Method and system for probability tree simplification

Abstract

Methods and systems for probability tree simplification are provided. A method for probability tree simplification includes receiving a probability tree structure having a plurality of nodes. At least one node structure value is associated with each of the plurality of nodes, and quantifies an entropy of a sub-tree extending from a respective one of the plurality of nodes. The method further includes receiving at least one parameter for removing one or more nodes of the probability tree structure; removing at least one node in the plurality of nodes from the probability tree structure according to the parameters; calculating an update entropy of each of the plurality of nodes upstream of the removed node; and outputting a simplified probability tree structure having no removed node and having an updated entropy for each of a plurality of nodes upstream of the removed node. Other example methods and systems for probability tree simplification are also disclosed.

Description

Technical Field

[0001] The information provided in this section is for the purpose of generally presenting the background of the present disclosure. To the extent described in this section, the work of the presently named inventors, and aspects that may otherwise not qualify as prior art at the time of filing, are neither explicitly nor implicitly admitted to be prior art to the present disclosure.

[0002] The present disclosure relates to methods and systems for probability tree simplification. Background Art

[0003] Artificial intelligence (AI) can be used in fully autonomous or semi-autonomous vehicles to determine the actions taken by the vehicle. For example, AI algorithms can be applied to calculate and determine the driving behavior of such a vehicle. In such examples, graphical models, such as probability trees, are often used for automated decision making. Probabilistic trees (e.g., rooted graphs with probabilities at each vertex) are common data structures used in many automated systems (e.g., systems or machines that make automated decisions, such as automated vehicles). An example of such a tree is Monte Carlo Tree Search (MCTS), which generates a probabilistic tree structure as an output for continuous decision making. In order to reach a decision, the algorithm builds a probabilistic tree data structure, where the root node is the current state and each vertex is a different action that can be taken from the root node. Summary of the invention

[0004] A method for probabilistic tree simplification is disclosed. The method includes receiving a probabilistic tree structure having a plurality of nodes. At least one node structure value is associated with each of the plurality of nodes, and the at least one node structure value quantifies the entropy of a subtree extending from a corresponding one of the plurality of nodes. The method also includes: receiving at least one parameter for removing one or more nodes of the probabilistic tree structure; removing at least one node of the plurality of nodes from the probabilistic tree structure according to the parameter; calculating an updated entropy of each of the plurality of nodes upstream of the removed node; and outputting a simplified probabilistic tree structure without the removed node and with an updated entropy of each of the plurality of nodes upstream of the removed node.

[0005] In other features, calculating the updated entropy of each of the plurality of nodes upstream of the removed node includes updating a visit count of each of the plurality of nodes upstream of the removed node.

[0006] In other features, removing at least one node of the plurality of nodes from the probabilistic tree structure comprises removing the at least one node and an entire subtree of the probabilistic tree structure downstream of the at least one node.

[0007] In other features, receiving at least one parameter for removing one or more nodes of the probabilistic tree structure includes receiving at least one defined node to be removed from the probabilistic tree structure.

[0008] In other features, receiving at least one parameter for removing one or more nodes of the probabilistic tree structure includes receiving at least one removal criterion for removing the one or more nodes from the probabilistic tree structure.

[0009] In other features, the at least one removal criterion includes at least one of removing all individual child nodes, removing each parent node having less than a defined number of child nodes, and removing each node having less than a defined number of branches extending therefrom.

[0010] In other features, one of the plurality of nodes is a parent node having a plurality of child nodes downstream of the parent node.

[0011] In other features, the method further comprises determining an optimal set of the plurality of child nodes to remove based on at least one removal criterion.

[0012] In other features, removing at least one of the plurality of nodes from the probabilistic tree structure includes removing an optimal set of a plurality of child nodes from the probabilistic tree structure.

[0013] In other features, the optimal set of the plurality of child nodes includes one or more child nodes downstream of the parent node.

[0014] In other features, determining an optimal set of multiple child nodes to be removed includes: for each possible set of multiple child nodes for removal, assuming that the possible set is removed, calculating the update entropy of each node in the multiple nodes upstream of the possible set; and assuming that the possible set is removed, calculating a trade-off score based on the update entropy and the size of the probabilistic tree structure.

[0015] In other features, determining the optimal set of the plurality of child nodes to remove includes selecting the possible set of the plurality of child nodes for removal having the highest tradeoff score value as the optimal set of the plurality of child nodes to remove.

[0016] In other features, the method further comprises generating a list of a plurality of possible sets including one or more child nodes for removal based on at least one removal criterion. Each possible set has a tradeoff score based on: an update entropy of each of a plurality of nodes upstream of the possible set assuming the possible set is removed, and a size of the probabilistic tree structure assuming the possible set is removed.

[0017] In other features, generating the list includes adding a possible set of one or more child nodes for removal only if a tradeoff score of the possible set is greater than a reference value.

[0018] In other features, generating the list includes adding a possible set of one or more child nodes for removal to the list only if the tradeoff score of the possible set of one or more child nodes is greater than the tradeoff score of a parent node associated with the one or more child nodes.

[0019] In other features, generating the list includes prioritizing multiple possible sets of the one or more child nodes in descending order based on their tradeoff scores.

[0020] In other features, removing at least one of the plurality of nodes from the probabilistic tree structure comprises: selecting a possible set of one or more child nodes having a highest tradeoff score value from a prioritized list; and removing the selected set of one or more child nodes from the probabilistic tree structure.

[0021] In other features, the method further comprises updating the tradeoff score of each possible set after removing the selected set of one or more child nodes from the probabilistic tree structure.

[0022] In other features, the method further comprises storing the reduced probability tree structure in a memory circuit.

[0023] An automated system includes a control module configured to receive a probabilistic tree structure having a plurality of nodes. At least one node structure value is associated with each of the plurality of nodes, and the at least one node structure value quantifies the entropy of a subtree extending from a corresponding one of the plurality of nodes. The control module is further configured to: receive at least one parameter for removing one or more nodes of the probabilistic tree structure; remove at least one node of the plurality of nodes from the probabilistic tree structure according to the parameter; calculate an updated entropy for each of the plurality of nodes upstream of the removed node; and output a simplified probabilistic tree structure without the removed node and with an updated entropy for each of the plurality of nodes upstream of the removed node.

[0024] In other features, the automated system further includes a memory circuit in communication with the control module. The control module is configured to store the reduced probability tree structure in the memory circuit.

