Data summarization for training machine learning models

Abstract

To provide a data summarization method, a computer, program, and a system for training a machine learning model.SOLUTION: A method includes obtaining a dataset including one or more data points. The method includes separating the dataset into one or more partitions on the basis of, a target number of subjects and a dimensionality of the data points included in the dataset. The method includes obtaining one or more weight vectors, each respective weight vector corresponding to a respective subject. The method includes selecting a first partition of the plurality of partitions which should be removed, from the dataset on the basis of, respective relationships between a first weighted centroid of the dataset and first partition weights corresponding to each of the partitions. The method includes obtaining a first subset of the dataset by removing the data points associated with the selected first partition from the dataset. The method includes training a machine learning model on the basis of, the first subset of the dataset.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present disclosure relates generally to data summarization for training machine learning models. [Background technology]

[0002] Machine learning models can be trained to analyze and / or perform a variety of tasks. A machine learning model may be trained using a training dataset that includes a number of data points that are relevant to the task to be performed by the machine learning model.

[0003] The subject matter claimed in this disclosure is not limited to embodiments that solve any disadvantages or that operate only in environments such as those described above. Rather, this background is provided only to illustrate one example technology area where some embodiments described in this disclosure may be practiced. Summary of the Invention

[0004] One or more embodiments of the present disclosure may include a method including obtaining a dataset including one or more data points. The method may include separating the dataset into one or more partitions based on a target number of objects and a dimensionality of the data points included in the dataset. The method may include obtaining one or more weight vectors, each corresponding to a respective object. The method may include selecting a first partition of a plurality of partitions to be removed from the dataset based on a respective relationship between a first weighted centroid of the dataset and a first partition weight corresponding to each of the partitions. The method may include obtaining a first subset of the dataset by removing data points associated with the selected first partition from the dataset. The method may include training a machine learning model based on the first subset of the dataset.

[0005] The object and advantages of the embodiments will be realized and attained at least by the elements, features, and combinations particularly pointed out in the claims. It is to be understood that both the foregoing general description and the following detailed description are explanatory and are not restrictive of the invention as claimed. [Brief explanation of the drawings]

[0006] Exemplary embodiments will be described and explained with additional specificity and detail through the accompanying drawings. [Figure 1A] FIG. 1 illustrates an exemplary system for training a machine learning model based on data points included in a core dataset according to the present disclosure. [Figure 1B] 1 illustrates the determination of a core data set based on one or more data points. [Figure 2] 1 is a flowchart of an exemplary method for training a machine learning model based on data points included in a core dataset according to the present disclosure. [Figure 3] 1 is a flowchart of an exemplary method for training a quantum machine learning model based on data points included in a core dataset according to the present disclosure. [Figure 4] 1 is an exemplary computing system. DETAILED DESCRIPTION OF THE INVENTION

[0007] Training a machine learning model may depend on the number of data points included in a dataset used to train the machine learning model. While training a machine learning model based on a training dataset that includes a large number of data points may offer various advantages, a training dataset that includes a large number of data points may include redundant data. The introduction of redundant data into a machine learning model may increase the time required to train the machine learning model without improving the accuracy of the machine learning model. Furthermore, in some instances, the amount of data in some datasets may make some techniques or systems used to train machine learning models (e.g., noisy intermediate-scale quantum (NISQ) devices) difficult, impractical, or impossible due to the large datasets potentially using more resources than may be available.

[0008] Carathéodory's theorem in convex geometry states that

number

number

[0009] The present disclosure may, among other things, facilitate training of machine learning models based on subsets of data points derived from a dataset containing multiple data points. In some embodiments, construction of the subset may be facilitated by the principles of Carathéodory's theorem, whereby the data points included in the subset are representative of the dataset from which the subset was constructed. These and other embodiments of the present disclosure may provide improvements over previous iterations of machine learning models and machine learning training processes. Thus, the functionality of a computing system implementing embodiments of the present disclosure may be improved by increasing the training speed of a machine learning model implemented on the computing system while maintaining a target level of accuracy for the trained model. Additionally or alternatively, the amount of processing resources that can be used to train the model may be reduced.

[0010] Additionally or alternatively, embodiments of the present disclosure may facilitate the implementation of quantum machine learning on noisy intermediate-scale quantum (NISQ) devices. NISQ devices include computing systems configured to perform quantum computing operations that are otherwise infeasible and / or impossible for classical computing systems to perform. Existing quantum computing devices obtain and process information using quantum bits (qubits), which represent fundamental units of quantum information about the state of a quantum system. NISQ devices may include fewer quantum bits (qubits) compared to the number of bits included in classical computing devices, and a large number of qubits may be required for a quantum computing system to perform operations that are infeasible in classical computing systems. Performing calculations for training a quantum machine learning model using an NISQ device may be impractical because the NISQ device may not include enough qubits to perform the operations necessary to train the quantum machine learning model. Therefore, training of quantum machine learning models implemented on one or more NISQ devices may be facilitated and / or improved by representing large datasets using a subset of data points that are representative of the larger dataset, in accordance with the present disclosure. Additionally, the ability to use a subset of data points may enable NISQ devices to be used to train quantum machine learning models based on data sets that may otherwise be too large.

[0011] Embodiments of the present disclosure will be described with reference to the accompanying drawings.

[0012] 1A is a diagram illustrating an example system 100 for training a machine learning model 140 based on data points included in a core dataset according to the present disclosure. The system 100 may include a data partitioning module 120, a data analysis module 130, and / or a machine learning model 140.

[0013] The data partitioning module 120, the data analysis module 130, and / or the machine learning model 140 may each include code and routines configured to enable a computing system to perform one or more operations. Additionally or alternatively, one or more of the respective modules may be implemented using hardware, including a processor, a microprocessor (e.g., for performing or controlling one or more operations), a field programmable gate array (FPGA), or an application-specific integrated circuit (ASIC). In some other examples, one or more of the respective modules may be implemented using a combination of hardware and software. In this disclosure, operations described as being performed by the data partitioning module 120, the data analysis module 130, and / or the machine learning model 140 may include operations that the data partitioning module 120, the data analysis module 130, and / or the machine learning model 140, respectively, may instruct the corresponding system to perform. The data partitioning module 120, the data analysis module 130, and / or the machine learning model 140 may be configured to perform a series of operations with respect to one or more data points 110, partitions 122-126, and / or data subsets 135, as described in further detail below with respect to at least methods 200 and / or 300 of Figures 2 and 3, respectively.

