Patent Application
20220245526
Time series data represents historic sequenced data over a range of time. Time series data may capture trends and patterns relating to events in different technology fields such as cloud usage, natural phenomenon prediction, service management, user activities, sales analysis, transaction management, etc. Predicting or forecasting time series may be performed by providing historical time series data to a predictive modeling system. The predictive modeling system can forecast those time series data into the future and generate time-series prediction results. The prediction results provide insights into activities or events that may occur in the future. The forecast results may provide valuable information to guide related users and entities to plan their future activities. There are technical challenges to forecast sparse time series that arise when making predictions based on events that occurred sporadically, as these events may not have repetitive patterns.
The foregoing and other aspects of embodiments are described in further detail with reference to the accompanying drawings, in which the same elements in different figures are referred to by common reference numerals. The embodiments are illustrated by way of example and should not be construed to limit the present disclosure.
Embodiments of the present disclosure provide forecasting techniques for accurately predicting sparse time series data relating to events in various technology fields.
Time series data may be categorized into different groups such as moderately sparse time series data and extremely sparse time series data based on sparsity levels representing extent of changes occurring in time series data over a range of time. The existing time series prediction models may predict sparse time series data with accurate mean/median values. However, there is a need to provide a modeling system to provide a prediction accuracy regarding prediction intervals and confidence bounds for the sparse time series data.
The existing time series prediction models may predict correct mean values for sparse time series data. However, the existing time series prediction models may generate a wide range of prediction intervals with a wide upper confidence bound and a wider upper confidence on both sides of the predicted mean values, which are caused by assuming Gaussian noise in the sparse time series data during the time series prediction process. The resulting prediction results, with a wide range of prediction intervals and wide confidence bounds, may lead to uncertain estimates of the prediction intervals and may not provide very useful prediction information for sparse time series data, thereby failing to predict related events that occur in the future. Further, the outputs of the existing time series prediction modes do not show that the sparse time series have Gaussian distribution features due to the non-Gaussian distribution of the prediction residuals associated with the prediction values and prediction intervals generated by the existing time series prediction models.
The present invention may provide a practical solution to problems described above with quantile hurdle modeling systems to generate accurate and useful prediction information for sparse time series data.
In one or more embodiments, a quantile hurdle modeling system may include a time series prediction model and a quantile regression model to perform prediction for moderate sparse time series data. The time series prediction model may generate the prediction values and prediction intervals for moderate sparse time series data. The quantile regression model may perform auto-regression to estimate different quantiles of the prediction residuals to generate adjusted prediction residuals with much tight prediction intervals and confidence bounds which are more relevant to time series data. A sparse time series prediction system may utilize the adjusted prediction residuals and the prediction values to generate accurate prediction explanation to be presented to users associated with the sparse time series data.
In one or more embodiments, for extremely sparse time series data, a quantile hurdle modeling system may include a Hurdle classifier, a time series prediction model and a quantile regression model considering period probabilities associated with extremely sparse time series data to generate accurate prediction result and improve prediction accuracy. The time series prediction model may generate the prediction values and prediction intervals for extremely sparse time series data. The quantile regression model may perform auto-regression to estimate different quantiles of the prediction residuals to generate adjusted prediction residuals with tight prediction intervals and confidence bounds which are more relevant to time series data. A Hurdle classifier may generate period probabilities of each sub-period extremely sparse time series data. A quantile hurdle modeling system may evaluate the generated prediction values and adjusted prediction residuals with the period probabilities of each sub-period of extremely sparse time series data to generate accurate prediction explanations and improve prediction accuracy.
A user computing device 130 may include a processor 131, memory 132, and an application browser 133. For example, a user device 130 may be a smartphone, personal computer, tablet, laptop computer, mobile device, or other device. Users may be registered customers or entities of the one or more online applications 123. Each user may create a user account with user information for subscribing and accessing an online software product or service provided by server computer 120. Each user account is stored as a user dataset associated with time series data or datasets described below.
