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REVIEW 3 major objections 6 minor 28 references

An Uncertainty-Aware ED-LSTM for Probabilistic Suffix Prediction

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Probabilistic suffix prediction—sampling many futures from an uncertainty-aware LSTM—can beat the single most-likely suffix and gives calibrated remaining-time distributions.

desk verdict Useful application-level combination of known uncertainty techniques, but the headline calibration claim is contradicted by the paper's own PIT plots. read the letter →

arxiv 2505.21339 v2 pith:5MD2PJJQ submitted 2025-05-27 cs.LG cs.AI

Henryk Mustroph , Michel Kunkler , Stefanie Rinderle-Ma This is my paper
classification cs.LGcs.AI
keywords probabilisticsuffixpredictionbusinessprocessmonitoringuncertaintyquantificationMCdropoutaleatoricencoder-decoderLSTMremainingtimePITcalibration
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that suffix prediction for business processes should return a distribution over possible futures rather than a single most-likely suffix. It builds an uncertainty-aware encoder-decoder LSTM that outputs per-event means and variances for continuous attributes and distributions over event labels, then samples 1000 suffixes with Monte Carlo dropout to approximate a posterior over suffixes. Across four real-life and one artificial event log, the authors report that the averaged probabilistic suffix often beats the greedy most-likely suffix on remaining-time error and suffix-length error, especially for short prefixes and long suffixes. They also argue, using probability integral transform calibration plots, that the predicted remaining-time distributions are well-calibrated enough to support downstream confidence-interval estimation. If the central claim holds, process analysts could plan with ranges and probabilities instead of one guess.

What carries the argument

The central mechanism is the U-ED-LSTM, an encoder-decoder LSTM in which each continuous event attribute is predicted as a mean and a log-variance pair and each categorical attribute as mean logits and a log-variance vector; the training losses are the negative log-likelihoods of those distributions, so the model learns an input-dependent noise level. Epistemic uncertainty is injected by Monte Carlo dropout with a fresh variational dropout mask per rollout, while aleatoric uncertainty is captured by the learned per-step variances. The MC suffix sampling algorithm then autoregressively draws continuous values from Normal distributions (or Log-Normal distributions for strictly positive durations) and categorical classes from softmaxed Gaussian logits, stopping at an end-of-sequence token or a maximum length, and 1000 such rollouts approximate the suffix posterior. The paper also tested a Log-Normal variant as Setting 3 and reports that it is sensitive to extreme sampled outliers.

What would settle it

Build a small synthetic event log with a known generative process so the exact conditional suffix distribution can be computed for every prefix, then compare the model's 1000-sample predictive distribution to the truth with a probability integral transform (PIT) histogram over many prefixes; a systematic U-shape or slope would show that the per-step distributional assumptions do not capture the true posterior.

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Extended reading notes

Core claim

The paper claims that suffix prediction should be framed as distribution prediction rather than point prediction. Its central empirical discovery is that on four real-life and one artificial event log, the mean over 1000 Monte-Carlo-sampled suffixes can outperform the autoregressively decoded most-likely suffix on remaining-time mean absolute error (MAE) and suffix-length MAE, especially for short prefixes and long suffixes, while the model's remaining-time predictions are calibrated well enough that probability integral transform (PIT) plots show no systematic location bias. For event-label accuracy, the most-likely suffix is usually better on low-variability logs, whereas the probabilistic suffix is competitive or better on high-variability logs such as Sepsis and BPIC-17. The paper concludes from these results that probabilistic suffix prediction is effective and can be used for advanced applications such as confidence interval estimation.

Load-bearing premise

The method assumes that the per-event Normal or Log-Normal distributions and the per-class logit distributions, combined through 1000 autoregressive rollouts, honestly represent the true distribution of possible suffixes; if single-step errors compound during sampling, the resulting distribution can drift away from reality.