[0014] In some embodiments, the data partitioning module 120, the data analysis module 130, and / or the machine learning model 140 may each be included in the same computing system, such as the exemplary computing system 400 described in connection with FIG. 4. Additionally or alternatively, the data analysis module 130 and / or the machine learning model 140 may be included in a first computing system, and the data partitioning module 120 may be included in a second computing system configured to interface with the first computing system. Furthermore, the data partitioning module 120, the data analysis module 130, and the machine learning model 140 are illustrated and described as separate elements to facilitate description of the present disclosure. Accordingly, any suitable hardware and / or software arrangement configured to perform the operations described as being performed by the data partitioning module 120, the data analysis module 130, and / or the machine learning model 140 is within the scope of the present disclosure.

[0015] A dataset comprising one or more data points 110 may be obtained by the data partitioning module 120. A dataset may include any number of d-dimensional data points 110. For example, in mathematical terms, a given dataset "V" may be expressed as follows:

number

[0016] In some embodiments, each of the data points 110 obtained by the data partitioning module 120 may comprise a vector with a dimensionality of "d". The dimensionality of a data point 110 describes the number of coordinates used to represent the location of each of the data points 110 in the vector space. For example, a particular data point located in cubic space may be represented by a set of three coordinates (e.g., a "<x,y,z> "), thereby making this particular data point contain a dimensionality of three. As another example, if a particular higher dimensional data point is represented by a set of six coordinates (e.g., "<x,y,z,α,β,γ> "), so that this particular higher dimensional data point contains a dimensionality of 6.

[0017] The data partitioning module 120 may separate the data points 110 included in the dataset into multiple disjoint partitions, such as a first partition 122, a second partition 124, and / or an Nth partition 126, where each data point 110 in the dataset is included in only one partition. In these and other embodiments, each of the partitions 122-126 may contain approximately the same number of data points, or the same number of data points 110. For example, a particular dataset may contain 12,000 data points, and the data partitioning module 120 may determine that this particular dataset can be separated into 12 partitions. The data points associated with the particular dataset may be divided into 12 partitions, with each partition containing approximately 1000 data points. In mathematical terms, a set "P" of "r" partitions may be defined as "{P1, P2, ..., P r}".

[0018] The data partitioning module 120 may determine the number of partitions into which the data points 110 may be divided (e.g., the number of partitions corresponding to the Nth partition 126) based on the dimensionality of the data points 110 and the target number of subjects to be represented. For example, in some embodiments, the number of partitions may be expressed as:

number

[0019] In some embodiments, the target number of objects to be represented may indicate the number of parameters associated with a topic associated with the machine learning model. The target number of objects to be represented may be an intrinsic aspect of the topic and / or task associated with the machine learning model. In some embodiments, the partitioning module 120 may obtain the objects to be represented from user input including information about the machine learning task. In these or other embodiments, the user input may specifically indicate the objects. Additionally or alternatively, the objects may be implicitly included in the user input based on information about the machine learning task, and the data partitioning module 120 may be configured to extract the objects based on information about the machine learning task. For example, the information about the machine learning task may relate to training a machine learning model to predict trends in a financial and / or economic dataset, which may include analyzing weighted averages, simple moving averages, and exponential moving averages of the financial and / or economic dataset. In such an example, the data partitioning module 120 may be configured to determine that the target number of objects to be represented is three based on three topics (weighted averages, simple moving averages, and exponential moving averages) of the financial and / or economic dataset to be analyzed.

[0020] One or more non-negative weight vectors associated with a dataset may be identified based on a target number of objects to be represented. In some embodiments, the data partitioning module 120 may obtain the weight vectors from user input, including information about the data points 110 and / or the machine learning task. In these and other embodiments, the user input may specifically indicate a weight corresponding to each data point. Additionally or alternatively, weights may be implicitly included in the user input based on information about the machine learning task, and the data partitioning module 120 may be configured to extract weights based on information about the machine learning task and / or the data points 110. Each element in a given weight vector may represent the importance of the corresponding data point with respect to the object to be represented. Thus, each weight vector may include a number of weight elements corresponding to the number of data points included in the dataset, and the number of weight vectors may correspond to the target number of objects to be represented. In some embodiments, the values ​​of each element in a particular weight vector may sum to 1. For example, in mathematical terms, a particular weight vector “a” including four weights (corresponding to a particular dataset including four data points) may be expressed as follows:

number

[0021] In some embodiments, the number of partitions may be determined according to equation (3) to ensure that the null space of matrix "M" is large enough to contain a number of vectors that satisfy conditions as described in more detail below with respect to data analysis module 130. Thus, the coefficient associated with the target number of objects to be represented in equation (3) may typically be greater than 1 (e.g., 2 as shown in equation (3)).

[0022] The data analysis module 130 may obtain one or more of the partitions 122-126 and perform one or more data analysis operations on the partitions 122-126 and / or data points associated with the partitions 122-126 to determine a data subset 135. In some embodiments, the data analysis module 130 may determine a partition weight corresponding to each of the partitions 122-126 and calculate a weighted centroid representative of the dataset based on the determined partition weights. Additionally or alternatively, the data analysis module 130 may determine a subset of the dataset (e.g., data subset 135) based on identifying one or more partitions that have the least influence on the weighted centroid of the dataset and excluding the one or more partitions identified as the least influence.

[0023] To facilitate the removal of one or more partitions, the data analysis module 130 can first determine a weighted centroid of the dataset corresponding to each respective weight vector. The weighted centroid of the dataset can describe a location in the vector space of the dataset that is identified as representative of the data points included in the dataset, taking into account the weight (e.g., significance) of each data point. Thus, the number of weighted centroids determined by the data analysis module 130 can correspond to the number of weight vectors and, by extension, the target number of represented objects. In other words, a weighted centroid can be determined for each represented object included in a particular dataset, because each data point 110 included in a particular dataset can include a different weight with respect to each represented object.

