Patent Publication Number: US-2023137184-A1

Title: Incremental machine learning for a parametric machine learning model

Description:
BACKGROUND 
     The present disclosure relates to machine learning, and more specifically, to methods, systems, and computer program products for incremental machine learning for a parametric machine learning model. 
     Machine learning is the science of getting computers to act without being explicitly programmed. In other words, machine learning is a method of data analysis that automates analytical model building. Machine learning is a branch of artificial intelligence based on the idea that computer systems can learn from data, identify patterns, and make decisions with minimal human intervention. 
     Most of machine learning uses supervised learning. Supervised learning is the task of learning a function that maps an input to an output based on example input-output pairs. Supervised learning infers a function, referred to as a machine learning model therein, from labeled training data consisting of a set of training examples, referred to as training samples therein. Each sample is a pair consisting of input values of features, which is typically a vector, and a value of output variable which can be continuous variable or categorial variable. 
     A supervised learning algorithm analyzes the training samples and produces a machine learning model, which can be used for mapping new samples to correctly determine the output values for unseen data. The algorithm for producing the machine learning model is learning from training samples, which can be thought of as a teacher. The algorithm iteratively makes predictions on the training data set and is corrected by the teacher. Learning stops when the algorithm achieves an acceptable level of performance. 
     BRIEF SUMMARY 
     This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. 
     According to a first aspect of the present disclosure, there is provided a computer-implemented method. The method may include processing samples comprising historical samples and new samples with an existing parametric machine learning model to obtain at least one prediction residual of each of the samples, wherein the existing parametric machine learning model was trained based on the historical samples. The method may further include clustering the samples based on the at least one prediction residual of each of the samples and features of each of the samples. The method may further include sampling samples in each cluster to ensure that each cluster includes substantially similar number of sampled samples. The method may further include updating the existing parametric machine learning model to obtain an updated parametric machine learning model based on sampled samples in each cluster. 
     According to a second aspect of the present disclosure, there is provided a system. The system comprises a first component with at least one processing unit in a cloud computing environment and a memory coupled to the at least one processing unit and storing instructions thereon. The instructions, when executed by the processing unit, perform actions of the above method. 
     According to a third aspect of the present disclosure, there is provided a computer program product comprising a computer-readable storage medium having program instructions embodied therewith. The program instructions are executable by a first component with at least one processing unit in a cloud computing environment to cause the at least one processing unit to perform actions of the above method. 
    
