Addressing Mark Imbalance in Integration-free Marked Temporal Point Processes
Authors: Sishun Liu
KE DENG
Yongli Ren
Yan Wang
Xiuzhen Zhang
Venue: NeurIPS 2025 poster ()
Keywords: Marked Temporal Point Process
Data Imbalance
Primary area: general_machine_learning

Abstract: Marked Temporal Point Process (MTPP) has been well studied to model the event distribution in marked event streams, which can be used to predict the mark and arrival time of the next event. However, existing studies overlook that the distribution of event marks is highly imbalanced in many real-world applications, with some marks being frequent but others rare. The imbalance poses a significant challenge to the performance of the next event prediction, especially for events of rare marks. To address this issue, we propose a thresholding method, which learns thresholds to tune the mark probability normalized by the mark's prior probability to optimize mark prediction, rather than predicting the mark directly based on the mark probability as in existing studies. In conjunction with this method, we predict the mark first and then the time.  In particular, we develop a novel neural Marked Temporal Point Process (MTPP) model to support effective time sampling and estimation of mark probability without computationally expensive numerical improper integration. Extensive experiments on real-world datasets demonstrate the superior performance of our solution against various baselines for the next event mark and time prediction. The code is available at https://github.com/undes1red/IFNMTPP.

Addressing Mark Imbalance in Integration-free Neural Marked Temporal Point Processes
Sishun Liu RMIT University Melbourne, Victoria 3000
Ke Deng RMIT University
Melbourne, Victoria 3000 ke deng@rmit edu au
sishun. Beshun..iu@studeene rmit edu.
Yongli Ren
Yan Wang
RMIT University Melbourne, Victoria 3000
Macquarie University Syndey, New South Wales 2000 yan. wang@mq edu. au
yongli, reng rew..ed.........mmmmmmmmmm... au
Xiuzhen Zhang RMIT University Melbourne, Victoria 3000
xiuzhen, changrrmit edu. au
Abstract
Marked Temporal Point Process (MTPP) has been well studied to model the event distribution marked event streams, which can used to predict the mark and arrival time of the next event. However, existing studies overlook that the distribution of event marks is highly imbalanced many real-world applications, with some marks being frequent but others rare. The imbalance poses significant challenge to the performance of the next event prediction, especially for events of rare marks. To address this issue, we propose thresholding method, which learns thresholds to tune the mark probability normalized by the mark's 's prior probability optimize mark prediction, rather than predicting the mark directly based on the mark probability as in existing studies. In conjunction with this method, we predict the mark first and then the time. In particular, develop a novel neural MTPP model to support effective time sampling and estimation of mark probability without computationally expensive numerical improper integration. Extensive experiments real-world datasets demonstrate the superior performance of our solution against various baselines for the next event mark and time prediction. The code is available at https: : /gghhu....b/g/////g com com/undest undeesll redd/ IFNMTPP.
Introduction
Marked Temporal Point Process (MTPP) models event sequences observed from natural phenomena (e.g. earthquakes) or generated in human activities (c.g. retweets), where each event has a mark and an arrival time. MTPP has attracted the attention of the research community (see Shchur et al. [34] for a comprehensive review). Typically, MTPP models the joint Probability Distribution Function (PDF) conditioned history, denoted p² (m,t) t)'. where and t the mark and arrival time? of the next event, respectively. Some studies are on the Poisson Process [37] and Hawkes process
'The asterisk reminds the probability is conditioned on history, i.e., the events the past.
2The time relative to the most recent event
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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[32. 16, 27]. Recently, we have witnessed rapid growth of neural MTPP, which models p" (m, t) using neural networks [24, 28, 41, 26, 43], due to the capability of learning complicated temporal patterns and computational efficiency [34].
However, existing studies overlook that the distribution of event marks is highly imbalanced in many real-world applications, with some marks being frequent but others rare, as shown in Figure 1 (a). Similar other machine learning tasks such as classification, the imbalance poses a significant challenge to the performance of the next event prediction, especially for events of rare marks, which are often more important than other marks (e.g., the occurrence of a 7-magnitude earthquake or a retweet from celebrities). By mitigating the impact of mark imbalance, this study aims to improve the performance of MTPP for next event prediction.
Various techniques have been investigated to improve the prediction performance of rare classes in classifiers, including resampling the training set, cost-sensitive approaches, and thresholding [17, 39.. Training data resampling requires a proper resampling ratio. Cost-sensitive approaches require domain knowledge on the importance of different marks in setting the cost [17]. To have a solution with minimum external knowledge and assumptions, this study adopts thresholding, which learns thresholds to tune the mark probability normalized by the prior probability of marks.
Addressing mark imbalance for MTPP using thresholding is not straightforward. In addition to mark prediction, MTPP also needs predict the time simuitaneously. In most existing MTPP studies, the strategy is to predict the time based on p" (t), the probability that the next event time is t, and then predict the mark based on p" (m](), the probability that the next event mark is at the predicted time f. Our analysis and experiments show that this strategy is unsuitable for addressing mark imbalance with thresholding. If time changes, the mark probability conditioned time typically changes and thus requires different tuning thresholds, However, it is implausible to learn the tuning thresholds at all times. So, we propose strategy that first predicts the mark based on p" (m). the probability that the next event mark is m, and then predicts the time based on p" (4/m), the probability that the next event time is on the condition that the predicted mark m is the next event mark. Since the mark probability p" (m) is independent of time, applying thresholding to handle mark imbalance is easy.
required for modeling p² (m) and time prediction, respectively. Second, sampling p (t/m) ) to predict time is inefficient because it needs the Cumulative Distribution Function (CDF) of p" (t]mm. but the CDF does not have a closed-form expression. To overcome these challenges, we find a way to unify the two improper integrations into one. Then, we develop novel MTPP model, called Integration-free Neural Marked Temporal Point Process (IFNMTPP), to approximate the unified improper integration, rather than using a computationally expensive numerical method. With IFNMTPP, we can directly model p" (m) and the CDF of p" (4]m). The CDF makes drawing samples from p" (1/m) efficient for time prediction. Based on p" (m). the thresholding method can be applied to address the mark imbalance. Extensive experiments on real-world datasets demonstrate the superior performance of our solution against various baselines for the next event mark and time prediction. The contributions of this study are threefold:
However, strategy has its challenges. First, two different improper integrations
This study investigates the impact of mark imbalance on MTPP for next event prediction, which is overlooked by existing MTPP studies.
This study introduces the first solution to address mark imbalance in MTPP, which learns thresholds to tune the mark probability normalized by the prior probability of marks to optimize mark prediction, rather than predicting marks based on mark probability directly in existing studies.
This study finds a way to unify two improper integrations into one, and proposes a novel Integration-free free Neural Marked Temporal Point Process (IFNMTPP) to approximate the unified improper integration to support time sampling and estimation of mark probability, rather than using computationally expensive numerical improper integration.
2 Preliminaries
2.1 Marked Temporal Point Process
The Marked Temporal Point Process (MTPP) a random process whose embodiment a sequence of discrete events, S {(m,, 44) h=),,, where i Z+ is the sequence order, t; R is the time

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when the ith event occurs, my is the mark of the ith event. This study only concerns a finite set of categorical marks M {K,, ,z,... ,KIM) ) and the simple MTPP, which allows most one event at every time, thus I, < 1j if < j. The time of the most recent event is 4,, and the current time is 44 The time interval between two adjacent events is the inter-event time. We assume that an event with particular mark at particular time may be triggered by past events. Let Hi, be the history up to (including) the most recent event, and Hi- be the history up to (excluding) the current time [31]. With these definitions, we can define the Conditional Intensity Function (CIF) of MTPP:
P(m k,, t E lt, (+)
X (m = ky t) = A(m = k, t(H,)) =
lim Ar-+0
(1)
At
With X" (m, t). the conditional joint PDF of the next event can be defined:
p" (mm, - (m,,t)-((mn p(m, p(m,) X3 (m, = X2 (),,)))xp(( S. Σ T(,,T)))
(2)
NEM
where 7 means integrating over time. (t) is the conditional PDF that no event has ever happened up to time I since 4,- We explain how to obtain Equation (2) from Equation (1) in Appendix A.
The simplest form of MTPP is the homogeneous Poisson process whose CIF merely contains positive number, i.c., X (m = kg,t) = c. Another example is the Hawkes process [14], belonging to the self-exciting point process family. Its CIF is X" (m k; () 14 + Ejt,et (4, (n) where K; (t, ()) > 0 represents the excite from previous events. Because it meets the real-world intuition that the influence of occurred events always drastically drops as time passes, the Hawkes process is widely used backbone process in various models [4, 27, 16, 15]. Recently, we have witnessed rapid growth of neural MTPP, which models p" (m, t) using neural networks [24, 28, 41, 26, 43], due to the capability of learning complicated temporal patterns and computational efficiency [34].
Based on (m, t), the mark m and time of the next event can be predicted. Most existing MTPP methods predict when the next event will occur first, and then predict what the mark is at the predicted time. Specifically, the expected time of the next event is noc
_(=,, Tp" (r) where (1) ΣmEm M.M. p" (m, t). A numerical method is typically used to calculate by sampling N times, denoted as {t' N. from pt)
(t) following Thinning Algorithm (TA) or Inverse Transform Sampling (ITS) [31] so that = N E.'t t., After that, the mark of the next event at f is predicted: my arg max M p" (m, t). Some studies predict the mark of the next event m = arg max 1" (m) and then predict the time of the next event Fm = s Tp" (rlm)dr given the predicted mark [36].
2.2 Mark Imbalance
In real-world scenarios, the mark distribution can be significantly imbalanced, i.e., some marks are persistent and others are rare. The imbalance hurts the performance of the next event prediction, especially for rare marks, which are often more important than other marks (e.g., the occurrence of 7-magnitude earthquake). Let us consider two marks 2 and 22 where k is much more frequent than & in the observed event sequence. Suppose the next event is mark kzg Because h is much more frequent than k2, it is very likely that p" (k1,t) p" (k2, t) for most of the time t, including 0o 7= S EmEm p" (m, (in,))de r)dr. If so, k- will be predicted as the next event, but the real mark is k2-
Figure (a) demonstrates the mark frequency distribution in three datasets, Retweet, USearthquake, and StackOverflow (see details in Section 4). Figure (b) shows p" (m, t) for each mark m in these datasets. The envelope covers p" (m, t) of all instances in the datasets, and the line is the average of p" pm(m,t) f) across these instances. These figures show that p" (k1,,) t) > p" (k2,, t) for most of the time k1 is frequent and hy is rare. Table 1 shows the mark prediction performance achieved by SAHP [41], a neural MTPP model, on rare and frequent marks, respectively, measured by macro-F1. We can see that the prediction performance for rare marks is significantly lower than that for frequent marks.
3 Methodology
To improve the performance of MTPP for next event prediction, this study handles mark imbalance with thresholding method, which learns thresholds to tune the mark probability normalized by the
3

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0.3
0.4
Table 1: Mark predic- tion performance mea- sured by macro-Fl using SAHP [41] for rare and frequent marks on three real-world datasets.
Pregentoe
2
0.1
81
0.0 Tspes
Mark Types
Types
Retweet
Rare
0.0266:amm
(a) The frequency distribution of marks in Retweet, USearthquake, and StackOverflow (from left to right).
Marks
Freq
0.6183+oomm
Marks
Mark Marc
USearthquake
Marks
Rare
0.0037=aumi
Probaggiis
Mark
Nark
Mark
Nark
0.00
Freq
0.00
0.2196
Marks
Mark
0.05
StackOvertlov
Marks
Rare
0.08631amm
50000
Time
0.00
0.00
(b) The p" (m, for each mark in Retweet, UScartqquake, and StackOverflow (from left right).
Freq
0.2054.amm
Marks
Figure I: A demonstration of the mark imbalance in various datasets and its influence on p" (m, t).
mark's prior probability to optimize mark prediction. In conjunction with the thresholding method, the proposed method predicts the mark based on p" (m) and then, given the predicted mark m, predicts the time based on p" (t/m).
3.1 Next Event Mark Prediction with Thresholding
The mark prediction of the next event depends on accurately modeling p" (m) for each mark m, the probability that the mark the next event m, based on p" (m, t). The expression p" (m) is:
p" (m)
p (m, T)dr
In general, the frequent mark has high p² and the rare mark has low (mm). Inspired by the thresholding method [19, 7]. we normalize the probability for each mark by its prior probability and leam to tune improve the prediction performance for rare marks. Specifically, for mark m, calculate the ratio between the probability of m, p" (m), and its prior probability, 5 (m):
p" (m)
Tm p (m)
In this paper, p" (m) is the proportion mark m in the training set. p" (m) measures the probability that the next event mark is If m is more frequent than m', p" (m) is expected be higher than p" (m'). In contrast, rm evaluates whether p" (m) is higher relative to its own proportion. A rare mark having low (mm) may have high rm to signal high chance of being the next event mark. In this way, the chance of rare marks in the next event prediction rectified.
With I'm for every mark the next event mark prediction mp is obtained by thresholding method:
mp arg max (rm Cm.)
(5)
where em the threshold rm. We learn em. which maximizes the accuracy mp on the training set. Specifically, for each mark m, if we predict the next mark m when I'm > 6m and not when I' fms the learned 6 maximizes the score the pairwise comparison, i.e., mark m vs. all other marks. The technical details of the thresholding method in Appendix C.2.