[0024] For example, a particular data set containing two represented objects may include two weight vectors. A weighted centroid for this particular data set may be calculated based on each of the two weight vectors and the data points contained in the particular data set, thereby determining two weighted centroids for the particular data set. In mathematical terms, the two weight vectors associated with a particular data set may be expressed as a first weight vector "a" and a second weight vector "b." Each of the weight vectors may include a first term "a1" or "b1," a second term "a2" or "b2," and an Nth term "a1" or "b2," as described above with respect to equation (4). n " or "b n The weighted centroid "x" of a particular data set including data points 110 as described above with respect to equation (2) associated with the first weight vector a ' may be calculated as the sum of the products of each data point 110 and the respective weights corresponding to each respective data point 110. The weighted centroid of a particular data set may be expressed as:

number

[0025] The data analysis module 130 can determine a weighted centroid corresponding to each partition for each respective represented object. The weighted centroid corresponding to a particular partition can indicate a location in the vector space of the particular partition that has been identified as representative of the data points included in the particular partition, taking into account the weight (e.g., significance) of each data point. In some embodiments, the number of weighted centroids determined for a particular partition can correspond to a target number of represented objects. For example, a particular dataset containing two represented objects may include two weight vectors, "a" and "b," and each partition containing data points from the particular dataset may include two weighted centroids, "μ" and "μ": j " and "λ j The weighted centroid for a particular partition may be calculated as the sum of the products of each data point 110 included in the particular partition and the respective weights corresponding to each respective data point 110. The weighted centroid corresponding to each partition may be expressed as:

number

[0026] In these and other embodiments, the data analysis module 130 may construct a matrix "M" to facilitate the identification and selection of a first partition for removal from the dataset. The dimensions of the matrix "M" may correspond to the number of dimensions "d" of the data points 110 included in the dataset and the number of partitions "r", such that the matrix is ​​a d by r matrix (e.g., the matrix includes "d" rows and "r" columns). Each column of the matrix "M" represents a weighted centroid (e.g., "μ" as described above with respect to equation (6)) associated with each of the partitions as determined by the following mathematical formula: j " and "λ j ").

number

number

[0027] The above operations described in relation to equations (7) to (9) are performed on the set of vectors {x1, x2, ..., x kr}" where each element in the non-zero index may represent a respective partition of the dataset to facilitate removal of one or more partitions from the dataset and / or re-weighting the remaining partitions after removal.

[0028] The data analysis module 130 can determine, for each respective represented object, a partition weight corresponding to each partition. The partition weight can indicate the importance of the partition associated with each respective partition weight with respect to each represented object. In some embodiments, a partition weight can be determined to be the total importance of the weights corresponding to the data points included in a particular partition. For example, a particular dataset including two represented objects can include two weight vectors "a" and "b", and each partition including data points from the particular dataset can include two partition weight vectors "c" and "c", expressed as follows: j " and "d j" may be included.

number

[0029] The data analysis module 130 can determine a first data subset 135 of the dataset. In some embodiments, the data analysis module 130 can select a first partition of the partitions 122-126 to remove from the dataset based on the respective relationships between the weighted centroids of the dataset and each of the partition weights. In these and other embodiments, the first data subset 135 can include the data points included in the partitions 122-126 minus the data points included in the selected first partition.

[0030] In some embodiments, selecting the first partition for removal from the dataset may include identifying the partitions that have the least influence on the determination of the weighted centroid of the dataset by comparing each partition's respective partition weight to the weighted centroid to determine which partition, corresponding to the partition weight, contributes least to the representation of the weighted centroid.

[0031] For each vector satisfying the conditions expressed in equations (8) and (9), one or more centroid-reduction factors may be calculated corresponding to a target number of represented objects. For example, a first centroid-reduction factor "α" may be calculated based on the partition weight of each partition corresponding to the first represented object. The first centroid-reduction factor "α" may indicate how to readjust the weight vector corresponding to the first represented object (e.g., weight vector "a" as described above) in response to the removal of the first partition. Thus, the first centroid-reduction factor "α" may be written according to the following equation:

number

[0032] In some embodiments where the number of represented target objects is two or more, the relational term "l" is used to establish a relationship between the index at which the first centroid reduction coefficient is determined and the index at which the second centroid reduction coefficient can be calculated. * " may be determined. * " may indicate which partitions may be selected for removal from the dataset and includes an index for which the first centroid reduction factor is determined. * " can be expressed as:

number

[0033] In these and other embodiments, the second centroid reduction factor "β" can indicate how to readjust the weight vector corresponding to the second represented object (e.g., weight vector "b" as described above) in response to the removal of the first partition. The index from which the second centroid reduction factor can be calculated is determined by the relation "l" according to the following formula: * " based on

number

number

[0034] The index corresponding to the first partition selected for removal may be set to zero based on one or more centroid reduction factors (e.g., “α” associated with the first represented object and / or “β” associated with the second represented object), and an updated partition weight vector (e.g., “c’ corresponding to the first represented object) may be set to zero. j ", and / or "d' corresponding to the second expressed object. j " ) may be determined. The updated partition weight vector may be calculated based on the following formula:

number

[0035] An updated set of partitions "S" may be constructed based on the updated partition weight vector by removing the index of the first partition that was removed from the updated partition weight vector. A subset "S" of the dataset may be identified by removing the partition corresponding to the jth term of the updated partition weight vector. In some embodiments, the construction of the updated set of partitions may be expressed as follows:

number

number

[0036] In some embodiments, one or more iteration conditions may be determined, and the operations of data analysis module 130 may be performed iteratively until the iteration conditions are met. In some embodiments, the iteration conditions may include specifying a number and / or percentage of partitions to be removed from the dataset, specifying a number and / or percentage of data points to be removed from data points 110, satisfying one or more data analysis metrics, achieving a threshold accuracy in the performance of the machine learning model, etc.

