This repository includes implementation of my research that propose novel methods for real-time event prediction for heterogeneous multivariate temporal data (time series, instantaneous events, and time intervals).
In the animation below, V1 and V2 are time series, V3 represents instantaneous events, and V4 represents time intervals.
Figure 1: The animation shows that the probability of experiencing an event of interest (heart attack in this example) increases over time (tc represents the current time), while the estimated time to event decreases.
Table of Contents
Symbolic time intervals (STIs) are a powerful way to represent time-series data and real-life events with varying duration, such as traffic light timing or medical treatments. STIs can be used to uniformly represent heterogeneous multivariate temporal data (time series, instantaneous events, or time intervals), including both event-driven measurements (e.g., traffic accidents) and manual measurements (e.g., blood tests). Temporal abstraction can be used to uniformly represent such heterogeneous multivariate temporal data using STIs. Frequent time intervals-related patterns (TIRPs) can be discovered from the STI data, which have proven to be valuable for knowledge discovery, as well as for use as features in classification and prediction tasks.
The completion of a TIRP can be inferred by calculating the probability of observing the remaining part of the pattern, given its observed part at a specific time.
A paper describing the idea of continuous completion prediction of a single temporal pattern instance at the Pacific-Asia Conference on Knowledge Discovery and Data Mining in 2023 [Link]:
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APA
Itzhak, N., Jaroszewicz, S., & Moskovitch, R. (2023, May). Continuously predicting the completion of a time intervals related pattern. In Pacific-Asia Conference on Knowledge Discovery and Data Mining (pp. 239-251). Cham: Springer Nature Switzerland. -
BibTeX
@inproceedings{itzhak2023continuously, title={Continuously predicting the completion of a time intervals related pattern}, author={Itzhak, Nevo and Jaroszewicz, Szymon and Moskovitch, Robert}, booktitle={Pacific-Asia Conference on Knowledge Discovery and Data Mining}, pages={239--251}, year={2023}, organization={Springer} }
An expanded version of this paper, including a detailed formulation of the problem, a description of the challenges, and the algorithms used to solve them, as well as a description of the fully continuous prediction model that incorporates the pattern’s components’ durations and more extensive experiments including various temporal abstraction methods, was accepted for publication in the Journal of Knowledge and Information Systems (KAIS) [Link]:
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APA
Itzhak, N., Jaroszewicz, S., & Moskovitch, R. (2023). Continuous prediction of a time intervals-related pattern’s completion. Knowledge and Information Systems, 1-50. -
BibTeX
@article{itzhak2023continuous, title={Continuous prediction of a time intervals-related pattern’s completion}, author={Itzhak, Nevo and Jaroszewicz, Szymon and Moskovitch, Robert}, journal={Knowledge and Information Systems}, pages={1--50}, year={2023}, publisher={Springer} }
A paper proposing a method for continuously predicting an event of interest using multiple instances of multiple temporal patterns has been accepted by the SIAM International Conference on Data Mining, 2024:
- APA
Itzhak, N., Jaroszewicz, S., & Moskovitch, R. (2024). Early Multiple Temporal Patterns Based Event Prediction in Heterogeneous Multivariate Temporal Data. In SIAM International Conference on Data Mining, Houston, TX, U.S., 2024.
To find more relevant papers on this topic or similar topics, please visit my Google Scholar profile.
Our methods build on the idea of real-time prediction of a single TIRP completion. The completion of a TIRP can be inferred by calculating the probability of observing the remaining part of the pattern, given its observed part at a specific time.
In the figure below, we observe a TIRP Q defined as
A overlaps B, A before y, B before y,
alongside four distinct time points denoted as tc^1, tc^2, tc^3, tc^4,
which have been selected to dissect the instance of the partial pattern.
Consider p_{t_c} as the observed part of the instance of Q at time point tc,
and correspondingly, s_{t_c} as the yet-to-occur portion of the instance of Q at tc.