[0025] In other features, at least one parameter is at least one removal criterion, one of the multiple nodes is a parent node, and there are multiple child nodes downstream of the parent node, and the control module is configured to: determine an optimal set of multiple child nodes to be removed based on the at least one removal criterion; and remove the optimal set of multiple child nodes from the probabilistic tree structure.

[0026] In other features, the at least one parameter is at least one removal criterion, and the control module is configured to generate a list of multiple possible sets of one or more child nodes for removal based on the at least one removal criterion. Each possible set has a tradeoff score based on: an update entropy of each of a plurality of nodes upstream of the possible set assuming the possible set is removed, and a size of the probabilistic tree structure assuming the possible set is removed.

[0027] In other features, the control module is configured to: prioritize multiple possible sets of one or more child nodes in descending order based on their tradeoff scores; and remove the possible set of one or more child nodes having the highest tradeoff score value from the list.

[0028] The present disclosure provides the following solutions:

[0029] 1. A method for probability tree simplification, the method comprising:

[0030] receiving a probabilistic tree structure having a plurality of nodes, wherein at least one node structure value is associated with each of the plurality of nodes, and the at least one node structure value quantifies an entropy of a subtree extending from a corresponding one of the plurality of nodes;

[0031] receiving at least one parameter for removing one or more nodes of a probabilistic tree structure;

[0032] removing at least one node from the plurality of nodes from the probabilistic tree structure according to a parameter;

[0033] calculating an update entropy for each of a plurality of nodes upstream of the removed node; and

[0034] A simplified probabilistic tree structure is output without the removed node and with updated entropy for each of the plurality of nodes upstream of the removed node.

[0035] 2. The method according to claim 1, wherein calculating the updated entropy of each of the plurality of nodes upstream of the removed node comprises updating the access count of each of the plurality of nodes upstream of the removed node.

[0036] 3. The method according to claim 1, wherein removing at least one node among a plurality of nodes from the probabilistic tree structure comprises removing at least one node and an entire subtree of the probabilistic tree structure downstream of the at least one node.

[0037] 4. The method of claim 1, wherein receiving at least one parameter for removing one or more nodes of a probabilistic tree structure comprises receiving at least one defined node to be removed from the probabilistic tree structure.

[0038] 5. The method according to claim 1, wherein receiving at least one parameter for removing one or more nodes of the probabilistic tree structure comprises receiving at least one removal criterion for removing one or more nodes from the probabilistic tree structure.

[0039] 6. A method according to Option 5, wherein at least one removal criterion includes at least one of the following: removing all single child nodes, removing each parent node with less than a defined number of child nodes, and removing each node with less than a defined number of branches extending from it.

[0040] 7. The method according to claim 5, wherein:

[0041] One of the plurality of nodes is a parent node, and has a plurality of child nodes downstream of the parent node;

[0042] The method further includes determining an optimal set of a plurality of child nodes to remove based on at least one removal criterion; and

[0043] Removing at least one node of the plurality of nodes from the probabilistic tree structure includes removing an optimal set of a plurality of child nodes from the probabilistic tree structure.

[0044] 8. A method according to Option 7, wherein the optimal set of multiple child nodes includes one or more child nodes downstream of the parent node.

[0045] 9. The method according to claim 7, wherein determining the optimal set of multiple child nodes to be removed comprises:

[0046] For each possible set of multiple child nodes for removal, assuming that the possible set is removed, calculating the update entropy of each node in the multiple nodes upstream of the possible set, and assuming that the possible set is removed, calculating a tradeoff score based on the update entropy and the size of the probability tree structure; and

[0047] The possible set of multiple child nodes for removal having the highest tradeoff score value is selected as the optimal set of multiple child nodes to be removed.

[0048] 10. The method according to Scheme 5 also includes generating a list of multiple possible sets including one or more child nodes for removal based on at least one removal criterion, wherein each possible set has a compromise score, and the compromise score is based on: the update entropy of each node in the multiple nodes upstream of the possible set assuming that the possible set is removed, and the size of the probabilistic tree structure assuming that the possible set is removed.

[0049] 11. The method according to embodiment 10, wherein generating the list comprises adding the possible set of one or more child nodes for removal to the list only when the tradeoff score of the possible set of one or more child nodes for removal is greater than a reference value.

[0050] 12. The method of claim 10, wherein generating the list comprises adding the possible set to the list only if the tradeoff score of the possible set of one or more child nodes for removal is greater than the tradeoff score of a parent node associated with the one or more child nodes.

[0051] 13. The method of claim 10, wherein generating the list comprises prioritizing multiple possible sets of one or more child nodes in descending order based on their tradeoff scores.

[0052] 14. A method according to scheme 13, wherein removing at least one node from multiple nodes from the probabilistic tree structure includes: selecting a possible set of one or more child nodes with the highest compromise score value from a prioritized list, and removing the selected set of one or more child nodes from the probabilistic tree structure.

[0053] 15. The method according to embodiment 14 further includes updating the tradeoff score of each possible set after removing the selected set of one or more child nodes from the probabilistic tree structure.

[0054] 16. The method according to claim 1 further comprises storing the simplified probability tree structure in a memory circuit.

[0055] 17. An automated system comprising:

[0056] The control module is configured to:

[0057] receiving a probabilistic tree structure having a plurality of nodes, wherein at least one node structure value is associated with each of the plurality of nodes, and the at least one node structure value quantifies an entropy of a subtree extending from a corresponding one of the plurality of nodes;

[0058] receiving at least one parameter for removing one or more nodes of a probabilistic tree structure;

[0059] removing at least one node from the plurality of nodes from the probabilistic tree structure according to a parameter;

[0060] calculating an update entropy for each of a plurality of nodes upstream of the removed node; and

[0061] A simplified probabilistic tree structure is output without the removed node and with updated entropy for each of the plurality of nodes upstream of the removed node.

[0062] 18. The automation system of claim 17, further comprising a memory circuit in communication with the control module, wherein the control module is configured to store the simplified probability tree structure in the memory circuit.

[0063] 19. The automated system of claim 17, wherein:

[0064] At least one parameter is at least one removal criterion;

[0065] One of the plurality of nodes is a parent node having a plurality of child nodes downstream of the parent node; and

[0066] The control module is configured to: determine an optimal set of multiple child nodes to be removed based on at least one removal criterion; and remove the optimal set of multiple child nodes from the probabilistic tree structure.

