Patent Publication Number: US-11042891-B2

Title: Optimizing revenue savings for actionable predictions of revenue change

Description:
BACKGROUND 
     General ledgers of a business contain valuable, fine-grained information about historical incoming revenues from various customers. Understanding whether the incoming revenue from a customer will increase or decrease would be very useful in targeting customers who are likely to slow down or stop purchasing services. Knowing which offerings would lead to a boost in incoming revenues would help create new bundled offerings that can be sold to attract more customers. 
     SUMMARY 
     Embodiments relate to optimizing potential revenue savings when predicting client revenue change. One embodiment provides a method for optimizing potential revenue savings when predicting client revenue change including receiving revenue data with timestamps for a number of historical periods at a particular level, with attributes of the particular level and a percentage of the required revenue change. The data is filtered. The filtered data is aggregated at the particular level for a selected prediction. A sliding window of the number of historical periods is moved over business periods, creating a data point for each historical period temporal window by extracting features. A required target output is created for each data point for at least one future time period. A weight is assigned to each data point proportional to value of revenue. A model is trained to optimize a weighted linear combination of losses over each data point. A set of recent histories is converted into a quantitative health value. 
     These and other features, aspects and advantages of the present invention will become understood with reference to the following description, appended claims and accompanying figures. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  depicts a cloud computing environment, according to an embodiment; 
         FIG. 2  depicts a set of abstraction model layers, according to an embodiment; 
         FIG. 3  is a network architecture for efficient representation, access and modification of variable length data objects, according to an embodiment; 
         FIG. 4  shows a representative hardware environment that may be associated with the servers and/or clients of  FIG. 1 , according to an embodiment; 
         FIG. 5  is a block diagram illustrating a revenue change prediction system, according to one embodiment; 
         FIG. 6  illustrates a block diagram for a process for predicting ledger revenue change behavior of clients receiving services, according to one embodiment; 
         FIG. 7  illustrates an example if a sliding window over data points, according to one embodiment; 
         FIG. 8  illustrates a block diagram for a process for optimizing revenue savings for actionable forecasts of revenue change, according to one embodiment; 
         FIG. 9  illustrates a block diagram for a process for optimizing predictive precision for actionable forecasts of revenue change, according to one embodiment; 
         FIG. 10  illustrates example graphs showing regularized precision being optimized using a Gaussian process, according to one embodiment; 
         FIG. 11  illustrates a set of example graphs showing Bayesian optimization over weight w that correctly explores the space and identifies a value of w to yield precision close to 1, according to one embodiment; 
         FIG. 12  illustrates another set of example graphs showing Bayesian optimization over weight w that correctly explores the space and identifies a value of w to yield precision close to 1, according to one embodiment; and 
         FIG. 13  illustrates yet another set of example graphs showing Bayesian optimization over weight w that correctly explores the space and identifies a value of w to yield precision close to 1, according to one embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     The descriptions of the various embodiments 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. 
     It is understood in advance that although this disclosure includes a detailed description of cloud computing, implementation of the teachings recited herein are not limited to a cloud computing environment. Rather, embodiments of the present invention are capable of being implemented in conjunction with any other type of computing environment now known or later developed. 
     One or more embodiments provide for optimizing potential revenue savings when predicting client revenue change. In one embodiment, actionable information is provided to the sales organization of a vendor of services by transforming recent ledger behavior of clients into a prediction of future client behavior including abandoning the vendor. Such predictions are particularly valuable in the context of cloud services where the client need not pay a penalty for abandoning the vendor and the client is only billed for services rendered by the vendor on a short term basis. Conventional approaches to prediction of client behavior are (1) focused on long running contractual behavior with penalties for cancelling the contract, (2) involve significantly more complex prediction methods that are not immediately understandable by the sales personnel, or (3) are often significantly less precise in the cloud context. One embodiment provides for a prediction if the cloud business (any account, or client, any revenue) account revenue will increase or decrease by x %. More precisely, will the average revenue of future two quarters for any given account (or offering or account-offering pair) grow or shrink by x % compared to current quarter. In one example, revenues are aggregated over all offerings sold to that account in a given country. Revenue is recorded on a quarterly basis due to accounting practices is a noisy target to make predictions on. In one embodiment, a prediction for two future quarters is provided. In one embodiment, inputs may include metadata about the customer such as country of business, past revenues, etc. The output may include a probability (risk score) indicating if revenue will increase by x % in two future quarters. 