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
       Through the more detailed description of some embodiments of the present disclosure in the accompanying drawings, the above and other objects, features and advantages of the present disclosure will become more apparent, wherein the same reference generally refers to the same components in the embodiments of the present disclosure. The various features of the drawings are not to scale as the illustrations are for clarity in facilitating one skilled in the art in understanding the disclosure in conjunction with the detailed description. The drawings are discussed forthwith below. 
         FIG.  1    depicts a cloud computing node according to some embodiments of the present disclosure. 
         FIG.  2    depicts a cloud computing environment according to some embodiments of the present disclosure. 
         FIG.  3    depicts abstraction model layers according to some embodiments of the present disclosure. 
         FIG.  4    depicts a diagram illustrating an example system for incremental machine learning for a parametric machine learning model according to some embodiments of the present disclosure. 
         FIG.  5    depicts a schematic diagram of a process implemented by a sampling module according to some embodiments of the present disclosure. 
         FIG.  6    depicts a schematic diagram of a process implemented by an updating module according to some embodiments of this disclosure. 
         FIG.  7    depicts a first incremental learning process according to some embodiments of this disclosure. 
         FIG.  8    depicts a second incremental learning process according to some embodiments of this disclosure. 
         FIG.  9    depicts a flowchart of an exemplary method for incremental machine learning for a parametric machine learning model according to some embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     The following description with reference to the accompanying drawings is provided to assist in a comprehensive understanding of exemplary embodiments of the disclosure as defined by the claims and their equivalents. It includes various specific details to assist in that understanding but these are to be regarded as merely exemplary. Accordingly, those of ordinary skill in the art will recognize that various changes and modifications of the embodiments described herein can be made without departing from the scope and spirit of the disclosure. In addition, descriptions of well-known functions and constructions may be omitted for clarity and conciseness. 
     In the following, reference is made to various embodiments of the disclosure. However, it should be understood that the disclosure is not limited to specific described embodiments. Instead, any combination of the following features and elements, whether related to different embodiments or not, is contemplated to implement and practice the disclosure. Furthermore, although embodiments may achieve advantages over other possible solutions and/or over the prior art, whether or not a particular advantage is achieved by a given embodiment is not limiting. Thus, the following aspects, features, embodiments, and advantages are merely illustrative and are not considered elements or limitations of the appended claims except where explicitly recited in a claim(s). 
     The terms and words used in the following description and claims are not limited to the bibliographical meanings, but are merely used to enable a clear and consistent understanding of the disclosure. Accordingly, it should be apparent to those skilled in the art that the following description of exemplary embodiments of the present disclosure is provided for illustration purpose only and not for the purpose of limiting the disclosure as defined by the appended claims and their equivalents. 
     It is to be understood that the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a component surface” includes reference to one or more of such surfaces unless the context clearly dictates otherwise. 
     It is to be understood that although this disclosure includes a detailed description on cloud computing, implementation of the teachings recited herein are not limited to a cloud computing environment. Rather, embodiments of the present disclosure are capable of being implemented in conjunction with any other type of computing environment now known or later developed. 
     Cloud computing is a model of service delivery for enabling convenient, on-demand network access to a shared pool of configurable computing resources (e.g. networks, network bandwidth, servers, processing, memory, storage, applications, virtual machines, and services) that can be rapidly provisioned and released with minimal management effort or interaction with a provider of the service. This cloud model may include at least five characteristics, at least three service models, and at least four deployment models. 
     Characteristics are as follows: 
     On-demand self-service: a cloud consumer can unilaterally provision computing capabilities, such as server time and network storage, as needed automatically without requiring human interaction with the service&#39;s provider. 
     Broad network access: capabilities are available over a network and accessed through standard mechanisms that promote use by heterogeneous thin or thick client platforms (e.g., mobile phones, laptops, and PDAs). 
     Resource pooling: the provider&#39;s computing resources are pooled to serve multiple consumers using a multi-tenant model, with different physical and virtual resources dynamically assigned and reassigned according to demand. There is a sense of location independence in that the consumer generally has no control or knowledge over the exact location of the provided resources but may be able to specify location at a higher level of abstraction (e.g., country, state, or datacenter). 
     Rapid elasticity: capabilities can be rapidly and elastically provisioned, in some cases automatically, to quickly scale out and rapidly released to quickly scale in. To the consumer, the capabilities available for provisioning often appear to be unlimited and can be purchased in any quantity at any time. 
     Measured service: cloud systems automatically control and optimize resource use by leveraging a metering capability at some level of abstraction appropriate to the type of service (e.g., storage, processing, bandwidth, and active user accounts). Resource usage can be monitored, controlled, and reported providing transparency for both the provider and consumer of the utilized service. 
     Service Models are as follows: 
     Software as a Service (SaaS): the capability provided to the consumer is to use the provider&#39;s applications running on a cloud infrastructure. The applications are accessible from various client devices through a thin client interface such as a web browser (e.g., web-based e-mail). The consumer does not manage or control the underlying cloud infrastructure including network, servers, operating systems, storage, or even individual application capabilities, with the possible exception of limited user-specific application configuration settings. 
     Platform as a Service (PaaS): the capability provided to the consumer is to deploy onto the cloud infrastructure consumer-created or acquired applications created using programming languages and tools supported by the provider. The consumer does not manage or control the underlying cloud infrastructure including networks, servers, operating systems, or storage, but has control over the deployed applications and possibly application hosting environment configurations. 
     Infrastructure as a Service (IaaS): the capability provided to the consumer is to provision processing, storage, networks, and other fundamental computing resources where the consumer is able to deploy and run arbitrary software, which can include operating systems and applications. The consumer does not manage or control the underlying cloud infrastructure but has control over operating systems, storage, deployed applications, and possibly limited control of select networking components (e.g., host firewalls). 
     Deployment Models are as follows: 
     Private cloud: the cloud infrastructure is operated solely for an organization. It may be managed by the organization or a third party and may exist on-premises or off-premises. 
     Community cloud: the cloud infrastructure is shared by several organizations and supports a specific community that has shared concerns (e.g., mission, security requirements, policy, and compliance considerations). It may be managed by the organizations or a third party and may exist on-premises or off-premises. 
     Public cloud: the cloud infrastructure is made available to the general public or a large industry group and is owned by an organization selling cloud services. 
     Hybrid cloud: the cloud infrastructure is a composition of two or more clouds (private, community, or public) that remain unique entities but are bound together by standardized or proprietary technology that enables data and application portability (e.g., cloud bursting for load-balancing between clouds). 
     A cloud computing environment is service oriented with a focus on statelessness, low coupling, modularity, and semantic interoperability. At the heart of cloud computing is an infrastructure that includes a network of interconnected nodes. 
     Referring now to  FIG.  1   , a schematic of an example of a cloud computing node is shown. Cloud computing node  10  is only one example of a suitable cloud computing node and is not intended to suggest any limitation as to the scope of use or functionality of embodiments of the disclosure described herein. Regardless, cloud computing node  10  is capable of being implemented and/or performing any of the functionality set forth hereinabove. 
     In cloud computing node  10  there is a computer system/server  12  or a portable electronic device such as a communication device, which is operational with numerous other general purpose or special purpose computing system environments or configurations. Examples of well-known computing systems, environments, and/or configurations that may be suitable for use with computer system/server  12  include, but are not limited to, personal computer systems, server computer systems, thin clients, thick clients, hand-held or laptop devices, multiprocessor systems, microprocessor-based systems, set top boxes, programmable consumer electronics, network PCs, minicomputer systems, mainframe computer systems, and distributed cloud computing environments that include any of the above systems or devices, and the like. 
