by half.

[0108] S4.3. Summarize all flow route combinations and construct a flow route probability distribution table. For example... Figure 3 Example;

[0109] S4.4 Calculate the entropy value CH for each flow path, as shown in Formula 1, where p(x j ) represents the xth j The probability distribution of the leaves:

[0110] CH=-∑p(x j )*log2(p(x j ))#(1)

[0111] S4.5 Calculate the flow probability for each flow route;

[0112] S4.6 Calculate the entropy TH of decision tree T, see Formula 2, where p k Indicates the probability of the k-th flow path:

[0113] TH=∑pk *CH#(2)

[0114] S4.7 Set all nodes to empty nodes and calculate the entropy value TH′ of the empty decision tree T;

[0115] S4.8. Based on the entropy value TH of decision tree T and the entropy value TH′ of empty tree, the information content T of decision tree T is calculated using formula (3). info Formula (3) is shown below;

[0116] T info =TH′-TH

[0117] S5. Based on the information content of each tree calculated in S4, obtain the information content of all federated decision trees in the forest. The e-commerce platform can determine the contribution of different business units to the product preference recommendation task based on the information content of the federated decision trees, and thus settle different revenues.

[0118] In summary, the information content measurement method for federated decision trees based on information entropy provided in this embodiment solves the problem of the inability to quantify the distribution of benefits among participants in federated decision trees in existing technologies. Because it introduces a step to screen for inferior participants, its training process requires less computational data compared to traditional federated forest algorithms, and has almost no impact on the computational workload of participants.

Claims

1. A method for measuring the information content of a federated decision tree based on information entropy, comprising the following training and measurement processes, characterized in that: The training process includes: S1. Configure the federated learning environment and prepare data: The federated learning environment configuration includes configuring a parameter server and connecting N participants and the parameter server to a private network; The data preparation includes sample data acquisition and preprocessing, and the sample data acquisition and preprocessing process is as follows: Each participant obtains their own sample data. With data tags and sample data With data tags Uploaded to the parameter server; sample data Includes sample ID, product ID, category, browsing time, and browsing duration. This represents the sample data of the i-th participant. This represents the data label for the i-th participant; user browsing behavior data and added-to-cart item labels are collected to obtain sample data. With data tags ; The parameter server merges the sample IDs uploaded by each participant to obtain a sample ID set D, and merges the tags uploaded by each participant. Obtain the label set F; S2. Joint participants and the parameter server jointly construct the CART tree: S2.1 The parameter server creates a decision tree T and an empty root node node on T to initialize the decision tree construction; S2.2 The parameter server distributes the structure of the decision tree T to each participant and marks the newly added empty nodes. S2.3 After updating their local decision tree structure based on the structure provided in S2.2, participants calculate the splitting parameters of the current node and feed the results back to the parameter server; the node splitting parameters include: the local optimal Gini index. Optimal segmentation label Optimal segmentation value and the probability of flow direction ; S2.4 The parameter server calculates global node segmentation parameters to determine the candidate participants for this communication round and screen out inferior participants to terminate the subsequent training process. S2.

5. Based on the candidate participants for this communication round determined by the parameter server in S2.4, the participants choose to delete or save node information and send the deleted or saved node information to the parameter server. S2.6 Repeat S2.2 to S2.5 to update the decision tree structure T until the federated decision tree is completed; S3. Combine multiple CART trees to form a federated decision tree forest: Add the federated decision trees to the federated decision tree forest, and determine the size of the forest as needed. If the forest is not large enough, repeat S2. The measurement process includes: S4. Calculate the information content of each tree; for participant i, the calculation process for the information content of each tree is as follows: S4.

