Adversarial Data Generation of Multi-category Marked Temporal Point Processes with Sparse, Incomplete, and Small Training Samples
Authors: Shashika Ranga Muramudalige
Anura Jayasumana
Haonan Wang
Venue:  (2021)
Keywords: Marked temporal point process
Stochastic process
Adversarial autoencoder
Incomplete data generation

Abstract: Asynchronous stochastic discrete event based processes are commonplace in application domains such as social science, homeland security, and health informatics.  Modeling complex interactions of such event data via marked temporal point processes (MTPPs) provides the ability of detection and prediction of specific interests or profiles. We present a novel multi-category MTPP generation technique for applications where training datasets are inherently sparse, incomplete, and small. The proposed adversarial architecture augments adversarial autoencoder (AAE) with feature mapping techniques, which includes a transformation between the categories and timestamps of marked points and the percentile distribution of the particular category.  The transformation of training data to the distribution facilitates the accurate capture of underlying process characteristics despite the sparseness and incompleteness of data. The proposed method is validated using several benchmark datasets. The similarity between actual and generated MTPPs is evaluated and compared with a Markov process based baseline. Results demonstrate the effectiveness and robustness of the proposed technique.

Under review as a conference paper at ICLR 2021
ADVERSARIAL DATA GENERATION OF MULTI- CATEGORY MARKED TEMPORAL POINT PROCESSES WITH SPARSE, INCOMPLETE, AND SMALL TRAINING SAMPLES
Anonymous authors Paper under double-blind review
ABSTRACT
Asynchronous stochastic discrete event based processes are commonplace in appli- cation domains such social science, homeland security, and health informatics. Modeling complex interactions of such event data via marked temporal point pro- cesses (MTPPs) provides the ability of detection and prediction of specific interests or profiles. We present novel multi multi-category MTPP generation technique for applications where training datasets are inherently sparse, incomplete, and small. The proposed adversarial architecture augments adversarial autoencoder (AAF) with feature mapping techniques, which includes a transformation between the categories and timestamps of marked points and the percentile distribution of the particular category. The transformation of training data to the distribution facilitates the accurate capture of underlying process characteristics despite the sparseness and incompleteness of data. The proposed method validated using several bench- mark datasets. The similarity between actual and generated MTPPs is evaluated and compared with a Markov process based baseline. Results demonstrate the effectiveness and robustness of the proposed technique.
INTRODUCTION
Marked Temporal Point Processes (MTPPs) are widely used for modeling and analysis of asyn- chronous stochastic discrete events in continuous time (Upadhyay et al. 2018 Türkmen et al., 2019, Yan, 2019) with applications in numerous domains such as homeland security, cybersecu- rity, consumer analytics, health care analytics, and social science. An MTPP models stochas- tic discrete events marked points (e;) defined by its time of the occurrence l; and its cat- egory G. Usually, point processes are characterized using the conditional intensity function, (t) = X(t) Pfevent [t, + /7t,), which given the past H, {e+ (2,,t,) It),t < f} specifies the probability of an event occurring at future time points. There are many popular intensity functional forms. Hawkes process (self-exciting process) (Hawkes) 1971) is point process used in both statistical and machine learning contexts where the intensity is a linear function of past events (Hz) (Türkmen et al., (2019) In traditional parametric models, the conditional intensity functions are manually pre-specified (Yan] 2019). Recently, various neural network models (generally called neural TPP) have been used to learn arbitrary and unknown distributions while eliminating the manual intensity function selection. Reinforcement learning (Zhu et al.) 2019 Li et al.) 2018), recurrent Neural Networks (RNN) (Du et al. 2016). and generative neural networks (Xiao al.) 2018) are used to approximate the intensity functions and learn complex MTPP distributions using larger datasets.
Recent advances in data collection techniques allow collecting complex event data which form heterogeneous MTTPs where marked point (c:z) defines time of occurrence (f;) and category (c₂) separately. Therefore, multi-category MTTPs not only concern about the time occurrence but also the category of the next marked point. The multi-category MTTPs append extra dimensionality to the distribution which complicates the learning using existing technologies. In fact, multi-cat matti-c MTPPs greatly helpful to model the behavioral patterns of suspicious specific individuals and groups in homeland security (Campedelli et al. 20196bal al Hung et al. 2018 2019), potential malicious network activities in cybersecurity (Peng al. 2017), recommendation systems in consumer anal malytics

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Vasssy et al., 2019), and the behavioral patterns of patients to determine certain illnesses Islam ct al. 2017 7 Mancini & Paganoni 2019).