     Computer system/server  12  may be described in the general context of computer system-executable instructions, such as program modules, being executed by a computer system. Generally, program modules may include routines, programs, objects, components, logic, data structures, and so on that perform particular tasks or implement particular abstract data types. Computer system/server  12  may be practiced in distributed cloud computing environments where tasks are performed by remote processing devices that are linked through a communications network. In a distributed cloud computing environment, program modules may be located in both local and remote computer system storage media including memory storage devices. 
     As shown in  FIG.  1   , computer system/server  12  in cloud computing node  10  is shown in the form of a general-purpose computing device. The components of computer system/server  12  may include, but are not limited to, one or more processors or processing units  16 , a system memory  28 , and a bus  18  that couples various system components including system memory  28  to processor  16 . 
     Bus  18  represents one or more of any of several types of bus structures, including a memory bus or memory controller, a peripheral bus, an accelerated graphics port, and a processor or local bus using any of a variety of bus architectures. By way of example, and not limitation, such architectures include Industry Standard Architecture (ISA) bus, Micro Channel Architecture (MCA) bus, Enhanced ISA (EISA) bus, Video Electronics Standards Association (VESA) local bus, and Peripheral Component Interconnect (PCI) bus. 
     Computer system/server  12  typically includes a variety of computer system readable media. Such media may be any available media that is accessible by computer system/server  12 , and it includes both volatile and non-volatile media, removable and non-removable media. 
     System memory  28  can include computer system readable media in the form of volatile memory, such as random access memory (RAM)  30  and/or cache memory  32 . Computer system/server  12  may further include other removable/non-removable, volatile/non-volatile computer system storage media. By way of example only, storage system  34  can be provided for reading from and writing to a non-removable, non-volatile magnetic media (not shown and typically called a “hard drive”). Although not shown, a magnetic disk drive for reading from and writing to a removable, non-volatile magnetic disk (e.g., a “floppy disk”), and an optical disk drive for reading from or writing to a removable, non-volatile optical disk such as a CD-ROM, DVD-ROM or other optical media can be provided. In such instances, each can be connected to bus  18  by one or more data media interfaces. As will be further depicted and described below, memory  28  may include at least one program product having a set (e.g., at least one) of program modules that are configured to carry out the functions of embodiments of the disclosure. 
     Program/utility  40 , having a set (at least one) of program modules  42 , may be stored in memory  28  by way of example, and not limitation, as well as an operating system, one or more application programs, other program modules, and program data. Each of the operating system, one or more application programs, other program modules, and program data or some combination thereof, may include an implementation of a networking environment. Program modules  42  generally carry out the functions and/or methodologies of embodiments of the disclosure as described herein. 
     Computer system/server  12  may also communicate with one or more external devices  14  such as a keyboard, a pointing device, a display  24 , etc.; one or more devices that enable a user to interact with computer system/server  12 ; and/or any devices (e.g., network card, modem, etc.) that enable computer system/server  12  to communicate with one or more other computing devices. Such communication can occur via Input/Output (I/O) interfaces  22 . Still yet, computer system/server  12  can communicate with one or more networks such as a local area network (LAN), a general wide area network (WAN), and/or a public network (e.g., the Internet) via network adapter  20 . As depicted, network adapter  20  communicates with the other components of computer system/server  12  via bus  18 . It should be understood that although not shown, other hardware and/or software components could be used in conjunction with computer system/server  12 . Examples, include, but are not limited to: microcode, device drivers, redundant processing units, external disk drive arrays, RAID systems, tape drives, and data archival storage systems, etc. 
     Referring now to  FIG.  2   , illustrative cloud computing environment  50  is depicted. As shown, cloud computing environment  50  includes one or more cloud computing nodes  10  with which local computing devices used by cloud consumers, such as, for example, personal digital assistant (PDA) or cellular telephone  54 A, desktop computer  54 B, laptop computer  54 C, and/or automobile computer system  54 N may communicate. Nodes  10  may communicate with one another. They may be grouped (not shown) physically or virtually, in one or more networks, such as Private, Community, Public, or Hybrid clouds as described hereinabove, or a combination thereof. This allows cloud computing environment  50  to offer infrastructure, platforms and/or software as services for which a cloud consumer does not need to maintain resources on a local computing device. It is understood that the types of computing devices  54 A-N shown in  FIG.  2    are intended to be illustrative only and that computing nodes  10  and cloud computing environment  50  can communicate with any type of computerized device over any type of network and/or network addressable connection (e.g., using a web browser). 
     Referring now to  FIG.  3   , a set of functional abstraction layers provided by cloud computing environment  50  ( FIG.  2   ) is shown. It should be understood in advance that the components, layers, and functions shown in  FIG.  3    are intended to be illustrative only and embodiments of the disclosure are not limited thereto. As depicted, the following layers and corresponding functions are provided: 
     Hardware and software layer  60  includes hardware and software components. Examples of hardware components include: mainframes  61 ; RISC (Reduced Instruction Set Computer) architecture based servers  62 ; servers  63 ; blade servers  64 ; storage devices  65 ; and networks and networking components  66 . In some embodiments, software components include network application server software  67  and database software  68 . 
     Virtualization layer  70  provides an abstraction layer from which the following examples of virtual entities may be provided: virtual servers  71 ; virtual storage  72 ; virtual networks  73 , including virtual private networks; virtual applications and operating systems  74 ; and virtual clients  75 . 
     In one example, management layer  80  may provide the functions described below. Resource provisioning  81  provides dynamic procurement of computing resources and other resources that are utilized to perform tasks within the cloud computing environment. Metering and Pricing  82  provide cost tracking as resources are utilized within the cloud computing environment, and billing or invoicing for consumption of these resources. In one example, these resources may include application software licenses. Security provides identity verification for cloud consumers and tasks, as well as protection for data and other resources. User portal  83  provides access to the cloud computing environment for consumers and system administrators. Service level management  84  provides cloud computing resource allocation and management such that required service levels are met. Service Level Agreement (SLA) planning and fulfillment  85  provide pre-arrangement for, and procurement of, cloud computing resources for which a future requirement is anticipated in accordance with an SLA. 
     Workloads layer  90  provides examples of functionality for which the cloud computing environment may be utilized. Examples of workloads and functions which may be provided from this layer include: mapping and navigation  91 ; software development and lifecycle management  92 ; virtual classroom education delivery  93 ; data analytics processing  94 ; transaction processing  95 ; and incremental machine learning  96 . 
     In machine learning, given historical training samples, each being a pair consisting of a set of values of input features and a value of an output variable, a machine learning model (model in short) can be built based on the historical training samples to represent the relationship between the set of input features and the corresponding output variable. For a new sample, which only contains a set of values of input features, the model can be used to predict a corresponding value of output variable for the new sample. 
     In some situations, over time, an existing model trained with historical samples can no longer be used to correctly predict values of output variables for new samples. It is needed to re-train the existing model to obtain a new model. This process is called incremental learning. There are two ways for incremental learning: one is to use the historical samples and the new samples to re-train the existing model to obtain the new model; the other is to use only the new samples to re-train the existing model to obtain the new model. 
     However, when the number of the new samples is not sufficient, it is difficult to get a new model with good quality. The reason is that if the historical samples and the new samples are combined to re-train the existing model, the patterns in the historical samples will dominate the new model, and the new model will not have a good performance for the new samples. On the other hand, if only the new samples are used to re-train the existing model, the new model may overfit the historical samples. 
     This disclosure proposes a method in which samples are selected from the historical samples and the new samples for incremental machine learning to ensure that an updated parametric machine learning model achieves a good prediction accuracy for new samples while keeps an acceptable level of prediction accuracy for the historical samples. 
     Table 1 shows an example data set including historical samples and new samples. The data set is two-dimensional. Each row is a record of a sample. A column “ID” represents an identification of a sample. Each of columns “X1”, “X2”, . . . , “Xn” represents a feature, and a vector {X1, X2, . . . , Xn} represents the input features. A column “Y” represents a corresponding output variable, which is categorical variable in this example, where “1” in the column Y represents that a corresponding sample belongs to a category “A” while “0” in the column “Y” represents that a corresponding sample belongs to a category of “B”. A column “New sample?” represents whether a sample is a historical sample or a new sample. For example, value “N” in the column “New sample?” represents that a corresponding sample is a historical sample while value “Y” in the column “New sample?” represents that a corresponding sample is a new sample. 
     
