Patent Publication Number: US-11640163-B1

Title: Event time characterization and prediction in multivariate event sequence domains to support improved process reliability

Description:
BACKGROUND 
     Technical Field 
     The present disclosure generally relates to plant optimization computer systems, and more particularly, to methods and systems for an automated generation of an optimization model for system-wide plant optimization based on multivariate event data. 
     Description of the Related Art 
     Manufacturing and process industries comprise a site-wide network of complex processes, each with a self-contained set of inputs and outputs. The variability in input flows, operational requirements, maintenance, breakdowns, changes in production plans, and the like, makes the production process dynamic. Plant-wide management may involve the ability to predict the dynamic process behavior and to alter any controls to adhere as closely as possible to the production plan. 
     Today, such plants generate multiple event streams providing multivariate data. A salient aspect of event sequence problems, is to be able to model and/or predict events arising from multiple event streams. These settings events often arrive in different channels at different times. For example, high dimensional event sequences often arise in IoT settings in process industries. In these settings, manufacturing processes may be well instrumented with sensors and control/monitoring systems. Understanding events generated by such control and monitoring systems, as well as providing early warning into future events is salient for safe and efficient operation of such processes. 
     Existing solutions for predicting events do not apply well to cases where there are large number of possible event types. A typical conversion of the of the multidimensional sequence to a univariate one may destroy the relationship between the event types, thereby losing valuable information. An understanding of the joint behavior of these multiple event streams can facilitate a better adjusted system. Manual optimization model generation is time-consuming, challenging, may involve both domain experts and optimization experts, and is often not practically possible in large scale operations. 
     SUMMARY 
     According to various embodiments, a computing device, a non-transitory computer readable storage medium, and a method are provided for administering a system. Multivariate data is received from a plurality of sensors of a system in an ambient state. Event sequences in the received multivariate data are identified. The multivariate event sequences are projected to a lower stochastic latent embedding. A temporal structure of the sequences is learned in a lower latent embedding. A probabilistic prediction in the lower latent space is provided. The probabilistic prediction in the lower stochastic latent space is decoded to an event prediction in the ambient state. 
     In one embodiment, the multivariate data comprises event sequences of different variables. 
     In one embodiment, at least some of the different variables are interrelated. 
     In one embodiment, the event sequences are compressed into a compact representation of latent variables. 
     In one embodiment, a recurrent neural network (RNN) is used to capture temporal dynamics of an event history from the compact representation. 
     In one embodiment, learned dynamics in the compact representation are used to detect a period of anomalous behavior of the system. 
     In one embodiment, projecting the multivariate event sequences to a lower stochastic latent embedding is by way of a variational auto encoder (VAE). 
     In one embodiment, an uncertainty of the prediction in the ambient state is provided. 
     In one embodiment, the system is an industrial plant. 
     In one embodiment, the variables comprise two or more of pressure, temperature, motion, volumetric flow, or sound level. 
     In one embodiment, one or more components of the system are adjusted to prevent the predicted event. 
     In one embodiment, multiple time step predictions are provided by autoregressively predicting latent variables at different future points in time. 
     These and other features will become apparent from the following detailed description of illustrative embodiments thereof, which is to be read in connection with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The drawings are of illustrative embodiments. They do not illustrate all embodiments. Other embodiments may be used in addition or instead. Details that may be apparent or unnecessary may be omitted to save space or for more effective illustration. Some embodiments may be practiced with additional components or steps and/or without all the components or steps that are illustrated. When the same numeral appears in different drawings, it refers to the same or like components or steps. 
         FIG.  1    illustrates an example architecture of a predictive variational autoencoder, consistent with an illustrative embodiment. 
         FIG.  2    illustrates an example time multivariate observation data in the form of a plurality of time series, consistent with an illustrative embodiment. 
         FIG.  3    provides a conceptual block diagram of a predictive latent variational autoencoder, consistent with an illustrative embodiment. 
         FIG.  4    is a conceptual block diagram of a predictive latent variational autoencoder configured to provide multiple predictive steps, consistent with an illustrative embodiment. 
         FIG.  5    presents an example processes, for an automated generation of an optimization model for system-wide plant optimization based on multivariate event data, consistent with illustrative embodiment. 
         FIG.  6    is a functional block diagram illustration of a particularly configured computer hardware platform that can communicate with various networked components, consistent with an illustrative embodiment. 
         FIG.  7    depicts a cloud computing environment, consistent with an illustrative embodiment. 