[0037] The iterative operation of data analysis module 130 may facilitate the removal of data points from data subset 135 such that the training dataset provided to machine learning model 140 includes fewer data points while maintaining a target level of accuracy for the machine learning training. In these and other embodiments, data analysis module 130 may update the weighted centroid of the dataset based on the data points 110 included in data subset 135 according to equation (5). Additionally or alternatively, data analysis module 130 may iteratively update partition weights associated with partitions 122-126 included in data subset 135. Additionally or alternatively, data analysis module 130 may iteratively select a second partition, a third partition, etc. for removal from data subset 135 to determine a second data subset, a third data subset, etc.

[0038] Machine learning model 140 may be trained to perform one or more tasks based on data subset 135. In some embodiments, training machine learning model 140 based on data subset 135 may facilitate categorizing data points based on a new data set, providing user recommendations, analyzing trends among data points, performing one or more tasks, etc. Additionally or alternatively, constructing data subset 135 may facilitate training a quantum machine learning model, as described in further detail below in connection with FIG.

[0039] Modifications, additions, or omissions may be made to Figure 1A without departing from the scope of this disclosure. For example, system 100 may include more or fewer elements than those illustrated and described in this disclosure.

[0040] FIG. 1B illustrates the determination of a core dataset for dataset 150a according to the present disclosure. Dataset 150a may include one or more two-dimensional data points 162, which may be representative of data points 110 described in connection with FIG. 1A. Data points 162 may be clustered into one or more disjoint partitions, such as partition 160a and / or partition 160b. Each partition may include an equal or approximately equal number of data points 162 and a weighted centroid 170, depicted as a red cross-shaped star. Additionally or alternatively, dataset 150a may include a weighted centroid 180, depicted as a green cross-shaped star.

[0041] One or more of the partitions may be identified as having the least influence on weighted centroid 180, as described above. As shown in data set 150b, five partitions, including partition 160b, are identified as having the least influence on weighted centroid 180. In some embodiments, each of the five partitions may be identified iteratively, as described above with respect to FIG. 1A.

[0042] Consequently, the remaining three partitions can be characterized as having the greatest influence on weighted centroid 180. The three partitions identified as having the greatest influence on weighted centroid 180, including partition 160a, can be categorized as a subset of dataset 150a, which may be representative of data subset 135 described in connection with FIG. 1A, and the five partitions identified as having the least influence on weighted centroid 180 can be excluded from the subset of dataset 150a.

[0043] Subset 150c of the dataset may be further partitioned (e.g., into partitions 190a and 190b). In some circumstances, updated weighted centroids of the partitions may be determined while weighted centroid 180 of the dataset remains unchanged. Additional partitions, such as partition 190b, may be identified as having the least impact on weighted centroid 180 and removed from subset 150d. Thus, subset 150d may include one or more partitions, such as partition 190a.

[0044] 2 is a flowchart of an example method 200 for training a machine learning model based on data points included in a core dataset according to the present disclosure. Method 200 may be performed by any suitable system, apparatus, or device. For example, data partitioning module 120, data analysis module 130, and / or machine learning model 140 may perform one or more of the operations associated with method 200. Although shown in discrete blocks, the steps and operations associated with one or more of the blocks of method 200 may be divided into further blocks, combined into fewer blocks, or eliminated depending on the particular implementation.

[0045] Method 200 may begin at block 210, where a dataset is obtained. The dataset may include one or more data points, such as data point 110 described above in connection with FIG. 1A. In some embodiments, the dataset may be a training dataset for a machine learning model. The data points included in the dataset may relate to a user question and / or a task the user wishes to perform, which the machine learning model may assist with after being trained. For example, the data points may include financial data, such as the price of an asset at a particular point in time. The machine learning model may be trained to determine financial data analysis metrics for the asset and / or related assets based on the financial data, predict future performance, etc.

[0046] The dataset may be separated into one or more partitions at block 220. Separation of the dataset into one or more partitions may be achieved as described above in connection with FIG. 1A.

[0047] At block 230, weight vectors associated with the dataset may be obtained. As described in connection with FIG. 1A , the number of weight vectors associated with a particular dataset may depend on the target number of represented objects corresponding to the particular dataset. In some embodiments, the represented objects and / or weight vectors may be inherent characteristics of the particular dataset based on the question the machine learning model is configured to answer and / or the task the machine learning model is configured to perform. Thus, the represented objects and / or weight vectors corresponding to a particular dataset may include user input provided to a particular computing system configured to train a machine learning model in accordance with the present disclosure. Additionally or alternatively, the represented objects and / or weight vectors corresponding to a particular dataset may be identified by a particular computing system based on previous datasets similar to the particular dataset.

[0048] One or more weighted centroids and one or more partition weights for the dataset may be determined in block 240. The determination of the weighted centroids and partition weights for the dataset may depend on the target number of objects to be represented and the weight vector associated with the dataset, as described above in connection with FIG.

[0049] At block 250, partitions may be selected for removal from the dataset. In some embodiments, the selection of partitions to be removed from the dataset may be based on the respective relationships between the weighted centroid of the dataset and each of the partition weights. In these and other embodiments, the partitions selected for removal from the dataset may include partitions identified as having the least impact on the dataset. The selection of partitions may be accomplished as described above in connection with FIG. 1A.

[0050] At block 260, a subset of the dataset may be obtained by excluding from the dataset the data points included in the partition identified at block 250. In some embodiments, the weight vector and / or partition weights may be re-evaluated based on the data points included in the subset, as described above in connection with FIG. 1A. In other words, method 200 may return to obtaining the weight vector at block 230, and blocks 230-260 of method 200 may be performed iteratively, as described above in connection with FIG. 1A.

[0051] A machine learning model may be trained based on the subset of the dataset at block 270. In some embodiments, the machine learning model may include a quantum machine learning model, and data points included in the subset of the dataset may be loaded onto qubits to facilitate training of the quantum machine learning model, as described below in connection with FIG.