We are thus interested in estimating Pr(Q | p_{t_c}), which represents the p_{t_c} at time t_c.
The simple computation (using SCPM) to compute this probability is Pr(Q)/Pr(p_{t_c}), which addresses the query:
"Among all instances where we observed p_{t_c}, how frequently was it succeeded by s_{t_c}?"
The computation of the numerator Pr(Q) is a relatively straightforward process,
involving the counting of Q instances.
Still, determining the denominator Pr(p_{t_c}) poses more intricate challenges in certain scenarios.
Challenges arise, such as at time point tc^2,
where STIs remain unfinished, rendering the description of p_{t_c} and s_{t_c}
using Allen's temporal relations unfeasible.
Figure 2: The objective is to determine, at various time points (e.g., tc^1, tc^2, tc^3, tc^4),
the probability and time of TIRP Q's eventual completion.
We also implemented an extension of the single TIRP completion model to be capable of estimating the TIRP's completion occurrence time, in addition to the completion probability.
Find more information about the challenges and the solutions, as well as more complex models for TIRP's completion (e.g., FCPM, or XGBoost-based models) in our papers.
By continuously aggregating multiple predictors for the completion of TIRPs that end with an event of interest, we learn a real-time event prediction model that is capable of estimating the event's occurrence probability and time. A model that leverages multiple TIRPs is expected to generalize better than a model that uses a single TIRP.
For example, the figure below presents TIRPs describing an entity with three symbols A, B, and C
until tc to several attributes of multiple detected TIRP instances.
In retrospect, it is known that this entity had an event of interest y in its data.
The continuous event prediction model consists three models m1, m2, m3 that estimates at
tc the y's occurrence probability, by continuously aggregating the Q1, Q2, and Q3 completion probabilities
and estimated times for the TIRP instances
p_{t_c}^{1.1}, p_{t_c}^{1.2}, p_{t_c}^{2.1},p_{t_c}^{2.2},p_{t_c}^{3.1}, detected until tc.
Figure 3: An example of detected prefix instances of three TIRPs Q1, Q2, and Q3 that end with the event of interest.
As shown with instances p_{t_c}^{1.1} and p_{t_c}^{1.2} (colored in blue),
the instances of a TIRP can be detected multiple times in the same entity before the event of interest occurs.
Additionally, p_{t_c}^{2.1} and p_{t_c}^{2.2} are prefixes of TIRP Q2 (colored in yellow)
and have a different number of tieps, in which the earlier instance (p_{t_c}^{2.1})
is more advanced than the later one (p_{t_c}^{2.2}).
Applying the simple mean function at tc resulted in:
mean { 0.75, 0.66, 0.87, 0.37, 0.52} = 0.634.
Thus, at tc=105 time units, the estimated probability of observing y is 63.4%.
Similarly, the event of interest occurrence time is computed by continuously aggregating all the predictors'
estimated TIRP completion times at tc.
Applying the simple mean function at tc resulted in:
mean {108, 112, 121, 110, 109} = 112 time units,
which is close to the actual occurrence time at time point 110.
Find more information about more complex continuous aggregation functions and TIRP selection methods, in our papers.
Our proposed methods require STI data. If you have heterogeneous multivariate temporal data (time series and events), you must transform it into STI format before using this repository. You must also provide time-intervals related patterns (TIRPs) as input.
Note: This repository does not include temporal abstraction methods or time-intervals mining algorithms because these are not part of our work' contributions. However, there are many other repositories that provide these methods, so you should use them before running this code.