Editorial extensions

If this is right

  • Process analysts can extract confidence intervals for remaining time directly from the 1000 sampled suffixes rather than treating one predicted trace as ground truth.
  • Probabilistic aggregation is most valuable in high-variability settings, where short prefixes and long suffixes make the greedy most-likely suffix least reliable.
  • Because the decoder outputs distributions for every event attribute, the same sampled suffix set can support questions about activity order, suffix length, and continuous attributes without retraining separate models.
  • The PIT calibration procedure gives process-mining teams a concrete way to test whether a predictor's uncertainty estimates are trustworthy before using them in decisions.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Editorial inference: if the mean over sampled suffixes beats the mode mainly because remaining-time distributions are skewed, probabilistic aggregation should pay off most in human-driven, high-variance logs and least in fully automated, low-variance ones.
  • Editorial inference: the Setting 3 log-normal outliers suggest a direct testable extension—clip predicted variances during sampling or replace the log-normal head with a quantile or mixture head, then rerun the same MAE and PIT comparisons.
  • Editorial inference: the empirical cumulative distribution functions behind the PIT plots could be queried directly for operational statements such as 'probability this case exceeds a 30-day deadline,' a use the paper names but does not evaluate.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper proposes probabilistic suffix prediction for business processes, in which an encoder-decoder LSTM (U-ED-LSTM) is trained with MC dropout for epistemic uncertainty and learned loss attenuation for aleatoric uncertainty, and a Monte Carlo suffix sampling algorithm generates an approximate distribution over suffixes. The approach is evaluated on four real-life and one artificial event log under three hyperparameter settings, comparing aggregated probabilistic predictions with greedy most-likely suffix predictions on suffix length, Damerau-Levenshtein similarity, and remaining-time MAE, and assessing calibration of remaining-time predictions via PIT plots. The central claims are that probabilistic suffix prediction can outperform most-likely suffix prediction, that the U-ED-LSTM has reasonable predictive performance, and that the model's predictions are well calibrated.

Significance. If the calibration claim were supported, the paper would make a useful contribution to predictive process monitoring: a calibrated distribution over suffixes would enable confidence-interval estimation and better handling of process variability. The manuscript has concrete strengths: it provides a public implementation, evaluates on multiple real-world datasets, reports three hyperparameter settings, and compares against existing suffix-prediction methods. However, the calibration evidence is central to the paper's novelty, and the paper's own PIT analysis contradicts the stated conclusions. The value of the contribution therefore depends on resolving an internal inconsistency rather than on a disagreement with existing consensus.