[0052] Modifications, additions, or omissions may be made to method 200 without departing from the scope of the present disclosure. For example, the designations of different elements in the described method are intended to aid in the explanation of the concepts described herein and are not intended to be limiting. Furthermore, method 200 may include any number of other elements or may be implemented in systems or contexts other than those described.

[0053] 3 is a flowchart of an exemplary method 300 for training a quantum machine learning model based on data points included in a core dataset according to the present disclosure. Method 300 may be performed by any suitable system, apparatus, or device. For example, data partitioning module 120, data analysis module 130, and / or machine learning model 140 may perform one or more of the operations associated with method 300. Although shown in discrete blocks, the steps and operations associated with one or more of the blocks of method 300 may be divided into further blocks, combined into fewer blocks, or eliminated, depending on the particular implementation.

[0054] The method may begin at block 310, where one or more data points are acquired and each data point is loaded into a quantum state. In some embodiments, the acquired data points may include data points 110 included in data subset 135, as described above in connection with FIG. 1A. The data points may include data represented in a classical state, and loading the data points into the quantum state may include converting classical bits representing the data points into a corresponding number of qubits.

[0055] At block 320, qubits representing data points may be acquired by a quantum machine learning model. In some embodiments, the quantum data points may be acquired by one or more NISQ devices on which the quantum machine learning model is implemented. At block 330, the quantum machine learning model may be trained based on the acquired quantum data points. In some embodiments, training the quantum machine learning model may include determining one or more machine learning parameters based on the training data. In some embodiments, the quantum machine learning model may acquire additional data points and / or load additional data points into the quantum state to satisfy one or more iteration conditions. The iteration conditions may include, for example, achieving a threshold accuracy of performance of the quantum machine learning model and / or passing a threshold number of training rounds. At block 340, the trained quantum machine learning model may be deployed to perform one or more machine learning tasks based on the machine learning parameters.

[0056] Modifications, additions, or omissions may be made to method 300 without departing from the scope of the present disclosure. For example, the designations of different elements in the described method are intended to aid in the explanation of the concepts described herein and are not intended to be limiting. Furthermore, method 300 may include any number of other elements or may be implemented in systems or contexts other than those described.

[0057] 4 illustrates an exemplary computing system 400 in accordance with at least one embodiment described in this disclosure. Computing system 400 may include a processor 410, a memory 420, a data storage device 430, and / or a communication unit 440, all of which may be communicatively coupled. Any or all of system 100 of FIG. 1, including data partitioning module 120, data analysis module 130, and / or machine learning model 140, may be implemented as a computing system consistent with computing system 400.

[0058] In general, processor 410 may include any suitable special purpose or general purpose computer, computing entity, or processing device, including various computer hardware or software modules, and may be configured to execute instructions stored on any applicable computer-readable storage medium. For example, processor 410 may include a microprocessor, microcontroller, digital signal processor (DSP), application specific integrated circuit (ASIC), field programmable gate array (FPGA), or any other digital or analog circuitry configured to interpret and / or execute program instructions and / or process data.

[0059] 4 as a single processor, it is understood that processor 410 may include any number of processors distributed across any number of networks or physical locations configured to individually or collectively perform any number of operations described in this disclosure. In some embodiments, processor 410 may interpret and / or execute program instructions and / or process data stored in memory 420, data storage device 430, or memory 420 and data storage device 430. In some embodiments, processor 410 may retrieve program instructions from data storage device 430 and load program instructions into memory 420.

[0060] After the program instructions are loaded into memory 420, processor 410 can execute the program instructions, such as instructions to perform any of methods 200 and / or 300 of Figures 2 and 3, respectively. For example, processor 410 can obtain a dataset, separate data points included in the dataset into multiple partitions, determine weights for each partition, determine a weighted centroid of the dataset, identify a first partition that has the least influence on the weighted centroid, obtain a first subset of the dataset by excluding the first partition, and / or train a machine learning model based on the first subset of the dataset.

[0061] Memory 420 and data storage 430 may include a computer-readable storage medium or one or more computer-readable storage media that carry or have stored thereon computer-executable instructions or data structures. Such computer-readable storage media may be any available media that can be accessed by a general-purpose or special-purpose computer, such as processor 410. For example, memory 420 and / or data storage 430 may store data sets obtained as described in connection with FIGS. 1A and 2. In some embodiments, computing system 400 may or may not include either memory 420 or data storage 430.

[0062] By way of example, and not limitation, such computer-readable storage media may include non-transitory computer-readable storage media including random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), compact disc read-only memory (CD-ROM) or other optical disk storage, magnetic disk storage or other magnetic storage devices, flash memory devices (e.g., solid-state memory devices), or any other storage medium that can be used to store desired program code in the form of computer-executable instructions or data structures and that can be accessed by a general-purpose or special-purpose computer. Combinations of the above may also be included within the scope of computer-readable storage media. Computer-executable instructions may include, for example, instructions and data configured to cause processor 610 to perform a certain operation or group of operations.

[0063] The communications unit 440 may include any component, device, system, or combination thereof configured to transmit or receive information over a network. In some embodiments, the communications unit 440 may communicate with other locations, other devices at the same location, or even other components within the same system. For example, the communications unit 440 may include a modem, a network card (wireless or wired), an optical communications device, an infrared communications device, a wireless communications device (such as an antenna), and / or a chipset (such as a Bluetooth® device, an 802.6 device (such as a metropolitan area network (MAN)), a WiFi device, a WiMax® device, a cellular communications facility, etc.). The communications unit 440 may enable data to be exchanged with a network and / or any other device or system described in this disclosure. For example, the communications unit 440 may enable the system 400 to communicate with other systems, such as computing devices and / or other networks.

[0064] Those skilled in the art, after reviewing this disclosure, may recognize that modifications, additions, or omissions may be made to system 400 without departing from the scope of the disclosure. For example, system 400 may include more or fewer components than explicitly illustrated and described.