Database 126 of the example system 100 may be included in server computer 120, or coupled to and in communication with the processor 121 of the server computer 120 via the network 110. Database 126 may be a shared remote database, a cloud database, or an on-site central database. Database 126 may receive instructions or data from, and send data to, server computer 120. In some embodiments, server computer 120 may retrieve and aggregate a large amount of time series data such as stream data, transaction data, text, image, video, etc., by accessing other servers or databases from various data sources 140 via network 110. Database 126 may store the aggregated time series data at a daily granularity, a weekly granularity, etc. The historical time series may be represented by time series datasets within a time span in a corresponding time step. Database 126 may store and update historical time series datasets 127 associated with events and corresponding users/entities via the network 110. Database 126 may store the time series datasets for building a Quantile hurdle modeling system 125 to forecast extremely sparse time series to generate prediction or predicted data 128 associated with events that may occur in the future. Database 126 may store prediction results as predicted data 128 to generate textual and or graphical reports for associated entities. Details related to building the Quantile Hurdle modeling system 125 will be described below.
Time series data may represent event data that includes, but is not limited to, cloud usage (e.g., storage usage or cost analysis), digital signal processing, audio/video processing, natural phenomenon data (e.g., weather information), entity activities or behaviors, national economy, market forecasting, financial service management data (e.g., transactions, payment, or sales), and any other time step data, etc.
A process of feature engineering may be performed by the server computer 120 to apply to historical time series data to extract and construct historical time series datasets 127 associated with time series events. Each time series dataset may be associated with a time series identifier and include a set of data points indicating values at respective time steps. The time step granularity of time series values may be represented by temporal features depending on the granularity of the prediction.
In the absence of any data points between previous adjacent time steps, the time series may be imputed with zeros to satisfy a constant granularity gap amongst data points.
System 200 may include a data processing model 124 to process and group time serial datasets 127 into two groups of moderately sparse time series datasets 202 and extremely sparse time series datasets 204. An appropriate time series predicting model may be selected to be particularly suited to the type of time series, such as a sparsity level of time series datasets. The grouped time serial datasets 127 may be used as time series training data and time series test data to train the corresponding models and molding system.
A given time series may consist of systematic components including the average value in the series, trend indicative of the increasing or decreasing value in the series, seasonality indictive of the repeating short-term cycle in the series, and one non-systematic random variation or noise in the series. A given time series dataset may include a value and a set of temporal features. A set of temporal features may include date, day, week, month, working day, day of the week, week of the month, quarter, month start, etc.
For moderate sparse time series datasets, Hurdle Regressor 208 may be used to generate time series prediction. As illustrated in
The time series prediction model 2081 may predict and generate a prediction value or a mean/median value {circumflex over (x)}t at a time step is (e.g., weekly, or monthly, etc.) based on a subset of time series datasets or a subset of previous data points with actual values (xt-n, . . . xt-1) before the time step ts corresponding to previous events. The time series prediction model 2081 may further generate a prediction interval and prediction residual (xt-{circumflex over (x)}t) at the time step is based on the subset of time series datasets. A prediction interval may represent a range of likely prediction values of an output variable from the time series prediction model 2081 at the time step ts. A residual (xt-{circumflex over (x)}t) may be calculated and determined as a difference between the actual time series value xt and the prediction value {circumflex over (x)} at the time step ts.
Quantile regressor 2082 may be a quantile regression based machine learning model. As illustrated in
Quantile regressor 2082 may be represented as an equation (1):
Q(xt-{circumflex over (x)}t)=g(t, t″, xt-1, {circumflex over (x)}t, {circumflex over (x)}t-1. . . {circumflex over (x)}t-n) (1)
Quantile regressor 2082 may be trained with prediction values {circumflex over (x)}t, the residuals (xt-{circumflex over (x)}t) from the time series prediction model 2081, and a set of parameters bi to estimate the probability distribution of the residuals (xt-{circumflex over (x)}t) around the mean/median value {circumflex over (x)}t. In some embodiments, the set of model parameter bi may be generated by fitting the residuals (xt-{circumflex over (x)}t) into the quantile regressor model 2082. For example, the set of parameters bi may comprise a set of quantile values and a plurality of temporal features (t, t″) including a date, day, week, month, day of the week, week of the month, etc. For example, Quantile regressor 2082 may be trained to estimate and predict the time series residuals at different quantiles such as 10%, 50%, 90%, etc. In some embodiments, the quantile regression may provide a non-parametric way of estimating probabilistic prediction by utilizing quantile loss to directly model the quantile level.
The Quantile regressor 2082 may perform auto-regression to estimate different quantiles of the residual distribution for Non-Gaussian noise to generate accurate prediction 210 for the moderate sparse time series datasets 202.