[0067] 20. The automated system of claim 19, wherein:

[0068] At least one parameter is at least one removal criterion; and

[0069] The control module is configured to:

[0070] generating a list of a plurality of possible sets including one or more child nodes for removal based on at least one removal criterion, wherein each possible set has a tradeoff score based on: an update entropy of each of a plurality of nodes upstream of the possible set assuming that the possible set is removed, and a size of a probability tree structure assuming that the possible set is removed;

[0071] prioritizing multiple possible sets of one or more child nodes in descending order based on their tradeoff scores; and

[0072] A possible set of one or more child nodes having the highest tradeoff score value is removed from the list.

[0073] Further areas of applicability of the present disclosure will become apparent from the detailed description, claims and drawings.The detailed description and specific examples are intended for purposes of illustration only and are not intended to limit the scope of the present disclosure. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] The present disclosure will become more fully understood from the detailed description and accompanying drawings, in which:

[0075] Figure 1 is a functional block diagram of an example system for probability tree simplification according to the present disclosure;

[0076] Figure 2 is an example probability tree structure in a non-simplified state according to the present disclosure;

[0077] Figure 3 is an example probability tree structure in a simplified state according to the present disclosure;

[0078] Figure 4is an example probabilistic tree structure according to the present disclosure, showing the general occurrence of a parent node and four child nodes downstream of the parent node;

[0079] Figure 5 According to the present disclosure Figure 4 The probability tree structure of , but two of the four child nodes are marked for removal;

[0080] Figure 6 is an example probabilistic tree structure having a plurality of nodes according to the present disclosure;

[0081] Figure 7 According to the present disclosure, Figure 1 The autonomous vehicle that is part of the system; and

[0082] Figure 8-10 is a flow chart of an example control process for probability tree simplification according to the present disclosure.

[0083] In the drawings, reference numerals may be repeated to identify similar and / or identical elements. DETAILED DESCRIPTION

[0084] AI algorithms are applied to calculate and determine automated decisions, such as driving behaviors of semi-autonomous and fully autonomous vehicles. In such examples, probability trees are often used for such features. For example, probability trees (e.g., MCTS, etc.) generate probability tree structures as outputs of continuous decision making. However, in many scenarios, when sequential decision making AI algorithms are applied to practical problems (e.g., autonomous driving, etc.), these probability trees may become very large and very complex. As an example, MCTS may contain most of the logic for selecting automated actions. For practical reasons, in many cases, it is desirable to better understand these trees, store them for debugging, compare them, or apply interpretability (XAI) algorithms, etc. Such actions are expensive in space (e.g., memory, etc.) and calculation (e.g., processing, etc.), due to the size and complexity of the probability tree structure. Therefore, it becomes a meaningful step to wisely reduce the size of the probability tree so that the size of the probability tree is reduced while maintaining the desired logic.

[0085] Systems and methods according to the present disclosure enable simplification of a probability tree by selectively removing nodes and their subtrees from the tree. In such an example, the selective removal of nodes and their subtrees is based on different received parameters, such as simplification criteria explained further below. In this way, and as explained further below, a compromise can be achieved to ensure a desired reduction in the size of the probability tree (e.g., reducing the size of the probability tree as much as possible) while minimizing changes in the tree's original entropy. Thus, through this compromise, the size of the probability tree can be significantly reduced while maintaining interest in the tree structure.

[0086] For example, the simplification criteria may consider a tradeoff between the size of the tree (e.g., the number of nodes) and the information / interest in the tree. For such an example, it may be desirable to keep wider subtrees of the tree because they generally contain more information, as opposed to subtrees that are thin (e.g., closer to the branch subtrees) and generally contain little information. In this way, the size of the probabilistic tree can be significantly reduced while maintaining the desired information.

[0087] The reduction in the size of the probability tree brings many benefits. For example, the amount of memory required to store the probability tree structure is reduced as the size of the probability tree is reduced compared to conventional systems. In addition, the amount of processing requirements (e.g., power, computation, etc.) for processing the probability tree structure is reduced as the size of the probability tree is reduced compared to conventional systems. In addition, the transmission requirements for transmitting the probability tree structure are reduced as the size of the probability tree is reduced compared to conventional systems.

[0088] Reference now Figure 1 , presents a block diagram of an example system 100 for probability tree simplification. For example, Figure 1 The system 100 is configured to convert Figure 2 The probability tree structure 200 of the probability tree is simplified to Figure 3 In other words, the probability tree structure 300 is Figure 2 A simplified version of the probability tree structure 200.

[0089] Figure 1 The system 100 may be employable in any suitable vehicle, such as an electric vehicle (e.g., a pure electric vehicle, a plug-in hybrid electric vehicle, etc.), an internal combustion engine vehicle, etc. In addition, the system 100 may be applicable to autonomous vehicles, such as semi-autonomous vehicles and fully autonomous vehicles. Figure 1 The system 100 and / or other systems and methods herein are described with respect to probability tree simplification for a vehicle implementation, but it should be understood that any of the systems and / or methods herein may be applicable to non-vehicle implementations, if desired.

[0090] like Figure 1 As shown, the system 100 generally includes a control module 102, a memory circuit 104, a probability tree module 108, and a parameter module 110. In such an example, the control module 102 can be connected to Figure 1 Each of the other components shown communicates with each other. Figure 1The system 100 is shown as including specific modules, but it should be understood that one or more other modules may be employed if desired. In addition, although the system 100 is shown as including multiple separate modules (e.g., control module 102, probability tree module 108, etc.), any combination of these modules and / or their functions may be integrated into one or more modules.

[0091] exist Figure 1 In an example of , the probability tree module 108 and the parameter module 110 can provide input to the control module 102. For example, the probability tree module 108 can store, generate and / or receive one or more probability tree structures, each probability tree structure having a plurality of nodes for the automated decision making process. Additionally, the parameter module 110 can store and / or receive parameters for removing one or more nodes of the probability tree structure of the probability tree module 108. In such an example, the control module 102 receives at least one probability tree structure and one or more parameters for removing nodes of the received probability tree structure, as further explained below. For example, Figure 2 The probability tree structure 200 may be provided by the probability tree module 108 to the control module 102 .

[0092] In various embodiments, Figure 1 The probability tree module 108 and / or parameter module 110 may include a storage structure (e.g., a database, a memory circuit, etc.) for storing the probability tree structure and / or the parameters. In such examples, the probability tree module 108 and / or the parameter module 110 may receive input (e.g., user input, etc.) that defines the parameters, the probability tree structure, etc. In other examples, if desired, the parameter module 110 may calculate or otherwise determine the parameters.