       
         
           
               
               
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 ID 
                 X1 
                 X2 
                 . . . 
                 Xn 
                 Y 
                 New sample? 
               
               
                   
               
             
            
               
                 1 
                 0.3 
                 0.7 
                 . . . 
                 0.2 
                 1 
                 N 
               
               
                 2 
                 0.5 
                 0.2 
                 . . . 
                 0.6 
                 0 
                 N 
               
               
                 3 
                 0.4 
                 0.3 
                   
                 0.5 
                 1 
                 N 
               
               
                 4 
                 0.2 
                 0.6 
                   
                 0.7 
                 1 
                 N 
               
               
                 5 
                 0.8 
                 0.4 
                   
                 0.6 
                 1 
                 N 
               
               
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
               
               
                 N 
                 0.9 
                 0.5 
                 . . . 
                 0.7 
                 0 
                 Y 
               
               
                   
               
            
           
         
       
     
     A parametric machine learning model (parametric model in short) means a model can be represented as some parameters which can be iteratively estimated using optimization method such as gradient descent. The parametric model may be, but not limited to, a linear regression model, a generalized linear model, a logistic regression model, a linear discriminant analysis model, a perceptron model, a naive Bayes model, a deep learning model, and the like. 
     If an output variable is a categorical variable, a value of the categorical variable may be defined as a one-hot-encode value of each category during training a parametric model. If the output variable is a continuous variable, the value of the output variable may be used directly during training the parametric model. After the parametric model is built, if the output variable is the categorical variable, a prediction probability value of each category for a sample can be obtained using the parametric model. Then a prediction residual of the sample for a category can be obtained by subtracting the prediction probability value of the sample for the category from the one-hot-encode value of the sample for the category. In addition, if the output variable is the continuous variable, a prediction value for a sample can be obtained using the parametric model. Then a prediction residual of the sample can be obtained by subtracting the prediction value of the sample from the value of the output variable of the sample. 
     Take the categorical variable as the output variable as an example. If the output variable takes two categories “A” and “B” and if a value of the output variable for a sample is “A”, a one-hot-encode value of the category “A” for the sample may be defined as “1”. And another one-hot-encode value of the category “B” for the sample may be defined as “0”. Table 2 shows example prediction residuals of some samples. In Table 2, each row represents a record of a sample. A column “ID” represents an identification of a sample. A column “Y_A” represents a one-hot-encode value for the category “A”. A column “Y_B” represents a one-hot-encode value for the category “B”. A column “P_A” represents a predicting value for the category “A” with a model. A column “P_B” represents a predicting value for the category “B” with the model. A column “R_A” represents a prediction residual of a sample for the category “A”. A column “R_B” represents a prediction residual of a sample for the category “B”. A column “Category” represents a labeled category of a sample. As indicated in Table 2, if prediction probability values for a sample obtained from the parametric model are 0.85 and 0.15 for category “A” and “B” respectively, then the residual of the sample for the category “A” is 1−0.85=0.15, and the residual of the sample for the category “B” is 0−0.15=−0.15. 
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                 ▪ 
                   
                   
                   
                   
                   
                   
                   
               
               
                 ID 
                 Y_A 
                 Y_B 
                 P_A 
                 P_B 
                 R_A 
                 R_B 
                 Category 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 1 
                 1 
                 0 
                 0.85 
                 0.15 
                 0.15 
                 −0.15 
                 A 
               