         FIG.  8    depicts abstraction model layers, consistent with an illustrative embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     Overview 
     In the following detailed description, numerous specific details are set forth by way of examples to provide a thorough understanding of the relevant teachings. However, it should be apparent that the present teachings may be practiced without such details. In other instances, well-known methods, procedures, components, and/or circuitry have been described at a relatively high-level, without detail, to avoid unnecessarily obscuring aspects of the present teachings. 
     The present disclosure generally relates to systems and methods for time to event characterization and prediction in multivariate event sequence domains to facilitate a more reliable large system having many components and sensors monitoring the same. Today, multivariate point processes (MPPs) are a salient class of temporal point processes (TPPs), which are configured to model random processes with complex temporal dynamics. While univariate TPP models can be successfully applied in various domains, MPPs have been largely unexplored. 
     Previous implementations using TPP mainly focus on the modelling univariate processes where only a single intensity function, sometimes referred to herein as a variable, is learned. Such framework, however, still faces several fundamental limits: (a) Univariate model input: at each gradient iteration, only an individual sequence is considered to update the parameters, making it hard for the model to learn complex interactions across different sequences; and (b) Intractable learning: maximum likelihood often leads to difficult learning due to the integration of the intensity embedded in the conditional density equation. These limits may be alleviated by assuming the intensity function has a simple exponential form, but such assumption reduces the expressiveness of the model. 
     Probabilistic prediction of high dimensional sequential data is generally a challenging task, both in terms of computational burden and distribution modelling. Sequential generative models, which have their roots in the variational autoencoder (VAE), can effectively learn from data with temporal dynamics. The teachings herein provide a novel sequential model for MPP applications. Learning of complex interactions between high dimensional event sequences is facilitated. In one aspect, the teachings herein use a novel VAE-based architecture that can capture the event interarrival time distribution, predict a next event in high-dimensional multivariate sequences and simulate the sequences for longer prediction horizons. 
     In one embodiment, the architecture described herein uses a sparse representation to enable capturing relationships in the presence of a large number of event types and can use strategies to ensure that temporal dynamics and correlation structures of the event sequence is captured. By virtue of the teachings herein, various technical benefits are achieved, including an accuracy of the computing platform coordinating a complex system, such as a manufacturing plant, is improved and the number of events in the complex system accurately calculated (e.g., predicted) and even avoided. The techniques described herein may be implemented in a number of ways. Example implementations are provided below with reference to the following figures. 
     Example Architecture 
       FIG.  1    illustrates an example architecture  100  of a predictive variational autoencoder (PVAE), consistent with an illustrative embodiment. There is a multivariate observation data  102  in the form of a plurality of time series that characterize the operation of a complex system, such as a manufacturing plant having many components (e.g., thousands, millions, etc.). This data  102  may be captured by various sensors, such as time, pressure, temperature, motion, volumetric flow, sound, etc. Each of these variables may have certain operation ranges for each component (e.g., piece of equipment). When the operation range is exceeded, it is recorded as an event. Each event is associated with a time stamp. An event in one parameter may be related to a separate parameter, such as increasing temperature with pressure. Such complex interactions between high dimensional event sequences can often arise in IoT settings in process industries. In these industries, complex manufacturing processes are well instrumented with sensors and control/monitoring systems. Understanding events generated by these control and monitoring systems is salient for safe and efficient operation of such processes. 
     The multivariate observation data  102  is used as a corpus of data from which a predictive model  104  can be constructed. The predictive model  104  is able to capture the event interarrival time distribution and provide a concise representation of the time series of the entire system  106 , as well as predict the next event  108  in high-dimensional multivariate sequences. In some embodiments, the model can perform long horizontal prediction without losing much accuracy  102 . The training of the predictive model  104 , sometimes referred to herein as the machine learning model, may be supervised or unsupervised. In supervised learning, a monitoring server may be presented with example data from the data store as being acceptable. Put differently, the time series observation data  102  acts as a teacher for the model. In unsupervised learning, there are no labels as what is acceptable; rather, it simply provides historic data to the model to find its own structure among the data. In one embodiment, the predictive model  104  is based on self supervised learning (SSL) and does not require any labels on the multivariate observation data  102 , which can be regarded as an intermediate form between supervised and unsupervised learning. Some of these concepts are discussed in more detail below 