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3.2 Next Event Time Prediction
After mark prediction, we predict the time. Let p" (f m) be the PDF of the next event time on the condition that the next event mark is m. Based on p" (tlm), we have:
fm (r
Tp" (rlm)dr
(6)
where Em is the expected time of the next event given the mark m.
3.3 Unifying Integral Functions
By the definition in Equation (3) and Equation (6), we must solve the improper integration of p" (m, 7) and rp" (p"(((mm for mark probability p" p"(m) and time prediction f, respectively. In general, improper integration does not have analytic solutions. This means that directly calculating p" (m) and fm following Equation (3) and Equation (6) is impossible. The solution is to approximate p" (m) and t. In partieular, is approximated the average of N samples {( JN from p" (4/m) as Equation (7).
N
I = (r(m) 2
1=1
To draw [ from p" (t)m). we use Inverse Transform Sampling (ITS), which takes the Cumulative Distribution Function (CDF) of the distribution that one wants to sample from. In our case, let F' (f/m) be the CDF of p" (t/m), i.e., (f = - p" (rIm)dT. (t(ma) refers to the probability of the next event happening in (t,, on the condition that its mark m. To draw a sample t' from p"(tt (t)m), we need to solve Equation (8).
(1 m)) =
where w' a random sample from uniform distribution (0, I). Since F= (1)m) is monotonic, Equation (8) is solvable by the bisection method. For each mark m, we obtain {())) yn by solving Equation (8) N times, which allows acquiring an arbitrary number samples for time prediction no matter rare frequent the mark m is. We can express F* (t|m) as follows:
F (+|mm)== = F* F'(m.)) p" (m)
Jr. ft (mm, r)dr ["d p" (m, r)dr
where (m) = f+t=0 p"(m,, r)dr is the probability that the mark of next event is m since 4, and F (m, t) = S1 p" (m, r)rr is the probability that the next event is mark m and happens in time interval (tt, We can further breakdown F" (m, t) shown in Equation (10).
('m,,t) S (m, F)dr (m, 1. +o0
p" (mmm, T)dr
p" (m,T)dd T)dr
(10)
For each mark m E M, we define I (m,t) t) as the integration starting from time f, any time after f t, to positive infinity:
(m, 1o1==]]] p² (m
(11)
(mm,, is monotonically decreasing as its derivative -p" (m, t) is always smaller than 0. We rewrite p" (m) in Equation (3) and F* (t/m) in Equation (9) using T' t):
(m) = [m,, 1z) F (f)mm) T [" 41) - (m,,
(12)
(13)
I (*m,ttt)
This means two improper integrations in Equation (3) and Equation (6) are now unified into one, i.e., [mmm, t), for modeling p" (m) and time prediction.
While drawing samples from a distribution can follow Thinning Algorithm (TA) or Inverse Transform Sampling (ITS) [31]. only ITS is suitable for integral function unification here. The basic idea in ITS is to simulate using CDF of p" (4)). Instead, Thinning Algorithm (TA) explicitly requires the expression of p" (t)mm), which is unknown typically.
5

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3.4 Integration-free Neural Marked Temporal Point Process (IFNMTPP)
With I* [mm,, t), we can model p'(m) and prediction time fm However, I* (m, is an improper integral with an infinite integration interval. Numerical methods are computationally expensive and can only be used to estimate integrals on finite interval. To avoid numerical methods, we introduce Integration- Segeee free Neural Marked Temporal Point Process (IFNMTPP) to approximate T (mm, l). For each mark m, IFNMTPP models the relationship between p" (m, 1) and its integral T ('m,t)
<mmm R1, (ms K
f(m Rr.
4 (mn k..
V Vennchy
+I" (m f..()
(()) 1/21 +
f(m f
k,
V Vm--h
Integral Estimation Module (IEM)
(mm = Rs.()
nnceasing
Nommaization
XN
App.
Full-cormecedd layers with non-negasiv weights
8
Vm-kaa
.I (mm kpn.f)
f(me - Ao.4)
fim f)
H4.
Encoder
b
Figure 2: Architecture of IFNMTPP where the history encoder is LSTM.
Figure sketches the architecture of IFNMTPP. For each mark m E M. we assign a vector Vm to prepare (m, 1) vm (t - 42) bm as input of the Integral Estimation Module (IEM), All parameters Vm are non-negative. IEM contains multiple fully-connected layers with non-negative weights, and monotonic-inccreasing and unbounded activation functions. Then, it ends with a monotonically decreasing function (xx) = 1 1/(1 + e*). So, IFNMTPP is intrinsically monotonically decreasing w.r.t. t. The outputs of IEM are scores s (m k1, f), (m (2.t)..... , (m kJMj t). The value of Emem s" (m, t) is not guaranteed to be 1. To produce the qualified probability distribution, they need to normalized. This is achieved by the Normalization module Figure that divides s" (m, t) by the partition function 7(Hr,) EmEm 8" (m, (4) for each m E M. Finally, IFNMTPP outputs 1 (m, t) for each mark m at the given time t:
s" sm,, t) (HH,,
(mm
(14)
With I' (m, t) and (m, ft), we have F* (f/m) by Equation (9) and Equation (10). Next, we calculate Im by drawing {(") from (4]m) following Equation (8). With the definition of IFNMTPP, we have the following proposition, with the proof in Appendix B, to guarantee that the model output is I' I'(m t):
Proposition 3.1. The oulput of IFNMTPP is D (m,, when its gradient is -p" (" (m, ().
We train IFNMTPP using the Negative Log-Likelihood (NLL) on event sequence S observed in time interval [to. T), where the time of the first event is t 2 to, and the time of the last event is T.
L = -logp(S) - Σ
log X" (mm(mtt
Σ (n,
(mSti)ES
to NEM
t Σ x((nT))dr)
Σ
(log X (m,,ti)
Σ (((,T))
J4-1 nEM
(ms
nEM
(15)
Σ
logp" (m,, t.) -log(1 Σ F (F,
(m..t)es
neMM
Σ (m.d)es
log (m;,t,) t,) log( Σ [*(n,T))
NEM
where p (m,,, 4) is the probability of the ith event conditioned on historical events. IFN- MTPP increases p' (m),t) where (m,,ty) E S are real events in event sequences. The term

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Table 2: Mark prediction performance measured by macro- Focro-F1/mmiro-F1 to evaluate thresholding and the prediction order of mark and time. The bold are the best values.
Retweet
SO
Tapbao
USeartqquke
M 0.4750 Lumes/00 jasess
0.1776 1177666mm00003337 Larnos 0.4190 0011900.mmme00044990000 junst
11.882/..mii003311188 jounzs
ours
M, 2=2010=amm:002200000
M, 0.6120 1012200:ummm00961222eeeee.
0.7441:aumeele
0.2773::ezzs0091188
M 0,4741=omzz00 100L-=mmm004438000uuu
0.3289 =0000
0.1214+60n2200.000 3009 +00003
Lime-mark-
with thresholddngg
M. 0.2000 wwtp::/www0000w0ooo/om 0.1023
juress
0.3054 wt07s/////00000mmmmmmm 0.02981ccoee:000
My 0.609---mmm0009590000orvv 0.2815==am2200.88885 -0880880000.08
0.7062+-nzsw0.7002-0oea
0.2436+602140099116
M 0.4269_ommmo0 http://oooo000000__eeeee0 i 0.12877.00m::0.55777 http:/0000777e_000e00 jureez
0.3968 1o.96%_omm
ours-
M. 00833--um:00003333-0mm 7.1065=+omm440.377666 300 =uurse
0.37599:omms/0077559
0.012
wo-Uhresholding
M, 0.66288
010000 0.2063:|jo::::0999990 (L00s
0.73111_mmcs007731111
0:25588:::::0004555555 jumm
0.4252=ammuu. 1815
0.0906+eomts//
+013355ommm000.334444444 0.1066+::x4000111 +0
time-mark-
w/o-thresholding
M. L0038/0000///0003333333 Laneyv
1.05667_.0mm:/0.221144
Lurees
0,2897
11997/ommm//058880 Lunser 1.000311omm20000144:33 1two://w000014omommoommmmo jomm
My 0.6208=-mmv00.997 a.000
0.2059:euss40991556:
0.2444+o0ms10 00
log(2 Emes I" (m, T)) is the survival term, which models no events after the last event i, in each event sequence until time T. In IFNMTPP, the expression of p" (mi, (4) is:
p (mm,, f,) a (m,, (4) 0t.
1 Os" (m4, (4) (m,,4)
(16)
Z(Hu) (f, t.) Öt:
Mei et al. [25] prove that an MTPP model converges to the true distribution when trained with the NLL loss defined in Equation (15). Combined with Proposition 3.1, IFNMTPP consistently estimates the true value of I (m, t).
4 Experiments
We run every experiment 5 times with different random seeds and report the mean and standard deviation (1 (I-sigma) of all results. The complete experiment settings are described in Appendix D.
Datasets Four real-world datasets include Retweet [42], StackOverflow(SO) [20], Taobao User Behavior Data(Taobao)) [2], and earthquake events over the Conterminous USUUSaart))aake) [38]. We split all marks of each dataset into two subsets, one containing frequent marks, denoted as My. the other containing rare marks, denoted as M,. M, n M, = Ø and M, U = M. The rare marks and frequent marks for each dataset are described in Appendix D.5.
Baseline Models* Our method, denoted as ours, uses IFNMTPP for predicting the mark of the next event, optimized with thresholding, then uses IFNMTPP to predict the time of the next event given the predicted mark. The first group of baselines includes: (i) t/otttrsssssoliinngggg to evaluate the effectiveness of the thresholding method. (ii) fime-mark-witee with-thresholding to evaluate the necessity to predict marks first for handling mark imbalance with thresholding. (iii) time-mark-w/d woo.rkwwwwotrrsshhddn www.-wtttthhhhoiiiiiii
same as second group of baselines evaluates thresholding against resampling. another classic technique to address data imbalance, including undersampling and oversampling. The third group of baselines includes existing MTPP methods. Since MTPP modeling has been well studied in the past decades, the state-of-the-arr methods demonstrate comparable performance. Among them, this study selects the most popular ones as baselines, including FullyNN [28]. THP [44], SAHP [41], AttHP [26], and Marked- LNM [36]. The details of these baselines available in Appendix D.4.
but mark prediction is not optimized with thresholding. The
Evaluation Metries We use macro-Fl and micro-F1, described in Appendix D.3.2, to evaluate mark predictions and use Mean Absolute Error (MAE), described in Appendix D.3.3, to evaluate time predictions on real- world datasets. The evaluation metries for mark and time are independent of each other. For each dataset, as discussed above, three sets M, M,, and M, are drawn from the original test set. Moreover, we evaluate the fidelity of IFNMTPP using five synthetic datasets. Experiment results on synthetic datasets (reported in Appendix E.2) demonstrate the high fidelity of IFNMTPP compared with other MTPP models.
RRetweet, StackOverflow, Taobao, and USearthquake are released under Apache-2.0 license[38). *Our codes will be released under MIT license.
7