[0093] The memory circuit 104 may be any suitable storage component as explained herein. In such an example, the memory circuit 104 receives the simplified probability tree structure from the control module 102 and stores the simplified probability tree structure for later implementation when desired. For example, Figure 3 The probability tree structure 300 is Figure 2 is a simplified version of the probability tree structure 200 and is generated by the control module 102 and stored in the memory circuit 104.

[0094] exist Figure 1In an example of the present invention, the probability tree module 108 can generate a probability tree structure based on one or more sensors. For example, the probability tree module 108 can be or be associated with an autonomous control module that generates a probability tree structure. In such an example, the probability tree module 108 can generate a tree structure in a decision-making process of an autonomous vehicle based on feedback from one or more sensors, wherein the one or more sensors are used to obtain information about the surroundings or environment of, for example, an autonomous vehicle. In such an example, the one or more sensors can include, for example, a camera, a lidar, a radar, a GPS, etc.

[0095] In various embodiments, the probability tree structure herein may be any suitable data structure used in an automated system. For example, Figure 2 The probability tree structure 200 of is a suitable example. As shown, the probability tree structure 200 includes a plurality of nodes 202 and edges 204 connecting any two nodes 202. Each node 202 represents a state of a system (e.g., an autonomous vehicle), and each edge 204 represents an action that takes the system from one state to another state (a subsequent state or a future state). The root node (e.g., the top node) of the probability tree structure 200 represents the current state of the system. Possible subsequent states are shown below the top node. Each action or edge has an associated probability.

[0096] A series of actions through the probability tree structure 200 is called a trajectory. In such an example, the control module (e.g., Figure 1 The probability tree module 108 of the control module starts with a root node (e.g., the current state of the system). The control module then selects an action to be taken from the probability tree evaluated from the root node. Once the action is executed, the system moves to the resulting state. The control module identifies the resulting state as the new root node and expands the new tree so that the optimization algorithm can be executed from the new root node.

[0097] In various embodiments, a probabilistic tree structure (e.g., Figure 2 Analysis of the probability tree structure 200 of the probability tree can provide a node structure value that describes the structure of the branches or subtrees spanning from a given node in the probability tree. Rather than going down the probability tree structure 200, the node structure value indicates that the probability tree structure 200 spans from each node. A larger node structure value reflects more uncertainty in the probability tree. This corresponds to a wider tree (e.g., more branches in different layers of a subtree). The node structure value can be standardized to reflect the uncertainty of each node so that a smaller subtree can be compared with a larger subtree.

[0098] Each node structure value provides an entropy value for a given node to describe the structure of the probability tree spanned from the node (e.g., a branch or subtree). For example, if a node does not include a branch or subtree, the node structure value of the node can be zero. Further information and examples about determining (e.g., calculating, etc.) a node structure value or entropy for a given node can be found in U.S. Application No. 18 / 336,115, filed June 16, 2023, which is incorporated herein in its entirety.

[0099] In the examples here, a simplified version of a given tree data structure can be calculated based on various parameters, such as Figure 2 The probability tree structure 200. For example, Figure 1 The control module 102 may implement one or more processes (e.g., a greedy simplification process down the tree, a two-stage greedy simplification, etc.) for removing subtrees from the probabilistic tree data structure, as further explained below. In such examples, the simplification of the tree data structure may be based on a simplification criterion, as further explained below. In various embodiments, when removing subtrees from the tree data structure, the control module 102 may rely on a tradeoff between the entropy and size of the tree data structure.

[0100] For example, in some cases, it may be desirable to reduce the size of the probabilistic tree structure as much as possible while reducing its original entropy as little as possible when necessary. To this end, a trade-off score based on the reduced size and entropy may be maximized. For example, the trade-off score may be maximized according to equation (1) below. In equation (1), H(T) refers to entropy (e.g., as explained in U.S. application Ser. No. 18 / 336,115 cited above), S is the size of the probabilistic tree structure (e.g., the number of nodes, the number of visits, etc.), A is the number of possible children that a node may have, and β is a trade-off parameter. In such an example, it is desirable to reduce the value of size S as much as possible, but to reduce the value of entropy H(T) as little as possible.

[0101] (1)max{H(T 0 )-β*log(|A|)*S}

[0102] In the above example, the tradeoff parameter β can be restricted. For example, since for any value of the tradeoff parameter β, it is possible to obtain zero due to an empty tree, the tradeoff parameter β can be restricted to a positive value. Therefore, under this restriction, the tradeoff parameter β can be restricted between a value greater than zero and an upper limit. For example, the following equation (2) shows the restriction of the tradeoff parameter β based on the above equation (1). In this example, βub represents the upper limit of the tradeoff parameter β.

[0103] (2)

[0104] In various embodiments, removing a node and its subtree from a probabilistic tree structure can be based on defining nodes. For example, the control module 102 can receive a probabilistic tree structure (e.g., Figure 2 The control module 102 may be configured to generate a probability tree structure 200 and receive parameters representing one or more defined nodes to be removed from the probability tree structure from the parameter module 110. In such an example, the control module 102 may then remove the defined node and the entire subtree downstream of the node.

[0105] Once removed, the control module 102 may then calculate updated values ​​for various data. For example, the control module 102 may update data associated with the size of the reduced probabilistic tree structure, such as a count of the number of visits, the number of nodes, etc. In addition, the control module 102 may calculate an updated entropy for each remaining node upstream of the removed node (e.g., as explained in U.S. Application No. 18 / 336,115 cited above).

[0106] The control module 102 may then output a simplified probability tree structure without the removed node and with updated entropy for each node upstream of the removed node (eg, Figure 3 In such an example, the simplified probability tree structure may be provided to the memory circuit 104 as explained above.

[0107] In other embodiments, the removal of a node and its subtrees from the probabilistic tree structure can be based on at least one removal criterion for removing one or more nodes from the probabilistic tree structure. In such examples, the control module 102 can receive the removal criterion (e.g., parameters) from the parameter module 110, as explained herein. The removal criterion can be any suitable criterion for node removal, such as removing all individual child nodes, removing each parent node with less than a defined number of child nodes, removing each node with less than a defined number of branches extending therefrom, etc.

[0108] An example process for removing nodes and their subtrees from a probabilistic tree structure based on a removal criterion is a greedy simplification process down the tree. In this process, the control module 102 may receive a probabilistic tree structure (e.g., Figure 2 ) and receives at least one removal criterion from the parameter module 110, as explained above.

