Classifications

• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N20/00—Machine learning
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N5/00—Computing arrangements using knowledge-based models
  • G06N5/01—Dynamic search techniques; Heuristics; Dynamic trees; Branch-and-bound
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N5/00—Computing arrangements using knowledge-based models
  • G06N5/02—Knowledge representation; Symbolic representation
  • G06N5/022—Knowledge engineering; Knowledge acquisition
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
  • G06N5/00—Computing arrangements using knowledge-based models
  • G06N5/04—Inference or reasoning models

Definitions

• the disclosed technology relates to a subgraph structure selection program, a subgraph structure selection device, and a subgraph structure selection method.
• graph kernel In order to use graph data as input for machine learning models, there is a technology called graph kernel that maps graph data to high-dimensional vectors. Examples of graph kernels include Random walk kernel, Graphlet kernel, Weisfeiler-Lehman kernel, and the like. These graph kernels often represent primitive subgraphs, with each element of the mapped vector representing a primitive subgraph. In graph XAI, it is desirable to obtain a vector representation of graph data that is as concise as possible.
• the Graphlet kernel enumerates graphlets consisting of a small number of nodes, counts the number of times each graphlet appears in the graph, and vectorizes the graph.
• a graphlet includes a predetermined number of nodes and lists all patterns of connections between nodes. When the number of nodes is ⁇ 3, 4, 5 ⁇ , the number of graphlets is 29, so the vector has 29 dimensions.
• Graph vectorization using graphlets has a problem in that the calculation cost of counting graphlets is high. In order to reduce the calculation cost, it is conceivable to reduce the number of graphlets by narrowing down the number of nodes, such as by setting the number of nodes in the graphlet to ⁇ 3, 4 ⁇ , for example. However, in this case, it is not possible to simply reduce the number of graphlets because it would have a negative impact on the accuracy of learning and prediction of a machine learning model using vectors of graph data.
• the disclosed technology aims to select a significant subgraph structure as a subgraph structure to be used in a graph kernel.
• the disclosed technique calculates the appearance frequency of each of a plurality of predetermined subgraph structures in each of one or more prediction target graphs including a plurality of nodes and a plurality of edges.
• the disclosed technique provides a method for determining the degree of contribution of each node or edge to a prediction result that is output when each of the one or more prediction target graphs is input to a trained machine learning model. Calculate explanation scores for each of a plurality of subgraph structures.
• the disclosed technology also provides, for each of the plurality of subgraph structures, the product of the average frequency of appearance, the standard deviation of the frequency of appearance, and the average of the explanation scores in the one or more prediction target graphs. Calculate.
• the disclosed technology selects one subgraph structure from among the plurality of subgraph structures and adds it to the list in descending order of the product.
• the disclosed technology calculates the accuracy of the machine learning model when inputting the graph of the prediction target that has been vectorized using the subgraph structure included in the list. Then, the disclosed technique selects the subgraph structure added to the list as the subgraph structure to be finally used when the change in accuracy satisfies a predetermined condition.
• One aspect is that a significant subgraph structure can be selected as the subgraph structure used in the graph kernel.
• FIG. 2 is a functional block diagram of a subgraph structure selection device. It is a figure which shows an example of an explanatory graph.
• FIG. 3 is a diagram for explaining a problem in selecting a graphlet. It is a figure which shows an example of a graphlet.
• FIG. 6 is a diagram for explaining the frequency of appearance of a graphlet and calculation of an explanation score.
• 1 is a block diagram showing a schematic configuration of a computer that functions as a subgraph structure selection device.
• FIG. 3 is a flowchart illustrating an example of subgraph structure selection processing.
• FIG. 3 is a diagram for explaining processing using a selected graphlet.
• a set of explanatory graphs is input to the subgraph structure selection device 10.
• the subgraph structure selection device 10 selects and outputs graphlets to be used in the graph kernel based on the explanatory graph set. Note that the graphlet is an example of a "subgraph structure" of the disclosed technology.
• An explanatory graph is a graph that includes multiple nodes and multiple edges that connect the nodes, and the contribution to the prediction result output when input to a trained machine learning model, that is, the contribution to the prediction.
• This is a graph in which a degree of contribution is assigned to each node or edge. In this embodiment, a case where a contribution degree is given to each node will be described as an example.