[0065] The foregoing disclosure is not intended to limit the disclosure to the precise form or particular field of use disclosed. Accordingly, various alternative embodiments and / or modifications to the disclosure, whether expressly described or implied herein, are contemplated in light of the present disclosure. While embodiments of the present disclosure have thus been described, it will be recognized that changes can be made in form and detail without departing from the scope of the present disclosure. Accordingly, the present disclosure is limited only by the scope of the claims.

[0066] In some embodiments, the different components, modules, engines, and services described herein may be implemented as objects or processes (e.g., as separate threads) executing on a computing system. Although some of the systems and processes described herein are generally described as being implemented in software (stored on and / or executed by general-purpose hardware), specific hardware implementations, or combinations of software and specific hardware implementations, are also possible and contemplated.

[0067] Terms used in this disclosure, particularly in the appended claims (e.g., the body of the appended claims), are generally intended to be "open" terms (e.g., the term "including" should be interpreted as "including but not limited to").

[0068] Furthermore, where a specific number of introduced claim recitations is intended, such intention will be explicitly stated in the claim; where such recitation is absent, such intention does not exist. For example, as an aid to understanding, the appended claims below may include the use of the introductory phrases "at least one" and "one or more" to introduce claim recitations. However, the use of such phrases should not be construed to imply that introducing a claim recitation with the indefinite article "a" or "an" limits any particular claim containing such introduced claim recitation to embodiments containing only one such recitation, even when the same claim includes the introductory phrase "one or more" or "at least one" and an indefinite article such as "a" (e.g., "a" and / or "an" should be interpreted to mean "at least one" or "one or more"). The same applies to the use of definite articles used to introduce claim recitations.

[0069] Furthermore, even when a particular number of introduced claim recitations is explicitly recited, those skilled in the art will recognize that such recitation should be interpreted to mean at least the recited number (e.g., the mere recitation of "two recitations" without other modifiers means at least two recitations, or more than two recitations). Furthermore, in instances where a definition similar to "at least one of A, B, and C, etc." or "one or more of A, B, and C, etc." is used, such a structure is generally intended to include A alone, B alone, C alone, A and B together, A and C together, B and C together, or A, B, and C together, etc.

[0070] Furthermore, any disjunctive word or phrase preceding two or more alternative terms, whether in the specification, claims, or drawings, should be understood to contemplate the possibility of including one of the terms, either of the terms, or both of the terms. For example, the phrase "A or B" should be understood to include the possibilities of "A" or "B" or "A and B."

[0071] All examples and conditional language set forth in this disclosure are intended for educational purposes to aid the reader in understanding the disclosure and the concepts the inventors have contributed to furthering the art, and should be considered as not being limited to the examples and conditions so specifically set forth. Although embodiments of the present disclosure have been described in detail, various changes, substitutions, and alterations can be made thereto without departing from the spirit and scope of the present disclosure.