[0109] The control module 102 may then determine the optimal set of nodes to remove from the probabilistic tree structure based on the removal criteria. Figure 4An example probabilistic tree structure 400 is depicted, which shows the general occurrence of parent nodes and child nodes, which can be repeated multiple times in the tree. Specifically, the probabilistic tree structure 400 is shown to include nodes 402, 404, 406, 408, 410, wherein node 402 represents a parent node, and nodes 404, 406, 408, 410 represent child nodes downstream of the parent node 402. In such an example, the control module 102 determines the optimal set of child nodes 404, 406, 408, 410 to be removed based on the removal criteria.

[0110] The determination of the optimal set may be based on the trade-off scores of different removal options. For example, given a parent node 402, the possible simplified set is all subsets of the child nodes 404, 406, 408, 410 (of the current parent node 402). For example, possible simplifications may include any combination of nodes to be removed, such as no nodes (e.g., retaining all child nodes 404, 406, 408, 410), removing child node 404 (e.g., retaining child nodes 406, 408, 410), removing child node 406 (e.g., retaining child nodes 404, 408, 410), removing child node 408 (e.g., retaining child nodes 404, 406, 410), removing child node 410 (e.g., retaining child nodes 404, 406, 408), removing child nodes 404, 406 (e.g., retaining child nodes 408, 410), removing child nodes 404, 408 (e.g., retaining child nodes 406, 410), etc. In such examples, the child nodes to be retained may be referred to as childrenToKeep.

[0111] Then, for each possible set of child nodes 404, 406, 408, 410 for removal, the control module 102 can recursively go up the tree and evaluate various data values. For example, the nodes to be removed can be a possible set of child nodes 408, 410, and the nodes to be retained (childrenToKeep) can be child nodes 404, 406. Figure 5 An example probability tree structure 500 is depicted, showing Figure 4 The general occurrence of nodes 402, 404, 406 of the possible set is calculated, and child nodes 408, 410 are removed. In this example, the access count of the child nodes 408, 410 is set to zero (0). Then, the control module 102 calculates the update entropy of each node (e.g., parent node 402) upstream of the possible set assuming that the child nodes 408, 410 are removed, and calculates the trade-off score (e.g., as explained above) based on the update entropy and the size of the probability tree structure assuming that the child nodes 408, 410 are removed.

[0112] The control module 102 recursively performs such calculations for each possible simplified set. Once completed, the control module 102 selects the optimal set for removal. For example, the control module 102 can select the possible set of child nodes 404, 406, 408, 410 for removal that have the highest tradeoff score value (on the entire tree) from the possible removals at the parent node 402 as the optimal set to be removed. With such a configuration, the control module 102 is able to identify local independent removals of a parent node and its set of child nodes.

[0113] The control module 102 may then remove the optimal set of nodes from the probabilistic tree structure and any subtrees of the nodes. Once the nodes are actually removed, the control module 102 may then calculate updated values ​​for various data, as explained herein. The control module 102 may then output a simplified probabilistic tree structure without the removed nodes (e.g., Figure 3 A simplified probabilistic tree structure 300) as explained herein.

[0114] Alternatively, the control module 102 may check for removal at the remaining children (childrenToKeep) and repeat the above process. For example, the greedy simplification process may continue down the tree, and the control module 102 performs the above process on the nodes that have not been removed. For example and referring to Figure 5 , the control module 102 may perform the above process on the nodes 404 and 406 that have not been removed.

[0115] Another example process for removing nodes and their subtrees from a probability tree structure based on a removal criterion is a two-stage greedy simplification. In the two-stage greedy simplification process, the control module 102 may receive a probability tree structure (e.g., Figure 2 ) and receives at least one removal criterion from the parameter module 110, as explained above.

[0116] The two-stage greedy simplification process generally includes two stages. The first stage includes moving down along the probability tree structure and generating a list (e.g., priority list pList) that may be removed. For example, after receiving the probability tree structure and the removal criteria, the control module 102 can determine (e.g., create) a list of possible (e.g., suggestions) sets of one or more nodes to be removed based on the removal criteria. In such an example, each possible set has a compromise score or value (e.g., calculated by the control module 102 as explained above), which is based on the updated entropy of each node upstream of the possible set and the size of the probability tree structure under the assumption that the possible set is removed. For example, for each suggested removal, the control module 102 can calculate the compromise score (e.g., β*log(|A|)*S) of the suggested removal by going up along the tree and adding each tree size reduction determination step. This results in a global removal set of simplified trees, rather than local independent removal.

[0117] In some examples, the control module 102 may add a possible set of one or more nodes for removal to the list only when certain conditions apply. For example, the control module 102 may add the possible set of nodes for removal only when the tradeoff score of the possible set of nodes is greater than a reference value. In such examples, the reference value may be user-defined, calculated by the control module 102, etc. For example, the control module 102 may calculate the reference value based on the specific removal criteria used and / or another received input. In other examples, the control module 102 may calculate the reference value based on the entropy-size tradeoff for a given value of the tradeoff parameter β.

[0118] Additionally and / or alternatively, the control module 102 may add a possible set of nodes for removal only if the tradeoff score of the possible set of nodes is greater than the tradeoff score of the parent node associated with one or more nodes. Thus, in order to be included on the list, a proposed removal must be better than the proposed removals of its ancestors (e.g., those that remove the current node).

[0119] For example, Figure 6A simplified probability tree structure 600 including nodes 602, 604, 606, 608, 610, 612 is depicted. As shown, nodes 602, 604 represent parent nodes, and nodes 604, 606, 608, 610, 612 represent child nodes. In this example, the control module 102 can suggest removing nodes as explained above. For example, at node 602, the control module 102 can suggest removing node 604 and retaining nodes 606, 608, all of which are children of node 602. In this example, node 602 is an ancestor of node 604 because node 602 suggests removing it. In addition, at node 604, the control module 102 can suggest removing node 610 and retaining node 612. In this example, node 604 is an ancestor of node 610 because node 604 suggests removing it. However, node 602 is not an ancestor of node 612 because node 604 suggests retaining it. In such an example, a proposed removal must be better than its ancestor's proposed removals to be included on the list.