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4.1 Experiment results
Impact of Thresholding on Mark Prediction For the mark prediction, we evaluate (i) the effec- tiveness of the proposed thresholding method by comparing ours with wyrss-/ooohrssolddie (ii) the necessity of the strategy to predict the mark first by comparing ours with The metric is macro-F1 and micro-F1, where the higher values indicate more accurate mark predic- experiment performs much better on rare and all mark prediction. ours also shows comparable performance on frequent mark prediction. It implies that the recall of frequent mark prediction is improved using thresholding.
with--titteeee wiith-ihressolding.
tions. The experimental results are reported in Table 2. Compared with ours-w/o-thie wursswootrressoldng ours
In Table 2, the performance of ours is better than time-mark- waitamarr-wwtttheeeeee with-thresholdingg on rare mark prediction on all datasets. To check whether the suboptimal performance of mark-withh-hrree to applying thresholding or not, we also compare time-mark mark-with withh-thresolliing with time-mar-we w/o- thresholding. The experimental results show that the performance of time-mark waat--aarr-wotaaaae w/oothhresholiig is lower than that of time-mark- seark-wwtt--heee wwth-wththeeeeee seath-ttreeholdin.. This indicates that predicting the mark first is more suitable for handling mark imbalance with thresholding.
is due
Time Prediction Performance For time pre- diction performance evaluation, we compare the time predicted using ours, i.e., based on (4)m)) and that using time-mark-with- thresholding, i.e., based on (t). The metric is MAE. Lower MAE means better. The ex- perimental results are reported in Table 3. We observe that predicting time based on p" (t]m) slightly outperforms that based on p" (t). The results indicate that the strategy to predict the mark first and then time also benefits the time prediction. The reason could be that I'm obtained by drawing samples from p" (t|m) is more spe- cific to the mark and thus tends to be more accu- rate compared to f obtained based on p" (t) for all marks.
Table 3: Time prediction performance to evaluate the order of time and mark predictions. The bold are the best values.
Retweet
SO
Taobao
UScarthquake
M 2515. s
0.6856:0m
ours
M, 3291 22zmee 4m49
0.6966
My 2198.7 (0006630.wer
g.2529
0.6713
time- mane-makk-oae
M 2504 0.64m =m64 0.2420 O 0.85 8516
with- M. 3223.2 3223.2-mmoss0.e 0.6515 soorr 0.2411 couus O. 0.7008 10007s
thresbolding My 2307.7=3 0.6095
0 I 1.2295
Table 4: Time prediction performance to evaluate thresholding vs. resampling. The bold are the best.
Retwett
SO
Taobao
UScarthquake
M. l 0.5212 0.3
0.6856=1100
ours
M, 3291, 2 0.4986
0.3385 -wr
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Thresholding vs. Resampling We compare the prediction performance of ours against re- sampling baselines oversampling and undersam- pling. As discussed in Section 1, resampling the training set and cost-sensitive approaches are two commonly used methods for handling data imbalance besides thresholding. According to López et al. [22], resampling the training set and cost-sensitive approaches are statistically equivalent. So, we focus resampling the training set only. The experiment results are reported in Table 5. We observe that ours consistently outperforms oversampling and undersampling. It is casy to see that the resampling ratio impacts the performance, but it is hard to figure out the correct ratio for different marks on different datasets.
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Table 5: Mark prediction performance to evaluate thresholding and resampling, measured by macro- Fl/micro-Fi F1, The bold are the best values.
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Oversampling
M. (002=-aomm0.115522o0a 0.04477-0021/03333340000
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Performance Comparison with Existing MTPP models
Table and Table report time predic-
tion performance and mark prediction performance, respectively, of ours and existing MTPP models,
8

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including FullyNN, THP, SAHP, AtNHH,, and Marked-LNM. Compared with existing MTPP models, ours demonstrates superior performance in both time prediction and mark prediction. For mark prediction, ours is the first MTPP model which addresses mark imbalance. For time prediction, the time for each mark m predicted by drawing samples from p" (f)m) based on 1 (m,,), t). The accurate approximation of I (m, t) leads to accurate time prediction. In particular, ours also outperforms Marked-LNN,, in time prediction. This demonstrates that modeling I (m, t) by neural networks is better than directly modeling p" (f)m) by the composition of log-normal distributions.
Table 7: Mark prediction performance to evaluate ours against existing MTPP models, measured by macro-F1/microo-1 The bold are the best values.
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5
Related Work
Marked Temporal Point Process Many MTPP studies specify a separate Conditional Inten- sity Function (CIF) X" (m, f) for each categori- cal mark m, based on which p² (m, 1) can be
Table 6: Time prediction performance evaluate ours vs. existing MTPP models. The bold are the best values.
formulated [10, 24, 44, 41, 12, 26, 29]. A more sophisticated intensity function [24, 44, 41, 26] can better capture the system dynam- ics but will require approximating the integral of X* (m,,) t) using a numerical method such as Monte Carlo. Recurrent Marked Temporal Point ProCess(RMTPP) [11] eludes numerical integral approximation as the CIF and its integral have closed form, which makes the log-likelihood easy to compute. Recent studies move away from directly modeling CIF. Shchur et al. [33] proposed an intensity-free solution, called Log- NormMix, to infer the density function p" (t) from a simple distribution such as the mixture of log-normal distributions. Omi et al. [28] pro- posed FullyNN to model the integral of CIF us- ing a neural network where CIF can be derived by differentiation, an operation computationally much easier compared with integration. All MTPP studies discussed so far predict the time of the
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next event first and then predict the mark. Recently, Waghmare et al. [36] proposes to model p" (m) using a classifier to predict the mark of the next event and modeling p" (4m) to predict the time of the event based on LogNorMMix.
9

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Recently, Yuan et al. [40] used a Denoising Diffusion Probabilistic Model (DDPM) to predict the next event the -patio-temporal point process. Lüdke et al. [23] developed Add-and-thin method for modifying event sequences sampled from a Poisson process to match a target distribution by adding or removing events. However, the mark of the spatio-temporal point process is continuous instead of discrete, and Add-and-thin is a temporal point process (TPP) model that does not consider marks. Therefore, these two approaches are out of the scope of our research.
Imbalanced Data Handling The techniques for handling imbalanced data, including data-level, algorithm-Ievel and classifier-Ievel approaches, are designed mainly for improving imbalanced classification tasks. The data-level approach is resampling the training set, including undersampling and oversampling [3]. Most existing resampling methods are based on the Synthetic Minority Over- sampling Technique (SMOTE) algorithm [13, 6, 5]. One benefit of data-level approaches is that they can cooperate with any classifiers. In contrast, algorithm-level approaches are more classifier-speciffe such as cost-sensitive methods [18, 21, 9]. The classifier-level method is also known as thresholding (or post-scaling) which learns thresholds to tune the obtained class probability [19, 7, 8, 35]. The effectiveness of resampling the train set is determined by the resampling ratio, but there is no easy way to figure it out for different classes on different datasets. The cost-sensitive approaches require domain knowledge regarding the importance of different marks to set the cost, but this is not always available [17]. To have a solution with minimum external knowledge and assumptions, this study adopts thresholding.
6 Conclusion and Limitation
Conclusion It is challenging for existing MTPP methods to accurately predict events of rare marks when the distribution of event marks is highly imbalanced. This is unacceptable in many applications if the rare mark is critical such as major earthquakes. This study introduces the first solution to address mark imbalance in MTPP. Instead of predicting mark based on mark probability directly as in existing studies, we learn thresholds to tune the mark probability normalized by the prior probability to optimize mark prediction. To achieve this goal, this study develops a strategy predict mark first and then the time by integrating two improper integrations into one and proposing novel Integration- -feee Neural Marked Temporal Point Process (IFNMTPP) to approximate the unified improper integration to support time sampling and estimation of mark probability, rather than using computationally expensive numerical improper integration. Extensive experiments on real-world datasets demonstrate the superior performance of our solution against various baselines in the next event mark and time prediction.
Limitation As the first effort to address the mark imbalance for MTPP, this study verifies the effec- tiveness of thresholding, but does not investigate (i) the opportunity to extend the thresholding method to incorporate domain knowledge, such as the importance of rare marks, and (ii) the effectiveness of resampling and cost- cest-sensitive approaches in this situation.
Broader Impact
This paper presents work whose goal is to advance the field of Machine Learning. Specifically, we want to reveal the mark imbalance to the MTPP community and propose relatively simple solution to inspire the development of more bias-aware MTPP approaches. There are many potential societal consequences of our work, none of which we feel must be specifically highlighted here.
Acknowledgement
This research is supported in part by the Australian Research Council (ARC) Discovery Projects DP20010144 and DP210100743.
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NeurIPS Paper Checklist
1. Claims
Question: Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope?
Answer: [Yes]
Justification: The contribution of this paper is first realizing the impact of mark imbalance to event predictions of MTPPs then devising an MTPP model and additional techniques to tackle this issue. They reflected in our abstract and introduction.
Guidelines:
The answer NA means that the abstract and introduction do not include the claims made paper.
The abstract and/or introduction should clearly state the claims made, including the contributions made in the paper and important assumptions and limitations. A No NA answer to this question will not be perceived well by the reviewers.
The claims made should match theoretical and experimental results, and reflect how much the results can be expected to generalize to other settings.
is fine to include aspirational goals as motivation as long as is clear that these goals not attained by the paper.
2. Limitations
Question: Does the paper discuss the limitations of the work performed by the authors?
Answer: [Yes]
Justification:
We have discussed the limit of our work in the main paper.
Guidelines:
The answer NA means that the paper has limitation while the answer No means that the paper has limitations, but those are not discussed in the paper.
The authors are encouraged to create a separate "Limitations" section in their paper.
The paper should point out any strong assumptions and how robust the results are to violations of these assumptions (c.g.. independence assumptions, noiseless settings, model sell-specfiiatiinn asymptotic approximations only holding locally). The authors should reflect on how these assumptions might be violated in practice and what the implications would be.
The authors should reflect the scope of the claims made, e.g. if the approach was only tested on few datasets or with few runs. In general, empirical results often depend on implicit assumptions, which should be articulated.
The authors should reflect on the factors that influence the performance of the approach. For example, facial recognition algorithm may perform poorly when image resolution low or images are taken in low lighting. Or speech-to-tex, system might not be used reliably to provide closed captions for online lectures because it fails handle technical jargon.
The authors should discuss the computational efficiency of the proposed algorithms and how they scale with dataset size.
If applicable, the authors should discuss possible limitations of their approach to address problems of privacy and faimesss.
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A The Conditional Joint PDF
This study concerns events with categorical marks. For mark m. define conditional intensity function X* (m, t):
(m ki; f) = 1(m ki t(Hee)
P(m k,, E [t, [t](H(-)
lim At-0
Al p(m = k,, E it,t + At) )
- lim
A1-0
P(Vj E Nt+,, & (41, 1),H,,) )1
(17)
p(m k, E 11,6+ H))
lim
26-0 P(vj E NN+,, ,4, & (4,, ()
p(m k, E [ HHu)
P(Vj E $ (4, 1) H.,)
where Hs, is the history up to (including) the most recent event, H. is the history up to (excluding) the current time, P(Vj E N+ tt (tt, H),) represents the probability that no event is observed in time interval (t,, t) given H4.
We denote Pm (tt. ()),) for the conditional probability that an event m happens in (t1, t2). Following the definition of simple TPP that most one event happens every timestamp t, the probability that no event occurs in (tz, t) is:
P(Vj N ty & (1H,))
Σ Pm ((ti, 1)())))
II (1- (((,)t))))) neM,ngf
MEM
P' ((ti,t)))H)
(18)
Σ
II (1((11,
1 Pa ((t t)(H4))
mEM
NEM
=1 - Σ F(m, - =1 Σ
F (mmmt)
mEM
mEM
where
((t,, Hlr)
('m, 1-PP ((t,, H),)
II wEM
(19)
The conditional joint PDF that the next event is and occurs in [t, t + dt) is:
p(m ki, [t, At) dF (m = Ku, t)
(20a)
dl
S pmm==k, [t,t+ At) dr F* ke,t) t)
(20b)
In this study. pmm, t). shorthand of p(m, t H2,)). is the formal representation of p(m k,,t t [1, 1,4+ + AH)) ). Note F* (m, 1) in Equation (19) is the probability that only one event happens in interval [t, + di) and the mark is m. This ensures the MTPP represented by p" (m, t) simple. By integrating Equation (20a) and Equation (18) in Equation (17), we have
px (m, = (m, t) - Σ (w,,
(21)
WEM
where EVEM (w, t) is calculated from the sum of Equation (17) over marker m:
F", 1) -xp(p- S: Σ (((n7))dT)
Σ
(22)
WEM
nEM
Then, we solve y" (m, l):
p' (m, (), /' Σ x),,T))d)
(23)
nEM
which is equivalent with Equation (2).
22

---

B Proof of the Proposition 3.1
Proof. The gradient IFNMTPP is -p" (m,, the function it learns take the form:
IFNMTPP(m, t)= - p' p' + C2
(24)
where C1 and C2 are two constants.
From IFNMTPP architecture, the Integral Estimation Module (IEM) consists of multiple fully connected layers with non-negative weights, and monotonic increasing and unbounded activation
functions. Then, it ends with monotonic decreasing function (xx Ite (as illustrated in
Figure 2). Since lim +oo o (z)
have:
S p" (m, C2 t1+
lim IFNMTPP(m, lim +
(25)
Substituting this into the earlier equation, obtain:
[" p" p'(m, [ore p 7"(m,
=
lim t-+
(26)
Substituting C2 back in Equation (24):
IFNMTPP(m,.) t) Jo. p" (m,,)) [ p" pm (m,,))d== f(a p" T (27)
Thus, the output of IFNMTPP is (*m, when its gradient is pp" pm,,
C Technical Details
C.1 Technical Details about IFNMTPP
In Appendix B, we show that IFNMTPP models (* t) when the activation function in the Integral Estimation Module (IEM) is monotonic increasing and unbounded. However, select tanh the activation function for training stability the implementation. tanh is monotonic but bounded, so lim IFNMTPP((m, t) C' > 0, making the implemented IFNMTPP slightly inaccurate. To mitigate this issue, we subtract the original output from the implemented IFNMTPP with C. The pseudo code is below:
for layer idx, layer enumerate (self.mlp)
# Hidden status at t for calculating \Gamma") * (m, t)
output layer (output) output self layer_yaerre wal.fllyyrr_cctacc aetivaaiotiviionnnoo (output)
Hidden status at t. for calculating \Gamma (m, t_) output_zeat zero = layer coutput_zeros output_zers zero self llayer_activation (output_zenn _errppuut_err)
11
if layer idx
12
# Hidden status at infinity for calculating \Gamma (m, +linfty) a. k.ka. C.
output_max torch, ones like (output))
self.tanh tanh parameter
14
else:
15
output_mat layer (output_maax _amppt___xx))
16
output max self self.layer activation (output_max) max)
18
probability inttryralnntalane from to inf self nonneg integral (-self. ( (output))
19
20
probability_ from_tttttt to inf self. nonneg_inteet (-self. aggregate (output_zznn
23