A number of challenges limit the collection and access to data in many fields often resulting in small and incomplete datasets. Scenarios involving social, political and crime behaviors are often incom- plete due to data collection challenges such data quality maintenance, privacy and confidentiality issues (National Institutes of Health & Services 2020), but still a rigorous analysis with complete data essential produce accurate and reliable outcomes. So, there is critical need for a technique to capture and learn from MTPP distribution, develop and apply machine learning algorithms, etc., for a small set of data some of which may be incomplete. We present an adversarial multi- multi-- MTPP generation technique which is capable of generating sparse, asynchronous, stochastic, multi-category. discrete events in continuous time based on a limited dataset. Adversarial training has recently evolved and is able to provide exceptional results in many data generation applications, mostly in image, audio, and video generation while precisely mimicking the features of an actual dataset. The primary GAN architecture (Goodfellow et al. 2014) only engages well for continuous and complete data distributions and GANs have not been used for learning the distribution of discrete variables (Choi et al.
2017). Later, GAN architectures for discrete events have been introduced (Makhzani Yu et al. 2017) and also applied for MTTP generation using extensive training data
jet al. 2015
(Xiao
al.
2018 2017).
Adversarial autoencoders (AAE) are fluent in capturing latent discrete or continuous distributions (Makhzani et al.] (015). In this work, we present feature mapping modules for accommodating incomplete data and make AAE capable of capturing the MTPP distributions of incomplete and small datasets. The incompleteness of the data points can be occurred in following ways. The marked points have been not collected or actors did not originally expose some marked points due to the dynamicity of these stochastic processes, which is the case especially in social and behavioral domains. Main contribution of the paper is novel technique to synthetically generate high-fidelity multi-category MTPPs using adversarial autoencoders and feature mapping techniques by leveraging sparse, incomplete, and small datasets. To the best of our knowledge, there is no technique available for multi-category MTTP generation using such a dataset which is significantly more challenging than the existing generation scenarios.
Section 2 reviews related literature on MTTPs and AAEs. Section 3 presents the definition of multi- category MTTPs and Section 4 discusses the usage of AAEs for incomplete, multi-categon MTTP generation. Then Section presents the unique preprocessing and postprocessing techniques include in the feature mapping encoder and the decoder. Section discusses the results of the experiment, and Section 7 ssmmmarises the conclusion and future work.
RELATED WORK
MTPPs are widely used for modeling of asynchronous stochastic discrete events continuous time (Upadhyay et al. 2018 Du et al. 2016 Li et al. 2018 Türkmen et al. 2019). Usually, an MTTP is defined using a conditional intensity function (Türkmen et al. 2019) which provides the instantaneous rate of events given previous points. Intensity functions are often approximated by various processes such as the Poisson process, Hawkes process (self-exciting process) (Hawkes) 1971). and self-correcting process (Isham & Westcott 1979p. In traditional MTPPs, the intensity function has to be explicitly defined; however any mismatch between the manually defined and the underlying intensity function of process can have a significant adverse impact on the accuracy of models and outcomes. Deep generative networks avoid the requirement of manually identifying the intensity and thus allows the use of arbitrary and complex distributions. Recurrent Neural Networks (RNNs) with reinforcement learning have been widely used in recent years (Du et al.) 2016 Li et al. 2018) as well as several hybrid and extended models are also presented. A stochastic sequential model is proposed in (Sharma et al.) 2019) as a combination of deep state space model and deterministic RNN for modeling MTPPs. FastPoint (Türkmen et al., 2019) uses deep RNNs to capture complex temporal patterns and self-excitation dynamics within each mark are modeled using Hawkes processes. A semi cami--arametric generative model is introduced in (Zhu et al. 2019) for centio- event data by combining spatial statistical models with reinforcement learning. The advanced data collection techniques and online social media platforms produce complex event data and thus social network analysis now be used to inform solutions many societal issues (Bonchi et al. 2011). Many such
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processes of heterogeneous and complex events require multi-category MTPP- brsPed representation. The data integrity is also a major concern in social networks as many fake and misleading data is not uncommon (Muramudalige
al. 2019). In many disciplines, such economies, biological and social sciences, removal of non-verifin verifalie entries is crucial for maintaining the required data integrity, which in turn leads incomplete and small datasets. Various techniques introduced handle missing data in different contexts (Folch-Fortuny et al.,