               
                 2 
                 0 
                 1 
                 0.45 
                 0.55 
                 −0.45 
                 0.45 
                 B 
               
               
                 3 
                 1 
                 0 
                 0.65 
                 0.35 
                 0.35 
                 −0.35 
                 A 
               
               
                   
               
            
           
         
       
     
     With reference now to  FIG.  4   , a diagram illustrating an example system  400  for incremental machine learning for a parametric machine learning model is depicted in accordance with some embodiments. The system  400  may be implemented in a network of data processing systems, such as the network data processing system  100  in  FIG.  1   , or a cloud computing environment, such as the cloud computing environment in  FIG.  3   . 
     The system  400  may comprise a training module  401 , a predicting module  402 , a clustering module  403 , a sampling module  404 , and an updating module  405 . Referring to  FIG.  4   , samples  410  may comprise historical samples and new samples. The training module  401  may be configured to produce an existing parametric machine learning model (“existing model”, in short)  411  by training the historical samples. After the existing model  411  is produced, the predicting module  402  may be configured to process the samples  410  including the historical samples and the new samples with the produced existing model  411  to obtain at least one prediction residual  412  of each of the samples  410 . The clustering module  403  may be configured to cluster the samples  410  based on the at least one prediction residual  412  of each of the samples  410  and respective features of each of the samples  410  to obtain clusters  413 . The sampling module  404  may be configured to sample the samples in each cluster  413  to obtain sampled samples  414  to ensure that each cluster includes substantially similar number of sampled samples. The updating module  405  may be configured to update the existing model  411  to obtain an updated parametric machine learning model (“updated model”, in short)  415  based on sampled samples  414  in each cluster. 
     In some embodiments, the training module  401  and the predicting module  402  may use any existing supervised learning technologies. The existing model  411  may be, but not limited to, one of the following models: a linear regression model, a generalized linear model, a logistic regression model, a linear discriminant analysis model, a perceptron model, a naive Bayes model, a deep learning model, and the like. 
     In some embodiments, Table 3 shows example clusters for the samples  410 , in which the output variable is the categorical variable. In Table 3, each row is a record of a sample. A column “ID” represents an identification of a sample. Each of columns “X1”, “X2”, . . . , “Xn” represents a feature of the sample. A column “R_A” represents a prediction residual of the sample for a category “A”. A column “R_B” represents a prediction residual of the sample for a category “B”. A column “Cluster_ID” represents which cluster the sample belongs to. The prediction residual set of a sample, i.e. R_A and R_B, may reflect whether the sample can be predicted by the existing model accurately. Thus, the prediction residual set can be added to the set of input features of the sample for clustering. The clustering module  403  may cluster the samples in Table 3, each sample including the set of input features {X1, X2, . . . , Xn, R_A, R_B}, and obtain clusters of the samples. The cluster ID of each sample in Table 3 is in the column “Cluster_ID”. Those skilled in the art my understand that the clustering module  403  may use any existing cluster methods, such as k-mean clustering, TwoStep clustering, or density-based special clustering of applications with noise (DBSCAN) or any future developed clustering methods. 
     
       
         
           
               
               
               
               
               
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                 ID 
                 X1 
                 X2 
                 . . . 
                 Xn 
                 R_A 
                 R_B 
                 Cluster_ID 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
            
               
                 1 
                 0.3 
                 0.7 
                 . . . 
                 0.2 
                 0.15 
                 −0.15 
                 1 
               
               
                 2 
                 0.5 
                 0.2 
                 . . . 
                 0.6 
                 0.65 
                 −0.65 
                 1 
               
               
                 3 
                 0.4 
                 0.3 
                   
                 0.5 
                 −0.35 
                 0.35 
                 2 
               
               
                 4 
                 0.2 
                 0.6 
                   
                 0.7 
                 −0.45 
                 0.45 
                 2 
               
               
                 5 
                 0.8 
                 0.4 
                   
                 0.6 
                 0.15 
                 −0.15 
                 1 
               
               
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
                 . . . 
               
               
                 N 
                 0.9 
                 0.5 
                 . . . 
                 0.7 
                 −0.25 
                 0.25 
                 2 
               
               
                   
               
            
           
         
       
     