major comments (3)
  1. [Abstract; Section 4.2] The calibration claim is contradicted by the paper's own PIT results. Section 4.2 defines a uniform PIT density as perfect calibration, a U-shape as underdispersion, a bell shape as overdispersion, and a slope or boundary peak as systematic bias. Figures 4 and 5 show a bell shape for Helpdesk, peaks at 1 for Sepsis and BPIC-17, a peak at 0 for PCR, and a peak near 0.2 for Repair, all of which the paper itself classifies as miscalibration. Nevertheless, the text states that 'our approach shows no systematic bias across all data sets' and the abstract concludes that 'the model's predictions are well calibrated.' This internal inconsistency directly undermines the central claim that probabilistic suffix prediction provides a calibrated distribution suitable for confidence-interval estimation, and it must be resolved before the headline conclusion can be accepted.
  2. [Section 3.1; Algorithm 1] There is an inconsistency between the dropout used for training and the dropout used for sampling. Section 3.1 states that variational dropout is applied in the U-ED-LSTM, with the same mask applied across time steps, and Figure 1 indicates this. Algorithm 1, however, samples the decoder weights with 'NaiveDropout(W_dec,p)' at each step (line 10). Since MC dropout as a Bayesian approximation relies on using the same dropout mechanism during inference as during training, and since naive dropout is known to be ineffective in recurrent networks, the epistemic-uncertainty quantification is not implemented as described. The authors need to correct the algorithm or justify why this discrepancy does not affect the uncertainty estimates.
  3. [Section 4.1, Table 4] The Setting 3 results illustrate that the assumed sampling distributions are fragile: the log-normal variant produces extreme outliers, e.g., a remaining-time sum MAE of 15,262 seconds for PCR versus roughly 160 seconds in Settings 1 and 2, and the text acknowledges that such outliers 'greatly influence the aggregated mean of all sampled suffixes.' This is not a peripheral issue, because the MC suffix sampler draws from these per-event distributions; pathological draws imply that the approximated suffix distribution is not reliable. This observation reinforces the calibration problem identified in the previous major comment and should be addressed explicitly in the evaluation.
minor comments (6)
  1. [Section 4.1] There is an unresolved placeholder 'Figure??' in the BPIC-17 discussion, and the accompanying figure reference should be corrected.
  2. [Table 3] Several numeric entries are concatenated without separators (e.g., '13.741.481.05' and '0.10.35 0.830.86'), which makes the table very difficult to read and should be reformatted.
  3. [Abstract; Section 1] The list in the abstract contains grammatical issues: 'probabilistic suffix prediction can outperform most likely suffix prediction, the U-ED-LSTM has reasonable predictive performance, and ii)' is not a well-formed parallel list, and the same problem appears in the introduction.
  4. [Algorithm 1] The symbols 'EOS' and the function 'GetActivity' are used without prior definition; the termination condition is unclear if the dataset does not contain an EOS activity, and the authors should state how the stopping criterion is defined for datasets without an explicit end marker.
  5. [Section 4.2] The PIT formula is not numbered, and the wording 'no systematic bias' appears immediately before a list of biased PIT shapes; the text should be aligned with the evidence presented in Figures 4 and 5.
  6. [Figures 2 and 3] The artificial dataset is called 'Repair' in the text and tables but 'Repair Shop' in Figure 3; the naming should be harmonized, and the y-axis label 'Remaining time MAE (days)' in Figure 3(b) should be checked against the Repair dataset's time unit.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the paper is an empirical benchmark; the calibration overstatement is an internal-consistency problem, not a circular derivation.

full rationale

The paper makes no derivational claim that reduces to its own inputs by construction or by self-citation. The U-ED-LSTM is trained using standard negative log-likelihood losses (Eqs. 3-5) adapted from external references, and the MC suffix sampling algorithm autoregressively draws from the learned per-event distributions against held-out ground-truth suffixes on external event logs. No fitted parameter is renamed as a prediction, no uniqueness theorem from the authors is invoked, and the loss functions do not encode the evaluation metrics. The calibration analysis uses PIT values computed on test data; the conclusion that predictions are 'well calibrated' is an interpretive statement, not a quantity forced by the training objective. One substantive non-circularity issue is that the paper's own PIT taxonomy (uniform = calibrated; U-shape, bell-shape, peaks, and slopes = miscalibration) conflicts with the non-uniform PIT histograms in Figs. 4-5, undermining the abstract's calibration claim. This is a correctness/falsification concern about the evidence, not a circularity of the derivation chain.

Assumptions & free parameters 10 free parameters · 5 assumptions · 0 invented entities

The central empirical claims rest on a stack of modeling and sampling assumptions rather than on a derivation. The main hand-chosen parameters are the network size, dropout, and sampling count; the main axioms are the validity of MC dropout as variational inference and the choice of Gaussian/log-Gaussian noise models. The paper introduces no new physical or conceptual entities.