2015 MacNeil Vroomen et al. 2016).
Generative adversarial networks (Goodfellow al. 2014) have become an alternative for data generation without extensive problem specific theoretical foundation or empirical verification (Yan) 2019). The initial GAN architecture (Goodfellow et al. 2014) is capable of capturing the exact distribution of continuous and complete data but cannot be used for learning the distribution of discrete variables (Choi et al.) 2017). The recent improvement in the form of Wasserstein GAN (Arjovsky et al. (017) is used to implement generative TPP models (Xiao et al. 2018). medGAN designed to learn the distribution of discrete features, such as diagnosis or medication codes, via combination of autoencoder and the adversarial framework (Choi et al. 2017). Adversarial probabilistic autoencoder which uses the GAN framework variational inference algorithm for both discrete and continuous latent variables. An aggregated posterior distribution of (()) on the latent code is defined with the encoding function (2(11) and the data distribution pa(x) as follows where denotes input sample
Autoencoder (AAE) (Makhzani et al. 2013)
<(2)= = /. ((2(x)p((x)dd
(1)
In general usage of AAE, represents consistent, discrete continuous data samples where almost all data points are captured or completed in given context. The challenge addressed in our paper apply an AAE for scattered and incomplete multi-category MTPPs generation using our proposed feature mapping techniques with a data approximation method. Details of such an AAE for sparse, incomplete, and multi-category MTPPs generation and feature mapping techniques are presented in Sections
and 5 respecttvvly
3 MULTTI-ATTEGORY MARKED TEMPORAL POINT PROCESSES
A marked temporal point process (MTPP) represents certain set of asynchronous stochastic discrete actions/events in continuous time (Upadhyay et al. 2018 Li et al. 2018). Due to the immense availability of heterogeneous and complex event data in recent years, is significant to model such complex events using multi-category MTPPs. multi-category marked point is denoted as follows.
(ti, cj)
time
Figure 1: A basic representation of a multi-category MTPP, marked point colors depict multiple categories a MTPP.
A marked point ezy is an event of category Gj occurring time t; shown in Figure I Tables in Appendix A illustrate categories (i.e., 0ÿ) in datasets, where these heterogeneous events exhibits complex dependencies and correlations. Usually, MTPP analysis deals with ensemble of marked temporal point processes (MTPPs). Multi-category MTPPs are described as follows. If the kth MTPP is HA and its marked points denoted as et He. Consider events (marked points) and m categories in the kth MTPP, then marked points are characterized as et = (fe, Cz) where E [1,m] and j E [1, m). Then,
ル- = (z), E H4: k E [1, where represents N number of multi-category MTPPs. However, without loss of generality, denote ety as Cij in the following discussion.
(2)
In some problem domains, i (time of occurrences) or j (categories) values may change rapidly and some categories may not be recorded frequently. More importantly, with many problems in
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Actual
MTTPs ci)
Generated casogoyoooyyy.o
Aupropaed posteior p(olfii))
e's digmtt
Pastin m eacppey Fricziir
Festur mexplin Decoddr
petho
parathi)
Encoder
Decocrr
pa(h))
Samples prior
disaibution
Discrininator
Real Fale??
Figure 2: Architecture of an AAE for sparse, incomplete, and multi-category MTPPs.
domains such social and behavioral sciences, not all marked points (Ezy) of MTPP are known or observable due to the limitations of information gathering process, confidentiality constraints, unverifiability, deception, etc. A notable aspect of our work, is the use of sparse, incomplete, and multi-category MTPPs where an actor (an MTTP) either did not carry out activities corresponding to certain event categories and marked points they carried them out, but such activities were not reported the reliable or permissible sources. address these challenges, we propose a feature mapping encoder and decoder which capable of capturing the sparseness and incompleteness of the data. The proposed feature mapping techniques consist of multiple steps including the calculation of cumulative probabilities for each category and a data approximation technique for incomplete data (briefly described in Algorithm|
More details of the feature mapping encoder and the decoder are
discussed in Section 5
3.1 MULTI-CATEGORY MTTP DATASETS
We evaluate the performance of our technique using real-world datasets from diverse range of domains.