Referring to in
The time series prediction model 2081 may predict a prediction value {circumflex over (x)}t at a time step is (e.g., weekly, or monthly, etc.) based on a subset of extremely sparse time series datasets 204 or a subset of previous data points with actual values (xt-n, xt-1) before the time step is corresponding to previous events. The time series prediction model 2081 may further generate a prediction interval and residual (xt-{circumflex over (x)}t) at the time step ts based on the subset of time series datasets or data points. Quantile regressor 2082 may perform Quantile-based confidence bound computation based on the residuals (xt-{circumflex over (x)}t) generated by the time series prediction model and a set of parameters ci to estimate the confidence bound to generate prediction intervals. The set of model parameters ci may be tuned to the extremely sparse time series datasets with different values for trend and/or seasonality components as opposed to the set of model parameters bi for the moderate sparse time series.
Hurdle regressor 208 may be implemented by respective algorithms of various machine learning models suitable for extremely sparse time series datasets 204.
Hurdle classifier 206 may predict whether an event relating to the time series is likely to occur by generating a probability of the event at a time step granularity (e.g., daily, weekly, etc.). For the extremely sparse time series datasets 204, Hurdle classifier 206 may be trained to predict the probability of the event for each data point the time step is daily. For example, Hurdle classifier 206 may generate a set of probabilities (p1, p2 . . . p7) for a sub-period of time series datasets within a week.
For a sub-period of time series datasets, the system 200 may use a probability filter 212 to determine a period probability p(w) of events occurred in a week based on an equation (2):
p(w)=1-(1-p1)*(1-p2)* . . . *(1-p7) (2)
The probability filter 212 may function as a binary filter by comparing the period probability p(w) to a probability threshold. The output of Hurdle Regressor 208 may be determined to be the prediction value for the set of corresponding datasets within in the week when the probability p(w) is above the probability threshold. Details about processes related to system 200 will be described below.
At 302, the processor 121 may receive historical time series datasets 127 from the database 126. For example, each time series dataset may represent time series digital values or numbers corresponding to a set of features associated with related events. Each time series dataset may be graphically presented as a set of data points indicative values at respective time steps over a time window or a time frame given the time series. The time series datasets may have varying sparsity levels. The sparsity level may be related to percentage of nonzero values, periodicity metrics, number of peaks, and length of time series.
At 304, the processor 121 may identify and determine a sparsity level of each time series dataset for determining whether each time series dataset is a sparse time series. The processor 121 may process each time series dataset to determine whether a time series data has the sparsity level beyond or below a sparsity threshold. For example, the sparsity levels for the time series datasets may be determined by calculating a percentage or a ratio of nonzero values of the time series dataset as each respective sparsity level of each time series dataset over a time period.
At 306, based on the sparsity levels of the time series datasets, the processor 121 may determine and group the time series datasets as two groups including moderately sparse time series datasets (e.g., a first set of time series datasets) and extremely sparse time series datasets (e.g., a second set of time series datasets). If the sparsity levels of time series datasets are determined lower than the sparsity threshold, the sparse time series datasets may be grouped as extremely sparse time series datasets. If the sparsity levels of time series datasets are determined above or equal to the sparsity threshold, the sparse time series datasets may be grouped as moderate sparse time series datasets. In some embodiments, the sparsity thresholds may vary across different ranges for time series data. The sparsity thresholds may depend on qualities of the time series, such as periodicity, non-stationarity, etc. In one or more embodiments, a time series dataset may be categorized or grouped as the extremely sparse time series dataset if a ratio of the number of data points to the length of the time series is less or equal to 0.1. A time series dataset may be categorized or grouped as the moderate sparsity time series dataset if the ratio of the number of data points to the length of the time series is more than 0.1 and less than or equal to 0.5. A time series dataset may be grouped as a non-sparse time series if the ratio of the number of data points to the length of the time series is more than 0.5. These values are presented as examples that can be used in some embodiments, although it may be possible to use different values to categorize sparsity in other embodiments.
For the moderately sparse time series datasets, the time series forecasting models 2081 may be able to predict the mean/median values accurately. However, the prediction may result in uncertainty with wide and inflated confidence bounds which may lead to uncertainty estimates of the prediction intervals and may not provide very useful prediction information for sparse time series data. The quantile regressor may be trained based on the residuals from the time series prediction models with a set of parameters bi to generate an accurate quantile-based confidence bound.