• the upper diagram in FIG. 2 shows an example of an explanatory graph.
• the upper diagram of FIG. 2 shows an example of a graph representing a chemical structure.
• the number written alongside each node (circle) is the degree of contribution.
• the contribution degree is used to select a graphlet on the assumption that the average contribution degree of nodes included in a significant portion with respect to the prediction result will be high.
• this assumption corresponds to an increase in the average contribution of nodes that constitute a chemically significant structure.
• Graph B has a higher average contribution. Therefore, subgraph B represents a more significant structure in the explanatory graph.
• graphlets with a small appearance frequency or standard deviation in the explanatory graph are deleted, and graphlets with high correlation with other graphlets are deleted.
• graphlets with high correlation with other graphlets are deleted.
• you want to remove redundant graphlets In the example of FIG. 2 above, if subgraph A and subgraph B appear simultaneously with high frequency, as shown in FIG .
• Graphlets whose structure matches the subgraph representing the graph may be deleted. In other words, significant graphlets may be excluded from the graphlets used for the graph kernel. Therefore, in this embodiment, as described above, the degree of contribution given to each node of the explanatory graph is used to select a graphlet.
• the subgraph structure selection device 10 functionally includes an appearance frequency calculation section 12, an explanation score calculation section 14, an evaluation value calculation section 16, a selection section 18, and a deletion section 20. Furthermore, a prediction model 30 that is a trained machine learning model is stored in a predetermined storage area of the subgraph structure selection device 10. Note that the evaluation value calculation unit 16 is an example of the “product calculation unit” of the disclosed technology.
• the appearance frequency calculation unit 12 calculates the appearance frequency of each of a plurality of predetermined graphlets in each of the explanatory graphs included in the explanatory graph set.
• the plurality of predetermined graphlets for example, as shown in FIG. 4, 29 graphlets g 1 to g 29 with the number of nodes ⁇ 3, 4, 5 ⁇ may be predetermined.
• the diagrams of graphlets used in FIG. 4 and part of FIGS. 5 and 8 described later are taken from the drawings in Non-Patent Document 1.
• the appearance frequency calculation unit 12 searches for and counts subgraphs whose structure matches each graphlet (graphlet g 6 in the example of FIG. 5) from the explanatory graph. Calculate the frequency.
• FIG. 5 the appearance frequency calculation unit 12 searches for and counts subgraphs whose structure matches each graphlet (graphlet g 6 in the example of FIG. 5) from the explanatory graph. Calculate the frequency.
• the appearance frequency calculation unit 12 calculates the appearance frequency of graphlet g6 as "2".
• the explanation score calculation unit 14 calculates the explanation score of each graphlet based on the degree of contribution of each node of the explanation graph. Specifically, the explanation score calculation unit 14 calculates the average contribution of nodes included in subgraphs that match the structure of the graphlet in the explanation graph as the explanation score of the graphlet.
• the explanatory score calculation unit 14 assigns the higher explanatory score calculated for each of the multiple subgraphs to that graphlet. This is a descriptive score.
• the explanation score calculation unit 14 calculates the average of the explanation scores for the plurality of subgraphs as the corresponding It may be calculated as the explanation score of the graphlet.
• the evaluation value calculation unit 16 calculates, as an evaluation value, the product of the average frequency of appearance, the standard deviation of the frequency of appearance, and the average of the description scores in the explanatory graph set for each of the plurality of graphlets. Specifically, the evaluation value calculation unit 16 calculates the average (hereinafter referred to as "average appearance frequency") ⁇ i of the appearance frequency calculated from each explanation graph over all explanation graphs for graphlet g i . The evaluation value calculation unit 16 also calculates the standard deviation ⁇ i of the appearance frequency calculated from each explanatory graph in all explanatory graphs for the graphlet g i .
• the evaluation value calculation unit 16 calculates the average (hereinafter referred to as "average explanation score") s i of the explanation scores calculated from each explanation graph over all explanation graphs for the graphlet g i . Then, the evaluation value calculation unit 16 calculates the product of the average appearance frequency ⁇ i , standard deviation ⁇ i , and average explanation score s i as the evaluation value ⁇ s i of the graphlet g i .