Radicalization Dataset The Western Jihadism Database (Klausen al. 2020) has almost all the incidents terrorist actions committed in western countries including timestamps and yet does not consist of unconfirmed undiscovered activities that cause incomplete dataset. We 135 detailed pathways (multi-category MTPPs) of home-grown jihadists (Klausen et al. (0188) which have been extracted from radicalization trajectories of 335 known American jihadists Klausen et 2016) as our real data distribution which covers over 24 behavioral indicators (categories). Table Appendix A describes the categories the radicalization dataset.
in
Mimic III Dataset MIMIC III medical dataset (Johnson et al. 2016) is a large, freely-available database of clinical visit records of Intensive Care Unit (ICU) patients between 2001 and 2012. We only use the SERVICES data table. which describes the services that patients were admitted under. We extract 500 patient records as MTTPs across different service types (categories). Service types are described in Table 2 in Appendix
A
Stack Overflow Dataset Stack Overflow is question answering website, which attains badges to encourage user engagement and guide behaviors. We use publicly available archived dataset (Internet) Archive, 2020) related to data science. Only 285 records (MTTPs) across 32 badges are extracted for evaluations where the dataset is sparse, incomplete, and small. The details of the badges (categories) are shown in Table 3 (Appendix A))
ADVERSARIAL AUTOENCODER (AAE) FOR SPARSE, INCOMPLETE, AND MULTI-CATEGGRR MTPPs
Figure shows the adversarial autoencoder architecture for sparse, incomplete, and multi-category MTPPs. The actual and generated aulti-category MTPPs are depicted in a tree structure where a root represents actor of MTTP. Square nodes stand for marked points, ej denotes the jth category,
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and the value 22 edge (connects actor and marked point) denotes the ith time of occurrence. The general AAE only includes an autoencoder and a discriminator (Makhzani et al. 2013). but our proposed architecture consists of an additional feature mapping encoder and decoder capture characteristics of the sparseness and incompleteness of the data. The feature mapping encoder transforms sparse, incomplete, and multi-category MTPPs (H) to a cumulative distribution-bn -hased representation ((H), which enables generating incomplete multi-category MTPPs through an AAE. The feature mapping decoder is able rearrange the generated multi-category MTPPs ((H') the actual format of
MTPPs (H').
The autoencoder forces a compressed knowledge representation of the original input which recon- structs the same data distribution. Initially, the original data distribution of multi-category MTTPs Pa(H) is fed into the feature mapping encoder which outputs the feature-mapped data distributions (H)). Then, the feature-mapped data is sent to the encoder where it compresses the data to latent code vector z. (()))(H)) and p(p(H))=) stand for the encoding and decoding distributions respectively. q(=) represents the aggregated posterior distribution of hidden code which forms through the encoding function and the feature- mappeeddappppdd data distribution. An aggregated posterior distribution (q())) of the hidden code vector of autoencoder for sparse, incomplete, and multi-categon, MTPPs can be defined as
((2)= = -Long g(alo((0))a((((())46)0)))
(3)
The operating principle of the AAE is that the autoencoder attempts to minimize the reconstruction error while the adversarial network tries to minimize the adversarial cost. Two simultaneous phases, reconstruction phase and regularization phase take place in each mini batch during training. The re- construction phase relates to the autoencoder of the network, and it minimizes the data reconstruction error, often referred to the loss. The regularization phase relates the adversarial component of the network, where it minimizes the adversarial cost to fool the discriminator by maximally regularizing an aggregated posterior distribution (22) ) to the prior p(z) distribution.
The simultaneous training process forces the discriminative adversarial network into thinking that the samples from hidden code q(z) come from the prior distribution p(z) (Makhzani al. 2015). In these experiments, normal distribution is used as the arbitrary prior p(z). After the training process, the decoder defines deep generative model that maps the prior distribution p(2) to the feapure-mapped data distribution pa() and generates data samples d(H'' from the prior and decoding distribution. The data generation can be interpreted as
pa(o(H()) J. p()(H))))p(=)dz where ((H)) ((H).