     In some embodiments,  FIG.  5    depicts a schematic diagram of a process implemented by the sampling module  404  according to some embodiments of the present disclosure. As shown in  FIG.  5   , clusters  501  including m clusters (m is an integer greater than or equal to 2) are obtained by the clustering module  403 . The different size of each cluster in the clusters  501  may indicate each cluster includes a different number of samples. The sampling module  404  may sample samples in each cluster of the clusters  501  to obtains clusters  502  in which each cluster includes substantially similar number of sampled samples. The user may define what the substantially similar number of sampled samples means. For example, if the difference in the number of samples in two clusters is within 5% of the number of samples in one cluster, it is considered that the number of samples in the two clusters is substantially similar. It can be understood that the above 5% is intended to be illustrative, a user may define any other percent or data. The sampling module  404  may use any existing re-sampling method, such as stratified sampling, over sampling, under sampling method, synthetic minority over-sampling technique (SMOTE) or any future developed re-sampling methods, to balance data size in each cluster so that the size of each cluster is almost equal. Suppose that cluster  3  includes 28 samples, which is the minimum number of samples in each cluster of the clusters  501 , while cluster  1  includes 900 samples, which is the maximum number of samples in each cluster of the clusters  501 . It is obvious that original cluster  1  in the clusters  501  includes a large number of the historical samples, which may be dominant in the existing model  411 . After being re-sampled by the sampling module  404 , each cluster in the clusters  502  may include nearly 28 samples. New cluster  1  in the clusters  502  also includes nearly 28 samples, a plurality of the history samples in the original cluster  1  is dropped by the sampling module  404 . The data pattern in the clusters  502  is more balanced considering the new samples. 
     In some embodiments,  FIG.  6    depicts a schematic diagram of a process implemented by the updating module  405  according to some embodiments of this disclosure. As shown in  FIG.  6   , the clusters  502  are obtained by the clustering module  403 , and each cluster in the clusters  502  includes substantially similar number of sampled samples. The updating module  405  may split the sampled samples  502  into training sampled samples  601 , historical testing sampled samples  602  and new testing sampled samples  603 . The split can be implemented in any existing methods. For example, a user may assign that 80% of the sampled samples in the clusters  502  is the training sampled samples  601 , 20% of the sampled samples in the clusters  502  is the testing sampled samples. Then the testing sampled samples may be divided into the historical testing sampled samples  602  and the new testing sampled samples  603  based on an attribute (i.e. the column “New Samples?” in Table 1) of each of the testing sampled samples. The updating module  405  may update the existing model  411  to obtain a temporary parametric machine learning model (temporary model in short) with the training sampled samples  601 . Specifically, during updating the existing model  411 , the original parameters, such as weights, in the existing model  411 , may be used as initial parameters, and the structure of the existing model  411  may be kept unchanged. The updating module  405  may iteratively train the existing model  411  by updating the weights with the training sampled samples  601  until an acceptable level of prediction accuracy for the training sampled samples  601  is achieved. After training, the existing model  411  has been trained to be the temporary model. 
     In some embodiments, the updating module  405  may then evaluate the temporary model with the historical testing sampled samples  602  and the new testing sampled samples  603 . Specifically, during evaluating the temporary model, features (i.e. input vector) of each of the historical testing sampled samples  602  and the new testing sampled samples  603  are input into the temporary model. Then a prediction value for each sample is output by the temporary model. The prediction accuracies for the historical testing sampled samples  602  and the new testing sampled samples  603  may be computed. If the prediction accuracy for the historical testing sampled samples  602  with the temporary model is not higher than a predefined threshold, or the prediction accuracy for the new testing sampled samples  603  with the temporary model is not higher than a prediction accuracy for the new testing sampled samples with the existing model, the updating module  405  may then determine that more new samples are needed for updating the existing model  411  to obtain an updated model. In other words, the updating module  405  may stop and suggest the user that more new samples may be needed to update the existing model. 
     In the following, the historical testing sampled samples  602  are taken as an example of a set of samples to compute prediction accuracy for the set of samples. If the output variable is the categorical variable, the prediction accuracies for the historical testing sampled samples  602  with a model can be computed as a percentage of correctly classified samples in the historical testing sampled samples  602 , and the predefined threshold can be set as a percentage, such as 80%. If the output variable is the continuous variable, the prediction accuracies for the historical testing sampled samples  602  with a model can be computed as a negative average of absolute difference between the predicted values and the values of the output variable of samples in the historical sample, and the predefined threshold can be set as a value, such as −1.8. The predefined thresholds may be defined by a user based on the user&#39;s requirements. 
     However, in some embodiments, if it is determined that the prediction accuracy for the historical testing sampled samples with the temporary model is higher than the predefined threshold and the prediction accuracy for the new testing sampled samples with the temporary model is higher than the prediction accuracy for the new testing sampled samples with the existing model  411 , the updating module  405  may determine that a first incremental learning process can be implemented. In other words, a better model (i.e. the temporary model) has been founded, which may be trained further. 
     In some embodiments,  FIG.  7    depicts the first incremental learning process according to some embodiments of this disclosure. Referring to  FIG.  7   , training samples  701 , training samples  703 , . . . , training samples  705  are used to indicate the training sampled samples  601  except for training sampled samples in the cluster  1 , in the cluster  2 , . . . , in the cluster m, respectively. The updating module  405  may train the temporary model to obtain a cluster-based parametric machine learning model (“cluster-based model”, in short) M (1)    702  with the training samples  701 . Similarly, the updating module  405  may train the temporary model to obtain a cluster-based model M (2)    704  with the training samples  703 , . . . , and train the temporary model to obtain a cluster-based model M (m)    706  with the training samples  705 . Steps of updating a model have been described before and are omitted here. Then the updating module  405  may evaluate the cluster-based models M (1)    702 , M (2)    704 , . . . , M (m)    706  respectively with the historical testing sampled samples  602  and the new testing sampled samples  603 . Steps of evaluating a model have been described before and are omitted here. From obtained m models M (1)    702 , M (2)    704 , . . . , M (m)    706 , the updating module  405  may then select cluster-based models whose prediction accuracy for the historical testing samples is higher than the predefined threshold. Suppose that p (p≤m) cluster-based models are selected. The updating module  405  may then select, from the selected p cluster-based models, a specific cluster-based parametric machine learning model (“specific cluster-based model”, in short), with the highest prediction accuracy for the new testing samples within the selected p cluster-based models. It is assumed that model M (1)    702  is selected as the specific cluster-based model. If it is determined that the prediction accuracy for the new testing sampled samples  603  with the specific cluster-based model M (1)    702  is not higher than the prediction accuracy for the new testing sampled samples with the temporary model, the updating module  405  may then determine the temporary model as the updated parametric machine learning model. 