     The resulting time series of prediction results  108  can be used in different ways. For example, forecasting outputs and the learned representation  110  can be used for event predictions and anomaly detection. In one embodiment, the learnt latent representation  106  can be used for downstream tasks, such as classification. By virtue of being able to accurately predict the different variables in a complex system, events can be planned for and optimized accordingly  114  to accommodate, or even to avoid, future events. To that end, the predicted data is used to adjust the complex manufacturing process  116  and the process continues iteratively by generating new event sequence data  118  which can be fed back to the predictive model  1104 . 
       FIG.  2    illustrates an example time multivariate observation data in the form of a plurality of time series  200 , consistent with an illustrative embodiment. For simplicity, three sequences  202 ( 1 ) to  202 ( 3 ) are shown in  FIG.  2   , while it will be understood that many (e.g., thousands) of time series are within the scope of the teachings herein. Each time series  202 ( 1 ) to  202 ( 3 ) includes an observation phase  204 , which is used by the predictive model to learn therefrom, and a prediction phase  206  of future events, where a continuation of each time series is determined by the model. Significantly, each time series (e.g.,  202 ( 1 ) to  202 ( 3 )) is not evaluated individually to determine its corresponding continuation; rather, all time series (e.g.,  202 ( 1 ) to  202 ( 3 )) are studied in aggregate to find interrelationships therebetween in order to provide a prediction of each respective time series during the prediction phase  206 . Stated differently, the model discussed herein can learn to correlate across different event sequences (e.g., time series  202 ( 1 ) to  202 ( 3 )). In one embodiment, the uncertainty prediction interval is provided as well (e.g., via probabilistic modeling of the event interarrival). 
     Example Block Diagram of a Predictive Latent Variational Autoencoder 
       FIG.  3    provides a conceptual block diagram of a predictive latent variational autoencoder (PVAE), consistent with an illustrative embodiment. A variational auto encoder (VAE) is an artificial neural network architecture that is operative to compress the input information into a constrained multivariate latent distribution (i.e., encode) to be able to later reconstruct it as accurately as possible (i.e., decode.) 
     The PVAE  300  of  FIG.  3    provides a new sequential VAE model for a prediction task. The architecture relies on the underlying assumption that the information describing the high dimensional data often lies on a much lower dimensional manifold. For example, in a Hawkes process, the free parameters can be limited by a small number of kernels representing the process, which can be shared across different dimensions. Thus, learning the temporal dependency of event inter-arrivals can essentially be distilled to learning the dynamics of the latent embedding, which is potentially easier to calculate by a computing device due to (a) dimensionality deduction, and (b) high level representation. To provide an accurate reconstruction, latent variables can be enforced to encode high level representation such as smoothness, and unnecessary information such as high frequency noise discarded. These smooth features can be dynamically easier to capture by a computing device via a recurrent network. The PVAE  300  is built on this assumption, and a temporal predictive model is introduced in the latent space to auto-regressively forecast the future (e.g., Z t ) and to infer this value back to the event sequence domain. To that end, a regularization is introduced that measures the proximity between the distribution of the past latent variables and that of the current time step. 
     In PVAE  300 , the rectangular shapes  302 ( 1 ) to  302 ( t ) indicate deterministic states  302 . There is a variational encoder  306  that include observed variables at different times x 1  to x t−1 . For example, x 1  represents all the event variables captured from various sensors when one of the variables exceeds a predetermined threshold. Thus, x 1  can be viewed as a large vector comprising various event types. The high-dimensional observed event inter-arrivals x i  at time i is mapped to a random variable z i  which lies on a lower dimensional manifold. A dimensional manifold is a topological space having the property that each point has a neighborhood that is homeomorphic to an open subset of n-dimensional Euclidean space. This mapping is the deep neural network encoder q(z i |x i ) of VAE. The PVAE  300  comprises t such separate mappings, which share the same VAE encoder with parameters θ  310 . The latent representations z 1 , . . . , z t  is expected to carry the temporal dynamics of the event sequence. This time-dependent variability is captured by a recurrent neural network (RNN) with deterministic states. Each state of the observed variables (e.g., x 1 ) has a corresponding output (e.g., C 2  ( 320 ( 2 )) for x 1 ). The outputs C 2  to Ct ( 320 ( 2 ) to  320 (T)) are used to provide a predicted output in the lower dimensional manifold Z t    330 , which is then used to predict the set of corresponding input variables x t    340 . 
     For example, output c t    320  of the recurrent neural network (RNN) is a random variable with distribution p(c t |h(z 1:t−1 )), where h is a deterministic function parametrized by γ−parameters of the RNN. The output c t    320  can be seen as the auxiliary random variable to constraint the two groups of latent random variables, namely (i) the prediction z t    330  and (ii) the observed history z 1:(t−1) . The prediction in the input domain, sometimes referred to herein as the ambient domain, is transferred from the prediction in the embedding space. 
     Given the observed input sequence x 1:(t−1) , the trained model generates M latent embeddings z 1:(t−1)   (m) , m=1, . . . , M via the variational distribution q(z i |x i ) with i=1, . . . , t−1. In this paper, q(z i |x i ) is a deep neural network parametrized by θ  310  with a simple distribution form, provided by the expression below:
 