At 402, server computer 120 may receive a first set of time series datasets 202 from database 126. The processor 121 may perform operations to generate different groups of time series datasets including actual past training datasets 51 and actual future test datasets 53. The first set of time series datasets 202 may each correspond to a data point indicative of a data value. Each data point or dataset may correspond to each respective subset of previous data points at a first time granularity within a time window. For example, a first time granularity may be a daily or weekly granularity. Referring to
At 404, the processor 121 may train a time series prediction model 2081 with actual past training datasets 51 and actual future test datasets 53. In some embodiments, a Bayesian linear model be trained with a set of coefficients ai to estimate the prediction values or mean/median values {circumflex over (x)}t for the respective time series datasets.
At 406, the time series prediction model 2081 may be executed by the processor 121 to apply to each respective subset of previous data points to generate a first set of predicted mean/median values (e.g., predicted past mean data 52) and a first set of time series residuals. The trained time series prediction model 2081 may generate accurate mean values as predicted past mean data or datasets 52. As illustrated in
A prediction interval 57 may represent a range of likely prediction values of an output variable from the time series prediction model 2081. A prediction interval 57 may be a range of values between a maximum upper confidence bound and a minimum lower confidence bound for each corresponding time serials dataset or data point. The existing models normally assume that the time series residuals are subject to Gaussian noise signal. As illustrated in
At 408, the processor 121 may train a quantile regressor 2082 to perform quantile-based confidence bound computation based on the time series residuals generated by the time series prediction model 2081 along with a first set of model parameters bi to predict the confidence bounds for improving the prediction interval estimation.
At 410, the processor 121 may apply the quantile regressor 2082 to the first set of residuals generated by the time series prediction model 2081 to generate a first set of adjusted residuals. The quantile regressor 2082 may perform quantile-based confidence bound computation based on the prediction residuals (xt-{circumflex over (x)}t) from the time series prediction model for actual past (training) data and actual future (test) data from the moderately sparse time series datasets 202. Quantile regressor 2802 may make no assumptions about the distribution of the prediction residuals from the time series prediction model 2081. Referring to
At 412, the processor 121 may generate a visualized explanation to present the generated prediction 210 including and or based on prediction values and prediction intervals for respective data points of the first time series datasets 202.
At 802, server computer 120 may receive extremely sparse time series datasets or a second set of time series datasets 204 from database 126. The processor 121 may perform operations to generate different groups of time series datasets including actual past training datasets 91 and actual future test datasets 93 as shown in
At 804, the processor 121 may train a time series prediction model 2081 with actual training datasets 91 and actual test datasets 93.
At 806, the trained time series prediction model 2081 may be executed by the processor 121 to apply to each respective subset of previous data points of the extremely sparse time series datasets to generate a second set of predicted mean/median values (e.g., predicted mean of (training) data 92), a second set of prediction values, a second set of prediction intervals, and a second set of time series residuals. As illustrated in
At 808, the processor 121 may train a quantile regressor 2082 to perform quantile-based confidence bound computation based on a second set of the time series residuals generated by the time series prediction model 2081 along with a second set of model parameters ci to predict the confidence bounds for improving the prediction interval estimation.
At 810, the processor 121 may apply the quantile regressor 2082 to the second set of residuals generated by the time series prediction model 2081 to generate a second set of prediction values and a second set of adjusted residuals. The Quantile regressor 2082 may perform quantile-based confidence bound computation based on the residuals (xt-{circumflex over (x)}t) from the time series prediction model for actual training datasets 91 and actual test datasets 93 from the extremely sparse time series datasets 204. Referring to
At 812, referring to
At 814, for the sub-period of time series datasets, the processor 121 may determine a period probability p(w) of events occurred in the time period based on equation (2) described above.
At 816, the processor 121 may execute an algorithm of a probability filter 212 to compare the period probability p(w) to a probability threshold. The probability threshold may be unique to respective time series datasets. The threshold value may be different for each time series and adjusted based on historic time series data.
At 818, when the processor 121 determines that the period probability p(w) is equal or below the probability threshold, the processor may set the prediction values or the output of Hurdle Regressor 208 to be 0 as the prediction result 214 for the corresponding sub-period of time series datasets within the time period.