---

probability integral minimal self. self. nonneg integral (-self aggregate (
output (ypput_maxx)
23
24
Shift the output with с when required.
if self wewoveestaall....
pro.aaiiity. intgyyraatgrral from inf hewpabiiitt_inttgrreeeeee hntyyyinneggiiiinanaaa minimal)
Lnteerral_rrom__ terrom__ttt___e t__t_innf___ inf
27
28
republrtieed.prrbbbiitty integral from t1 to inf intaggrratyitteralla self epsilon
probability integral from tl to inf probability integral minimal) +
29
30
else:
inntberrrtt__ttgralll. from t t_to_int- inf probability integral from t to inf
32
33
regularized probability integral from tl to inf iaobability.integraaae ltt_l_frroooo_o__eeee____e + self epsilon
C.2
Technical Details about Thresholding
We use the classic threshold-tuning method [19, 7] to obtain the optimal 6m Specifically, the method obtains optimal by taking three steps for each mark m. In step 1, we draw the precision-recall curve of m. This curve shows us the precision and recall across all possible thresholds. In step since our target is to maximize the Fl score, which is the harmonic mean of the precision and recall, we compute the Fl score for all possible threshold using the precision and recall obtained the first step. In step 3, the threshold that yields the maximum Fl value is the Em The pseudo code is below:
For each mark $m \in M$ for i in range (num_ _
Step 1: draw the precision-recall curve. precision[i], recall[i], thresholds = precision recall curve ( training results events next == i) astype il)
# Step 2: Calculate the F1 score across all possible threshold.
fls (2 * precision[i] * recall(i]) (precision[i] recall(i]) fls np to num (fls)
10
11
Step 3: Pick the threshold that yields the maximal F1 value. ix = np. arg.aaxx (fis)
12
13
fi[i] = fis [ix]
threshold. append (thresholds [ix])
Once cm is known for each mark m E M, we predict the next mark as m if rm Em is maximum. Why? because such m will lead higher Fl value compared other marks.
Please note that we did not train a machine learning model like a neural network to obtain the optimal Gn- Conceptually,
predict by selecting with the maximum r., Cm (i.e., argmaz) and use the prediction loss to update the parameters of the model producing 6m However, argmaz is non-differentiable that backpropagation is not allowed to update model parameters. This is why we did not use this method.
D Experiment Settings
D.1 Real-world Datasets
We use the following four datasets to evaluate the performance IFNMTPP.
Retweet dataser[42] records when users Retweet a particular message on Twitter. This dataset distinguishes all users into three different types: (1) normal user, whose followers

---

count is lower than the median, (2) influence user, whose followers count is higher than the median but lower than the 95th percentile, (3) famous user, whose followers count higher than the 95th percentile. About 2 million Retweets are recorded, and the average sequence length is This dataset is released under the Apache-2.0 license[38].
SteckOverflow dataser(SO)[20] was collected from Stackoverflow", popular question- answering website about various topics. Users providing decent answers will receive different badges rewards. This dataset collects the timestamps when people obtain 22 badges from the website, and the average sequence length is 72.This dataset released under the Apache-2.0 license[38).
[2 records users' interactions on Taobao, an online shopping website from China. These actions include user clicking and buying online items, viewing reviews and comments, or searching for items. The average length of sequences in this dataset is 58, and 17 different marks are available. This dataset is released under the Apache-2.0 license[38].
USearthquake [38] records all earthquakes happened in the continental US from USGS This dataset has 7 marks, referring to earthquakes with magnitude 2.0 to 2.9, 3.0 3.9, 4.0 to 4.9, 5.0 to 5.9, 6.0 to 6.9, 7.0 to 7.9, or 8 and higher. The average sequence length is 16. This dataset is released under the Apache-2.0 license[38].
D.2 Synthetic Datasets
All synthetic datasets are generated so we do not have any licenses information for them. The code to generate all synthetic datasets comes from the codebase of [28] https: :/s:://o //gi thub. com com/omin tt any licenses.
which publicly accessible without
Hawkes process dataset Hawkes_1 was generated utilising Hawkes process:
A (t) μ40 + exp((b(tt
(28)
where = 0.2, 0.8, and = 1.0.
Hawkes process dataset Hawkes.2 was generated utilising Hawkes process:
(1) = 140 Σ exp(- by (t. (4) + a2 expe (4))
(29)
where 0.2, 0i
0.4, bi = 1.0, and b2 20.
Homogeneous Poisson process dataset was generated using the Homogeneous Poisson process where the conditional intensity function (+(t) is constant over the entire timeline.
This paper assumes X (t) =
Self-correct process dataset was generated using the temporal point process whose intensity significantly drops when an event happens. The definition of the conditional intensity function is (1) exp(u(( 4) aN) where N the number of occurred events, and μ and are fixed parameters. In our experiments, we set a = 1.
Stationary renewal process dataser was generated using stationary renewal process, which directly defines the probability distribution over time p" (t) as a log- normal distribution as shown Equation (30).
log² (4)
p (1la)
exp(
(30)
alv
20
where a is the standard deviation. Here, we set 1. With Equation (30) and TPP's definition, one could solve the corresponding intensity function by Wolframalpha":
-0. -0.79788 exp(-0.5 (o))
X²(1) -1 (0.707077
(31)
where er((x) 2 Jo exp(-13)dl.
hhape://taackOveffow.com/
https://www.oolfraaaapp...ommm
25

---

These five synthetic distributions cooperate with synthetic marking methods. This method generates discrete marks sampled from uniform distribution. All synthetic datasets have different marks,
D.3
Metries
D.3.1 Metrics for Synthetic Datasets
For synthetic datasets, the real distribution p" (m,, known. We can compare the generated (m,,() () against the real one. Most papers report the relative NLL loss, that is, the average of the absolute difference between - log 5 (m, t) and - log (m, t) on the observed events(if markers unavailable, log (t) and log p" (t)[28, 33). The lower relative NLL loss indicates better performance. However, such metric only evaluates performance at discrete events, which cannot gauge the overall discrepancy between 3 (m, t) and p" (m,t) t). So, this paper selects Spearman Coefficient and L distance to measure the discrepancy between 6* (m, t) and p" (m, t) over time, while we also report the relative NLL loss for reference.
Spearman Coefficient p( ((X,Y) Y) measures the relationship between two arbitrary value sequences, X and Y, defined by Equation (32). If X and Y are more correlated, p(X, ) is higher; lower otherwise. Compared with the Pearson coefficient which is suitable if the relationship between X and Y is linear, Spearman coefficient could better deal with non-linear relationships. Because most probability distributions of TPP are non-linear, we select Spearman coefficient.
p(X, Y) Cov(Rank(X) Rank(() E [
(32)
oxoy where ox and are the standard deviations of the values in sequence X = 12. ... .nn] and
Y (8i. Ve. }, respectively. We expect p between 6r (m, and p" (m, is close 1.
1 distance measures how different two arbitrary functions are interval [a,
gf())))= = J. lf(z) - g(x)ldx >
(33)
The smaller the L' distance is, the more similar f(x) and g(z) are. When L' (f 0, f(z) almost equals to g(x) in interval [a, b] for any f(x and g(x), or f(x) = g(x) at every x E [a, bj both f() and g(x) continuous.
D.3.2 Metrics for Real-World Datasets macro-F1 micro-F1
The macro-F1 value and micro-F1 value derives from the F1 value. Fl value has been widely used in almost all binary classification tasks because, compared with accuracy that might be fooled by false positives, Fl value takes accuracy and recall rate in its mind, where the model should correctly mark out positive samples for a better accuracy and negative samples for better recall rate. The definition of value is:
2 Acc Recall
F1
(34)
Acc + Recall
F1 value is only for the binary classification. Some researchers realise that a multi-class classification can be evaluated by decomposing the original classification task into multiple binary classification tasks and averaging every obtained Fl values. This is how macro-F1 devised. The expression of macro-F1 is:
M
macro-FF F1 =
Fim
(35)
M
m=1
where Fim is the F1 value for marker m. macro-F1 treats all classes equally, so it has been widely used in studies addressing class imbalance.
On the other hand, micro-Fl a global average of Fl values. Specifically, micro-Fl computes the sum of true positives, false negatives, and false positives over all classes then use Equation (34) to obtain the micro-F1. micro-F1 shows the overall performance regardless of the class.
If the mark prediction is based on (m) like our solution, macro-F1 and micro-F1 are independent of time prediction by nature. For baselines where mark prediction is based on p" (m/[() the mark involved in macro-FI and micro-F1 is conditioned on the real time of the next event to ensure that macro-F1 and micro-F1 are independent of the time prediction. Specifically, for each real next event (m ks, t') in test set, we compute macro-FI and micro-FI using the mark predicted from p(m[t').
26

---

D.3.3 Metrics for Real- World Datasets Mean Absolute Error (MAE)
The test dataset T' contains subset of real next events. We denote T Tm=k; C T as those real next events where the mark is k; E M. The number of events in Tm=k, is [m==k]- For each real next event (m k, t) E T m. are interested in the evaluation of time prediction. Consider all real next events in mm=k, MAEm=k; can be defined:
MAE
Σ
t Em=kil
(36)
[Tm=k (m=kk.0)E7=>k
The absolute difference It - fmmmky between real time t and the predicted time fm=n, for mark kG is the prediction error for the real next event (m = k., 1). Here, ky is not necessarily the predicted mark so that the time prediction evaluation is independent of mark prediction. MAEM, is the geometric mean of MAE across all marks in M,. M, can be M, My, or M,::
MAEM.
IM. II
MAEm=k;
(37)
KEM.
where M..] is the number of marks in M..
D.4
Baselines
D.4.1
Group One
The first group of baselines includes: (i) ours-woothhresholddng which is the same as our method but the mark prediction is not optimized with thresholding. The mark prediction returns the mark with the highest mark probability as described in Section 2. The purpose is to evaluate the effectiveness thiithhhrrhhhngg that uses IFNMTPP to predict the time of the next event first, and then predicts the mark with the same thresholding method as ours. To do that, we predict time f which is the mean of N samples from p" (t) Emem p" (m, t) first, and then modify p" (m) in Equation (4) p" (mz[F ()) for mark prediction following the procedure described in Section 3.1. The purpose is to evaluate the necessity to predict mark first for handling mark imbalance with thresholding. (iii) time-mark-wie www-ttheesooliiig mark prediction is not optimized with thresholding.
of the thresholding method. (ii) time-mark-with, mirk--wwth-hrreshlldde
same as time-mark-i witt wet---w-ththhhhohiing thresholding but
D.4.2 Group Two
The second group of baselines evaluates thresholding against resampling, another classic technique to address data imbalance, including undersampling and oversampling. For undersampling, we reduce the frequency of other marks to ensure that they have the same number of training events as the rarest mark. For oversampling, we increase the frequency of other marks so that they have the same number of training events the most frequent mark. For fair comparison, the backbone MTPP method IFNMTPP. After training completes for both baselines, the mark with the highest probability is predicted as the next event mark.
D.4.3 Group Three
The third group of baselines includes existing MTPP methods. Since MTPP modeling has been well studied in the past decades, the state-of-the- methods demonstrate comparable performance. Among them, this study selects the most popular ones as baselines. Four neural MTPP methods based on conditional intensity function (CIF) are FullyNN (28), THP [44], SAHP [41], and AtNHP [26]. Besides these four, another baseline Marked-LNNy [36] models p" (m) using a classifier to prediet the mark of the next event and models p² (t)m) using LogNormMix to predict the time of the event.
Fully Neural for the history embedding and inter-event time I. Then the density function is formu- lated to predict the time of the next event. We rewrote FullyNN in PyTorch[30] based on the official implementation available at https://g/ / thub com/ om t kahi ro/ which is publicly accessible without any license.
uses neural network to estimate the integral of X (t)
27