 z   i   (m) ˜ ( z   i   ;g   μ ( x   i ), g   σ ( x   i ) i= 1, . . . , t− 1  (Eq. 1)
 
     The average of these latent sample 
                 z   ¯     i     =       1   M     ⁢       ∑   m       z   i     (   m   )                 
can be used as the input to the RNN, and the M output samples c (m)  is produced by sampling from Gaussian distribution, provided by the expression below:
 
 c   t   (m) ˜ ( h   μ (   z     1:(t−1) ), h   σ (   z     1:(t−1) ))  (Eq. 2)
 
     The  c   t —the average over m samples c t   (m)  can be seen as the proxy for the latent code z t . The prediction {circumflex over (x)} t  is obtained from sampling, as provided by the expression below:
 
 x   t ˜ ( f   μ (   c     t ), f   σ (   c     t ))  (Eq. 3)
 
     Then, taking the mean over these samples. The multiple step-ahead prediction can be produced as follows: once the average sample z t  is attained, it can be used as the input to the recurrent network to produce samples z t+1  and consequently yield the output {circumflex over (x)} t+1 . The procedure can be repeated n times to predict n value z t:t+n  and their associated {circumflex over (x)} t:t+n . 
     Accordingly, the multivariate event sequences x 1  to x t−1  are projected to a lower stochastic latent embedding  312 . The temporal structure of the multivariate event sequences is learned in the latent space  302 . A probabilistic prediction in the stochastic latent space Ct  320  is transferred to the event prediction Z t    330 . C t  captures the dynamics of latents z 1 , . . . , z t−1  via LSTM and is considered as the surrogate of z t . Thus, the output C t  is 320 is mapped back to the input domain to calculate the prediction x t    340 . The representation  312  is modelled probabilistically. Thus, the prediction samples are obtained by sampling. 
     The parameters ϕ and γ of the neural network are learned via maximizing the sum of the log likelihood log p(x 1:t ) with respect to these parameters. Due to the intractability of the likelihood, in one embodiment, a variational distribution q(c t , z 1:t |x 1:t ) is introduced that approximates the posterior p(c t , z 1:t |x 1:t ). The evidence lower bound ELBO is derived from Jensen inequality, as provided by the expression below: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
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     In one embodiment, the variational distribution can be parametrized by a deep neural network with parameters θ and γ, which can be decomposed as provided below: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
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     With the Markov assumption on the variational factor that q(c t |z 1:t ,x 1:t )=q(c t |z 1:(t−1) ), the second term yields the following expression: 
     
       
         
           
             
               
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     The above expression is the KL divergence between two distributions: the factor q(c t |z 1:(t−1) ) and p(c t |z t ). 
     The last term can also be simplified to: 
     
       
         
           
             
               
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     Equation 10 above measures the KL divergence between the factor q(z i |x i ) of the variational approximation and the latent prior p(z t ). 
     In one embodiment, parameters ϕ, θ, and γ of the network are learned by minimizing the sum of lower bounds over training samples:
 
 (ϕ,θ,γ)=Σ x     1:t     (ϕ,θ,γ; x   1:t )  (Eq. 11)
 
     In equation 11 above, the  (ϕ, θ, γ; x 1:t ) is the sum of three components: 
     
       
         
           
             