     One or more embodiments provide for predictive accuracy that treats each prediction loss equally. In predicting future revenue growth or shrinkage, all data points are not equally important. Risk of revenue losses from higher revenue clients are more important than lower revenue clients. One embodiment optimizes returning high revenue accounts at risk of shrinkage. One embodiment ranks accounts using monetary risk instead of just a probability risk. 
     Conventional prediction methods that optimize for accuracy would not perform well on real, imbalanced business datasets. Some business divisions that may see predominant growth have fewer data points whose target is 1 when predicting shrinkage by some percentage. Some business divisions that may see predominant shrinkage have fewer data points whose target is 1 when predicting growth by some percentage. In one embodiment, datasets specific to each business division are often imbalanced, and accuracy is therefore a poor metric to optimize for. Typically, sales resources are sufficient to take actions on saving only the top-k accounts predicted to shrink (top-k offerings predicted to grow). Thus, it is more important to have high quality predictions in the top-k with a minimum overall accuracy rather than lower-quality predictions in the top-k and higher overall accuracy. In one embodiment, obtaining the highest prediction precision (which corresponds to high quality leads) with a minimum recall (which corresponds to quantity) is provided. One embodiment uses machine learning classifiers that optimize for accuracy. Optimizing for precision and recall is computationally difficult since these are non-convex functions. 
     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 (VMs), 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 and 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 data center). 
     Rapid elasticity: capabilities can be rapidly and elastically provisioned and, 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 consumer accounts). Resource usage can be monitored, controlled, and reported, thereby 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 the ability 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 email). 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 consumer-specific application configuration settings. 
     Platform as a Service (PaaS): the capability provided to the consumer is the ability 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 the ability 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 a service oriented with a focus on statelessness, low coupling, modularity, and semantic interoperability. At the heart of cloud computing is an infrastructure comprising a network of interconnected nodes. 
     Referring now to  FIG. 1 , an illustrative cloud computing environment  50  is depicted. As shown, cloud computing environment  50  comprises 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 the 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. 2 , a set of functional abstraction layers provided by the cloud computing environment  50  ( FIG. 1 ) is shown. It should be understood in advance that the components, layers, and functions shown in  FIG. 2  are intended to be illustrative only and embodiments of the invention 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, a 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 comprise 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 optimizing potential revenue savings when predicting client revenue change processing  96 . As mentioned above, all of the foregoing examples described with respect to  FIG. 2  are illustrative only, and the invention is not limited to these examples. 
     It is understood all functions of one or more embodiments as described herein may be typically performed by the processing system  300  ( FIG. 3 ) or the autonomous cloud environment  410  ( FIG. 4 ), which can be tangibly embodied as hardware processors and with modules of program code. However, this need not be the case for non-real-time processing. Rather, for non-real-time processing the functionality recited herein could be carried out/implemented and/or enabled by any of the layers  60 ,  70 ,  80  and  90  shown in  FIG. 2 . 
     It is reiterated 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, the embodiments of the present invention may be implemented with any type of clustered computing environment now known or later developed. 
       FIG. 3  illustrates a network architecture  300 , in accordance with one embodiment. As shown in  FIG. 3 , a plurality of remote networks  302  are provided, including a first remote network  304  and a second remote network  306 . A gateway  301  may be coupled between the remote networks  302  and a proximate network  308 . In the context of the present network architecture  300 , the networks  304 ,  306  may each take any form including, but not limited to, a LAN, a WAN, such as the Internet, public switched telephone network (PSTN), internal telephone network, etc. 