The generated feature mapped data (o(H)) by the AAE is fed into the feature mapping decoder to transform the actual format of multi-category MTPPs (H(). Further details of the feature mapping encoder and the decoder are discussed in Section
5 FEATURE MAPPING
The major challenge of applying the AAE framework to multi-category MTPPs is that the data representation is structured; that is, each MTPP consists of set of marked points belonging to various categories. In addition, each MTPP starts from an initial point (in the radicalization dataset, the date of birth of an actor) and continues with exposed multi-category marked points at different times. To implement the AAE framework discussed in the previous section, we propose a feature mapping which essentially maps the complicated MTPPs into the Euclidean space. This is achieved by a set of preprocessing steps including data transformation for each category. The architecture of our proposed method is shown in Figure 2 and its functionality is summarized in Algorithm
There are two major components: a feature mapping encoder (steps 1-3) and a decoder (steps 5-6) and the data generation (step 4). In step 1, all the marked point times (f,) are transformed to the days (a,) based on the initial point of each actor and shifted to a same days range. As result, the updated marked points can be denoted eij- (aphifted cy). For each MTPP, the value 0 is assigned to those categories that do not occur. As explained earlier, the absence of a certain category in MTPP instance may be due to either that category not being associated with the MTPP, or
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Algorithm 1 Feature mapping & MTPP generation pipeline
Input: H. (real MTTPs), eG (t,, E H
Output: H'' (generated MTTPs), Eiy = (1, E
7t
Step Convert timestamps to days Cgy (a. (agifteed .cy)
Step 2 Replace with percentiles Eaj = (g)
Step 3 Data approximation technique for incomplete marks
Step 4 Data generation via AAE PH()(H)) - Pa()(H')) where l/g (g) E EH'
Step 5 Replace percentiles with actual values l/g (a, shifted .4))
Step Convert days to timestamps e/y (t,,,))
Guevent
ThAnhs
State loewar villane
90X
0:0
605
8.005
5
400
100
200
200
300
15.3
0.
23.8
50.0
1205
0.0
25.3
505
15.0
3003
Figure 3: (Inverse) percentile graphs for categories in radicalization dataset ('Convert date', 'Trauma', and 'Step towards violence'), )) In this example, Y-axis represents days (a.). Day O indicates the unavailability of marked points (eg: There are 70.37%, 80.74%, and 35.55% of unavailability of marked points for "Convert date', 'Trauma', and 'Step towards violence' categories respectively).
limitations of data collection, or its presence not being recorded. The (inverse) percentile graphs for three categories (Convert date, Trauma, and Step towards violence) in the radicalization dataset are depicted Figure To measure the dissimilarity between two marked points in the same category, the difference of their shifted time is sufficient. However, such time difference varies a lot across different categories. In step we propose to use the inverse percentiles instead. helps to overcome the effect of sparseness and incompleteness of the marked processes some extent. For instance, the shifted time of the marked point eij can be transformed using P. (a (aahifted) where Fr, is the inverse cumulative distribution function of the category Cj.
The inverse percentile distributions are shown in Figure 3 depict that there is a significance un- availability of marked points in categories. Therefore, unavailable marked points obtain higher percentile values which are sufficient to confuse the MTTP distribution. In step 3, we present a data approximation technique to further mitigate the effect of the sparseness and the incompleteness of the data by changing the percentile values only for unavailable marked points (where aj using uniform distribution. Pe, (0) denotes the percentile value of unavailable marked points in jth category. The percentile values (Pt)) of unavailable marked points are substituted by randomly generated values (e, where values are changed as follows. For percentile value of jth category ith time occurrence,
shifted 0)
Pc, (0)) from the uniform distribution Then, the percentile
Pgj
if a shifted # E.
Pg =
(5)
otherwise
After applying the data approximation technique. the updated marked points can be indicated as eg cy), Steps 1-3 describe the sequential steps of pre-processing encoder and produces feature mapped multi-category MTPPs @(H) as the input to the AAE (see
the feature mapping
Figure 2. The feature mapped multi-categon categoy MTPPs can be denoted as follows. The ktth feature mapped MTPP is Φ(H() and Cij E d(H(.), then
((H) = {eig (P)j. E d(Hx);k E [I,
where ((H) is N number of feature mapped multi-category MTPPs.