               
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     For example, in the equation of  (ϕ, θ, γ; x 1:t ), the first component plays the roll of reconstructing the original input data, the last component represents the divergence of the variational distribution q(z i |x i ) from the prior p(z i ), which can be assumed to be Gaussian with zero mean and unit norm standard deviation. The second regularization enforces the variational condition q(c t |z 1:(t−1)  to be closed to the distribution p(c t |z t ) in the latent space. This condition implies that the output random variable of the recurrent network conditioned on the inputs z 1:(t−1)  has similar distribution as that of c t  conditioned on z t . In one embodiment, both distributions have Gaussian forms with means h(z 1:(t−1) ) and z t , respectively. This regularization imposes the predictive capability of the latent embedding: the random variable z t  is the proximity of the encoded h(z 1:(t−1) ). This proximity is translated to the input domain via minimizing the reconstruction error between the actual x t  and the sample from decoder. This sample is the function of the observed history x 1:(t−1) . 
     To make the loss function more flexible in term of assigning different weights for each loss component, in one embodiment, regularization parameters α and β are introduced on KL divergences to control the balance between reconstruction and KL losses. Furthermore, Monte Carlo estimates of the expectation in equation 12 above can be formed via the K samples {z 1:t   (k) } k=1   K . The objective may have the following approximation form:
 
 (ϕ,θ,γ; x   1:t )=   1 ( x   1:t )+α   2 ( x   1:t )+β   3 ( x   1:t )  (Eq. 13)
         Where:       

     
       
         
           
             
               
                 
                   
                     
                       
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     In one embodiment, the variational factor is q(c t |z 1:(t−1) ˜ (c t ; μ t , σ t   2 ), which is the multivariate Gaussian with diagonal covariance matrix with variance σ t   2 . Here, μ t , σ t   2  is parametrized by RNN with parameters γ: μ t =h μ (z 1:(t−1) ) and σ t   2 =h σ (z 1:(t−1) . Additionally, we make the assumption p(c t |z t )˜ (c t ; z t , I). With these assumptions, the KL divergences are analytically derived. In one embodiment, a reparameterization trick is applied to optimize equation 11 above. 
     In one embodiment, the variational distribution q(c 1:t , z 1:t |x 1:t ) can be introduced to monitor the divergence between q(c i |z 1:(i−1) ) and p(c i |z i ) for all i, which we skip due to the similar derivation. In this embodiment, only    2  is changed to the following expression: 
     
       
         
           
             
               
                 
                   
                     