1. Divide the tree nodes according to the participant number. The node division rule is: retain the node information where the candidate participant number in the communication round is the same as the participant i number, and set the remaining nodes as empty nodes. S4.2 Find the combination of node flow routes, which includes finding all node flow routes and calculating the flow probability; the flow routes are found using the decision tree sample prediction principle, and the flow route probability is obtained by a preset calculation rule; S4.3 Summarize all flow route combinations and construct a flow route probability distribution table; S4.4 Calculate the entropy value CH of each flow path using formula (1), as shown in formula (1) below: ； in, Indicates the first The probability distribution of the leaves; S4.5 Calculate the flow probability for each flow route; S4.6 Calculate the entropy value TH of decision tree T using formula (2), as shown below: ； in, This represents the probability of the k-th flow route. S4.7 Set all nodes to empty nodes and calculate the entropy of the empty decision tree T. ; S4.

8. Based on the entropy value TH of decision tree T and the entropy value of the empty tree... The information content of decision tree T is calculated using formula (3). Formula (3) is shown below: 。 2. The information content measurement method for federated decision trees based on information entropy as described in claim 1, characterized in that, The method in S2.2 for the parameter server to distribute the structure of the decision tree T to each participant includes: S2.2.1 The parameter server obtains a global sample ID sampling set by randomly sampling from D with an 80% probability. A global data label sampling set is obtained by randomly sampling from F with an 80% probability. ; S2.2.2, For all Perform the following operations: Will and Find the intersection to obtain the sample set of participant i's sample IDs. ,Will and Find the intersection to obtain the sample set of data labels for participant i. Distribute to the i-th participant and .

3. The information content measurement method for federated decision trees based on information entropy as described in claim 2, characterized in that, The method for calculating the segmentation parameters of the current node in S2.3 includes: S2.3.1 Receiving and ; S2.3.2 Calculation based on the principle of constructing a CART tree Local optimal Gini index Optimal segmentation label With the optimal split value ; S2.3.3 Calculate the probability of flow direction , representing the percentage of samples flowing to the left child node and the percentage of samples flowing to the right child node after segmentation according to the optimal segmentation label and the optimal segmentation value, respectively.

4. The information content measurement method for federated decision trees based on information entropy as described in claim 1, characterized in that, The detailed process of step S2.4 is as follows: The parameter server aggregates the local optimal Gini index, optimal split label, optimal split value, and flow probability of all participants. The participant with the highest local Gini index will be selected as the candidate participant for this communication round. If the candidate participants in this communication round are the same as those in the previous round, then the participant with the second highest local Gini index will be selected as the candidate participant for this communication round; the candidate participants in this communication round will be notified to save node information, i.e., send... Notify other participants to delete node information, i.e., send ; If a participant is not selected as a candidate participant in any of the N*|F|*2 communication rounds, then that participant is considered a poor participant and the subsequent training process for that participant ends.

5. The information content measurement method for federated decision trees based on information entropy as described in claim 1, characterized in that, The detailed process of S2.5 is as follows: S2.5.1 Receive the signal from the parameter server to save and delete node information. and perform the following operations: like Then delete the local optimal Gini index. Optimal segmentation label Optimal segmentation value With flow direction probability At the same time, it does not screen for inferior participants; like If so, store it in the currently empty node. Optimal segmentation label Optimal segmentation value With flow direction probability ; S2.5.2, Based on the optimal segmentation label With the optimal split value segmentation This yields the subset of data samples flowing to the left child node under participant i. The subset of data samples flowing to the right child node under participant i. ; S2.5.3, Extraction and The data labels are used to obtain the subset of sample IDs flowing to the left child node under participant i. The subset of sample IDs flowing to the right child node under participant i. ; S2.5.4, will and Send to the parameter server.

6. The information content measurement method for federated decision trees based on information entropy as described in claim 5, characterized in that, The detailed process of S2.6 is as follows: S2.6.1 Store in the newly added node the candidate participant number for this communication round, as well as the participant's local optimal Gini index, optimal split label, optimal split value, and flow probability; receive data from the candidate participants for this communication round. and and set it as and ;like The length is less than 5% of D or If the length of is less than 5% of D, then stop this communication round and do not execute the remaining steps. S2.6.2, Create the left and right child nodes of the node; S2.6.

3. For the left child node, create a new communication round. Let the left child node be node, and let... for And recursively execute S2.3 to S2.6; for the right child node, create a new communication round, let the right child node be node, and let... for And recursively execute S2.3 to S2.6.

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