---

Transformer Hawkes Process(TH]][44] uses Transformer- based encoder to represent history as a hidden state The softplus-based intensity function and the density function are modelled to predict the time of next event. We reproduce this model in Py PyToochh based on the paper.
Self-Attentive Hawkes Process(SAHP)]44) is based on the same intuition as Continuous- time LSTM(CTLSTMM)224, which generalizes the classical Hawkes process by parameterizing its intensity function with recurrent neural networks. CTLSTM is interpolated version of the standard LSTM, allowwng us to generate outputs in a continuous-time domain. SAHP further improves performance by replacing LSTM with Transformers, Because the only difference between SAHP and CTLSTM is the history encoder, and SAHP has reported achieving better performance than CTLSTM, only evaluate SAHP in this paper. We reproduce this model in Py Torch based on the paper.
AnNHP[26] is another Transformer-bais based MTPP model. Different from THP and SAHP, where Transformer only encodes history, and the distribution is extracted from history repre- sentations using another deep module, AttNHP merges these two modules into one by di- rectly extracting the distribution from historical events using a Transformer. We use the code provided by the author at ht tt / /git hub. com/ wangaangaaaaaa 1anna3nn1/1.// 2aa.///aaapp////ea anaaaahhaaaaae andtt.
Marked LogNormMMxxMarreed (3M is an MTPP extension the LogNormMix(33) Marked-LNM also follows the MT paradigm by modeling p" (m) first, then using position of log Gaussian distribution to represent p (t]mm. To the best of our knowledge, Marked-LNM is the only MTPP approach predicting the mark of the next event first and then predicting the time of the event. However, Marked-LNM limits the form of p² (4/m) the composition of log Gaussian distributions. This setting introduces induc- tive biases into the model, which could compromise the model prediction performance. We implement this model in PyTorch by modifying the official LogNorrMix code https: /////ttttte //ggtttubb../////// com/ shohur moturrifii ifl-tpp. The official codes are released under the MIT license.
D.5 Data Preprocessing
We prepare synthetic and real-world datasets with normalization. For each dataset, normalization scales the time t of every event in each event sequence by the time mean i of all events in all event sequences and standard deviation as shown in Equation (38);
Escated
(38)
Normalization is useful when the time is relatively large, such as in the Retweet dataset. Table 8 shows how normalization is applied on various datasets.
Table 8: Data preprocessing.
Dataset
Retweet
StackOverflow
Taobao
USearthquake
five synthetic datasets
Normalization
Our work focuses on predicting when the next event will happen provided mark, especially rare mark. For each dataset, we classify if one mark is rare or frequent. The percentages of marks in each dataset are presented in Figure 3. Table shows which marks are classified as frequent and which are classified as rare.
Table 9: Rare marks and frequent marks.
Dataset name
The number marks
Rare Mark
Frequent Mark
Retweet
3
[2] 12, 13, 14, 15, 16. 17, 18. 19, 21]
[0, I]
StackOverflow
22
21. 2, 10. 11,
3, 8]
Taohao
17
10, 1, 3,4,, 4,5,
9,
10, 11, 12, 13, 14, 15]
[16]
USearthquake
7
13, 4, 5, 61
[0, 1, 21
28

---

0.5
0.4
Paremrac
0..3
Rargrrooo
83.3
Rencembat
2022
0.
0.1
0.1
6.1
0.0
0.0
Mark Types
Mark
Mark Types
Mark Types
(a) Retweet
(b) SverfOve
(c)
Taobao
(d) USearthquake
Figure 3: The frequency distribution of marks in real-world datasets.
D.6 Model Training
This section introduces the hyperparameter settings for all MTPP models used in this paper. The two values of "Steps" refer to the number of warm-up steps and total training steps, respectively. "BS" refers to batch size, and "LR" refers to the learning rate. Unless otherwise specified, train a model 3 times with different random seeds and report the mean and standard deviation of the results. We conduct all experiments A100-PCIE GPUs. All codes will be release upon acceptance under the MIT license.
repeatedly
internal cluster. It includes Intel Xeon CPUs and NVIDIA
For each mark we sample N times {(* m from F* (4]mm) to predict the time of the next event on condition that its mark is m by the inverse transform sampling:
F" m) =u
(39)
where u' is random sample from uniform distribution. The common practice samples u, from the standard uniform distribution u' ~ L( 1). MTPP allows &ę to go to positive infinity. When w' is very close to 1, the time drawn from Equation (39) will be meaninglessly big and cause a negative impact to the accuracy of evaluation. To avoid this, we let u² ~ (O, 0.9). We find this trick can significantly stabilize the sampling process.
D.6.1 IFNMTPP Configurations
Table 10 lists the hyperparameter settings for IFNMTPP. The three values of "MS" (model structure) refer the number of dimensions for history embedding h, the number of dimensions for vm and bm and the number of non-negative fully-connected layers in the IEM module, respectively.
Table 10: Hyperparameter settings for IFNMTPP.
Datasets
Steps
MS
BS
Retweet
[80,000, 400,000]
[32, 16, 4]
0.002
Stackoverflow
[40,000, 200,000]
[32, 32, 21
32
0.002
Taobao
[16,000, 80,000)
[32, 16, 4]
32
0.002
UScarthquake
[40,000, 200,000]
[32, 16,1 4]
32
0.002
Synthetic
120,000, 100,000]
[32, 64, 3]
32
0.002
D.6.2 FullyNN Configurations
Table 11 shows hyperparameter settings for FullyNN. The three numbers in column "MS" share the same meaning as those in IFNMTPP.
D.6.3 THP Configurations
Table 12 shows all hyperparameter settings for THP. The six values "MS" are the number of dimensions of the Transformer input vectors, the number of dimensions of the hidden outputs from an RNN which is on top of the Transformer encoder, the number of dimensions the vectors used by self-attentions (g. k, and v), the number of Transformer layers, and heads.
and bn always have the number of dimensions.
29

---

Table 11: Hyperparameter settings for FullyNN.
Datasets
Steps
MS
BS
LR
Retweet
[80,000, 400,000]
[32. 16, 4]
32
0.002
Stackoverflow
[40,000, 200,000]
[32, 32, 2]
32
0.002
Taobao
[16,000. 80,000]
[32. 16,
32
0.002
USearthquake
[40,000, 200,000]
[32, 16, 4]
0.002
Synthetic
[20,000, 100,000]
[32, 64, 31
32
0.002
Table 12: Hyperparameter settings for THP.
Datasets
Steps
MS
Retweet
180,000, 400,000)
[16, 16, 32,
8, 3. 3]
0.002
Stackoverflow
[40,000, 200,000]
[16, 16, 32,
8, 3.
32
0.002
Taohao
[16,000, 80,000]
[16, 16, 32,
8, 31
32
0.002
USearthquake
[40,000, 200,000]
[16, 16, 32,
8.
3, 3.
32
0.002
Synthetic
[20,000. 100,000]
[16, 32, 64,
16, 3, 41
32
0.002
D.6.4 SAHP Configurations
The hyperparameter settings for SAHP are available Table 13. The first six values of "MS" share the same meaning as those in THP while the last is the dropout rate.
Table 13: Hyperparameter settings for SAHP.
Datasets
Steps
MS
BS
LR
Retweet
180,000, 400,000)
[16, 16, 32, 8, 3, 0.11
32
0.002
Stackoverflow
[40,000, 200,000]
[16, 16, 32, 3, 3.1,
32
0.002
Taobao
[16,000, 80,000]
[16, 16,
32, 8, 3,
32
0.002
USearthquake
[40,000, 200,000]
[16, 16, 32,
3, 0.1]
32
0.002
Synthetic
120,000, 100,000]
[16, 32, 64,
3,4,,
32
0.002
D.6.5 AUNHP Contigurations
The hyperparameter settings for AttNHP available in Table 14. The first six values of "MS" share the same meaning as those in THP while the last is the dropout rate.
Table 14: Hyperparameter settings for SAHP.
Datasets
Steps
MS
BS
LR
Retweet
[80,000, 400,000]
[16, 16, 64, 8, 3, 0.0]
32
0.002
Stackoverflow
[40,000, 200,000]
[16,
64,
3.00
0.002
Taobao
[16,000, 80,000]
[16. 16,
64,
3,3,
0.002
USearthquake
[40,000, 200,000]
[16. 16, 64,
3. 3, 0.0]
32
0.002
Synthetic
120,000, 100,000]
[16, 16, 64,
3,
32
0.002
D.6.6 Marked-LNM Configurations
The hyperparameter settings for Marked-LNN, are presented in Table 15. The three values of "MS" the number of the dimensions of LSTM, the number of the dimensions of mark embedding, and the number of Gaussian distributions, respectively.
E
Additional Experiment Results
E.1 Performance of LFNMTPP for modeling p² (m,
For better and integration- solution, IFNMTPP models the improper integration of p" (m, t). The advantage has been verified by the experiment results reported in Table 6. IFNMTPP models
30

---

Table 15: Hyperparameter settings for Marked-LNM.
Datasets
Steps
MS
BS
LR
Retweet
180,000, 400,000)
[32, 32, 16]
32
0.002
Stackoverflow
[40,000, 200,000]
[32, 32, 16]
32
0.002
Taobao
[16,000, 80,000]
[32. 32, 16]
0.002
USearthquake
[40,000, 200,000]
[32, 32, 16]
32
0.002
Synthetic
[20,000, 100,000)
[32, 32, 16]
32
0.002
p"(m. t) at the same time while modeling the improper integration of p" (m, t). Compared to other existing MTPP models, the performance of IFNMTPP in modeling p" (m, is evaluated and reported in Table 16. The evaluation metric is NLL loss, the average of the - log p* (m, t) at the observed events. The lower NLL loss indicates better performance. We observe that IFNMTPP shows competent performance.
Table 16: Accuracy of p² (m, t) measured by NLL loss on real-world datasets. Lower is better.
IFNMTPP (Ours)
FullyNN
SAHP
THP
AttNHP
Marked-LNN
Retweel
6.3225=0.007 -0.0007
6.6437
10.379 6.19
6.0084
6.5292:+o.044
Stackoverflow
2.0540 0.0029
3.6984-10002
2.0713-0.0022
2.5565
2.081 11 1:00004
2.0992.10.014
Taobao
-0.7762
-0.0431 100ms
-1.2779
0.0421
140.91
-1.2190.1..0m6:
1.2720
USearthquake
1.3278 0.0533
1.8664
1.3544
0.0300
2.0744103174
1.4120
1.051
E.2 Evaluating Model Fidelity on Synthetic datasets
In this section, report the full result of model fidelity test synthetic datasets involving IFNMTPP and other baselines. The IFNMTPP consistently learns more accurate p (m, t) than other baselines supported by the lower L' distnace and higher Spearman coefficient. These findings suggest that predictions based on IFNMTPP should be more reliable and accurate.
Table 17: Model fidelity test performance on synthetic datasets; higher Spearman, lower T,1 and relative NLL loss better; the bold and underline indicate the best and the second-hest values, respectively.
Hawkes_1
Hawkes_2
Poisson
Self-correct
Stationary Renewal
IFNMTPP (Ours)
1.0000 0.00000
0.9999 1000000
1.0000 0.0000
0.9551 1000009
0.9999 1000000
Spearman
FullyNN
0,9952 100004
0,9963 +0.0002
0.9722
::00018
0.9477+10000
0.9998 #.00000
SAHP
0.9959 0047
0.9862+tn.0mm
0.9615 0225
0.9492:t0004
0.9990
THP
0.9266
0.7366220.05
1.0000
0.6969400017
0.0413
AttNHP
Marked-LNM
0.9924+00007
0.9971
0.9713
0.9491
0.9999:4.0000
IFNMTPP (Ours)
0.1480
0.3105-100432
0.01333:..000
0,5163
0.0654::000i
FullyNN
0.6225100227
10.088
0.2973 0.0000
1.1889
0.0710=0009
SAHP
1.0245+o.900 2966
4.7867++0270
0.6893+4o022
L.3333+00196
0.4872++a1188
THP
25.500+03364
0.0203
10.656+00065
9.9230#400451
AtNHH
Marked-LNN
0.69941100177
2.6446110063
0.3620
0.7406
0.0402:10.001
Relative NLL
IFNMTPP (Ours)
0.0000
0.0001
0.0000
0.0007+t0.0m1
0.0000=:0.000
FullyNN
40000
0.0008
0.0002
0.0015 0000
0.0000==0.000
SAHP
0.0086++0001
0.03 12312+40000 4.00195
0.0092++.0008
+000002
0.0072
0.0009
+.00034+00000
THP
0.2137
0,6663
0.0029
0.0000
:-0.0000
0.12622
0-0000
0.077 1 4-00000
AtNHΩ
0.8202++0000
0.0387+400144
0.263
+-0,0009
0.0820
(5620++0.000
0.3065 +000007
Marked-LNMM
0.0004-100000
0.0010+0.000
0.0006+400000
0.0018
0.0000=:4.00m
31