[0120] In various embodiments, the list of possible sets of nodes can be prioritized as desired. For example, the control module 102 can prioritize them in descending order based on the compromise scores of the possible sets of nodes on the list. In other words, the control module 102 can prioritize the list of suggested removals from high to low. In such an example, the list is sorted, where the suggested removals are shown as being more beneficial at the top, and above the suggested removals shown as being less beneficial. In other examples, the list of possible sets of nodes for removal can be prioritized, sorted, etc. (or not prioritized, sorted, etc.) in another suitable manner.

[0121] In some examples, the lists of possible sets of nodes for removal may overlap. For example, a list may contain a current suggestion to remove a node that has an ancestor. In other words, the parent node has already suggested removing the subtree that contains the current suggestion. This scenario can be handled in a variety of ways. One option may be to update the value of the ancestor parent based on the advantage provided by the ancestor parent (through its suggested removal) after the currently suggested removal, or relative to the currently suggested removal. In other words, measure the removals in the ancestors assuming that the current removal has already been performed. By doing so, the priority list better reflects the advantage of the removal of the ancestors, which only appears after the removal is completed in the current node. In other examples, all possible removals from the ancestors may be considered (e.g., by recalculating the best removal option) assuming that the currently suggested removal has already been performed.

[0122] Then, once the list of suggested sets is complete, the control module 102 can begin removing sets of nodes from the probabilistic tree structure. This can be referred to as the second phase of the two-phase greedy simplification process. For example, the control module 102 can traverse the generated list and apply the suggested removals (one by one), and update the probabilistic tree structure after each removal.

[0123] For example, the control module 102 may select a possible set (e.g., a suggested set) of nodes having the highest tradeoff score value from the prioritized list (e.g., the suggested set at the top of the list), and then remove the selected set from the probabilistic tree structure. Once removed, the control module 102 may calculate updated values ​​for various data (e.g., tradeoff score, entropy, number of visits, size, etc.), as explained herein.

[0124] In various embodiments, if desired, the control module 102 may optionally re-prioritize the possible set of nodes for removal in descending order based on the updated tradeoff scores. In such an example, the control module 102 may re-evaluate the suggested removals in the priority list before implementing such re-prioritization. With such a configuration, the computational effort to re-prioritize the possible set of nodes for removal may be significant.

[0125] The control module 102 may then select the next possible (or suggested) set of nodes for removal from the prioritized (or re-prioritized) list and again calculate updated values ​​for the various data. This may continue as desired. For example, the selection and removal of nodes may continue until a defined condition applies. For example, the process may continue until the probabilistic tree structure is left with a defined number of nodes, a defined value, a defined tradeoff, a defined entropy, etc. Then, once the removal of the set of suggested nodes is complete, the control module 102 may output a simplified probabilistic tree structure without the removed nodes (e.g., Figure 3 A simplified probabilistic tree structure 300) as explained herein.

[0126] As explained above, system 100 and / or other similar automated systems may be employed in any suitable autonomous vehicle. For example, Figure 7 Describes the Figure 1 The system 100 is configured to operate a vehicle 700 in an autonomous mode or automatic mode. For example, the vehicle 700 includes Figure 1 The control module 102, the probability tree module 108, and the probability tree module 108, as well as one or more sensors 712 that can be used for the automatic decision making process of the vehicle 700. In such an example, the control module 102 can reduce the size of the probability tree structure as explained herein.

[0127] Figure 8-10 It shows that Figure 1The system 100 is used for the example control processes 800, 900, 1000 of probability tree simplification. Although the example control processes 800, 900, 1000 are relative to the control module 102, Figure 1 Although described with reference to a system, any of the control processes 800, 900, 1000 may be adopted by any suitable system.

[0128] exist Figure 8 In the example, the control process 800 begins at 802, where the control module 102 receives a probability tree structure. In such an example, the probability tree structure can be obtained from Figure 1 The control module 102 receives the probability tree module 108 or another suitable source, as explained above. Control then proceeds to 804, where the control module 102 receives one or more defined nodes for removal from the probability tree structure. The defined nodes may be Figure 1 The control module 102 may provide a parameter to the node 110 or another suitable source, as explained above. Control then proceeds to 806 where the control module 102 selects a defined node for removal. Control then proceeds to 808.

[0129] At 808, the control module 102 determines whether the selected node has a parent node. If the selected node does not have a parent node (e.g., the selected node is a root node), control proceeds to 816. However, if the selected node does have a parent node (e.g., the selected node is not a root node), control proceeds to 810.

[0130] At 810, the control module 102 removes the selected node and the entire subtree downstream of the selected node. Control then proceeds to 812, 814. The control module 102 updates the visit count (eg, the size of the tree) at 812 and updates the entropy at 814, as explained herein. Control then proceeds to 816.

[0131] At 816, the control module 102 determines whether there are any more nodes defined for removal. If so, control returns to 806. Otherwise, control proceeds to 818, where the control module 102 outputs a simplified probability tree structure. For example, the control module 102 may send Figure 1 Then, at 820, control may store the simplified probability tree structure in the memory circuit 104 as explained herein.

[0132] exist Fig. 9 , the control process 900 begins at 902, where the control module 102 receives, for example, Figure 1 The probability tree module 108 or another suitable source receives the probability tree structure, as explained above. Control then proceeds to 904, where the control module 102 receives one or more removal criteria. In such an example, the removal criteria may be Figure 1 The parameters of the module 110 or another suitable source are provided, as explained above. Control then proceeds to 906, where the control module 102 selects a node (eg, a root node) of the probability tree structure. Control then proceeds to 908.

[0133] At 908, the control module 102 determines whether the selected node has any child nodes. If not, control proceeds to 910, where the control module 102 selects another node (e.g., the next node) of the probability tree structure. Control then returns to 908. However, if the selected node has child nodes, control proceeds to 912.

[0134] At 912, the control module 102 evaluates each set of child nodes from all possible sets of the selected node. For example, and as explained above, the control module 102 can recursively go up the tree and evaluate various data values ​​for each possible set of child nodes for removal. In such an example, the evaluation values ​​can include, for example, an evaluation entropy, an evaluation size, an evaluation tradeoff score, etc. for each node upstream of the possible set. Control proceeds to 914.

[0135] At 914, the control module 102 selects the optimal set of child nodes for removal based on the evaluation of all possible sets. In such an example, the control module 102 may select the set of child nodes with the highest tradeoff score as the optimal set for removal. Control proceeds to 916, where the control module 102 removes the optimal set and the entire subtree downstream of the optimal set.