In step 4. feature mapped MTTPs d(?) are fed to the AAE and data similar to the actual data is generated. The details of statistical methods that inspect the similarity between the datasets and the

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10
64
Catogory ID (or)
ID Ioy
Canaaoy tb iCd
64
64
24
24
Category 1D (CO
Cetegary ID (CX)
Caoegory 10 (C4)
a) Actual trans. prob. matrix
5) Avg. generazed trane, prob. mabri
<) (Tt--al)
Figure 4: Conditional probability matrices for actual and generated datasets, and the difference. (radicalization data)
results are presented in the Section Let M denotes the number of MTTPs ((H'), that are generated by the AAE. Then, the generated MTTPs can be denoted as follows.
((H() = (d, = ( E (HH')); E [1.
Then, the feature mapping decoder (see Figure 2 applied transform generated percentile values to the actual multi-category MTPP format. In step 5, a generated percentile value of a marked point of jth category ith time occurrence P is converted to its day, based on the inverse percentile graphs in each category Fe, (Figure 3). and reshifted to the actual days range. Then, marked point is redefined as, Eij = (a4, Cj). In step 6, pre-defined or any distribution-bann -baed on the initial point can be utilized to convert days real timestamps (t²) of the marked points. The advantage is that, allows selecting any date range where provides flexibility to generate even future marked points based upon the requirement of the analysis. After the conversion, generated marked point (e(y) of jth category at the ith occurrence is denoted c/y (y)) The kth generated MTTP is H' and e/e H' k. can define the generated multi-category MTTP (H') as
= = cz) E H'i; []].
(8)
The introduced feature mapping techniques generate multi-category MTPPs similar the actual MTPPs. In Section we show the similarity between AAE-based generated and actual MTPPs for radicalization using different statistical measurements.
RESULTS
In our experiment, the AAE is configured for 10K epochs with 32 mini-batch sizes in the training phase. The MTPP generation runs for 100 times and yields 10K MTPPs in each run. A Keras Tensorflow codebase is used for the AAE implementation. The typical MTTP baselines like Reinforcement Learning, RNNs, Wasserstein GANs require significant amount of data to train network. Therefore, such techniques are not applicable our proposed approach. As the baseline, we compare the proposed data generation technique with Markov chain approach which was applied to the same dataset in (Klausen et al., 20185). compare with AAE-based generated MTTPs, we produce datasets using their conditional probability diagrams of the Markov chain by running 100 times and obtain 10K pathways each run. Conditional probability calculation is performed after applying the data approximation technique (step 3) described in Section 5 Here, the pre- rre-processed data o(H) used to calculate actual conditional probability which provides further validation on our proposed feature mapping techniques. In the same way, generated data o(H') by AAE (before enter the feature-mapping decoder) is utilized to calculate generated conditional probabilities.
Figure 4 depicts the conditional probability matrices for actual data (panel (a)), generated data (panel (b)). and their difference (panel (c)) for the radicalization data using a color map. In each matrix, cell (x, y) denotes the conditional probability p(y|æ) of category y given category æ. Here, the probability is calculated based on the marked points Eij = (tz, cj). The probability difference matrix
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highlights the accuracy and the robustness of our proposed generation method by showing that the real and generated conditional probabilities are almost the same for every pair of categories. The only noticeable difference arises in Category 24 (max val 0.35), which is due to the fact that "date of criminal action' is the last marked point for almost all observations. The marginal distributions for radicalization and mimic data in Figure 5 further corroborates the similarity of the actual and the AAE-based generated datasets. The generated marginals are calculated based on over 100 runs.
0.00
0.0
NarloW
Marooy
AAE
0.9
ART
0.25
8.15
2.05
8.05
0.0
20
Catagary
(a) Radicalization data
(b) Mimic data
Figure 5: Marginal distribution for each category: column sum for the conditional probability matrix; Real (green), Markov generated (orange), and AAE generated (red) data.
20.0
Markov
17.5
AAE
Percertage
20
5.-
2.5
0.0
15
25
Categery ID
Coteggoy ID
(a) Radicalization data
(b) Mimic data
Figure 6: Bar plots for the probability of occurrence for each category based on real (green), Markov (orange), and AAE (red) generated data. Error bars (blue) represent the standard error over 100 runs.