• the selection unit 18 selects one graphlet from the plurality of graphlets and adds it to the list in descending order of the evaluation value calculated by the evaluation value calculation unit 16. Each time, the selection unit 18 calculates the accuracy of the prediction model 30 when input is an explanatory graph vectorized using graphlets included in the list. The selection unit 18 passes the list to the deletion unit 20 when the change in accuracy satisfies a predetermined condition. The selection unit 18 may set the predetermined condition to a case where the accuracy no longer increases or a case where the accuracy decreases. The selection unit 18 may determine that the accuracy has stopped increasing when the difference between the accuracy calculated last time and the accuracy calculated this time is within a predetermined value. Furthermore, the selection unit 18 may determine that the accuracy is decreasing when the accuracy calculated this time is lower than the accuracy calculated last time.
• the deletion unit 20 calculates an index indicating the correlation between all pairs of graphlets added to the list, and deletes the graphlet with the lower average explanation score s from the list for the pairs whose index is equal to or higher than a predetermined value. do.
• the deletion unit 20 may calculate a cross-correlation c as an index indicating correlation. If both highly correlated graphlets are left, it would be redundant, so one is deleted. At this time, by deleting graphlets with a lower average explanation score s, graphlets with significant structures are more likely to remain.
• the deletion unit 20 outputs the graphlets remaining in the list as graphlets that are finally used in the graph kernel.
• the subgraph structure selection device 10 may be realized, for example, by a computer 40 shown in FIG. 6.
• the computer 40 includes a CPU (Central Processing Unit) 41, a memory 42 as a temporary storage area, and a nonvolatile storage section 43.
• the computer 40 also includes an input/output device 44 such as an input section and a display section, and an R/W (Read/Write) section 45 that controls reading and writing of data to and from a storage medium 49 .
• the computer 40 also includes a communication I/F (Interface) 46 connected to a network such as the Internet.
• the CPU 41, memory 42, storage section 43, input/output device 44, R/W section 45, and communication I/F 46 are connected to each other via a bus 47.
• the storage unit 43 may be realized by a HDD (Hard Disk Drive), an SSD (Solid State Drive), a flash memory, or the like.
• a subgraph structure selection program 50 for causing the computer 40 to function as the subgraph structure selection device 10 is stored in the storage unit 43 as a storage medium.
• the subgraph structure selection program 50 includes an appearance frequency calculation process 52, an explanation score calculation process 54, an evaluation value calculation process 56, a selection process 58, and a deletion process 60.
• the storage unit 43 includes an information storage area 70 in which information constituting the prediction model 30 is stored.
• the CPU 41 reads the subgraph structure selection program 50 from the storage unit 43, expands it into the memory 42, and sequentially executes the processes included in the subgraph structure selection program 50.
• the CPU 41 operates as the appearance frequency calculation unit 12 shown in FIG. 1 by executing the appearance frequency calculation process 52. Further, the CPU 41 operates as the explanation score calculation unit 14 shown in FIG. 1 by executing the explanation score calculation process 54. Further, the CPU 41 operates as the evaluation value calculation unit 16 shown in FIG. 1 by executing the evaluation value calculation process 56. Further, the CPU 41 operates as the selection unit 18 shown in FIG. 1 by executing the selection process 58. Further, the CPU 41 operates as the deletion unit 20 shown in FIG. 1 by executing the deletion process 60.
• the CPU 41 reads information from the information storage area 70 and develops the prediction model 30 in the memory 42 .
• the computer 40 that has executed the subgraph structure selection program 50 functions as the subgraph structure selection device 10. Note that the CPU 41 that executes the program is hardware.
• subgraph structure selection program 50 can also be realized by, for example, a semiconductor integrated circuit, more specifically, an ASIC (Application Specific Integrated Circuit).
• ASIC Application Specific Integrated Circuit
• the subgraph structure selection device 10 executes the subgraph structure selection process shown in FIG. Note that the subgraph structure selection process is an example of the subgraph structure selection method of the disclosed technology.
• step S10 the appearance frequency calculation unit 12 acquires the explanatory graph set input to the subgraph structure selection device 10.
• step S12 the appearance frequency calculation unit 12 calculates the appearance frequency of each graphlet in each explanation graph by searching and counting subgraphs whose structure matches the graphlet.
• step S14 the explanation score calculation unit 14 calculates the average contribution of nodes included in subgraphs that match the structure of the graphlet in the explanation graph as the explanation score of the graphlet.