free parameters (10)
  • MC dropout probability p = 0.1
    Set constant during training and MC sampling, following [26].
  • Sequence length S = 5
    Loss is computed on fixed-length sequences of 5 events following [9].
  • Teacher forcing probability = 0.8 initial, decayed after 20% of epochs
    Chosen following [25] to balance target and predicted inputs.
  • Hidden size = 128
    Used for both encoder and decoder LSTMs in all three settings.
  • Number of MC samples T = 1000
    The posterior distribution of suffixes is approximated from 1000 samples per prefix.
  • Learning rate = 1e-4 to 1e-6 per dataset
    Tuned after extensive testing on each dataset.
  • Number of training epochs = 200 for setting 1, 100 for settings 2 and 3
    Set by observed stagnation in learning curves.
  • L2 regularization lambda = 1e-4
    Applied to encoder and decoder parameters.
  • Embedding dimension D = min(600, round(1.6*(K+2)^0.56))
    Heuristic from [27]; depends on the number of categories K.
  • Maximum case length padding cutoff = Excludes top 1.5% longest cases
    Padding length chosen following [27].
assumptions (5)
  • domain assumption MC dropout is a valid variational approximation to the posterior over LSTM weights.
    Section 3.1 uses dropout in stochastic LSTM cells and an L2 penalty following [7,8], but the paper does not verify that the variational assumptions hold for its architecture and datasets.
  • domain assumption Per-event continuous attributes follow Normal or Log-Normal noise and categorical logits follow independent Normal noise.
    Equations 3 and 4 assume these distributions for loss attenuation; the PIT analysis is the only check and it contradicts the assumption.
  • ad hoc to paper Autoregressive sampling with T=1000 approximates the true suffix distribution.
    Algorithm 1 fixes T=1000 without a convergence study or comparison of sample sizes.
  • domain assumption The case-level 65/15/20 split yields independent and identically distributed test cases.
    Section 4 splits cases at random; temporal drift or inter-case dependence in the event logs is not analyzed.
  • domain assumption Pooled PIT values can be read as a single calibration diagnostic.
    Section 4.2 pools PIT values across all test cases and interprets the histogram shape; this assumes exchangeability across cases.

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Cite this review

Pith. "Pith review of An Uncertainty-Aware ED-LSTM for Probabilistic Suffix Prediction." pith.science (2026). https://pith.science/paper/5MD2PJJQ

@misc{pith2026250521339,
  author       = {Pith},
  title        = {Pith review of: An Uncertainty-Aware ED-LSTM for Probabilistic Suffix Prediction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5MD2PJJQ}},
  note         = {Machine review of arXiv:2505.21339}
}
read the original abstract

Suffix prediction of business processes forecasts the remaining sequence of events until process completion. Current approaches focus on predicting the most likely suffix, representing a single scenario. However, when the future course of a process is subject to uncertainty and high variability, the expressiveness of such a single scenario can be limited, since other possible scenarios, which together may have a higher overall probability, are overlooked. To address this limitation, we propose probabilistic suffix prediction, a novel approach that approximates a probability distribution of suffixes. The proposed approach is based on an Uncertainty-Aware Encoder-Decoder LSTM (U-ED-LSTM) and a Monte Carlo (MC) suffix sampling algorithm. We capture epistemic uncertainties via MC dropout and aleatoric uncertainties as learned loss attenuation. This technical report presents a comprehensive evaluation of the probabilistic suffix prediction approach's predictive performance and calibration under three different hyperparameter settings, using four real-life and one artificial event log. The results show that: i) probabilistic suffix prediction can outperform most likely suffix prediction, the U-ED-LSTM has reasonable predictive performance, and ii) the model's predictions are well calibrated.

Figures

Figures reproduced from arXiv: 2505.21339 by the authors.

Figure 1
Figure 1. U-ED-LSTM Architecture and Training Pipeline [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Predictive Performance - Setting 2 for the Datasets: Helpdesk, Sepsis, and BPIC-17 [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Predictive Performance - Setting 2 for the Datasets: PCR and Repair [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Model Calibration of Remaining Time Predictions - Setting 2 for the Datasets: Helpdesk, [PITH_FULL_IMAGE:figures/full_fig_p018_4.png]
Figure 5
Figure 5. Figure 5: Model Calibration of Remaining Time Predictions - Setting 2 for the Datasets: PCR and [PITH_FULL_IMAGE:figures/full_fig_p018_5.png]

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