---

E.3 Comparing IFNMTPP with Marked-LNM and thresholding
Among baselines, only Marked-LNM follows the mark-time modeling paradigm and is suitable with thresholding. We therefore compare the mark prediction accuracy of our method and Marked- LNM under thresholding. The results, summarized in the table below, demonstrate that our method outperforms Marked-LNM in mark prediction. Note that we do not report time prediction results for this comparison, as the time prediction is unaffected by the method used for predicting marks. Nonetheless, as shown in Table 6, our method also achieves strong performance in time prediction.
Table 18: Comparison of IFNMTPP with Lognormmix thresholding four data sets, measured by macro-F1/miero-d The bold are the best values.
8.473) 1L0093 BL0053
0.1776=0.0631 B.126
0.4199-0.0044
0.132--0U071 (1.3199:0.00255
0.2011:2.0882 0.2010
0.1476=000011
/1.755N==000185
10.11110000
0.2799 0.0014 0.87740
H. 0.9181--00000
Mrkaed-LNM-
Hucsiooling
0.5477-0.000/
0.42 (13N76620008 0093
1330-0003//
0.1004-0.0004
0.1519-0,01//0 5662+000000
0.1121=000077
05055000055
44692400114
0.1558
10.79455000000
0.2271+000116)
0.119620000 DU7S -0.3438-000080
32