The following files are required as input:
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Training set (see for example
input/STI data/sti_train.csv) - A set that is used to learn the models. The format should be as following:SeriesID,VarID,SymbolID,StartTime,EndTime 1.0,1.0,3.0,2.0,49.0 1.0,1.0,2.0,50.0,67.0 1.0,2.0,4.0,9.0,10.0 ... 1512.0,9.0,27.0,2.0,25.0 1512.0,10.0,28.0,2.0,25.0 1512.0,11.0,33.0,2.0,25.0 1512.0,999.0,999.0,26.0,27.0Where the columns are:
SeriesID- float; the entity ID (for example, patient ID)VarID- float; the variable ID (for example, blood pressure)SymbolID- float; the symbol ID (for example, high blood pressure). Mote: the symbol ID must be unique even if the VarId is different. The event of interest's index is defined in theconstfile as explain later. We defined the event of interest's index to be 999.0 and in the last row of the CSV it can be seen that the event of interest was occurred (1512.0,999.0,999.0,26.0,27.0).StartTime- float; the symbol's start timeEndTime- float; the symbol's end time
It's very important to make sure that in entities that the event of interest has occurred, the event of interest will have the latest start time and the latest end time of other STIs will be earlier to the event of interest's start time. This means only temporal relations of meets or before are supported with the event of interest.
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Testing set (see for example
input/STI data/sti_test.csv) - Same format as the training set descriptions but used of evaluation of the methods instead of learning the methods. -
Patterns (see for example
input/STI data/patterns.csv) - Provided TIRPs that are relevant for the model learning (pattern selection methods can be applied on this file). For the provided TIRPs, only those that ends with the event of interest are used. Note: the index of the event of interest needs to be defined in theconstfile. The format should be as following:STIs,TempRels,VerSupp,HorSupp "[1, 10, 6]","['c', 'c', 'b']",0.06097560975609756,7.8 "[1, 10, 6, 1]","['c', 'c', 'b', 'b', 'b', 'b']",0.06097560975609756,7.8 ... "[1, 5, 999]","['c', 'b', 'b']",0.17682926829268292,2.413793103448276 "[1, 5, 15, 999]","['c', 'c', 'b', 'b', 'b', 'b']",0.054878048780487805,6.888888888888889Where the columns are:
STIs- str; represents an array of STIsTempRels- str; represents an array of Allen's seven temporal relations (with the following chars:BEFORE = 'b',MEETS = 'm',CONTAINS = 'c',EQUALS = 'e',FINISHED_BY = 'f',OVERLAPS = 'o',STARTS = 's')VerSupp- float; currently not used; represents the vertical support of a TIRP, which means the percentage of entities found to have at least one instance of the TIRP).HorSupp- float; currently not used; represents the mean horizontal support of a TIRP, which represents the averaged number of a TIRP's instances that were discovered in an entity
We defined the event of interest's index to be 999.0. Thus, the first two rows will be ignored as they represent TIRPs that not end with the event of interest. In contrast, the last rows will be used as they TIRPs that end with the event of interest.
For example, the last row (
"[1, 5, 15, 999]","['c', 'c', 'b', 'b', 'b', 'b']") represents a TIRP with the STIs "1", "5", "15", and "999" with the following temporal relations:5 15 999 1 'c' 'c' 'b' 5 'b' 'b' 15 'b'while the indices of the temporal relations in the array
['c', 'c', 'b', 'b', 'b', 'b']are located in this order:5 15 999 1 0 1 3 5 2 4 15 5Examples of TIRP instances could be:
----------------1------------------- -------------5--------- -------15------ -999-OR:
----------------1------------------- -------5----- -15- -999-OR:
----------------1------------------- --------------5----------------- -------------15-------------- -999-and many more...
The raw data are used to compare our methods with baseline models.
The following files are required as input:
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Training set (see for example
input/Raw data/raw_train.csv) - A set that is used to learn the baseline models.The format should be as following:
SeriesID,VarID,TimeStamp,VarVal 1.0,1.0,6.0,0.15908584402322806 1.0,1.0,7.0,0.15908584402322806 1.0,1.0,8.0,0.15908584402322806 ... 1730.0,12.0,6.0,-0.9177692310061688 1730.0,12.0,9.0,-0.9177692310061688 1730.0,12.0,15.0,-0.9177692310061688Where the columns are:
SeriesID- float; the entity ID (for example, patient ID)VarID- float; the variable ID (for example, blood pressure)TimeStamp- float; timestampVarVal- float; the variable value at the timestamp
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Training classes (see for example
input/Raw data/train_class.csv) - The classes that are used to learn the baseline models.The format should be as following:
SeriesID,Class 1578.0,1 1557.0,1 1607.0,1 ... 1407.0,0 1291.0,0 66.0,0Where the columns are:
SeriesID- float; the entity ID (for example, patient ID)Class- int; whether the event of interest was occurred or not. Note: For entities with an event of interest, the data should be provided in a way that shows the event occurred one timestamp after the entity's data ends. In other words, provide the data until the event of interest.