     In some embodiments, if it is determined that a prediction accuracy for the new testing sampled samples  603  with the specific cluster-based model M (1)    702  is higher than a prediction accuracy for the new testing sampled samples  603  with the temporary model, the updating module  405  may then execute a second incremental learning to train the specific cluster-based model M (1)    702  corresponding to a first cluster (i.e., cluster  1 ) being excluded in updating the specific cluster-based model. 
     In some embodiments,  FIG.  8    depicts the second incremental learning process according to some embodiments of this disclosure. Referring to  FIG.  8   , training samples  801 , training samples  803 , . . . , training samples  805  are used to indicate the training sampled samples  601  except for training sampled samples in the first cluster (being excluded during generating the specific cluster-based model), and also except for training sampled samples in the cluster  2 , in the cluster  3 , . . . , in the cluster m respectively. The updating module  405  may train the specific cluster-based model to obtain a next cluster-based parametric machine learning model (next cluster-based model in short) M 1   (1)    802  with the training sampled samples  801 . Similarly, the updating module  405  may train the specific cluster-based model to obtain a next cluster-based model M 1   (2)    804  with the training sampled samples  803 , . . . , and train the specific cluster-based model to obtain a next cluster-based model M (m−1)    806  with the training sampled samples  805 . Steps of updating a model have been described before and are omitted here. Then the updating module  405  may evaluate the next cluster-based models M 1   (1)    802 , M 1   (2)    804 , . . . , M 1   (m−1)    806  respectively with the historical testing sampled samples  602  and the new testing sampled samples  603 . Steps of evaluating a model have been described before and are omitted here. From obtained m models M 1   (1)    802 , M 1   (2)    804 , . . . , M 1   (m−1)    806 , the updating module  405  may then select next cluster-based models whose prediction accuracy for the historical testing samples is higher than the predefined threshold. Suppose that q (q≤m−1) next cluster-based models are selected. The updating module  405  may then select, from the selected q next cluster-based models, a specific next cluster-based parametric machine learning model (“specific next cluster-based model”, in short), with the highest prediction accuracy for the new testing sampled samples  603  within the selected q next cluster-based models. It is assumed that model M 1   (m−1)    806  is selected as the specific next cluster-based model. If it is determined that a prediction accuracy for the new testing sampled samples  603  with the specific next cluster-based model M 1   (m−1)    806  is not higher than the prediction accuracy for the new testing sampled samples  603  with the specific cluster-based model M (1)    702 , the updating module  405  may then determine the specific cluster-based model M (1)    702  as the updated model. 
     In some embodiments, if it is determined that a prediction accuracy for the new testing sampled samples  603  with the specific next cluster-based model M 1   (m−1)    806  is higher than a prediction accuracy for the new testing sampled samples  603  with the specific temporary model M (1)    702 , the updating module  405  may then iteratively execute a next incremental learning similar to  FIG.  8    by further exclude the second cluster, a third cluster, . . . and so on until a prediction accuracy for the new testing sampled samples  603  with a next selected model is not higher than an existing selected model. The updating module  405  may then determine the selected model in the last iteration as the updated model. 
       FIG.  9    depicts a flowchart of an exemplary method  900  for incremental machine learning for a parametric machine learning model according to some embodiments of the present disclosure. The method  900  may be implemented by the system  400 , or other suitable computer/computing systems. For ease of understanding, the method  900  will be described with reference to  FIG.  4   . 
     At  910 , the system  400  may process the samples  410  comprising historical samples and new samples with an existing parametric machine learning model  411  to obtain at least one prediction residual  412  of each of the samples, where the existing parametric machine learning model  411  was trained based on the historical samples. In some embodiments, the prediction residual  412  of a sample is obtained by one of the following: subtracting a prediction value of the sample predicted by the existing parametric machine learning model from a value of an output variable of the sample if the output variable is a continuous variable; or subtracting a prediction probability value of the sample for the category predicted by the existing parametric machine learning model from a one-hot-encode value of the sample for the category if the output variable is a category variable and the category variable being defined as the one-hot-encode value of the sample for the category. 
     At  920 , the system  400  may cluster the samples  410  based on the at least one prediction residuals  412  of each of the samples and features of each of the samples  410 . 
     At  930 , the system  400  may sample samples in each cluster to ensure that each cluster includes substantially similar number of sampled samples  414 . 
     At  940 , the system  400  may update the existing parametric machine learning model  411  to obtain an updated parametric machine learning model  415  based on sampled samples. 
     In some embodiments, the system  400  may split the sampled samples  414  into training sampled samples, historical testing sampled samples and new testing sampled samples. Then the system  400  may train the existing parametric machine learning model  411  to obtain a temporary parametric machine learning model with the training sampled samples. The system  400  may then evaluate the temporary parametric machine learning model with the samples  603  and  604 . If a prediction accuracy for the historical testing sampled samples with the temporary parametric machine learning model is not higher than a predefined threshold or a prediction accuracy for the new testing sampled samples with the temporary parametric machine learning model is not higher than a prediction accuracy for the new testing sampled samples with the existing parametric machine learning model, the system  400  may determine that more new samples are needed for updating the existing parametric machine learning model to obtain an updated parametric machine learning mode. 
     In some embodiments, if the prediction accuracy for the historical testing sampled samples with the temporary parametric machine learning model is higher than the predefined threshold and the prediction accuracy for the new testing sampled samples with the temporary parametric machine learning model is higher than the prediction accuracy for the new testing sampled samples with the existing parametric machine learning model, the system  400  may execute a first incremental learning process. 