• the explanation score calculation unit 14 calculates the explanation score of each graphlet in each explanation graph.
• step S16 the evaluation value calculation unit 16 calculates, for each graphlet, the average appearance frequency that is the average of the appearance frequencies calculated from each explanatory graph, the standard deviation of the appearance frequency, and the average appearance frequency calculated from each explanatory graph.
• the average explanation score which is the average of the explanation scores obtained, is calculated. Then, the evaluation value calculation unit 16 calculates the product of the average appearance frequency, standard deviation, and average explanation score as the evaluation value of each graphlet.
• step S18 the selection unit 18 creates a list L in which the graphlets are sorted in descending order of the evaluation value calculated in step S16.
• step S20 the selection unit 18 selects the graphlet with the highest evaluation value from the list L, adds it to the list L', and deletes it from the list L.
• step S22 the selection unit 18 calculates the accuracy of the prediction model 30 when inputting the explanatory graph vectorized using the graphlets included in the list L' as graph kernels.
• step S24 the selection unit 18 determines whether the accuracy calculated in step S22 is lower than the previously calculated accuracy. If the accuracy has not decreased, the process returns to step S20, and if it has decreased, the process proceeds to step S26.
• step S26 the selection unit 18 deletes the last graphlet added to the list L' from the list L', and passes the list L' to the deletion unit 20.
• step S28 the deletion unit 20 calculates an index indicating the correlation of all pairs of graphlets in the list L'. Then, the deletion unit 20 deletes the graphlet with the lower average explanation score s from the list L' for the pairs in which the index indicating correlation is equal to or greater than a predetermined value.
• the deletion unit 20 outputs the graphlets remaining in the list L' as graphlets to be finally used by the graph kernel, and ends the subgraph structure selection process.
• the subgraph structure selection device calculates the appearance frequency of each of a plurality of predetermined graphlets in each of one or more explanatory graphs including a plurality of nodes and a plurality of edges. calculate. Further, the subgraph structure selection device calculates an explanation score for each of the plurality of graphlets based on the degree of contribution of each node given to the explanation graph. Further, the subgraph structure selection device calculates, for each of the plurality of subgraphlets, the product of the average appearance frequency, the standard deviation of the appearance frequency, and the average explanation score in the explanatory graph set as an evaluation value. Further, the subgraph structure selection device selects one graphlet from among the plurality of graphlets in descending order of evaluation value and adds it to the list.
• the subgraph structure selection device calculates the accuracy of the prediction model when input is an explanatory graph vectorized using graphlets included in the list. Then, when the change in precision satisfies a predetermined condition, the subgraph structure selection device selects the graphlet added to the list as a subgraph structure to be finally used in the graph kernel. Thereby, a significant subgraph structure can be selected as the subgraph structure to be used in the graph kernel.
• this embodiment selects a graphlet to be used in the graph kernel using an explanatory score based on the degree of contribution in the explanatory graph, without losing significant subgraph structure.
• a concise combination of graphlets can be selected.
• the prediction result explanation obtained along with the prediction result can be concise and concise without losing its significance.
• FIG. 8 shows an example in which, among the selected graphlets, a subgraph whose structure matches the graphlet surrounded by a broken line (bold line part) is identified as a subgraph contributing to prediction.
• causal inferences when performing subsequent causal inferences based on the prediction results and prediction result explanations, significant causal relationships are likely to be estimated as causal relationships between subgraphs within the graph. For example, in the case of a graph representing a chemical structure, performing causal inference can contribute to discovering subgraphs related to reaction mechanisms.
• the subgraph structure selection program is stored (installed) in the storage unit in advance, but the present invention is not limited to this.
• the program according to the disclosed technology can also be provided in a form stored in a storage medium such as a CD-ROM, DVD-ROM, or USB memory.
• Subgraph structure selection device 10
• Appearance frequency calculation unit 14
• Evaluation value calculation unit 16
• Selection unit 20
• Deletion unit 30
• Prediction model 40
• Computer 41
• Memory 43
• Storage section 44
• Input/output device 45
• R/W section 46
• Communication I/F 47
• Bus 49
• Subgraph structure selection program 52
• Appearance frequency calculation process 54
• Evaluation value calculation process 56
• Deletion process 60
• Information storage area Information storage area

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• 2022
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