We further calculate the probabilities of occurrence for the categories described in Appendix A [ compares the percentages of categories in actual and generated datasets. The error bar shows the standard error (s.d./ /n where = 100) of each category and proves the robustness of the proposed multi-category MTPP generation technique. The 3rd (stackoverflow) dataset also performs the same in all experiments.
CONCLUSION & FUTURE WORK
We propose a novel multi-category MTPP generation technique using adversarial autoencoders for sparse, incomplete, and small datasets, where it is challenging to mimic an actual data distribution using existing techniques. The performance of our proposed method is demonstrated through real data examples. A cumulative distribution based preprocessing technique is introduced capture the sequence pattern of the categories and reduce the dominance of the unavailable categories. The statistical similarity between the generated and actual data is demonstrated via diverse descriptive statistics. Ongoing work includes extending to the data anonymization applications and applying our proposed multi-category MTPP generation technique to address data privacy concern..
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A APPENDIX
The multi-category MTPP datasets
1. Radicalization dataset
ID
Name
ID
Name
ID
Name
ID
Name
Convert Date
Rebellion
13
Dawa-Rea Real Life
19
Desire for Action
2 Disillusionment
Lifestyle Changes
14
Epiphany
20
Passive Support
Trauma
/dee/Oce
Peer-Immersion
Foreign Org.
4 Personal Crisis
10
Drop Out Date
16
Phy Training
22
Issues Threats
Soeking Information
Underemployment
Marriage Secking
Steps towards Violence
New Authority Figures
12
Dawa-Virtul
18
Socictal Discngagement
24
Date of Criminal Action
Table 1: Category IDs and category names in the radicalization dataset
2. Mimic III dataset
ID
Name
Description
CMED
Cardine Medical - for non-surgical cardine related admissions
Cardiac Surgery for surgical cardiac
MED
Medical general service for internal medicine
SURG
Surgical general surgical service not classified elsewbere
NSURG
Neurologic Surgical surgical, relating the brain
TRAUM
Trauma injury or damage caused by physical harm from an externa sourze
Table 2: Category IDs and category names in the mimic IIII dataset
3. Stack Overflow dataset
Question
Autubiographer
2 Enthusiast
10
Curious
Notable Question
Tumbleweed
Good Answer
11
Critic
Editor
Explainer
4
Excuvator
12
Popular Question
Necromancer
Commentator
5
Nice Question
13
Yearling
21
Custodian
Promoter
Rovival
Constitucut
Caucus
Teacher
Quorum
15
Informed
23
Enlightened
31
Organizer
Famous Question
Supporter
Table 3: Category IDs and category names in the stackoverflow dataset
11


Reviews:
[{"review_id": "HeGtEvLLnnA", "reviewer": "AnonReviewer3", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "Summary:\nThe authors propose a method for multi-category marked temporal point processes (MTPPs) generation with sparse, incomplete, and small training dataset. They apply Adversarial Autoencoder (AAE) and feature mapping techniques, which include a transformation between the categories and timestamps of marked points and the percentile distribution of the category.  The paper shows effectiveness and robustness of the proposed method by comparing with Markov chain approach on three datasets: Radicalization Dataset, Mimic III Dataset and Stack Overflow Dataset.\n\nStrength:\n1.\tThe paper is clear in general. Firstly, they define MTPP and multi-category MTPP. Then, the multi-category MTPP generation with sparse, incomplete, small training data problem is addressed.  The authors argue that it is a popular real-world problem where we only can access small and incomplete data.\n2.\tThe description of the overall method is reasonable. But more details can improve understanding.\n\nWeakness:\n1.\tThe authors should provide justification of choosing to use AAE in the work. In particular, why is AAE an attractive approach for MTPP? \n2.\t The authors mention: \"The typical MTTP baselines like Reinforcement Learning, RNNs, Wasserstein GANs require a significant amount of data to train a network. Therefore, such techniques are not applicable to our proposed approach. As the baseline, we compare the proposed data generation technique with a Markov chain approach which was applied to the same dataset in (Klausen et al., 2018b).\" The authors could try to apply Reinforcement Learning, RNNs, Wasserstein GANs with data filled by simple methods, to empirically validate that these methods are not suitable for incomplete, small data.\n3.\tIn feature mapping method, the authors could provide justification for converting marked point times t_ij to days a_i. Besides, the method to convert t_ij to a_i and examples are not provided. If this is a common preprocessing method in MTPP, the authors should cite the relevant work. Overall, Step 1 of Algorithm 1 is not clear. \n4.