A Unified Particle Filter LSTM for Data-Driven Process Simulation

Data-driven process simulation aims to generate realistic case trajectories from historical event logs without requiring an explicitly specified model of the underlying dynamics. Deep sequence models can capture complex temporal dependencies through next-activity probabilities and conditional time distributions. However, event logs provide only a partial view of the underlying process state, often recording activity completions without the corresponding service-start times. Consequently, the same observed process history may be consistent with multiple plausible latent process conditions, whereas standard recurrent models compress each process prefix into a single deterministic recurrent state. We propose a Unified Particle Filter LSTM (Unified PF-LSTM) that maintains and sequentially updates a weighted set of recurrent-state hypotheses. We summarize this particle belief using its weighted mean and learned features based on the moment-generating function. The resulting representation is used to predict a categorical distribution over the next activity and conditional quantiles of the current activity's sojourn time. The framework is trained end-to-end from event-log data and evaluated on three real-world emergency department datasets. The results show that the proposed framework consistently outperforms the considered data-driven baselines in reproducing routing, duration, and system-level behavior across all datasets, with particularly strong gains in settings where complex process dynamics are only partially reflected in the available event logs.

Mind the Long Tail: Understanding the Difficulty of Delay Detection in Business Processes

The early detection of delayed cases in business processes is a critical capability for organizations. Predictive process monitoring (PPM) supports this task by using historical event logs to predict the remaining time of ongoing cases, enabling timely interventions to avoid missed deadlines and service level violations. Although remaining time prediction has advanced considerably through sophisticated deep learning architectures, little is known about the intrinsic difficulty of delay detection itself. Since performance is typically assessed using aggregate metrics, prior work provides limited insight into how models perform across the target distribution, especially on the operationally most critical cases with large delays. In this paper, we address this gap by analyzing the difficulty of delay detection. Across 14 event logs, we show that remaining times are typically strongly right-skewed, with only a small fraction of cases exhibiting large delays. Existing models capture the mode of this distribution well but perform poorly on high-delay cases. We further uncover pronounced heteroscedasticity, showing that predictive uncertainty increases with delay magnitude. Based on these findings, we evaluate approaches to mitigate the imbalance problem, but find only limited benefits, suggesting that the key underlying problem may not be imbalance but higher uncertainty associated with delayed cases. We show that this correlation can be exploited to substantially improve the identification of delayed cases. Overall, our work provides new insights into the sources of difficulty in delay detection and identifies uncertainty-aware modeling as a promising direction for future PPM research.

Uncertainty-Aware Probabilistic Constrained Clustering from Entangled Pairwise Supervision

Pairwise constrained clustering typically relies on hard must-link/cannot-link labels, whereas realistic pairwise supervision may be real-valued and entangle intrinsic ambiguity, expert judgment, and stochastic corruption. Existing deep constrained clustering (DCC) methods mainly target hard, expert-agnostic constraints, treating soft labels mostly numerically rather than semantically. We formalize this setting as uncertainty-aware probabilistic constrained clustering (UPCC), defining a canonical aleatoric target through a heterogeneous observation process and analyzing its conditional identifiability. We introduce ProbPair, an angular pairwise objective for probabilistic relations, and build ECI-PP, an estimator--corrector--integrator framework that refines imperfect supervision via belief estimation, correction, and reliability-aware integration. Across challenging probabilistic supervision settings, experiments on diverse benchmarks show that ECI-PP outperforms state-of-the-art DCC methods and remains robust with a shared default configuration.

Learning What Not to Impute: An Uncertainty-Aware Diffusion Framework for Meaningful Missingness

Missing value imputation is a fundamental task in machine learning, with most existing methods assuming that all missing entries correspond to unobserved regular values. In many real-world datasets, however, missingness may arise from two distinct sources: some entries are meaningfully missing (intrinsically absent and semantically valid), while others are missing due to the observation process and should be imputed. We formalize this distinction as a selective imputation problem, where the goal is to jointly infer which missing entries should be preserved and which should be recovered. To address this challenge, we propose Diff-Joint, a diffusion-based framework that jointly models tabular data together with a latent missingness mask. The method alternates between conditional sampling and uncertainty-aware aggregation to iteratively refine both imputed values and missingness labels. Empirical results on synthetic and real-world datasets demonstrate that Diff-Joint effectively identifies meaningfully missing entries while achieving competitive imputation accuracy and improved downstream task performance.