Reviews:
[{"review_id": "FKDkkhj0mq", "reviewer": "Reviewer_P9hy", "summary": "The paper claims to achieve high performance in discrete imbalanced temporal processes.", "questions": "..", "limitations": "How do these algorithms scale?", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 2, "strengths_and_weaknesses": "First, my understanding is that  the key idea of the paper is to predict separately for the different marks. If I understand right, this by itself does not help much, but makes it possible to generate samples for the rare marks, and then do thresholding.?\n\nThe way the authors approach the thresholding is to spend 3.3 to motivate a  complex NN  that includes  a History Encoder, plus a linear stages.  I didn´t quite get it  how you use the LSTM. Would it make sense to  try a regression based approach?\n\nResults:\nThere are maybe too many results. Namely, always presenting the three configurations makes it difficult to focus on the rare marks, Also, you have different notions of \"rare\" comparing USearthquake  an say TaoBao. It would be helpful to know basic dataset info such as size and marks frequency.\n\nMacro F1-Micro F1: why these two.  Why not Precision and REcall?", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate your review.\n\n> First, my understanding is that the key idea of the paper is to predict separately for the different marks. If I understand right, this by itself does not help much, but makes it possible to generate samples for the rare marks, and then do thresholding?\n\nResponse:\n\nWe respectively disagree. Our problem aims at predicting the time and mark of the next event, instead of predicting separately for different marks. Specifically, we investigate how to predict events of rare marks more accurately without sacreficing the prediction accuracy on frequent marks. Our solution includes the proposed IFNMTPP and thresholding.\n \n> The way the authors approach the thresholding is to spend 3.3 to motivate a complex NN that includes a History Encoder, plus a linear stages. I didn´t quite get it how you use the LSTM. Would it make sense to try a regression based approach?\n\nResponse:\n\nThe target function of IFNMTPP $\\Gamma^\\*(m, t)$  is defined conditional on the history sequence $\\mathcal{H}\\_{t\\_l}$. To properly capture this dependency, we first encode $\\mathcal{H}_{t_l}$ into a vector using an LSTM, which is well-suited for processing sequential data with temporal dependencies. This history vector is then fed into the Integral Estimation Module (IEM) of IFNMTPP to model $\\Gamma^\\*(m, t)$, ensuring that the conditional structure of the problem is preserved.\n\nGiven this formulation, we argue that using a standard regression-based approach to model $\\Gamma^*(m, t)$ would be inappropriate. Regression methods typically do not account for rich temporal structures or dynamic conditioning on sequences, which are central to the IFNMTPP framework. Therefore, a history-aware encoding followed by conditional modeling is both a principled and necessary design choice.\n\n> Results: There are maybe too many results. Namely, always presenting the three configurations makes it difficult to focus on the rare marks, Also, you have different notions of \"rare\" comparing USearthquake an say TaoBao. It would be helpful to know basic dataset info such as size and marks frequency.\n\nResponse:\n\nFirst, presenting the macro-F1/micro-F1 for all classes, rare classes, and frequent classes is widely used in research of data imbalanced classification. Following that, we evaluate performance of our model in terms of macro-F1/micro-F1 for all marks, rare marks, and frequent marks in our study. We agree that the result can be a lot, but they comprehensively present the mark prediction performance of our model.\n\nSecond, we present the basic dataset info, including dataset size and mark frequency, in Appendix C.5. We place it in the Appendix because we do not have sufficient space in the main paper.\n\n> Macro F1-Micro F1: why these two. Why not Precision and REcall?\n\nF1 value is the harmonic mean of precision and recall, defined as:\n$$\nF1 = \\frac{2}{\\frac{1}{\\mathrm{recall}} + \\frac{1}{\\mathrm{precision}}}\n$$\n\nF1 value is for binary classification. For multiclass classification, we have Macro F1 and Micro F1. Macro F1 is a macro-averaged F1 score of different marks, while Micro F1 is the harmonic mean of micro precision and micro recall. Macro F1 and Micro F1 have considered precision and recall of different marks, so there is no need to present precision and recall.\n\n> How do these algorithms scale?\n\nThe scalability to large mark vocabularies is an important concern. Training MTPP models on datasets with hundreds or thousands of marks is a well-known challenge, as it requires computing the integral of $\\lambda^*(m, t)$ for every mark, which incurs high computational cost.\n\nOur proposed IFNMTPP model is integration-free, which avoids this costly computation and makes it more efficient than many intensity-based baselines. However, as noted, the normalization operation across all marks could still become a performance bottleneck when the number of marks is very large. Therefore, while IFNMTPP is well-suited for applications involving dozens of marks—a common setting in many real-world scenarios—scaling to hundreds or thousands of marks remains an open challenge and a promising direction for future work."}, {"review_id": "wpqmAx69za", "reviewer": "Reviewer_nnTx", "summary": "This work studies the class imbalance problem in MTPP.\nThe authors propose a novel two-part solution: (1) a thresholding method that adjusts predicted mark probabilities by each mark’s prior frequency to better handle class imbalance, and (2) an Integration-Free Neural MTPP (IFNMTPP) model that predicts the next event’s mark first and then its time without requiring expensive numeric integration.", "questions": "- Why not learn thresholds on a validation set instead of the training set to prevent overfitting?\n- The Integral Estimation Module (IEM) enforces monotonicity via non-negative weights and activation functions. Does this constraint reduce the flexibility of IFNMTPP in modeling highly non-linear or non-monotonic dynamics?\n- The loss includes a log survival term. How sensitive is model performance to this term?", "limitations": "1. Thresholding is Post-hoc and Static\n2. A mark-specific monotonic neural network (Integral Estimation Module) must be trained for each mark.\n3. Applicability Limited to Discrete Marks", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Strengths\n- It is the first work on class imbalance in MTPPs.\n- The proposed thresholding method is an original adaptation of imbalance handling to sequential event prediction.\n- the IFNMTPP model introduces a new “integration-free” approach to neural point process modeling.\n- The method yields large improvements in rare event prediction (several-fold increases in rare-mark F1 over baselines) while maintaining or improving overall performance.\n\nWeakness\n- The IFNMTPP architecture introduces additional complexity (an LSTM history encoder plus a specialized IEM network for each mark) compared to simpler models. Training this model with the monotonic constraints could be challenging too.\n- The thresholds for each mark are learned to maximize F1 on the training set. This could potentially overfit those thresholds to training characteristics.\n- The study focuses on thresholding vs basic resampling. Other imbalance-handling strategies (e.g., cost-sensitive learning where rare events incur higher loss, or more advanced oversampling like SMOTE variants) are not explored or compared with.", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate your review.\n\n> Weakness: The IFNMTPP architecture introduces additional complexity (an LSTM history encoder plus a specialized IEM network for each mark) compared to simpler models. Training this model with the monotonic constraints could be challenging too.\n>\n> Q2: The Integral Estimation Module (IEM) enforces monotonicity via non-negative weights and activation functions. Does this constraint reduce the flexibility of IFNMTPP in modeling highly non-linear or non-monotonic dynamics?\n>\n>Limitation: A mark-specific monotonic neural network (Integral Estimation Module) must be trained for each mark.\n \n \nResponse:\n \nFirst, IFNMTPP does not need a dedicated LSTM history encoder plus a specialized IEM network for each mark, as the reviewer said. As shown in Figure 2, we only have one LSTM providing history information to all marks, and one IEM calculating the value of $\\Gamma^\\*(m, t)$ for all marks in one forward propagation.\n \nSecond, IFNMTPP must be monotonic. Note IFNMTPP is used to model $\\Gamma^\\*(m, t)$, the integration of the joint distribution $p^\\*(m, t)$ from time $t$ to infinity. Clearly, the integration decreases when $t$ increases. So, IFNMTPP must be constrained monotonic. \n\nFinally, the monotocity of IFNMTPP can be easily guaranteed by fully-connected layers of non-negative weights, the monotonic-increasing activation functions, and a monotonically decreasing function $\\sigma(x) = 1/(1 + e^x)$, as stated in line 181-183 in section 3.4. The monotonic-increasing activation functions and $\\sigma(x)$ are easy to implement. As for fully-connected layers with non-negative weights, we only need to rewrite the ```forward()``` function of the ```nn.Linear``` module as follows:\n \n```python\n    def forward(self, inputs):\n        weight = self.weight > 0\n        weight = self.weight * weight.float()\n        self.weight.data = torch.clamp(weight, min=self.eps)\n        return F.linear(inputs, self.weight, self.bias)\n```\nwhere ```torch.clamp``` will ensure that no negative number exists in the weight of the ```Linear``` module.\n \n> Weakness: The thresholds for each mark are learned to maximize F1 on the training set. This could potentially overfit those thresholds to training characteristics.\n>\n> Q1: Why not learn thresholds on a validation set instead of the training set to prevent overfitting?\n \nResponse:\n \nWhen developing the solution, we were aware that the thresholds fit the training dataset well but may not generalize effectively. However, we would like to emphasize that validation data cannot assist in this case. Typically, during training, a model's performance is evaluated on both training and validation sets. While training loss steadily decreases, validation loss may initially drop and then rise if overfitting occurs. However, as discussed in the last paragraph of Appendix B, we cannot train a model like a neural network to directly optimize thresholds due to the non-differentiable nature of the argmax operation.\n \nInstead, our thresholding method follows [19,7], which determines the optimal threshold for each mark using the training data. Specifically, for each mark $m$, all training events get a probability. These events are then sorted by the probability, and there is a threshold between each pair of consecutive probabilities. For a given threshold, we predict an event as having mark $m$ if its probability exceeds the threshold, and not $m$ otherwise. We compute the F1 score for each possible threshold and select the one yielding the highest F1 as the optimal threshold for that mark.\n \nIn theory, one could evaluate different combinations of thresholds across all marks using validation data. However, this approach is impractical for overfitting detection due to (i) the exponential growth in the number of combinations and (ii) the absence of a well-defined analogue to typical model overfitting behavior (i.e., validation loss increasing after an initial decrease), as threshold tuning is a discrete, non-parametric process.\n \n> Weakness: The study focuses on thresholding vs basic resampling. Other imbalance-handling strategies (e.g., cost-sensitive learning where rare events incur higher loss, or more advanced oversampling like SMOTE variants) are not explored or compared with.\n \nResponse:\n \nFirst, Section 4.1 (line 254) of our paper explains why cost-sensitive approaches are not included in our comparison. As noted by Lopez et al. [22], resampling methods and cost-sensitive approaches are statistically equivalent. Therefore, by comparing with resampling methods, we effectively cover the evaluation of cost-sensitive strategies as well.\n \nSecond, while SMOTE is a well-known oversampling technique, it is not applicable to our problem. SMOTE works by generating synthetic samples for minority classes to balance the dataset. However, applying SMOTE to a multivariate temporal point process (MTPP) would require an MTPP model capable of generating samples conditioned on a specific mark. To the best of our knowledge, no such MTPP model currently exists. This is why SMOTE is not considered in our study.\n \n> Q3: The loss includes a log survival term. How sensitive is model performance to this term?\n \nResponse:\n \nThe loss function in Equation (12) is widely used in MTPP research. For clarity, we present its derivation below:\n\n$$\nL = -\\log p(\\mathcal{S}) = -\\sum_{(m_i, t_i) \\in \\mathcal{S}}{\\log\\lambda^\\*(m_i, t_i)} + \\int_{0}^{T}{\\sum_{n \\in M}{\\lambda^\\*(n, \\tau)d\\tau}}\n$$\n\n$$\n= - \\sum_{(m_i, t_i) \\in \\mathcal{S}}{(\\log\\lambda^\\*(m_i, t_i)} - \\int_{t_{i-1}}^{t_i}{\\sum_{n \\in M}{\\lambda^\\*(n, \\tau)d\\tau})} + \\int_{t_l}^{T}{\\sum_{n \\in M}{\\lambda^\\*(n, \\tau)d\\tau})}\n$$\n\n$$\n= - \\sum_{(m_i, t_i) \\in \\mathcal{S}}{\\log p^\\*(m, t)} - \\log(1 - \\sum_{n \\in M}{F^\\*(m, T)})\n$$\n\n$$\n= - \\sum_{(m_i, t_i) \\in \\mathcal{S}}{\\log p^\\*(m, t)} - \\log(\\sum_{n \\in M}{\\Gamma^\\*(m, T)})\n$$  \n\nHere, all events occur within the time interval $[0, T]$. The term, $\\log(\\sum_{n \\in M}{\\Gamma^\\*(m, T)})$, is a log survival term derived from the definition of $p^\\*(m,t)$, which represents the conditional density and is the modeling objective in MTPP. \n\nImportantly, this survival term is not a regularization parameter—it cannot be omitted or tuned as a hyperparameter. Excluding it would render the loss function logically incorrect, as it would violate the mathematical formulation of the conditional likelihood in temporal point processes. Therefore, this term is essential for maintaining the theoretical soundness of the model.\n \n> Limitation: Thresholding is Post-hoc and Static\n \nResponse:\n \nThe reviewer may be concerned that the thresholds might become ineffective if the true distribution $p^\\*(m, t)$ of the data shifts. In our work, $p^\\*(m, t)$ is modeled by the MTPP based on historical data. If the MTPP model successfully captures such distributional shifts during training, the predicted probabilities—and thus the derived thresholds—will adapt accordingly. However, if the model fails to capture the shift, the thresholds will remain outdated. Therefore, the adaptability of the thresholds ultimately depends on the MTPP model’s ability to reflect changes in the underlying distribution. In this sense, it is more appropriate to discuss adaptive mechanisms in the context of MTPP modeling rather than thresholding itself, which is beyond the scope of our paper.\n\n> Limitation: Applicability Limited to Discrete Marks\n \nResponse:\n \nOur problem definition specifically focuses on marked temporal point processes (MTPPs), which model events associated with discrete marks. MTPP with dicrete marks is a well-established framework, with substantial prior research as summarized in Shchur's review [34]. Our paper addresses the rare mark prediction problem within this framework, and therefore, our scope is intentionally limited to discrete marks. We do not consider this a limitation of our work, but rather a deliberate and well-justified modeling choice aligned with the goals of our study."}, {"review_id": "hC16UJ3mi2", "reviewer": "Reviewer_iCwh", "summary": "This paper proposes a new modeling approach for marked temporal point processes with the intentions of mitigating the impact that imbalance in mark frequencies has on downstream mark prediction. This is done through a combination of two techniques: (i) a proposed MTPP architecture that is integration free through directly parameterizing mark-specific survival functions with monotonic networks, and (ii) by applying a thresholding method when predicting next marks in a sequence to help account for frequency imbalance.", "questions": "1. The model proposed probably most resembles the Fully-NN model, which the paper does compare to. I do think the paper does warrant a more in depth comparison in the methodology between these two given their similarities. It is worth noting though that the Fully-NN model was not designed to model marks as it was just a pure TPP model. How then was this model used to compare with in the experiments?\n2. If my understanding is correct, the thresholding is applied after the model is initially trained using the log-likelihood objective. From the experiments, it is clear that the thresholding seems to have some positive impact in correcting for mark imbalance. Do you have any potential thoughts on how these lessons could be incorporated into the training of the model directly, to potentially allow for better predictions out of the box without having the transform the distribution post-hoc?", "limitations": "yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n1. Mark imbalance is a real problem that is common in many datasets, so explicitly targeting this as a problem is well motivated. I also do appreciate that that is the primary focus of the paper as well, compared to say presenting the work as a generic MTPP model (which it admittedly is) and then over index on the next event prediction metrics after the fact.\n2. The model presented takes advantage of a clever reformulation of the typical joint distributions that define MTPPs, allowing for direct targets to parameterize to avoid approximating integrals during training. \n3. Empirically the method does appear, on average, to perform well and achieves the improvement in next mark prediction that it aimed for.\n\n**Weaknesses:**\n1. I felt that the technical details surrounding the proposed model (sections 3.3, 3.4) were a bit lacking in detail and explanation. These sections could have benefited a lot from more text concerning what equations represented and how they pieced together. \n2. The empirical results shown established that within the proposed model, thresholding was superior for next mark prediction compared to no thresholding, time then mark prediction (w/ and w/o thresholding), over-sampling, and under-sampling. It also shows that the proposed model with thresholding is in general superior in performance compared to other modeling baselines. Importantly, what it does not show is whether the improvement over baselines is primarily due to the proposed model or thresholding. To have a proper comparison, an additional ablation should be done to apply thresholding (when applicable) to the baseline methods -- at least for some of the experiments as this can understandably be a large undertaking.\n3. A minor note, but the empirical results presented in the paper largely consisted of tables of numbers which can be hard to parse at times. Some visualizations of them could go a long way towards improving the readability of the experiments section.", "was_revised": true, "final_justification": "I believe this paper to provide a meaningful contribution towards an under-evaluated topic in MTPPs. While the authors did address the points I raised, I do think the paper would require a good bit of editing to tighten up the messaging and properly showcase their contributions. As such, I will keep my score as-is with hopes of seeing this work accepted, if not here then shortly thereafter in the future after further polishing.", "rebuttal": "We appreciate your review.\n\n> Weaknesses: I felt that the technical details surrounding the proposed model (sections 3.3, 3.4) were a bit lacking in detail and explanation. These sections could have benefited a lot from more text concerning what equations represented and how they pieced together.