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     With the foregoing explanation of providing a predictive state of a complex system, reference now is made to  FIG.  4   , which is a conceptual block diagram  400  of a predictive latent variational autoencoder (PVAE) configured to provide multiple predictive steps, consistent with an illustrative embodiment. Similar to the architecture discussed in the context of  FIG.  3   , the multivariate event sequences are projected to a lower stochastic latent embedding. The temporal structure of the sequences is learned in the latent space. A probabilistic prediction in the stochastic latent space is transferred to the event prediction. In addition, the architecture of  FIG.  4    can provide multiple step prediction by autoregressively predicting latent variables at different future points in time x t , x t +1, x t +2, etc. In one embodiment, the model can stay in the latent space and does not need to go back to the ambient (e.g., original data) space at every prediction step. Stated differently, intermediate predictions may not be necessary in order to make a more long-term prediction. For example, a weekly prediction is not necessary to make a prediction for next month. 
     The teachings herein use a novel VAE-based architecture, referred to herein as a PVAE, which can be used to capture the event interarrival time distribution, predict the next event in high-dimensional multivariate sequences, as well as simulate the sequences for longer prediction horizons. The architecture uses novel strategies to ensure that temporal dynamics and correlation structures of the event sequence is captured. The architecture efficiently learns the correlation across different event sequences, capture temporal dynamics of the sequences, learns a representation that can be used for other tasks, and probabilistically predicts multiple steps into the future. In some embodiments, the architecture also employs strategies to ensure that learning complex event sequences is possible by imposing a sparse representation on the underlying model. 
     By virtue of the teachings herein a holistic view of a complex system, such as a manufacturing plant is provided, as well as accurate predictions in different points in time. These predictions are not based on a review of variables individually; rather, all the variables in the data are analyzed together to find relationships between them, to provide a more accurate prediction of events. In this way, a better understanding of the complex system is facilitated by an appropriately configured computing device and the control thereof simplified and made more efficient. Events can be predicted and even avoided. While, to facilitate the present discussion, a manufacturing plant is used as an example of a complex system, it will be understood that other large and complex systems that cannot be practically coordinated by a human, such as healthcare, time series forecasting, video activity predictions, and others are within the scope of the teachings herein. 
     Example Process 
     With the foregoing overview of the example architecture  100  of  FIG.  1    and example PVAEs  300  and  400  of  FIGS.  3  and  4   , it may be helpful now to consider a high-level discussion of an example process. To that end,  FIG.  5    presents an example processes  500 , for an automated generation of an optimization model for system-wide plant optimization based on multivariate event data, consistent with illustrative embodiment. Process  500  is illustrated as a collection of blocks in a logical flowchart, which represents sequence of operations that can be implemented in hardware, software, or a combination thereof. In the context of software, the blocks represent computer-executable instructions that, when executed by one or more processors, perform the recited operations. Generally, computer-executable instructions may include routines, programs, objects, components, data structures, and the like that perform functions or implement abstract data types. In each process, the order in which the operations are described is not intended to be construed as a limitation, and any number of the described blocks can be combined in any order and/or performed in parallel to implement the process. For discussion purposes, the process  500  is described with reference to the architectures  100  and  300  of  FIGS.  1  and  3   , respectively. 
     At block  502  multivariate data  102  from a plurality of sensors (e.g., components of a plant) in an ambient state is received, for one or more observation points (e.g., x 1  to x t−1 ). For example, the multivariate data  102  from the sensors may comprise event sequences. 
     At block  504 , event sequences in the received multivariate data are identified. 
     At block  506 , the multivariate event sequences are projected to a lower stochastic latent embedding. 
     At block  508 , a temporal structure of the sequences is learned in the latent embedding (e.g.,  310 ). A correlation (e.g.,  302 ) between variables in the sequences in the lower latent space is determined. 
     At block  512 , a probabilistic prediction (e.g.,  330 ) is provided in the lower latent space. 
     At block  514 , the probabilistic prediction in the lower stochastic latent space is decoded to an event prediction in the ambient state (e.g., x t    340 ). 
     Example Computer Platform 
     As discussed above, functions relating to methods and systems for the automated generation of an optimization model for system-wide plant optimization based on multivariate event data can be performed with the use of one or more computing devices connected for data communication via wireless or wired communication.  FIG.  6    is a functional block diagram illustration of a computer hardware platform that can communicate with various networked components, such as a training input data source, the cloud, etc. In particular,  FIG.  6    illustrates a network or host computer platform  600 , as may be used to implement a server, such as an analytics server that can support the predictive model  104  of  FIG.  1   . 
     The computer platform  600  may include a central processing unit (CPU)  604 , a hard disk drive (HDD)  606 , random access memory (RAM) and/or read only memory (ROM)  608 , a keyboard  610 , a mouse  612 , a display  614 , and a communication interface  616 , which are connected to a system bus  602 . 
     In one embodiment, the HDD  606 , has capabilities that include storing a program that can execute various processes, such as the PVAE engine  640 , in a manner described herein. The analytics engine  640  may have various modules configured to perform different functions. For example, there may be an interaction module  642  that is operative to interact with one or more sensors of a complex system to receive data therefrom, such as multivariate observation data in the form of time series at different points in time. There may be an encoding module  644  that is operative to map data from an ambient state (e.g., x 1 ) to a lower dimensional manifold (e.g., z 1 ). There may be a decode module  646  that is operative to go in the reverse direction as the encoder, namely decode data from the lower dimensional manifold (e.g., Z t ) to the ambient state (e.g., x t ). There may be a representation module that is operative to provide a latent representation of multiple time series of an entire system. In one embodiment, there is a prediction module  650  operative to predict a next event. In one embodiment there is a recurrent neural network (RNN) module configured to capture temporal dynamics of an event history from the compact representation of latent variables of a complex system. 