At 820, when the processor 121 determines that the period probability p(w) is above the probability threshold, the processor may confirm the second set of the prediction values and the second set of the adjusted prediction intervals from quantile regressor 2082 for the sub-period of datasets within the time period. The prediction result 214 may include the second set of the prediction values and the second set of the adjusted prediction intervals on a weekly granularity. The prediction result 214 may be aggregated to a suitable prediction granularity, such as a monthly granularity.
At 822, the processor 121 may generate a visualized explanation to present the generated prediction 214 including or based on the second set of the prediction values and a second set of the adjusted prediction intervals for respective data points of the second time series datasets 204.
Referring to
In some embodiments, different time series prediction models or algorithms may be selected for quantile hurdle modeling systems to perform sparse time series data prediction based on the model performance evaluation. A metric called Normalized Mean Absolute Error (NMAE) may be used to evaluate the improvement and compare the models or quantile hurdle modeling system performance among the different models and algorithms.
The MAE of trivial predictor refers to predictions determined using mean of historic data. This metric compares the performance of the algorithm to the mean prediction of the historic data. A model or quantile hurdle modeling system may quantify a better performance with the lower NMAE value. If the NMAE value is larger than 1, the model may generate prediction with a lower accuracy performance compared with the mean of historic data.
In some embodiments, the disclosed principles provide a practical technological solution to effectively and accurately generate predicted time series data. Embodiments of the present disclosure provide advantages and improvements of processing moderately and extremely sparse time series datasets for predicting future values embedding. For example, the embodiments described herein provide computational efficiency and predictive accuracy with related machine learning tasks. The advantages of the disclosed principles include providing accuracy in extremely sparse time series prediction. The disclosed methods may assist users to process historical time series to predict corresponding events that may occur in the future. The generated prediction explanations may provide better service and or personalized service tailored to associated users or entities.
The embodiments described herein may provide a real time solution with faster processing and delivery of event predication that satisfy user expectations and improve user experience when the users interact with the system for managing event-related time series activities and obtaining related information and advice to manage their registered accounts with the online services.
Processor(s) 1202 may use any known processor technology, including but not limited to graphics processors and multi-core processors. Suitable processors for the execution of a program of instructions may include, by way of example, both general and special purpose microprocessors, and the sole processor or one of multiple processors or cores, of any kind of computer. Generally, a processor may receive instructions and data from a read-only memory or a random-access memory or both. The essential elements of a computer may include a processor for executing instructions and one or more memories for storing instructions and data. Generally, a computer may also include, or be operatively coupled to communicate with, one or more mass storage devices for storing data files; such devices include magnetic disks, such as internal hard disks and removable disks; magneto-optical disks; and optical disks. Storage devices suitable for tangibly embodying computer program instructions and data may include all forms of non-transitory memory, including by way of example semiconductor memory devices, such as EPROM, EEPROM, and flash memory devices; magnetic disks such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM and DVD-ROM disks. The processor and the memory may be supplemented by, or incorporated in, ASICs (application-specific integrated circuits).
Input devices 1204 may be any known input devices technology, including but not limited to a keyboard (including a virtual keyboard), mouse, track ball, and touch-sensitive pad or display. To provide for interaction with a user, the features and functional operations described in the disclosed embodiments may be implemented on a computer having a display device 1206 such as a CRT (cathode ray tube) or LCD (liquid crystal display) monitor for displaying information to the user and a keyboard and a pointing device such as a mouse or a trackball by which the user can provide input to the computer. Display device 1206 may be any known display technology, including but not limited to display devices using Liquid Crystal Display (LCD) or Light Emitting Diode (LED) technology.
Communication interfaces 1208 may be configured to enable computing device 1200 to communicate with other another computing or network device across a network, such as via a wired connection, a wireless connection, or a combination of wired and wireless connections. For example, communication interfaces 1208 may include an Ethernet interface, an optical interface, a coaxial interface, an infrared interface, a radio frequency (RF) interface, a universal serial bus (USB) interface, a Wi-Fi interface, a cellular network interface, or the like.