     In some embodiments, in the first incremental learning process, for each specific cluster in all clusters, the system  400  may train the temporary parametric machine learning model to obtain a cluster-based parametric machine learning model with the training sampled samples in all clusters except for those in the specific cluster, and then evaluate the cluster-based parametric machine learning model with historical testing sampled samples and new testing sampled samples respectively. Then the system  400  may select, from all cluster-based parametric machine learning models, cluster-based parametric machine learning models whose prediction accuracy for the historical testing sampled samples is higher than a predefined threshold. The system  400  may then select from the selected cluster-based parametric machine learning models, a specific cluster-based parametric machine learning model with the highest prediction accuracy for the new testing sampled samples within the selected cluster-based parametric machine learning models. If a prediction accuracy for the new testing sampled samples with the specific cluster-based parametric machine learning model is not higher than a prediction accuracy for the new testing sampled samples with the temporary parametric machine learning model, the system  400  may determine the temporary parametric machine learning model as the updated parametric machine learning model. 
     In some embodiments, if the prediction accuracy for the new testing sampled samples with the specific cluster-based parametric machine learning model is higher than the prediction accuracy for the new testing sampled samples with the temporary parametric machine learning model, the system  400  may execute a second incremental learning process. 
     In some embodiments, in the second incremental learning process, for each specific cluster in all clusters except for a first cluster which is excluded in updating the specific cluster-based parametric machine learning model, the system  400  may train the specific cluster-based parametric machine learning model with the training sampled samples in all clusters except for those in both the cluster and the first cluster to obtain a next cluster-based parametric machine learning model, and evaluate the next cluster-based parametric machine learning model with the historical testing sampled samples and the new testing sampled samples respectively. Then the system  400  may select, from all next cluster-based parametric machine learning models, next cluster-based parametric machine learning models whose prediction accuracy for the historical testing sampled samples is higher than the predefined threshold. The system  400  may then select, from the selected next cluster-based parametric machine learning models, a specific next cluster-based parametric machine learning model with the highest prediction accuracy for the new testing sampled samples within the selected next cluster-based parametric machine learning models. Again, if a prediction accuracy for the new testing sampled samples with the specific next cluster-based parametric machine learning model is not higher than a prediction accuracy for the new testing sampled samples with the specific cluster-based parametric machine learning model, the system  400  may determine the specific cluster-based parametric machine learning model as the updated parametric machine learning model. 
     In some embodiments, if it is determined that a prediction accuracy for the new testing sampled samples  603  with the specific next cluster-based parametric machine learning model is higher than a prediction accuracy for the new testing sampled samples  603  with the specific cluster-based parametric machine learning model, the system  400  may then iteratively execute a next incremental learning by further exclude the second cluster, a third cluster, . . . and so on until a prediction accuracy for the new testing sampled samples  603  with a next selected model is not higher than an existing selected model. The system  400  may then determine the selected model in the last iteration as the updated parametric machine learning model. 
     In some embodiments, the clustering step  920  is implemented using one of following methods: K-mean clustering, TwoStep clustering, or DBSCAN and the like. 
     In some embodiments, the sampling step  930  is implemented using one of following method: stratified sampling, over sampling, or under sampling. 
     The samples of the present disclosure may be industrial measurement data, image data, video data, big data collected on the Internet, commercial data, and the like, and the features of the samples may be those commonly used in data processing for those data. 
     In this way, the updated parametric machine learning model  415  is obtained which may achieve a good prediction accuracy for new samples while keeping an acceptable level of prediction accuracy for the historical samples. 
     The present disclosure may be a system, a method, and/or a computer program product at any possible technical detail level of integration. The computer program product may include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present disclosure. 
     The computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of the computer readable storage medium includes the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire. 
     Computer readable program instructions described herein can be downloaded to respective computing/processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and/or a wireless network. The network may comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and/or edge servers. A network adapter card or network interface in each computing/processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing/processing device. 
     Computer readable program instructions for carrying out operations of the present disclosure may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, configuration data for integrated circuitry, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++, or the like, and procedural programming languages, such as the “C” programming language or similar programming languages. The computer readable program instructions may execute entirely on the user&#39;s computer, partly on the user&#39;s computer, as a stand-alone software package, partly on the user&#39;s computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user&#39;s computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present disclosure. 
     Aspects of the present disclosure are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the disclosure. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer readable program instructions. 
     These computer readable program instructions may be provided to a processor of a computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. These computer readable program instructions may also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and/or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function/act specified in the flowchart and/or block diagram block or blocks. 
     The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions/acts specified in the flowchart and/or block diagram block or blocks. 
     The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the blocks may occur out of the order noted in the Figures. For example, two blocks shown in succession may, in fact, be accomplished as one step, executed concurrently, substantially concurrently, in a partially or wholly temporally overlapping manner, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions. 
     The descriptions of the various embodiments of the present disclosure have been presented for purposes of illustration, but are not intended to be exhaustive or limited to the embodiments disclosed. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The terminology used herein was chosen to best explain the principles of the embodiments, the practical application or technical improvement over technologies found in the marketplace, or to enable others of ordinary skill in the art to understand the embodiments disclosed herein.