     Example Cloud Platform 
     As discussed above, functions relating to an for an efficient symbolic sequence analytics using random sequence embeddings, may include a cloud. 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.  7   , an illustrative cloud computing environment  700  is depicted. As shown, cloud computing environment  700  includes one or more cloud computing nodes  710  with which local computing devices used by cloud consumers, such as, for example, personal digital assistant (PDA) or cellular telephone  754 A, desktop computer  754 B, laptop computer  754 C, and/or automobile computer system  754 N may communicate. Nodes  710  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  750  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  754 A-N shown in  FIG.  7    are intended to be illustrative only and that computing nodes  710  and cloud computing environment  750  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.  8   , a set of functional abstraction layers provided by cloud computing environment  750  ( FIG.  7   ) is shown. It should be understood in advance that the components, layers, and functions shown in  FIG.  8    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  860  includes hardware and software components. Examples of hardware components include: mainframes  861 ; RISC (Reduced Instruction Set Computer) architecture based servers  862 ; servers  863 ; blade servers  864 ; storage devices  865 ; and networks and networking components  866 . In some embodiments, software components include network application server software  867  and database software  868 . 
     Virtualization layer  870  provides an abstraction layer from which the following examples of virtual entities may be provided: virtual servers  871 ; virtual storage  872 ; virtual networks  873 , including virtual private networks; virtual applications and operating systems  874 ; and virtual clients  875 . 
     In one example, management layer  880  may provide the functions described below. Resource provisioning  881  provides dynamic procurement of computing resources and other resources that are utilized to perform tasks within the cloud computing environment. Metering and Pricing  882  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  883  provides access to the cloud computing environment for consumers and system administrators. Service level management  884  provides cloud computing resource allocation and management such that required service levels are met. Service Level Agreement (SLA) planning and fulfillment  885  provide pre-arrangement for, and procurement of, cloud computing resources for which a future requirement is anticipated in accordance with an SLA. 
     Workloads layer  890  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  891 ; software development and lifecycle management  892 ; virtual classroom education delivery  893 ; data analytics processing  894 ; transaction processing  895 ; and PVAE  896 , as discussed herein. 
     CONCLUSION 
     The descriptions of the various embodiments of the present teachings 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. 
     While the foregoing has described what are considered to be the best state and/or other examples, it is understood that various modifications may be made therein and that the subject matter disclosed herein may be implemented in various forms and examples, and that the teachings may be applied in numerous applications, only some of which have been described herein. It is intended by the following claims to claim any and all applications, modifications and variations that fall within the true scope of the present teachings. 
     The components, steps, features, objects, benefits and advantages that have been discussed herein are merely illustrative. None of them, nor the discussions relating to them, are intended to limit the scope of protection. While various advantages have been discussed herein, it will be understood that not all embodiments necessarily include all advantages. Unless otherwise stated, all measurements, values, ratings, positions, magnitudes, sizes, and other specifications that are set forth in this specification, including in the claims that follow, are approximate, not exact. They are intended to have a reasonable range that is consistent with the functions to which they relate and with what is customary in the art to which they pertain. 
     Numerous other embodiments are also contemplated. These include embodiments that have fewer, additional, and/or different components, steps, features, objects, benefits and advantages. These also include embodiments in which the components and/or steps are arranged and/or ordered differently. 
     Aspects of the present disclosure are described herein with reference to a flowchart illustration and/or block diagram of a method, apparatus (systems), and computer program products according to embodiments of the present 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, 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 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 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 herein 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 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. 
     While the foregoing has been described in conjunction with exemplary embodiments, it is understood that the term “exemplary” is merely meant as an example, rather than the best or optimal. Except as stated immediately above, nothing that has been stated or illustrated is intended or should be interpreted to cause a dedication of any component, step, feature, object, benefit, advantage, or equivalent to the public, regardless of whether it is or is not recited in the claims. 
     It will be understood that the terms and expressions used herein have the ordinary meaning as is accorded to such terms and expressions with respect to their corresponding respective areas of inquiry and study except where specific meanings have otherwise been set forth herein. Relational terms such as first and second and the like may be used solely to distinguish one entity or action from another without necessarily requiring or implying any actual such relationship or order between such entities or actions. The terms “comprises,” “comprising,” or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. An element proceeded by “a” or “an” does not, without further constraints, preclude the existence of additional identical elements in the process, method, article, or apparatus that comprises the element. 
     The Abstract of the Disclosure is provided to allow the reader to quickly ascertain the nature of the technical disclosure. It is submitted with the understanding that it will not be used to interpret or limit the scope or meaning of the claims. In addition, in the foregoing Detailed Description, it can be seen that various features are grouped together in various embodiments for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the claimed embodiments have more features than are expressly recited in each claim. Rather, as the following claims reflect, inventive subject matter lies in less than all features of a single disclosed embodiment. Thus, the following claims are hereby incorporated into the Detailed Description, with each claim standing on its own as a separately claimed subject matter.