[0072] The following notes are provided regarding the above embodiment. (Appendix 1) obtaining a dataset comprising a plurality of data points; Separating the dataset into a plurality of partitions based on a target number of subjects and a dimensionality of the data points included in the dataset, each of the partitions including one or more data points of the plurality of data points; obtaining a plurality of weight vectors, each respective weight vector corresponding to a respective object of the target number of objects; determining a plurality of first weighted centroids of the data set, each respective first weighted centroid corresponding to a respective object of the target number of objects, and determined based on the plurality of data points and a respective weight vector associated with the respective object corresponding to the respective first weighted centroid; determining a plurality of first partition weights, each of the first partition weights being determined based on a respective data point included in a respective partition and one or more elements of a respective weight vector associated with the respective data point; selecting a first partition of the plurality of partitions to remove from the dataset based on a respective relationship between the first weighted centroid and each of the first partition weights; obtaining a first subset of the dataset by removing data points associated with the first partition from the dataset; training a machine learning model based on the first subset of the dataset; A method comprising: (Appendix 2) determining one or more second weighted centroids of the data set, each corresponding to a respective subject of the target number of subjects, each second weighted centroid determined based on the data points included in the first subset and a respective weight vector associated with each subject; determining one or more second partition weights for the first subset, each of the second partition weights being determined based on one or more elements of a weight vector associated with each of the target number of objects; identifying a second partition of the partitions in the first subset that has the least influence on determining the second weighted centroid based on the second partition weights; obtaining a second subset by removing data points associated with the second partition from the first subset; training the machine learning model based on the second subset of the dataset; 2. The method of claim 1, further comprising: (Appendix 3) determining an iteration condition; determining whether the iteration condition is met; 3. The method of claim 2, further comprising: (Appendix 4) 2. The method of claim 1, wherein the dataset is separated into 2k(d+1) partitions, where "k" represents the target number of points and "d" represents the dimensionality of the data points. (Appendix 5) 2. The method of claim 1, wherein selecting the first partition of the plurality of partitions to remove from the dataset includes identifying a partition of the dataset that has the least influence on determining the first weighted centroid by comparing the first partition weight with the first weighted centroid to determine which partition corresponding to the first partition weight contributes least to the representation of the first weighted centroid. (Appendix 6) the machine learning model is a quantum machine learning model; Training the quantum machine learning model includes: loading each data point in the first subset into a quantum state; determining one or more machine learning parameters based on the quantum data points; 2. The method of claim 1, comprising: (Appendix 7) 7. The method of claim 6, wherein the quantum machine learning model is configured to be implemented on one or more noisy intermediate-scale quantum (NISQ) devices. (Appendix 8) the plurality of data points included in the dataset include financial or economic data; the machine learning model is trained to perform analysis of financial or economic data; The method described in Appendix 1. (Appendix 9) One or more non-transitory computer-readable storage media configured to store instructions that, in response to being executed by one or more processors, cause the system to perform operations, the operations including: obtaining a dataset comprising a plurality of data points; Separating the dataset into a plurality of partitions based on a target number of subjects and a dimensionality of the data points included in the dataset, each of the partitions including one or more data points of the plurality of data points; obtaining a plurality of weight vectors, each respective weight vector corresponding to a respective object of the target number of objects; determining a plurality of first weighted centroids of the data set, each respective first weighted centroid corresponding to a respective object of the target number of objects and determined based on the plurality of data points and a respective weight vector associated with the respective object corresponding to the respective first weighted centroid; determining a plurality of first partition weights, each of the first partition weights determined based on a respective data point included in a respective partition and one or more elements of a respective weight vector associated with the respective data point; selecting a first partition of the plurality of partitions to remove from the dataset based on a respective relationship between the first weighted centroid and each of the first partition weights; obtaining a first subset of the dataset by removing data points associated with the first partition from the dataset; training a machine learning model based on the first subset of the dataset; one or more non-transitory computer-readable storage media, (Appendix 10) The operation is determining one or more second weighted centroids of the dataset, each corresponding to a respective subject of the target number of subjects, each second weighted centroid determined based on data points included in the first subset and a respective weight vector associated with each subject; determining one or more second partition weights for the first subset, each of the second partition weights being determined based on one or more elements of a weight vector associated with each of the target number of objects; identifying a second partition of the partitions in the first subset that has the least influence on determining the second weighted centroid based on the second partition weights; obtaining a second subset by removing data points associated with the second partition from the first subset; training the machine learning model based on the second subset of the dataset; 10. The one or more non-transitory computer-readable storage media of claim 9, further comprising: (Appendix 11) The operation is determining an iteration condition; determining whether the iteration condition is satisfied; and 11. The one or more non-transitory computer-readable storage media of claim 10, further comprising: (Appendix 12) 10. The one or more non-transitory computer-readable storage media of claim 9, wherein the dataset is separated into 2k(d+1) partitions, where "k" represents the target number of points and "d" represents the number of dimensions of the data points. (Appendix 13) 10. The one or more non-transitory computer-readable storage media of claim 9, wherein selecting the first partition of the plurality of partitions to remove from the dataset includes identifying a partition of the dataset that has the least influence on determining the first weighted centroid by comparing the first partition weight to the first weighted centroid to determine which partition corresponding to the first partition weight contributes the least to the representation of the first weighted centroid. (Appendix 14) the machine learning model is a quantum machine learning model; Training the quantum machine learning model includes: loading each data point in the first subset into a quantum state; determining one or more machine learning parameters based on the quantum data points; 10. One or more non-transitory computer-readable storage media as described in Appendix 9, including: (Appendix 15) 15. The one or more non-transitory computer-readable storage media of claim 14, wherein the quantum machine learning model is configured to be implemented on one or more noisy intermediate-scale quantum (NISQ) devices. (Appendix 16) the plurality of data points included in the dataset include financial or economic data; the machine learning model is trained to perform analysis of financial or economic data; 10. One or more non-transitory computer-readable storage media as described in Appendix 9. (Appendix 17) 1. A system comprising: one or more processors; one or more non-transitory computer-readable storage media configured to store instructions that, in response to being executed, cause the system to perform operations, the operations including: obtaining a dataset comprising a plurality of data points; Separating the dataset into a plurality of partitions based on a target number of subjects and a dimensionality of the data points included in the dataset, each of the partitions including one or more data points of the plurality of data points; obtaining a plurality of weight vectors, each respective weight vector corresponding to a respective object of the target number of objects; determining a plurality of first weighted centroids of the data set, each respective first weighted centroid corresponding to a respective object of the target number of objects and determined based on the plurality of data points and a respective weight vector associated with the respective object corresponding to the respective first weighted centroid; determining a plurality of first partition weights, each of the first partition weights determined based on a respective data point included in a respective partition and one or more elements of a respective weight vector associated with the respective data point; selecting a first partition of the plurality of partitions to remove from the dataset based on a respective relationship between the first weighted centroid and each of the first partition weights; obtaining a first subset of the dataset by removing data points associated with the first partition from the dataset; training a machine learning model based on the first subset of the dataset; Including, the system. (Appendix 18) The operation is determining one or more second weighted centroids of the dataset, each corresponding to a respective subject of the target number of subjects, each second weighted centroid determined based on data points included in the first subset and a respective weight vector associated with each subject; determining one or more second partition weights for the first subset, each of the second partition weights being determined based on one or more elements of a weight vector associated with each of the target number of objects; identifying a second partition of the partitions in the first subset that has the least influence on determining the second weighted centroid based on the second partition weights; obtaining a second subset by removing data points associated with the second partition from the first subset; training the machine learning model based on the second subset of the dataset; 18. The system of claim 17, further comprising: (Appendix 19) The operation is determining an iteration condition; determining whether the iteration condition is satisfied; and 19. The system of claim 18, further comprising: (Appendix 20) the machine learning model is a quantum machine learning model; Training the quantum machine learning model includes: loading each data point in the first subset into a quantum state; determining one or more machine learning parameters based on the quantum data points; 18. The system of claim 17, comprising:

Claims

1. A processor-executed method comprising: obtaining a dataset comprising a plurality of data points; Separating the dataset into a plurality of partitions based on a target number of subjects and a dimensionality of the data points included in the dataset, each of the partitions including one or more data points of the plurality of data points; obtaining a plurality of weight vectors, each respective weight vector corresponding to a respective object of the target number of objects; determining a plurality of first weighted centroids of the data set, each respective first weighted centroid corresponding to a respective object of the target number of objects and determined based on the plurality of data points and a respective weight vector associated with the respective object corresponding to the respective first weighted centroid; determining a plurality of first partition weights, each of the first partition weights determined based on a respective data point included in a respective partition and one or more elements of a respective weight vector associated with the respective data point; selecting a first partition of the plurality of partitions to remove from the dataset based on a respective relationship between the first weighted centroid and each of the first partition weights; obtaining a first subset of the dataset by removing data points associated with the first partition from the dataset; training a machine learning model based on the first subset of the dataset; A method comprising:

2. determining one or more second weighted centroids of the dataset, each corresponding to a respective subject of the target number of subjects, each second weighted centroid determined based on the data points included in the first subset and a respective weight vector associated with each subject; determining one or more second partition weights for the first subset, each of the second partition weights being determined based on one or more elements of a weight vector associated with each of the target number of objects; identifying a second partition of the partitions included in the first subset that has the least influence on determining the second weighted centroid based on the second partition weights; obtaining a second subset by removing data points associated with the second partition from the first subset; training the machine learning model based on the second subset of the dataset; The method of claim 1 further comprising:

3. determining an iteration condition; determining whether the iteration condition is met; The method of claim 2 further comprising:

4. 2. The method of claim 1, wherein the dataset is separated into 2k(d+1) partitions, where "k" represents the target number of points and "d" represents the dimensionality of the data points.