\n> \n> A minor note, but the empirical results presented in the paper largely consisted of tables of numbers which can be hard to parse at times. Some visualizations of them could go a long way towards improving the readability of the experiments section.\n\nResponse:\n\nAfter carefully reviewing section 3.3 and 3.4, we will add the following content in the final version. \n\n- present the formulas of $F^\\*(m|t)$ and $p^\\*(m)$ based on $\\Gamma^\\*(m, t)$ as follows:\n$$\nF^\\*(m|t) = \\frac{F^\\*(m, t)}{p^\\*(m)} = \\frac{1}{\\int_{t_l}^{+\\infty}{p^\\*(m, \\tau)d\\tau}}\\int_{t_l}^{t}{p^\\*(m, \\tau)d\\tau} = \\frac{\\Gamma^\\*(m, t_l) - \\Gamma^\\*(m, t)}{\\Gamma^\\*(m, t_l)}\n$$\n$$\np^\\*(m) = \\int_{t_l}^{+\\infty}{p^\\*(m, \\tau)d\\tau} = \\Gamma^\\*(m, t_l)\n$$\n\n- explain the loss function (Equation 12) in details as follows:\n\nThe loss function is widely used in MTPP research. For clarity, we present its derivation below:\n$$\nL = -\\log p(\\mathcal{S}) = -\\sum_{(m_i, t_i) \\in \\mathcal{S}}{\\log\\lambda^\\*(m_i, t_i)} + \\int_{0}^{T}{\\sum_{n \\in M}{\\lambda^\\*(n, \\tau)d\\tau}}\n$$\n\n$$\n= - \\sum_{(m_i, t_i) \\in \\mathcal{S}}{(\\log\\lambda^\\*(m_i, t_i)} - \\int_{t_{i-1}}^{t_i}{\\sum_{n \\in M}{\\lambda^\\*(n, \\tau)d\\tau})} + \\int_{t_l}^{T}{\\sum_{n \\in M}{\\lambda^\\*(n, \\tau)d\\tau})}\n$$\n\n$$\n= - \\sum_{(m_i, t_i) \\in \\mathcal{S}}{\\log p^\\*(m, t)} - \\log(1 - \\sum_{n \\in M}{F^\\*(m, T)})\n$$\n\n$$\n= - \\sum_{(m_i, t_i) \\in \\mathcal{S}}{\\log p^\\*(m, t)} - \\log(\\sum_{n \\in M}{\\Gamma^\\*(m, T)})\n$$  \nHere, all events occur within the time interval $[0, T]$. The term, $\\log(\\sum_{n \\in M}{\\Gamma^\\*(m, T)})$, is a log survival term derived from the definition of $p^\\*(m,t)$, which represents the conditional density and is the modeling objective in MTPP. This survival term is not a regularization parameter—it cannot be omitted or tuned as a hyperparameter. Excluding it would render the loss function logically incorrect, as it would violate the mathematical formulation of the conditional likelihood in temporal point processes. Therefore, this term is essential for maintaining the theoretical soundness of the model.\n\n> Weaknesses: The empirical results shown established that within the proposed model, thresholding was superior for next mark prediction compared to no thresholding, time then mark prediction (w/ and w/o thresholding), over-sampling, and under-sampling. It also shows that the proposed model with thresholding is in general superior in performance compared to other modeling baselines. Importantly, what it does not show is whether the improvement over baselines is primarily due to the proposed model or thresholding. To have a proper comparison, an additional ablation should be done to apply thresholding (when applicable) to the baseline methods -- at least for some of the experiments as this can understandably be a large undertaking.\n\nResponse:\n \nFour of the baselines—FullyNN, SAHP, THP, and AttNHP—are popular intensity-based MTPP models that follow the modeling paradigm of $p^\\*(t)$ followed by $p^\\*(m|t)$. That is, they first model the event time distribution $p^\\*(t)$ to predict the next event time and then predict the mark distribution $p^\\*(m|t)$ conditioned on the predicted time. As discussed in Section 1 (paragraph starting at line 40), this paradigm is not suitable for addressing mark imbalance via thresholding, which motivates our alternative modeling paradigm of $p^\\*(m)$ followed by $p^\\*(t|m)$. This formulation naturally supports thresholding on the mark prediction step and has been empirically validated, as shown in Table 2.\n\nAs a result, we do not apply thresholding to the four intensity-based baselines. However, we are still able to compare our method without thresholding (denoted as “ours-w/o-thresholding” in Table 2 for mark prediction and Table 3 for time prediction) against these four baselines (Table 7 for mark prediction and Table 6 time prediction). The results show that our method outperforms the four baselines even without the use of thresholding.\n\nAmong all baselines, only Marked-LNM follows the mark-time modeling paradigm and is suitable with thresholding. We therefore compare the mark prediction accuracy of our method and Marked-LNM under thresholding. The results, summarized in the table below, demonstrate that our method outperforms Marked-LNM in mark prediction. Note that we do not report time prediction results for this comparison, as the time prediction is unaffected by the method used for predicting marks. Nonetheless, as shown in Table 6, our method also achieves strong performance in time prediction.\n\n|                     |       | Retweet                        | SO                             | Taobao                          | USearthquake                   |\n|---------------------|-------|--------------------------------|--------------------------------|---------------------------------|--------------------------------|\n| **ours**            | $M$     | **0.4750±0.0033** / **0.4394±0.0093** | **0.1776±0.0030** / **0.6376±0.0026** | **0.4190±0.0104** / 0.7499±0.0151 | **0.1382±0.0071** / 0.3189±0.0125 |\n|                     | $M_r$    | **0.2010±0.0082** / **0.2010±0.0082** | **0.1476±0.0041** / **0.4530±0.0026** | **0.3987±0.0108** / 0.7558±0.0185 | 0.0339±0.0051 / 0.1111±0.0098 |\n|                     | $M_f$    | **0.6120±0.0013** / **0.9612±0.0021** | **0.2795±0.0014** / **0.8974±0.0042** | 0.7441±0.0060 / 0.7441±0.0060 | **0.2773±0.0215** / **0.9181±0.0102** |\n|Lognormmix + thresholding| $M$ | 0.4228±0.0014 / 0.3876±0.0093 | 0.1121±0.0007 / 0.4469±0.0124 | 0.1558±0.0623 / **0.7945±0.0060** | 0.1198±0.0078 / **0.3438±0.0035** |\n| | $M_r$ | 0.1730±0.0033 / 0.1730±0.0033 | 0.1004±0.0004 / 0.3527±0.0065 | 0.1181±0.0653 / **0.8318±0.0019** |  **0.0393±0.0004** / **0.1740±0.0074** |\n| | $M_f$ | 0.5477±0.0004 / 0.8687±0.0005 | 0.1519±0.0017 / 0.5662±0.0209 | **0.7589±0.0133** / **0.7589±0.0133** | 0.2271±0.0169 / 0.6810±0.0427 |\n\n> Q1: The model proposed probably most resembles the Fully-NN model, which the paper does compare to. I do think the paper does warrant a more in depth comparison in the methodology between these two given their similarities. It is worth noting though that the Fully-NN model was not designed to model marks as it was just a pure TPP model. How then was this model used to compare with in the experiments?\n\nResponse:\n\nYes, the original FullyNN is a TPP model that does not support marks. To adapt FullyNN as a baseline for marked TPP models, we modify the input to the \"Cumulative Hazard Function Network\" (as shown in Figure 1 of the FullyNN paper) by replacing the single time input $\\tau$ with a time vector $\\tau = [\\tau_1, \\tau_2, \\cdots, \\tau_k]$, where each $\\tau_i$ corresponds to the time associated with mark $k_i$. Accordingly, the output of the \"Cumulative Hazard Function Network\" is extended from a scalar to a vector $\\Phi = [\\Phi(\\tau_1), \\Phi(\\tau_2), \\cdots, \\Phi(\\tau_k)]$. The gradient $d\\Phi/d\\tau$ is the intensity function for each mark. We will include this description in the final version.\n\n> Q2: If my understanding is correct, the thresholding is applied after the model is initially trained using the log-likelihood objective. From the experiments, it is clear that the thresholding seems to have some positive impact in correcting for mark imbalance. Do you have any potential thoughts on how these lessons could be incorporated into the training of the model directly, to potentially allow for better predictions out of the box without having the transform the distribution post-hoc?\n\nResponse:\n\nAt present, we do not have an effective approach for training a rare-mark-aware MTPP model that outperforms simple thresholding. However, we consider this an important problem and are actively exploring potential solutions."}, {"review_id": "vRQJLDLMyK", "reviewer": "Reviewer_cXr5", "summary": "The work tackles a practical but under-explored problem—class-imbalance in Marked Temporal Point Processes (MTPPs)—and proposes a neat pipeline that (i) predicts the mark first with per-class F1-optimal thresholds, then (ii) predicts the time using an integration-free neural model that directly approximates a unified tail integral.  Empirical gains on four datasets are convincing, but several methodological assumptions and scalability questions remain unresolved.", "questions": "Please refer to the \"weaknesses\" section above.", "limitations": "Please refer to the \"weaknesses\" section above.", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "Strengths\nPractical relevance: Rare marks often correspond to critical events (e.g., large quake), yet are poorly handled in existing MTPPs; the paper addresses this gap head-on.\nConceptual simplicity: Thresholding at the probability level leaves the generative time model untouched, avoiding the negative side-effects of resampling or cost-sensitive losses on continuous-time likelihood.\nIntegration-free inference: The unified-integral trick yields a truly quadrature-free model, leading to faster inference and simpler implementation.\nComprehensive evaluation: Four real-world datasets, ablations on thresholding, mark-first vs. joint prediction, and synthetic studies on integral approximation.\n\nWeaknesses \n1.Independence assumption may be too strong. The key factor enabling thresholding is assuming p(m | H_t) is independent of Δt.  Yet many domains exhibit mark–time dependence (e.g., “long silence → rare fault”).  The paper does not measure this dependence nor analyze its impact when violated.\n\n2.Static thresholds under distribution drift. F1-optimal thresholds are learned offline once. In streaming settings where class priors evolve (common in social and medical data), static thresholds can quickly become sub-optimal. No adaptive mechanism is discussed.\n\n3.Scalability to large mark vocabularies. All datasets have ≤ 17 marks.  Threshold search cost is O(|M|·S) and the integral network stores per-class parameters. Feasibility for hundreds or thousands of marks is unclear.\n\n4.Lack of theoretical error bounds. IFNMTPP approximates \\Gamma(m,t) with a monotone network, but no approximation error or convergence analysis is provided. It is therefore hard to judge robustness on long horizons or extreme marks.\n\n5.Baseline fairness. The study compares against resampling but omits cost-sensitive loss baselines that are strong for imbalance problems. Without them, the advantage of thresholding may be overstated.\n\n6.End-to-end performance not fully reported. The paper reports MAE conditioned on the true mark and separately macro-F1 for marks. It would be more informative to provide joint metrics (e.g., time MAE using the predicted mark) to quantify error compounding.", "was_revised": true, "final_justification": "Thanks the authors for their comprehensive and thoughtful response to my feedback. I decide to raise my score to 4.", "rebuttal": "We appreciate your review.\n\n> Independence assumption may be too strong. The key factor enabling thresholding is assuming $p(m | H_t)$ is independent of Δt. Yet many domains exhibit mark–time dependence (e.g., “long silence → rare fault”). The paper does not measure this dependence nor analyze its impact when violated.\n\nResponse:\n\nWe respectfully disagree with the claim that our model makes an \"independence assumption.\" While $p^\\*(m)$ is the marginal distribution of $p^\\*(m, t)$ and thus does not depend on $t$, this alone does not imply that $m$ and $t$ are independent. According to the definition of independence, $m$ and $t$ would be independent only if $p^\\*(m, t) = p^\\*(m)p^\\*(t)$, which is not the case in our model. Instead, we factor the joint distribution as $p^\\*(m, t) = p^\\*(m)p^\\*(t|m)$, as shown in Equations (3) and (6). This formulation preserves the dependence between mark and time via the conditional distribution $p^\\*(t|m)$. Therefore, our approach does not assume independence between mark and time.\n\n> Static thresholds under distribution drift. F1-optimal thresholds are learned offline once. In streaming settings where class priors evolve (common in social and medical data), static thresholds can quickly become sub-optimal. No adaptive mechanism is discussed.\n\nResponse:\n\nIt is true that thresholds may become ineffective if the true data distribution $p^\\*(m, t)$ shifts. In our work, $p^\\*(m, t)$ is modeled by the MTPP based on historical data. If the MTPP model successfully captures such distributional shifts during training, the predicted probabilities—and thus the derived thresholds—will adapt accordingly. However, if the model fails to capture the shift, the thresholds will remain outdated. Therefore, the adaptability of the thresholds ultimately depends on the MTPP model’s ability to reflect changes in the underlying distribution. In this sense, it is more appropriate to discuss adaptive mechanisms in the context of MTPP modeling rather than thresholding itself, which is beyond the scope of our paper.\n\n> Scalability to large mark vocabularies. All datasets have ≤ 17 marks. Threshold search cost is O(|M|·S) and the integral network stores per-class parameters. Feasibility for hundreds or thousands of marks is unclear.\n\nResponse:\n\nWe would like to clarify that the StackOverflow dataset in our experiments contains 22 marks. \n\nWe agree that scalability to large mark vocabularies is an important concern. Training MTPP models on datasets with hundreds or thousands of marks is a well-known challenge, as it requires computing the integral of $\\lambda^\\*(m, t)$ for every mark, which incurs high computational cost.\n\nOur proposed IFNMTPP model is integration-free, which avoids this costly computation and makes it more efficient than many intensity-based baselines. However, as noted, the normalization operation across all marks could still become a performance bottleneck when the number of marks is very large. Therefore, while IFNMTPP is well-suited for applications involving dozens of marks—a common setting in many real-world scenarios—scaling to hundreds or thousands of marks remains an open challenge and a promising direction for future work.\n\n> Lack of theoretical error bounds. IFNMTPP approximates $\\Gamma(m,t)$ with a monotone network, but no approximation error or convergence analysis is provided. It is therefore hard to judge robustness on long horizons or extreme marks.\n\nResponse:\n\nThe reviewer may be concerned that the gradient of IFNMTPP is $-p^*(m, t)$, and questions why IFNMTPP is able to learn the cumulative tail probability $\\Gamma(m, t) = \\int_{t}^{+\\infty} p^\\*(m, \\tau) , d\\tau$. We next address this by analyzing how IFNMTPP is trained and what it learns.\n\nWe use Maximum Likelihood Estimation (MLE) to train IFNMTPP, a continuous neural network whose gradient with respect to time is $-p^\\*(m, t)$. The training loss is the negative log-likelihood (NLL) of $p^\\*(m, t)$. Mei et al. (2020) have shown that training with NLL leads to an unbiased MTPP model, meaning the model will learn the true distribution $p^\\*(m, t)$ under ideal conditions.\n\nSince IFNMTPP is designed such that its gradient is $-p^\\*(m, t)$, the function it learns must take the form:\n$$\n\\mathrm{IFNMTPP}(m, t) = -\\int_{C_1}^{t}{p^\\*(m, \\tau)d\\tau} + C_2\n$$\nwhere $C_1$ and $C_2$ are two constants. \n\nFrom IFNMTPP architecture (lines 181–183), the Integral Estimation Module (IEM) consists of multiple fully connected layers with non-negative weights and monotonic increasing, unbounded activation functions. It terminates with a monotonic decreasing function $\\sigma(x) = \\frac{1}{1 + e^x}$ for each mark. Since $\\lim_{x \\to +\\infty} \\sigma(x) = 0$, and the unbounded activations ensure the IEM’s hidden state diverges as $t \\to \\infty$, we have:\n$$\n\\lim_{t\\rightarrow+\\infty}{\\mathrm{IFNMTPP}(m, t)} = \\lim_{t\\rightarrow+\\infty}{-\\int_{C_1}^{t}{p^\\*(m, \\tau)d\\tau} + C_2} = 0\n$$\nSubstituting this into the earlier equation, we obtain:\n$$\nC_2 = \\lim_{t\\rightarrow+\\infty}{\\int_{C_1}^{t}{p^\\*(m, \\tau)d\\tau}} = \\int_{C_1}^{+\\infty}{p^\\*(m, \\tau)d\\tau} \n$$\nSubstituting $C_2$ back in:\n$$\n\\mathrm{IFNMTPP}(m, t) = \\int_{C_1}^{+\\infty}{p^\\*(m, \\tau)d\\tau}-\\int_{C_1}^{t}{p^\\*(m, \\tau)d\\tau} = \\int_{t}^{+\\infty}{p^\\*(m, \\tau)d\\tau} = \\Gamma^\\*(m, t)\n$$\nThus, IFNMTPP always learns the true value of $\\Gamma(m, t)$, given that it learns the true density $p^*(m, t)$ through MLE. This theoretical guarantee is a key strength of our method.\n\nMei, H., Wan, T., & Eisner, J. (2020). Noise-Contrastive Estimation for Multivariate Point Processes. In H. Larochelle, M. Ranzato, R. Hadsell, M. F. Balcan, & H. Lin (Eds.), Advances in Neural Information Processing Systems (Vol. 33, pp. 5204–5214).\n\n> Baseline fairness. The study compares against resampling but omits cost-sensitive loss baselines that are strong for imbalance problems. Without them, the advantage of thresholding may be overstated.\n\nResponse:\n\nSection 4.1 (line 254) of our paper explains why cost-sensitive approaches are not included in our comparison. As noted by Lopez et al. [22], resampling methods and cost-sensitive approaches are statistically equivalent. Therefore, by comparing with resampling methods, we effectively cover the evaluation of cost-sensitive strategies as well.\n\n> End-to-end performance not fully reported. The paper reports MAE conditioned on the true mark and separately macro-F1 for marks. It would be more informative to provide joint metrics (e.g., time MAE using the predicted mark) to quantify error compounding.\n\nResponse:\n\nWhen designing our evaluation, we considered the option of measuring \"time MAE using the predicted mark.\" However, we believe this is not a valid evaluation metric. A proper metric must isolate the effect of the variable being. This rule is called *ceteris paribus*, meaning all other influencing factors must be held constant. In the context of MTPP models, the predicted mark directly influences the predicted time through $p^\\*(t|m)$. As different models may predict different marks, time errors computed based on these varying predicted marks are not directly comparable. This violates the *ceteris paribus* principle and renders \"time MAE using the predicted mark\" an invalid metric for evaluating time prediction.\n\nIn contrast, \"MAE conditioned on the true mark\" is a valid and widely accepted metric because the true mark is the same across all models, ensuring fair comparison. This principle also underpins existing evaluation practices in MTPP literature, where time prediction is evaluated via MAE between real and predicted times (from $p^\\*(t)$), and mark prediction is assessed via accuracy or NLL conditioned on true times.\n\nIn our study, we also use negative log-likelihood (NLL) to evaluate the joint modeling of $p^\\*(m, t)$. This provides a unified metric that reflects the model’s performance across both time and mark dimensions simultaneously."}]

Author rebuttal:

Meta-review: Following the final round of reviews, the paper received one borderline reject and three borderline accept recommendations. The reviewers recognized the significance and novelty of the work, which focuses on developing Marked Temporal Point Process (MTPP) models to address class imbalance, a common issue in real-world datasets. The paper proposes a thresholding method in which class-specific thresholds are learned to maximize the F1 score on the training data. This approach demonstrated strong performance across several MTPP datasets. Reviewers appreciated the empirical results but expressed concerns regarding the sensitivity of the method to the choice of thresholds. They also noted that the proposed architecture introduces additional complexity compared to existing models. The authors’ rebuttal addressed several of these concerns effectively and had a positive influence on the reviewers’ overall assessment. Although some limitations remain, the Area Chair concluded that the paper's strengths outweigh its weaknesses and therefore recommended acceptance.
Decision: Accept (poster)