     In use, the gateway  301  serves as an entrance point from the remote networks  302  to the proximate network  308 . As such, the gateway  301  may function as a router, which is capable of directing a given packet of data that arrives at the gateway  301 , and a switch, which furnishes the actual path in and out of the gateway  301  for a given packet. 
     Further included is at least one data server  314  coupled to the proximate network  308 , which is accessible from the remote networks  302  via the gateway  301 . It should be noted that the data server(s)  314  may include any type of computing device/groupware. Coupled to each data server  314  is a plurality of user devices  316 . Such user devices  316  may include a desktop computer, laptop computer, handheld computer, printer, and/or any other type of logic-containing device. It should be noted that a user device  311  may also be directly coupled to any of the networks in some embodiments. 
     A peripheral  320  or series of peripherals  320 , e.g., facsimile machines, printers, scanners, hard disk drives, networked and/or local storage units or systems, etc., may be coupled to one or more of the networks  304 ,  306 ,  308 . It should be noted that databases and/or additional components may be utilized with, or integrated into, any type of network element coupled to the networks  304 ,  306 ,  308 . In the context of the present description, a network element may refer to any component of a network. 
     According to some approaches, methods and systems described herein may be implemented with and/or on virtual systems and/or systems, which emulate one or more other systems, such as a UNIX system that emulates an IBM z/OS environment, a UNIX system that virtually hosts a MICROSOFT WINDOWS environment, a MICROSOFT WINDOWS system that emulates an IBM z/OS environment, etc. This virtualization and/or emulation may be implemented through the use of VMWARE software in some embodiments. 
       FIG. 4  shows a representative hardware system  400  environment associated with a user device  316  and/or server  314  of  FIG. 3 , in accordance with one embodiment. In one example, a hardware configuration includes a workstation having a central processing unit  410 , such as a microprocessor, and a number of other units interconnected via a system bus  412 . The workstation shown in  FIG. 4  may include a Random Access Memory (RAM)  414 , Read Only Memory (ROM)  416 , an I/O adapter  418  for connecting peripheral devices, such as disk storage units  420  to the bus  412 , a user interface adapter  422  for connecting a keyboard  424 , a mouse  426 , a speaker  428 , a microphone  432 , and/or other user interface devices, such as a touch screen, a digital camera (not shown), etc., to the bus  412 , communication adapter  434  for connecting the workstation to a communication network  435  (e.g., a data processing network) and a display adapter  436  for connecting the bus  412  to a display device  438 . 
     In one example, the workstation may have resident thereon an operating system, such as the MICROSOFT WINDOWS Operating System (OS), a MAC OS, a UNIX OS, etc. In one embodiment, the system  400  employs a POSIX® based file system. It will be appreciated that other examples may also be implemented on platforms and operating systems other than those mentioned. Such other examples may include operating systems written using JAVA, XML, C, and/or C++ language, or other programming languages, along with an object oriented programming methodology. Object oriented programming (OOP), which has become increasingly used to develop complex applications, may also be used. 
       FIG. 5  is a block diagram illustrating a revenue change prediction system  500 , according to one embodiment. In one embodiment, the revenue change prediction system  500  includes client devices  510  (e.g., mobile devices, smart devices, computing systems, etc.), a cloud or resource sharing environment  520 , and servers  530 . In one embodiment, the client devices are provided with cloud services from the servers  530  through the cloud or resource sharing environment  520 . 
       FIG. 6  illustrates a block diagram for a process  600  for predicting ledger revenue change behavior of clients receiving services, according to one embodiment. In one embodiment, the inputs to the process  600  may include: revenue for historical periods with timestamps (e.g., month, quarter, year, etc.) for each account-offerings pair and attributes (e.g., brand and geography, etc.); whether the required prediction is for growth or shrinkage of account/offering revenue; and percentage of growth or shrinkage. In one embodiment, the outputs may include: prediction (binary variable indicating the prediction by the machine learning algorithm of specified growth/shrinkage happening by specified percentage); probability (probability of specified growth/shrinkage happening by specified percentage); and ranked list of accounts/offerings in descending order of monetary gain/risk for growth/shrinkage. 