[0136] Then, the control module 102 calculates the updated entropy for each node (e.g., parent node 402) upstream of the possible set assuming that the child nodes 408, 410 are removed, and calculates a tradeoff score (e.g., as explained above) based on the updated entropy and the size of the probability tree structure assuming that the child nodes 408, 410 are removed. Control then proceeds to 918, 920.

[0137] At 918 , the control module 102 updates the number of visits count (eg, the size of the tree), as explained above. At 920 , the control module 102 updates the entropy, as explained herein. Control then proceeds to 922 .

[0138] At 922, the control module 102 determines whether there are any more nodes. In other words, the control module 102 can determine whether control has reached the end state of the trajectory in the probabilistic tree structure (e.g., a leaf node equals a node with no children). If there are more nodes, control returns to 910. Otherwise, control proceeds to 924, where the control module 102 outputs a simplified probabilistic tree structure, as explained above. Then, control proceeds to 926, where control can store the simplified probabilistic tree structure in the memory circuit 104, as explained herein.

[0139] exist Fig.10 In the control process 1000, it is similar to Fig. 9 900, but with additional and / or alternative control features. For example, Fig.10 The control process 1000 includes the above relative Fig. 9 The control process 900 of FIG. 100 is explained in steps 902, 904, 906, 908, 910, 912. In such an example, if the control module 102 determines at 908 that the selected node has no child nodes, control proceeds to 910. Otherwise, if the control module 102 determines at 908 that the selected node has child nodes, control proceeds to 912, where control evaluates each set of child nodes from all possible sets of the selected node, as explained above. Control then proceeds to 1014.

[0140] At 1014, the control module 102 determines whether to add the evaluated set of nodes (e.g., one node, two nodes, etc.) to the priority list. For example, in some embodiments, the evaluation set can be added to the priority list only when the updated data value (e.g., the compromise score) of the node set for removal is greater than the reference value and / or greater than the compromise score of the parent node associated with one or more nodes in the evaluation set, as explained herein. If the control module 102 determines that the evaluation set should not be added to the priority list, control returns to 910, where the control module 102 selects another node (e.g., the next node). Otherwise, if the control module 102 determines that the evaluation set should be added to the priority list, control proceeds to 1016, where the control module 102 adds the evaluation set to the list as a suggested set for removal. Control then proceeds to 1018.

[0141] At 1018, the control module 102 determines whether there are any more nodes, as explained above. If yes, control returns to 910. If no, control proceeds to 1020, where the control module 102 prioritizes the suggested node sets on the list. For example, the control module 102 may prioritize the suggested sets for removal in descending order based on their tradeoff scores, as explained above. Control then proceeds to 1022.

[0142] At 1022, the control module 102 selects one of the suggested sets of nodes to remove. For example, the control module 102 may select the set of suggestions that is highest (e.g., first) on the sorted priority list or another suitable set of suggestions. Control then proceeds to 1024, where the control module 102 removes the selected set of suggestions and the entire subtree downstream of the set. Control then proceeds to 1026, 1028. The control module 102 updates the number of visits count (e.g., the size of the tree) at 1026 and updates the entropy at 1028, as explained herein. Control then proceeds to 1030.

[0143] At 1030, the control module 102 determines whether a condition is met to stop selecting and removing the suggestion set from the priority list. For example, the selection and removal of nodes can continue until the probabilistic tree structure has a predefined number of nodes, a predefined value, a predefined entropy, etc., as explained above. If no at 1030, control returns to 1022, where the control module 102 selects another one of the suggestion node sets for removal (e.g., the next suggestion set of one or more nodes on the priority list). Otherwise, if yes at 1030 (e.g., the condition is met), control proceeds to 1034.

[0144] At 1034, control module 102 outputs the reduced probability tree structure, as explained above. Control then proceeds to 1036, where control may store the reduced probability tree structure in memory circuit 104, as explained herein.

[0145] The foregoing description is merely illustrative in nature and is by no means intended to limit the present disclosure, its application or use. The broad teachings of the present disclosure can be implemented in various forms. Therefore, although the present disclosure includes specific examples, the true scope of the present disclosure should not be so limited, because after studying the drawings, the specification and the appended claims, other modifications will become apparent. It should be understood that one or more steps in the method can be performed in different orders (or concurrently) without changing the principles of the present disclosure. In addition, although each embodiment is described above as having certain features, any one or more of those features described with respect to any embodiment of the present disclosure can be implemented in the features of any other embodiment and / or combined with the features of any other embodiment, even if the combination is not explicitly described. In other words, the described embodiments are not mutually exclusive, and the replacement of one or more embodiments with each other is still within the scope of the present disclosure.

[0146] Spatial and functional relationships between elements (e.g., between modules, circuit elements, semiconductor layers, etc.) are described using various terms, including "connected," "engaged," "coupled," "adjacent," "next to," "on top of," "above," "below," and "disposed." Unless explicitly described as "direct," when describing the relationship between a first and a second element in the above disclosure, the relationship can be a direct relationship between the first and second elements with no other intervening elements, but can also be an indirect relationship between the first and second elements with one or more intervening elements (spatially or functionally) present. As used herein, the phrase at least one of A, B, and C should be construed to mean a logical (A or B or C), using a non-exclusive logical or, and should not be construed to mean "at least one of A, at least one of B, and at least one of C."

[0147] In a diagram, the direction of the arrow indicated by the arrow generally indicates the flow of information (such as data or instructions) of interest to the diagram. For example, when component A and component B exchange various information, but the information transmitted from component A to component B is relevant to the diagram, the arrow may point from component A to component B. This one-way arrow does not mean that no other information is transmitted from component B to component A. In addition, for information sent from component A to component B, component B may send a request or a receipt confirmation of the information to component A.

[0148] In this application, including the definitions below, the term "module" or the term "controller" may be replaced with the term "circuit". The term "module" may refer to part of or include: an application specific integrated circuit (ASIC); a digital, analog or mixed analog / digital discrete circuit; a digital, analog or mixed analog / digital integrated circuit; a combinational logic circuit; a field programmable gate array (FPGA); a processor circuit (shared, dedicated or grouped) that executes code; a memory circuit (shared, dedicated or grouped) that stores code executed by the processor circuit; other suitable hardware components that provide the described functionality; or a combination of some or all of the above, such as in a system on a chip.

