We introduce a novel machine learning method called the Penalized Profile Support Vector Machine based on the Gabriel edited set for the computation of the probability of failure for a complex system as determined by a threshold condition on a computer model of system behavior. The method is designed to minimize the number of evaluations of the computer model while preserving the geometry of the decision boundary that determines the probability. It employs an adaptive sampling strategy designed to strategically allocate points near the boundary determining failure and builds a locally linear surrogate boundary that remains consistent with its geometry by strategic clustering of training points. We prove two convergence results and we compare the performance of the method against a number of state of the art classification methods on four test problems. We also apply the method to determine the probability of survival using the Lotka--Volterra model for competing species.

The Kalman filter (KF) is one of the most widely used tools for data assimilation and sequential estimation. In this work, we show that the state estimates from the KF in a standard linear dynamical system setting are equivalent to those given by the KF in a transformed system, with infinite process noise (i.e., a ``flat prior'') and an augmented measurement space. This reformulation---which we refer to as augmented measurement sensor fusion (SF)---is conceptually interesting, because the transformed system here is seemingly static (as there is effectively no process model), but we can still capture the state dynamics inherent to the KF by folding the process model into the measurement space. Further, this reformulation of the KF turns out to be useful in settings in which past states are observed eventually (at some lag). Here, when the measurement noise covariance is estimated by the empirical covariance, we show that the state predictions from SF are equivalent to those from a regression of past states on past measurements, subject to particular linear constraints (reflecting the relationships encoded in the measurement map). This allows us to port standard ideas (say, regularization methods) in regression over to dynamical systems. For example, we can posit multiple candidate process models, fold all of them into the measurement model, transform to the regression perspective, and apply $\ell_1$ penalization to perform process model selection. We give various empirical demonstrations, and focus on an application to nowcasting the weekly incidence of influenza in the US.

This paper proposes a new meta-learning method -- named HARMLESS (HAwkes Relational Meta Learning method for Short Sequences) for learning heterogeneous point process models from a collection of short event sequence data along with a relational network. Specifically, we propose a hierarchical Bayesian mixture Hawkes process model, which naturally incorporates the relational information among sequences into point process modeling. Compared with existing methods, our model can capture the underlying mixed-community patterns of the relational network, which simultaneously encourages knowledge sharing among sequences and facilitates adaptively learning for each individual sequence. We further propose an efficient stochastic variational meta-EM algorithm, which can scale to large problems. Numerical experiments on both synthetic and real data show that HARMLESS outperforms existing methods in terms of predicting the future events.

Process discovery algorithms automatically extract process models from event logs, but high variability often results in complex and hard-to-understand models. To mitigate this issue, trace clustering techniques group process executions into clusters, each represented by a simpler and more understandable process model. Model-driven trace clustering improves on this by assigning traces to clusters based on their conformity to cluster-specific process models. However, most existing clustering techniques rely on either no process model discovery, or non-stochastic models, neglecting the frequency or probability of activities and transitions, thereby limiting their capability to capture real-world execution dynamics. We propose a novel model-driven trace clustering method that optimizes stochastic process models within each cluster. Our approach uses entropic relevance, a stochastic conformance metric based on directly-follows probabilities, to guide trace assignment. This allows clustering decisions to consider both structural alignment with a cluster's process model and the likelihood that a trace originates from a given stochastic process model. The method is computationally efficient, scales linearly with input size, and improves model interpretability by producing clusters with clearer control-flow patterns. Extensive experiments on public real-life datasets demonstrate that while our method yields superior stochastic coherence and graph simplicity, traditional fitness metrics reveal a trade-off, highlighting the specific utility of our approach for stochastic process analysis.

A spatial point process can be characterized by an intensity function which predicts the number of events that occur across space.

We call (1) the process model and (2) the measurement model.

Thank you for your encouraging comments. Thank you for your thorough and helpful review. We appreciate all of your feedback. This is explained in the "sensor selection" paragraph at the end of the paper and We are glad that you understand and appreciate the significance of Theorem 2. Empirical results/better demonstrations It also suggests that with the "right" constraints put in place, a nonlinear method should do very well. For example, we can try multiple process models on the flu data.

Context: Ensuring high levels of dependability in modern computer-based systems has become increasingly challenging due to their complexity. Although systems are validated at design time, their behavior can be different at run-time, possibly showing control-flow anomalies due to "unknown unknowns". Objective: We aim to detect control-flow anomalies through software monitoring, which verifies run-time behavior by logging software execution and detecting deviations from expected control flow. Methods: We propose a methodology to develop software monitors for control-flow anomaly detection through Large Language Models (LLMs) and conformance checking. The methodology builds on existing software development practices to maintain traditional V&V while providing an additional level of robustness and trustworthiness. It leverages LLMs to link design-time models and implementation code, automating source-code instrumentation. The resulting event logs are analyzed via conformance checking, an explainable and effective technique for control-flow anomaly detection. Results: We test the methodology on a case-study scenario from the European Railway Traffic Management System / European Train Control System (ERTMS/ETCS), which is a railway standard for modern interoperable railways. The results obtained from the ERTMS/ETCS case study demonstrate that LLM-based source-code instrumentation can achieve up to 84.775% control-flow coverage of the reference design-time process model, while the subsequent conformance checking-based anomaly detection reaches a peak performance of 96.610% F1-score and 93.515% AUC. Conclusion: Incorporating domain-specific knowledge to guide LLMs in source-code instrumentation significantly allowed obtaining reliable and quality software logs and enabled effective control-flow anomaly detection through conformance checking.

Identifying interpretable patterns in multi-electrode recordings is a longstanding and increasingly pressing challenge in neuroscience.

Event logs extracted from information systems offer a rich foundation for understanding and improving business processes. In many real-world applications, it is possible to distinguish between desirable and undesirable process executions, where desirable traces reflect efficient or compliant behavior, and undesirable ones may involve inefficiencies, rule violations, delays, or resource waste. This distinction presents an opportunity to guide process discovery in a more outcome-aware manner. Discovering a single process model without considering outcomes can yield representations poorly suited for conformance checking and performance analysis, as they fail to capture critical behavioral differences. Moreover, prioritizing one behavior over the other may obscure structural distinctions vital for understanding process outcomes. By learning interpretable discriminative rules over control-flow features, we group traces with similar desirability profiles and apply process discovery separately within each group. This results in focused and interpretable models that reveal the drivers of both desirable and undesirable executions. The approach is implemented as a publicly available tool and it is evaluated on multiple real-life event logs, demonstrating its effectiveness in isolating and visualizing critical process patterns.