\tAt the data approximation technique (step 3 of the Algorithm 1), the author randomly chooses a probability for the appearance of an unobservable data point but there is a lack of explanations. Can the authors explain the reason of selecting from [0, Pcj(0)]?\n5.\tThe authors should provide more details of incomplete and small dataset, and compare with their method when training with full data. This is to understand that if generated data is still good when training with small dataset\n\n\n=============== \nafter rebuttal: I thank authors for the responses. After reviewing the authors' response and other reviewers' comments, I keep my original rating. \n", "extra_scores": {}, "extra_text": {}}, {"review_id": "A7ouY0w7wMb", "reviewer": "AnonReviewer1", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "This work studies the generation technique for multi-category MTPP using adversarial autoencoders for sparse and incomplete datasets. To address the sparsity and incompleteness, some pre-processing and post-processing methods are utilized to adapt the data to AAE.\n\nStrengths: The model setup is reasonable, and the idea is straightforward to understand. \n\nI recommend rejection of the paper for the reasons below.\n\nWeakness: The major concern is the contribution of the work is very limited. The generation framework is a combination of adversarial auto-encoder and feature mapping encoder (decoder), where the AAE part is completely same as the original work in [Makhzani et al., 2015]. In my eyes, the only contribution is the addition of the feature encoder and decoder. Although the author named it like that, the so-called encoder and decoder are in fact some heuristic pre-processing and post-processing (shift and normalization) of the raw data. \n\nSome specific concerns: the notation in Eq.(2) is confused. If c_j is defined as the category, then c_j should \\in [1,m] not j. I understand what the author means by the current notation. It is better to define e_i=(t_i,c_i) where i \\in [1,n] and c_i \\in [1,m]. \nIn algorithm 1, the steps 1-3 are some heuristic pre-processing of the raw data. Why do that? Why change the timestamps to days and scale it to a probability value? Any intuition behind this operation? My understanding is the raw data is shifted, scaled and normalized to [0,1]. Add some theoretical analysis why performing that pre-processing will help AAE handle the sparse and incomplete data. \nIn experiments, there is only one baseline model to compare with. Add more DNN-based generative baseline models will make the experiment more convincing. \nIn experiments, although the author claimed 3 real datasets, I did not see any experimental results of the 3rd (stackoverflow) dataset. \n\nTypo: above Eq.(5), significance-->significant", "extra_scores": {}, "extra_text": {}}, {"review_id": "5Ugsi6Eaam-", "reviewer": "AnonReviewer4", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "", "summary_of_the_review": "", "strength_and_weaknesses": "", "limitations_and_societal_impact": "", "review_text": "The paper is concentrated at dealing with the data missing problem of MTPP and applies an AAE for the “incomplete multi-categorical MTPPs”.  First, the problem description appears questionable. Point processes are a class of stochastic processes for modelling discrete event sequences in a continuous time domain. They are statistical models and have a well-defined mathematical meaning. The expression of “incomplete point process” is quite confusing. One possible reason is that the authors fail to distinguish between the model and the data. One can say “incomplete data” or “incomplete observations of a model”, but “incomplete model” is not acceptable unless properly defined. Therefore, the proposed method seems not specifically for point processes but for the sequential data. \n\nThe authors seem to misunderstand the difference between empirical distribution and probabilistic distribution. The probabilities, e.g., $p_d(\\mathcal{H})$, are actually empirical distributions of the time. Here the authors see the arrival time of the events as a random variable, and $t_{ij}$’s are independent samples of the random variable, which is unrelated to point processes. The percentiles used in the algorithm are essentially the cumulative empirical distributions of the arrival time. If point processes need to be considered here, the authors should define their probabilistic structures as they are probabilistic models, where the intensity function is often inevitable unless otherwise defined. I believe the confusing mathematical formulation should be considered as a fatal flaw.\n", "extra_scores": {}, "extra_text": {}}]

Author rebuttal:

Meta-review: This paper proposes a new generation technique for multi-category marked temporal point processes.  The paper was reviewed by three expert reviewers who expressed concerns for limited novel contributions, theoretical justification, and empirical evidence. The authors are encouraged to continue research, taking into consideration the detailed comments provided by the reviewers.
Decision: Reject