     In one embodiment, in block  610  ledger data input is obtained, and is cleaned/filtered for invalid values of brands/business divisions, revenue, etc., which are invariably present in a large database exported file. Revenue for a business-offering pair, for any periods where revenue is not mentioned for a business-offering pair is assumed to be zero. In one embodiment, revenues are aggregated. For example, revenues are generated for each combination of customer identification (ID), offering ID, account year, account quarter, brand/business division, geographical location of business such as country name, etc. In one example, process  600  may be applied to any revenue change prediction at any granular level: accounts, offerings, or account-offerings pair (or any other granular level). Quarters are specific instantiations, but process  600  is not limited to quarters. 
     In one embodiment, in block  620 , from the client device or user, process  600  obtains the following inputs: growth or shrinkage, and its percentage. In one embodiment, the following inputs may also be taken to filter data points on each of them: brand/business division, country, continent, etc. In block  630 , for each combination of customer ID, offering ID, brand/business division, geographical location of business such as country name, continent, etc. In one embodiment, a sliding window is moved a number of time periods (e.g., five time periods) over the business periods (e.g., quarters).  FIG. 7  illustrates an example if a sliding window (grey boxes) over data points, according to one embodiment. Returning back to  FIG. 6 , for each five temporal window periods (Q−2, Q−1, Q, Q+1, Q+2), a data point is created by extracting features (as indicated below). Each data point also has a target output used to predict given percentage of growth/shrinkage of revenues of future two time periods (Q+1, Q+2). 
     In one embodiment, the features may include the following. ID: customer ID, offerings ID, or customer-offerings pair ID+year of current business quarter (e.g. 2014)+Quarter index of current business quarter (e.g. 1, 2, 3, 4)+geography (e.g., Country ID where company is located)+Brand/Business Division Name. Q: revenue for current business quarter Q. Q−1: revenue for business quarter Q−1; Q−2: revenue for business quarter Q−2; BACKWARD RATIO: Q−2/(Q−1+Q); FORWARD RATIO: Q/(Q−1+Q−2); LOG(BACKWARD RATIO): log of BACKWARD_RATIO; LOG(FORWARD RATIO): log of FORWARD_RATIO; SIGN(BACKWARD RATIO): sign of BACKWARD_RATIO; SIGN(FORWARD RATIO): sign of FORWARD_RATIO; and NUMBER OF POSITIVE QUARTERS: number of positive revenue quarters out of Q, Q−1, and Q−2. The GROWTH(XX)/SHRINKAGE(XX) is the target indicator variable indicating if average revenue of two future quarters grew/shrunk by XX percent. 
     In one embodiment, in block  640  training of a statistical classification model (e.g., using boosted classification trees) is performed. In one example, one hundred trees are used in each learned gradient boosted classifier. 
     In one embodiment, in blocks  650 - 670 , outputs are obtained as follows. In one embodiment, the binary predictions and the prediction probability for each data point in a test dataset is obtained using the statistical classification model learned in block  640 . Prediction and prediction probabilities are used to output goodness of classification metrics such as accuracy, precision, recall, area under the ROC (Receiver Operating Characteristic) curve. Offerings in a test dataset are sorted in decreasing order of growth probability and presented to a user as actionable (ie, for further action). Customers in the test dataset are sorted in decreasing order of shrinkage probability and presented to user for further action. In block  650 , classification metrics (accuracy, precision, recall, and AUC (Area under ROC curve) are output using the statistical classification model on test data points. In block  660 , a list of accounts in descending order of Growth/Shrinkage probability is output. In block  670 , a list of offerings in decreasing order of revenue Growth/Shrinkage probability is output. One or more embodiments aim at helping the cloud business predict shrinking and abandoned accounts so that it can save the revenue coming from shrinking or abandoning. This is in the range of millions each quarter. One or more embodiments aim at predicting offerings that are expected to grow. This is very useful for business as it can upsell/cross-sell such offerings and the predictions can be also used in business sales planning. 
       FIG. 8  illustrates a block diagram for a process  800  for optimizing revenue savings for actionable forecasts of revenue change, according to one embodiment. In one embodiment, the inputs for process  800  include: revenue for some historical periods with timestamps (e.g., month, quarter, year, etc.) for each account-offerings pair and attributes (e.g., brand and geography, etc.); whether the required prediction is for growth or shrinkage of account/offering revenue; and percentage of growth or shrinkage. The outputs for process  800  may include: prediction (binary variable indicating the prediction by the machine learning algorithm of specified Growth/Shrinkage happening by specified percentage); probability (probability of specified Growth/Shrinkage happening by specified percentage); and ranked list of accounts/offerings in descending order of monetary gain/risk for growth/shrinkage. 
     The terminology used herein includes the following. 
     TP=True Positives 
     FP=False Positives 
     TN=True Negatives 
     FN=False Negatives 
     N=Total number of data points 
     Classification Evaluation Metrics 
     