5. 2. The method of claim 1, wherein selecting the first partition of the plurality of partitions to remove from the dataset comprises identifying a partition that has the least influence on determining the first weighted centroid of the dataset by comparing the first partition weight to the first weighted centroid to determine which partition corresponding to the first partition weight contributes least to the representation of the first weighted centroid.

6. the machine learning model is a quantum machine learning model; Training the quantum machine learning model includes: loading each data point in the first subset into a quantum state; determining one or more machine learning parameters based on the quantum data points; The method of claim 1 , comprising:

7. 10. The method of claim 6, wherein the quantum machine learning model is configured to be implemented on one or more noisy intermediate-scale quantum (NISQ) devices.

8. the plurality of data points included in the dataset include financial or economic data; the machine learning model is trained to perform analysis of financial or economic data; The method of claim 1.

9. 1. A computer program that causes one or more processors to perform operations, said operations comprising: obtaining a dataset comprising a plurality of data points; Separating the dataset into a plurality of partitions based on a target number of subjects and a dimensionality of the data points included in the dataset, each of the partitions including one or more data points of the plurality of data points; obtaining a plurality of weight vectors, each respective weight vector corresponding to a respective object of the target number of objects; determining a plurality of first weighted centroids of the data set, each respective first weighted centroid corresponding to a respective object of the target number of objects and determined based on the plurality of data points and a respective weight vector associated with the respective object corresponding to the respective first weighted centroid; determining a plurality of first partition weights, each of the first partition weights determined based on a respective data point included in a respective partition and one or more elements of a respective weight vector associated with the respective data point; selecting a first partition of the plurality of partitions to remove from the dataset based on a respective relationship between the first weighted centroid and each of the first partition weights; obtaining a first subset of the dataset by removing data points associated with the first partition from the dataset; training a machine learning model based on the first subset of the dataset; a computer program comprising:

10. The operation is determining one or more second weighted centroids of the dataset, each corresponding to a respective subject of the target number of subjects, each second weighted centroid determined based on data points included in the first subset and a respective weight vector associated with each subject; determining one or more second partition weights for the first subset, each of the second partition weights being determined based on one or more elements of a weight vector associated with each of the target number of objects; identifying a second partition of the partitions included in the first subset that has the least influence on determining the second weighted centroid based on the second partition weights; obtaining a second subset by removing data points associated with the second partition from the first subset; training the machine learning model based on the second subset of the dataset; 10. The computer program of claim 9, further comprising:

11. The operation is determining an iteration condition; determining whether the iteration condition is satisfied; and The computer program of claim 10, further comprising:

12. 10. The computer program of claim 9, wherein the dataset is separated into 2k(d+1) partitions, where "k" represents the target number of points and "d" represents the dimensionality of the data points.

13. 10. The computer program product of claim 9, wherein selecting the first partition of the plurality of partitions to remove from the dataset comprises identifying a partition that has the least influence on determining the first weighted centroid of the dataset by comparing the first partition weight to the first weighted centroid to determine which partition corresponding to the first partition weight contributes least to the representation of the first weighted centroid.

14. the machine learning model is a quantum machine learning model; Training the quantum machine learning model includes: loading each data point in the first subset into a quantum state; determining one or more machine learning parameters based on the quantum data points; 10. The computer program of claim 9, comprising:

15. 15. The computer program of claim 14, wherein the quantum machine learning model is configured to be implemented on one or more Noisy Intermediate-Scale Quantum (NISQ) devices.

16. the plurality of data points included in the dataset include financial or economic data; the machine learning model is trained to perform analysis of financial or economic data; 10. A computer program according to claim 9.

17. 1. A system comprising: one or more processors; one or more non-transitory computer-readable storage media configured to store instructions that, in response to being executed, cause the system to perform operations, the operations including: obtaining a dataset comprising a plurality of data points; Separating the dataset into a plurality of partitions based on a target number of subjects and a dimensionality of the data points included in the dataset, each of the partitions including one or more data points of the plurality of data points; obtaining a plurality of weight vectors, each respective weight vector corresponding to a respective object of the target number of objects; determining a plurality of first weighted centroids of the data set, each respective first weighted centroid corresponding to a respective object of the target number of objects and determined based on the plurality of data points and a respective weight vector associated with the respective object corresponding to the respective first weighted centroid; determining a plurality of first partition weights, each of the first partition weights determined based on a respective data point included in a respective partition and one or more elements of a respective weight vector associated with the respective data point; selecting a first partition of the plurality of partitions to remove from the dataset based on a respective relationship between the first weighted centroid and each of the first partition weights; obtaining a first subset of the dataset by removing data points associated with the first partition from the dataset; training a machine learning model based on the first subset of the dataset; Including, the system.

18. The operation is determining one or more second weighted centroids of the dataset, each corresponding to a respective subject of the target number of subjects, each second weighted centroid determined based on data points included in the first subset and a respective weight vector associated with each subject; determining one or more second partition weights for the first subset, each of the second partition weights being determined based on one or more elements of a weight vector associated with each of the target number of objects; identifying a second partition of the partitions included in the first subset that has the least influence on determining the second weighted centroid based on the second partition weights; obtaining a second subset by removing data points associated with the second partition from the first subset; training the machine learning model based on the second subset of the dataset; 20. The system of claim 17, further comprising:

19. The operation is determining an iteration condition; determining whether the iteration condition is satisfied; and 20. The system of claim 18, further comprising:

20. the machine learning model is a quantum machine learning model; Training the quantum machine learning model includes: loading each data point in the first subset into a quantum state; determining one or more machine learning parameters based on the quantum data points; 20. The system of claim 17, comprising:

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