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Testing set (see for example
input/Raw data/raw_test.csv) - Same as the training set but used to evaluate the baseline models. -
Testing classes (see for example
input/Raw data/test_class.csv) - Same as the training classes but used to learn the baseline models.
The cont.py file contains configuration that can be changed for the experiments.
EVENT_INDEX- Represent the index of the event. The data should contain events with symbol and variable id with the same value. The default is 999.TAU_EXP- an array oftauvalues (time delays) that used for the model prediction.W_EXP- an array ofwvalues (window sizes) that used for the model prediction.- Input folders and files names - define the input folder and the input files as describe above.
- Model parameters - Dictionaries with all relevant parameters can be defined and provided for the experiments. Some models using these dictionaries for hyperparameters to find the best parameters for the model.
The requirements.txt file lists all Python libraries that the project depend on,
and they will be installed using:
pip install -r requirements.txtThe code is divided as follows
main.py: This Python file contains the main code for running the model learning process.core_comp: This folder contains all the files for the core classes of time intervals components.tirp_prefixes: This folder contains all the files for the TIRP-Prefix definitions and detection.prediction: This folder contains all the files for the prediction classes of TIRP's completion (e.g., SCPM, FCPM, and XGBoost-based models).
The flow
The given code processes and evaluates predictive models for events of interest using time interval data.
Let's break down the flow of the code step by step:
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Load Data: The code starts by defining various file paths. These paths point to different CSV files that contain data. It includes paths for STI data, raw data, and pattern data. The code also loads the training and test sets. It also extracts labels for the test set and the time of the event of interest from the test set. This is used for model evaluation.
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Pattern Data: It loads patterns data. This patterns data will be used to build models.
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Model Building Loop: The code then enters a loop that iterates over patterns that end with the event of interest. For each pattern, it does the following:
- Learns probability models for the pattern. It learns different probability models for the given pattern using different methods or parameters.
- Learns a time model for the pattern.
- Performs post-training cleanup.
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Prediction Loop: After building the models for all patterns end with the event of interest, the code enters another loop that iterates over entities in the test set. For each entity, it does the following:
- Predicts the probability and time to event using specific models.
- Aggregates the predicted probability and time.
- Stores the aggregated prediction.
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Model Evaluation: After making predictions for all test entities, the code evaluates the learned models. It calculates metrics like AUC-ROC and AUPRC using specific evaluation parameters (tau and w). Then, the code prints the metrics to the console.
Any contributions you make are greatly appreciated.
If you have a suggestion that would make this better, please fork the repo and create a pull request. You can also simply open an issue with the tag "enhancement".
Don't forget to give the project a star!
Thanks again!
Distributed under the MIT License. See LICENSE.txt for more information.
I would like to thank Tali Malenboim, Lior Tkach, and Shani Bahat for their help in debugging this repository, asking questions, and providing comments.
These students plan to continue my PhD work, and they have done a great job of understanding all the complex aspects of this research in order to implement their own ideas in the future.
I wish you all the best with your research, and I hope this repository will help you achieve your academic goals.
In memory of Lior Tkach (M.Sc. student in Prof. Robert Moskovitch's lab), who was tragically killed in a terror attack on October 7th, 2023.
Lior's passion for knowledge and dedication to his work were evident in his constructive comments and pivotal role in debugging the code for this repository. His memory lives on in our hearts and in the work we continue to do.