       
         
           
             Accuracy 
             = 
             
               
                 
                   TP 
                   + 
                   TN 
                 
                 
                   TP 
                   + 
                   TN 
                   + 
                   FP 
                   + 
                   FN 
                 
               
               = 
               
                 
                   TP 
                   + 
                   TN 
                 
                 N 
               
             
           
         
       
       
         
           
             Precision 
             = 
             
               TP 
               
                 TP 
                 + 
                 FP 
               
             
           
         
       
       
         
           
             Recall 
             = 
             
               TP 
               
                 TP 
                 + 
                 FN 
               
             
           
         
       
       
         
           
             AUC 
             ⁢ 
             
                 
             
             ⁢ 
             
               ( 
               
                 Area 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 under 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 ROC 
                 ⁢ 
                 
                     
                 
                 ⁢ 
                 curve 
               
               ) 
             
           
         
       
     
     In one embodiment, for process  800  blocks  610 - 630  are the same as described above in process  600 . Block  840  provides for optimizing for revenue savings instead of predictive accuracy. In one embodiment, a weighted dataset is built or generated such that each data point is weighted by a value proportional to the company&#39;s revenue. Better to use a slowly growing function like log of revenue to avoid extreme values of revenue dominating the entire loss function being optimized. Hence, the data point weights w i  are logarithmic value of absolute value of the total revenue over past three quarters i.e. Q, Q−1, Q−2. A value of two (2) is added to each weight to prevent negative or zero weights, particularly to prevent a weight of negative infinity at zero revenues. 
     In one embodiment, in block  850  process  800  trains a statistical classification model (e.g., a boosted classification trees, etc.). Most machine learning classifiers optimize for unweighted loss function. 
                     max   ⁡     (     TP   +   TN     )       =       ⁢     max   ⁡     (     N   -   FP   -   FN     )                   =       ⁢     min   ⁡     (     FP   +   FN     )                   =       ⁢     min   ⁢       ∑   i     ⁢     loss   ⁡     (     datapoint   i     )                       
The loss function that is optimized is a weighted linear combination of the losses over each data point.
 
             min   ⁢       ∑   i     ⁢       w   i     *     loss   ⁡     (     datapoint   i     )                 
This ensures that losses over higher revenue data points are given more importance in the minimization since weights are monotonically increasing in revenue magnitude. Additionally, the loss function provides higher revenue savings since the customers detected to have shrinking future revenues are also likely to be high-paying customers.
 
     In one embodiment, blocks  860 - 880 , outputs are obtained as follows. In one embodiment, the binary predictions and the prediction probability for each data point in a test dataset are obtained using the statistical classification model learned in block  850 . Prediction and prediction probabilities are used to output goodness of classification metrics such as accuracy, precision, recall, area under the ROC (Receiver Operating Characteristic) curve. Offerings in a test dataset are sorted in decreasing order of growth probability and presented to a client of a user for further actionability. In block  860 , classification metrics (accuracy, precision, recall, and AUC are output using the statistical classification model on test data points. In block  870 , a list of accounts in descending order of Growth/Shrinkage probability is output. In block  880 , a list of offerings in decreasing order of revenue Growth/Shrinkage probability is output. In one embodiment, the customers/offerings/customer-offerings pairs are ranked by the probability of shrinkage by x %. In another embodiment, the customers are ranked by monetary risk as follows: Monetary risk=Probability of shrinkage by x %*Revenue lost due to x % shrinkage. A metric provides a complete picture of the risk associated with an account. The metric is expected to provide higher revenue savings since the customers predicted to have shrinking future revenues are also likely to be high-paying customers. A difference from just using monetary risk is that process  800  weighs data points by their corresponding revenues in learning the model to get more confident prediction of shrinkage probabilities before calculating monetary risk. Conventional methods put an equal weight on each data point during the learning phase of the classifier. Process  800  gives a significantly higher potential revenue saving since it puts shrinking accounts with “highest” revenue on top (gives a higher monetary risk to save in terms of accounts and a higher one to gain in terms of offerings). 
       FIG. 9  illustrates a block diagram for a process  900  for optimizing predictive precision for actionable forecasts of revenue change, according to one embodiment. In one embodiment, The inputs for process  900  include: revenue for some historical periods with timestamps (e.g., month, quarter, year, etc.) for each account-offerings pair and attributes (e.g., brand and geography, etc.); whether the required prediction is for growth or shrinkage of account/offering revenue; percentage of growth or shrinkage; and recall threshold or percentile for calculating recall threshold. In one embodiment, the outputs for process  900  include: prediction (binary variable indicating the prediction by the machine learning algorithm of specified Growth/Shrinkage happening by specified percentage); probability (probability of specified Growth/Shrinkage happening by specified percentage; and ranked list of accounts/offerings in descending order of probability of growth/shrinkage. These outputs are at maximum precision and at least the given/calculated minimum recall R 0 . 
     In one embodiment, blocks  610 - 630  are the same as described above. In one embodiment, in block  940  optimization is performed for predictive precision instead of predictive accuracy. Most machine learning classifiers optimize for accuracy.
 
max(TP+TN)=max( N −FP−FN)=min(FP+FN)=min Σ i  loss(datapoint i )
 
In one embodiment, process  900  optimizes a modified parametrized objective function such that parameter balances tradeoff between precision and accuracy
 
min{ w ·FP+(1 −w )·FN}
         w is a parameter between (0,1)
 