Memory 1210 may be any computer-readable medium that participates in providing computer program instructions and data to processor(s) 1202 for execution, including without limitation, non-transitory computer-readable storage media (e.g., optical disks, magnetic disks, flash drives, etc.), or volatile media (e.g., SCRAM, ROM, etc.). Memory 1210 may include various instructions for implementing an operating system 1214 (e.g., Mac OS®, Windows®, Linux). The operating system may be multi-user, multiprocessing, multitasking, multithreading, real-time, and the like. The operating system may perform basic tasks, including but not limited to: recognizing inputs from input devices 1204; sending output to display device 1206; keeping track of files and directories on memory 1210; controlling peripheral devices (e.g., disk drives, printers, etc.) which can be controlled directly or through an I/O controller; and managing traffic on bus 1212. Bus 1212 may be any known internal or external bus technology, including but not limited to ISA, EISA, PCI, PCI Express, USB, Serial ATA or FireWire.
Network communications instructions 1216 may establish and maintain network connections (e.g., software applications for implementing communication protocols, such as TCP/IP, HTTP, Ethernet, telephony, etc.). Application(s) 1220 and program modules 1218 may include software application(s) and different functional program modules which are executed by processor(s) 1202 to implement the processes described herein and/or other processes. The program modules 1218 may include but are not limited to software programs, machine learning models, objects, components, data structures that are configured to perform tasks or implement the processes described herein. The processes described herein may also be implemented in operating system 1214.
The features and functional operations described in the disclosed embodiments may be implemented in one or more computer programs that may be executable on a programmable system including at least one programmable processor coupled to receive data and instructions from, and to transmit data and instructions to, a data storage system, at least one input device, and at least one output device. A computer program is a set of instructions that can be used, directly or indirectly, in a computer to perform a certain activity or bring about a certain result. A computer program may be written in any form of programming language (e.g., Objective-C, Java), including compiled or interpreted languages, and it may be deployed in any form, including as a stand-alone program or as a module, component, subroutine, or other unit suitable for use in a computing environment.
The described features and functional operations described in the disclosed embodiments may be implemented in a computer system that includes a back-end component, such as a data server, or that includes a middleware component, such as an server computer or an Internet server, or that includes a front-end component, such as a user device having a graphical user interface or an Internet browser, or any combination thereof. The components of the system may be connected by any form or medium of digital data communication such as a communication network. Examples of communication networks include, e.g., a telephone network, a LAN, a WAN, and the computers and networks forming the Internet.
The computer system may include user computing devices and server computers. A user computing device and server may generally be remote from each other and may typically interact through a network. The relationship of user computing devices and server computer may arise by virtue of computer programs running on the respective computers and having a client-server relationship to each other.
Communication between various network and computing devices 1200 of a computing system may be facilitated by one or more application programming interfaces (APIs). APIs of system may be proprietary and/or may be examples available to those of ordinary skill in the art such as Amazon® Web Services (AWS) APIs or the like. The API may be implemented as one or more calls in program code that send or receive one or more parameters through a parameter list or other structure based on a call convention defined in an API specification document. One or more features and functional operations described in the disclosed embodiments may be implemented using an API. An API may define one or more parameters that are passed between an application and other software instructions/code (e.g., an operating system, library routine, function) that provides a service, that provides data, or that performs an operation or a computation. A parameter may be a constant, a key, a data structure, an object, an object class, a variable, a data type, a pointer, an array, a list, or another call.
While various embodiments have been described above, it should be understood that they have been presented by way of example and not limitation. It will be apparent to persons skilled in the relevant art(s) that various changes in form and detail can be made therein without departing from the spirit and scope. In fact, after reading the above description, it will be apparent to one skilled in the relevant art(s) how to implement alternative embodiments. For example, other steps may be provided, or steps may be eliminated, from the described flows, and other components may be added to, or removed from, the described systems. Accordingly, other implementations are within the scope of the following claims.
In addition, it should be understood that any figures which highlight the functionality and advantages are presented for example purposes only. The disclosed methodology and system are each sufficiently flexible and configurable such that they may be utilized in ways other than that shown.
Although the term “at least one” may often be used in the specification, claims and drawings, the terms “a”, “an”, “the”, “said”, etc. also signify “at least one” or “the at least one” in the specification, claims and drawings.
Finally, it is the applicant's intent that only claims that include the express language “means for” or “step for” be interpreted under 35 U.S.C. 112(f). Claims that do not expressly include the phrase “means for” or “step for” are not to be interpreted under 35 U.S.C. 112(f).