[0149] The module may include one or more interface circuits. In some examples, the interface circuit may include a wired or wireless interface connected to a local area network (LAN), the Internet, a wide area network (WAN), or a combination thereof. The functions of any given module of the present disclosure may be distributed between multiple modules connected by the interface circuit. For example, multiple modules may allow load balancing. In another example, a server (also referred to as a remote or cloud) module may perform some functions on behalf of a client module.

[0150] The term code used above may include software, firmware, and / or microcode, and may refer to programs, routines, functions, classes, data structures, and / or objects. The term shared processor circuit encompasses a single processor circuit that executes some or all code from multiple modules. The term group processor circuit encompasses such a processor circuit, which is combined with additional processor circuits, to execute some or all code from one or more modules. References to multiple processor circuits encompass multiple processor circuits on discrete dies, multiple processor circuits on a single die, multiple cores of a single processor circuit, multiple threads of a single processor circuit, or a combination of the above. The term shared memory circuit encompasses a single memory circuit that stores some or all code from multiple modules. The term group memory circuit encompasses such a memory circuit, which is combined with additional memory, to store some or all code from one or more modules.

[0151] The term memory circuit is a subset of the term computer-readable medium. The term computer-readable medium as used herein does not cover transient electrical or electromagnetic signals propagated through a medium (e.g., on a carrier wave); thus, the term computer-readable medium may be considered to be tangible and non-transitory. Non-limiting examples of non-transitory tangible computer-readable media are non-volatile memory circuits (e.g., flash memory circuits, erasable programmable read-only memory circuits, or mask read-only memory circuits), volatile memory circuits (e.g., static random access memory circuits or dynamic random access memory circuits), magnetic storage media (e.g., analog or digital magnetic tape or hard drive), and optical storage media (e.g., CD, DVD, or Blu-ray disc).

[0152] The apparatus and methods described in this application may be implemented in part or in whole by a special-purpose computer, which is created by configuring a general-purpose computer to perform one or more specific functions embodied in a computer program. The functional blocks, flow chart components and other elements described above act as software specifications, which can be translated into computer programs by the routine work of a skilled technician or programmer.

[0153] The computer program includes processor executable instructions stored on at least one non-transitory tangible computer readable medium. The computer program may also include or rely on stored data. The computer program may include a basic input / output system (BIOS) that interacts with the hardware of the special-purpose computer, device drivers that interact with specific devices of the special-purpose computer, one or more operating systems, user applications, background services, background applications, etc.

[0154] A computer program may include: (i) descriptive text to be parsed, such as HTML (Hypertext Markup Language), XML (Extensible Markup Language), or JSON (JavaScript Object Notation); (ii) assembly code; (iii) object code generated by a compiler from source code; (iv) source code executed by an interpreter; (v) source code compiled and executed by a real-time compiler, etc. By way of example only, the source code may be compiled using languages ​​including C, C++, C#, Objective-C, Swift, Haskell, Go, SQL, R, Lisp, Fortran, Perl, Pascal, Curl, OCaml, HTML5 (Hypertext Markup Language Fifth Revision), Ada, ASP (Active Server Pages), PHP (PHP: Hypertext Preprocessor), Scala, Eiffel, Smalltalk, Erlang, Ruby, Visual Lua, MATLAB, SIMULINK, and The grammar of the language is used to write it.

Claims

1. A method for probability tree simplification, the method comprising: receiving a probabilistic tree structure having a plurality of nodes, wherein at least one node structure value is associated with each of the plurality of nodes, and the at least one node structure value quantifies an entropy of a subtree extending from a corresponding one of the plurality of nodes; receiving at least one parameter for removing one or more nodes of a probabilistic tree structure; removing at least one node from the plurality of nodes from the probabilistic tree structure according to a parameter; Calculate the update entropy of each of the multiple nodes upstream of the removed node; as well as A simplified probabilistic tree structure is output without the removed node and with updated entropy for each of the plurality of nodes upstream of the removed node. 2 . The method of claim 1 , wherein receiving at least one parameter for removing one or more nodes of the probabilistic tree structure comprises receiving at least one defined node to be removed from the probabilistic tree structure. 3 . The method of claim 1 , wherein receiving at least one parameter for removing one or more nodes of the probabilistic tree structure comprises receiving at least one removal criterion for removing one or more nodes from the probabilistic tree structure.

4. The method according to claim 3, wherein: One of the plurality of nodes is a parent node, and has a plurality of child nodes downstream of the parent node; The method further includes determining an optimal set of a plurality of child nodes to remove based on at least one removal criterion; and Removing at least one node of the plurality of nodes from the probabilistic tree structure includes removing an optimal set of a plurality of child nodes from the probabilistic tree structure.

5. The method of claim 4, wherein determining an optimal set of multiple child nodes to be removed comprises: For each possible set of multiple child nodes for removal, assuming that the possible set is removed, calculating the update entropy of each node in the multiple nodes upstream of the possible set, and assuming that the possible set is removed, calculating a tradeoff score based on the update entropy and the size of the probability tree structure; as well as The possible set of multiple child nodes for removal having the highest tradeoff score value is selected as the optimal set of multiple child nodes to be removed.

6. The method according to claim 3 also includes generating a list of multiple possible sets including one or more child nodes for removal based on at least one removal criterion, wherein each possible set has a compromise score, and the compromise score is based on: the update entropy of each node in the multiple nodes upstream of the possible set assuming that the possible set is removed, and the size of the probabilistic tree structure assuming that the possible set is removed. 7 . The method of claim 6 , wherein generating the list comprises prioritizing multiple possible sets of one or more child nodes in descending order based on their tradeoff scores.

8. The method of claim 7, wherein removing at least one of the plurality of nodes from the probabilistic tree structure comprises: A possible set of one or more child nodes having a highest tradeoff score value is selected from the prioritized list, and the selected set of one or more child nodes is removed from the probabilistic tree structure.

9. The method of claim 1, further comprising storing the reduced probability tree structure in a memory circuit.

10. An automated system comprising: The control module is configured to: receiving a probabilistic tree structure having a plurality of nodes, wherein at least one node structure value is associated with each of the plurality of nodes, and the at least one node structure value quantifies an entropy of a subtree extending from a corresponding one of the plurality of nodes; receiving at least one parameter for removing one or more nodes of a probabilistic tree structure; removing at least one node from the plurality of nodes from the probabilistic tree structure according to a parameter; Calculate the update entropy of each of the multiple nodes upstream of the removed node; as well as A simplified probabilistic tree structure is output without the removed node and with updated entropy for each of the plurality of nodes upstream of the removed node.

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