Using one amongst various meta-optimization techniques such as grid search, line search, Bayesian optimization (based on Gaussian processes), simulated annealing, genetic algorithms, etc., process  900  determines the parameter w such that a parametrized algorithm returns the highest precision with a specified minimum recall R 0 . In one embodiment, a statistical classification model (e.g., a boosted classification trees) is trained. Process  900  searches over the parameter w that trades off between precision and recall to obtain a statistical model that provides maximum precision for a certain minimum recall. In one embodiment, In one embodiment, in process  900  a Gaussian process based Bayesian optimization provides better results than a uniform grid search. Gaussian processes are good for exploration versus exploitation tradeoff in optimization. Process  900  focuses on areas of parameter space that have higher chances of attaining maximum objective value. In other embodiment, the framework is not limited to Gaussian processes as any general or unidimensional optimization algorithm such as grid search, line search, genetic algorithms, simulated annealing gradient ascent, etc. may be used. The minimum recall R 0  can be specified in one of several ways: user-specified, inferred as a suitable percentile (e.g. top 20 th  percentile, etc.) from the histogram of recall values obtained from the precision-recall curve of a baseline tree boosting classifier that optimizes vanilla accuracy, as a fraction of the precision (e.g., recall must be at least ¼ th  of the precision), etc.
       

     In one embodiment,  FIG. 10  illustrates example graphs showing regularized precision being optimized using a Gaussian process, according to one embodiment.  FIG. 11  illustrates a set of example graphs showing Bayesian optimization over weight w that correctly explores the space and identifies a value of w to yield precision close to 1, according to one embodiment.  FIG. 12  illustrates another set of example graphs showing Bayesian optimization over weight w that correctly explores the space and identifies a value of w to yield precision close to 1, according to one embodiment.  FIG. 13  illustrates yet another set of example graphs showing Bayesian optimization over weight w that correctly explores the space and identifies a value of w to yield precision close to 1, according to one embodiment. 
     Returning to  FIG. 9 , in one embodiment, in blocks  950 - 970 , outputs are obtained as follows. In one embodiment, the binary predictions and the prediction probability for each data point in a test dataset is obtained using the statistical classification model learned in block  940 . Prediction and prediction probabilities are used to output goodness of classification metrics such as accuracy, precision, recall, area under the ROC curve. Customers in the test dataset are sorted in decreasing order of monetary risk and presented to user for further actionability, where monetary risk=probability of shrinkage by x %*Revenue lost due to x % shrinkage. Offerings in test file are sorted in decreasing order of growth probability and presented to user for further actionability. In block  950 , classification metrics (accuracy, precision, recall, and AUC) are output using the statistical classification model on test data points. In block  960 , a list of accounts in descending order of Growth/Shrinkage probability is output. In block  970 , a list of offerings in decreasing order of revenue Growth/Shrinkage probability is output. In one embodiment, process  900  provides a significantly higher potential revenue saving since it puts shrinking accounts with “highest” chances of being shrunk or abandoned on top and thus acting on those would yield a higher probability of revenue savings. 
     As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a system, method or computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a “circuit,” “module” or “system.” Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied thereon. 
     Any combination of one or more computer readable medium(s) may be utilized. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, 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), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. 
     A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. 
     Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing. 
     Computer program code for carrying out operations for aspects of the present invention may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like and conventional procedural programming languages, such as the “C” programming language or similar programming languages. The program code 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). 
     Aspects of the present invention are described below with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. 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 program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose 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 program instructions may also be stored in a computer readable medium that can direct a computer, other programmable data processing apparatus, or other devices to function in a particular manner, such that the instructions stored in the computer readable medium produce an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks. 
     The computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing 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 invention. 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 block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, 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. 
     References in the claims to an element in the singular is not intended to mean “one and only” unless explicitly so stated, but rather “one or more.” All structural and functional equivalents to the elements of the above-described exemplary embodiment that are currently known or later come to be known to those of ordinary skill in the art are intended to be encompassed by the present claims. No claim element herein is to be construed under the provisions of 35 U.S.C. section 112, sixth paragraph, unless the element is expressly recited using the phrase “means for” or “step for.” 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
     The corresponding structures, materials, acts, and equivalents of all means or step plus function elements in the claims below are intended to include any structure, material, or act for performing the function in combination with other claimed elements as specifically claimed. The description of the present invention has been presented for purposes of illustration and description, but is not intended to be exhaustive or limited to the invention in the form 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 invention. The embodiment was chosen and described in order to best explain the principles of the invention and the practical application, and to enable others of ordinary skill in the art to understand the invention for various embodiments with various modifications as are suited to the particular use contemplated.