We consider the problem of designing a data-driven nonlinear state estimation (DANSE) method that uses (noisy) nonlinear measurements of a process whose underlying state transition model (STM) is unknown. Such a process is referred to as a model-free process. A recurrent neural network (RNN) provides parameters of a Gaussian prior that characterize the state of the model-free process, using all previous measurements at a given time point. In the case of DANSE, the measurement system was linear, leading to a closed-form solution for the state posterior. However, the presence of a nonlinear measurement system renders a closed-form solution infeasible. Instead, the second-order statistics of the state posterior are computed using the nonlinear measurements observed at the time point. We address the nonlinear measurements using a reparameterization trick-based particle sampling approach, and estimate the second-order statistics of the state posterior. The proposed method is referred to as particle-based DANSE (pDANSE). The RNN of pDANSE uses sequential measurements efficiently and avoids the use of computationally intensive sequential Monte-Carlo (SMC) and/or ancestral sampling. We describe the semi-supervised learning method for pDANSE, which transitions to unsupervised learning in the absence of labeled data. Using a stochastic Lorenz-$63$ system as a benchmark process, we experimentally demonstrate the state estimation performance for four nonlinear measurement systems. We explore cubic nonlinearity and a camera-model nonlinearity where unsupervised learning is used; then we explore half-wave rectification nonlinearity and Cartesian-to-spherical nonlinearity where semi-supervised learning is used. The performance of state estimation is shown to be competitive vis-à-vis particle filters that have complete knowledge of the STM of the Lorenz-$63$ system.

Understanding post-wildfire vegetation loss is critical for developing effective ecological recovery strategies and is often challenging due to the extended time and effort required to capture the evolving ecosystem features. Recent works in this area have not fully explored all the contributing factors, their modalities, and interactions with each other. Furthermore, most research in this domain is limited by a lack of interpretability in predictive modeling, making it less useful in real-world settings. In this work, we propose a novel end-to-end ML pipeline called MVeLMA (\textbf{M}ultimodal \textbf{Ve}getation \textbf{L}oss \textbf{M}odeling \textbf{A}rchitecture) to predict county-wise vegetation loss from fire events. MVeLMA uses a multimodal feature integration pipeline and a stacked ensemble-based architecture to capture different modalities while also incorporating uncertainty estimation through probabilistic modeling. Through comprehensive experiments, we show that our model outperforms several state-of-the-art (SOTA) and baseline models in predicting post-wildfire vegetation loss. Furthermore, we generate vegetation loss confidence maps to identify high-risk counties, thereby helping targeted recovery efforts. The findings of this work have the potential to inform future disaster relief planning, ecological policy development, and wildlife recovery management.

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.

Abstract-- The oscillations of the human heart rate are inherently complex and non-linear--they are best described by mathematical chaos, and they present a challenge when applied to the practical domain of cardiovascular health monitoring in everyday life. In this work, we study the non-linear chaotic behavior of heart rate through mutual information and introduce a novel approach for enhancing heart rate estimation in real-life conditions. Our proposed approach not only explains and handles the non-linear temporal complexity from a mathematical perspective but also improves the deep learning solutions when combined with them. We validate our proposed method on four established datasets from real-life scenarios and compare its performance with existing algorithms thoroughly with extensive ablation experiments. Our results demonstrate a substantial improvement, up to 40%, of the proposed approach in estimating heart rate compared to traditional methods and existing machine-learning techniques while reducing the reliance on multiple sensing modalities and eliminating the need for post-processing steps. Healthy biological systems exhibit complex patterns of variability that can be described by mathematical chaos [1], [2]. A healthy heart is not a metronome; instead, its complex and constantly changing oscillations enable the cardiovascular system to rapidly adjust to sudden physical and psychological challenges to homeostasis [2]. Therefore, measuring heart rate (HR) during daily life has significant importance in monitoring individuals' health.

Recent theoretical advancement of information density in natural language has brought the following question on desk: To what degree does natural language exhibit periodicity pattern in its encoded information? We address this question by introducing a new method called AutoPeriod of Surprisal (APS). APS adopts a canonical periodicity detection algorithm and is able to identify any significant periods that exist in the surprisal sequence of a single document. By applying the algorithm to a set of corpora, we have obtained the following interesting results: Firstly, a considerable proportion of human language demonstrates a strong pattern of periodicity in information; Secondly, new periods that are outside the distributions of typical structural units in text (e.g., sentence boundaries, elementary discourse units, etc.) are found and further confirmed via harmonic regression modeling. We conclude that the periodicity of information in language is a joint outcome from both structured factors and other driving factors that take effect at longer distances. The advantages of our periodicity detection method and its potentials in LLM-generation detection are further discussed.

In this paper, we study the problem of online sparse linear regression (OSLR) where the algorithms are restricted to accessing only $k$ out of $d$ attributes per instance for prediction, which was proved to be NP-hard. Previous work gave polynomial-time algorithms assuming the data matrix satisfies the linear independence of features, the compatibility condition, or the restricted isometry property. We introduce a new polynomial-time algorithm, which significantly improves previous regret bounds (Ito et al., 2017) under the compatibility condition that is weaker than the other two assumptions. The improvements benefit from a tighter convergence rate of the $\ell_1$-norm error of our estimators. Our algorithm leverages the well-studied Dantzig Selector, but importantly with several novel techniques, including an algorithm-dependent sampling scheme for estimating the covariance matrix, an adaptive parameter tuning scheme, and a batching online Newton step with careful initializations. We also give novel and non-trivial analyses, including an induction method for analyzing the $\ell_1$-norm error, careful analyses on the covariance of non-independent random variables, and a decomposition on the regret. We further extend our algorithm to OSLR with additional observations where the algorithms can observe additional $k_0$ attributes after each prediction, and improve previous regret bounds (Kale et al., 2017; Ito et al., 2017).

Due to the growing concern about unsavory behaviors of machine learning models toward certain demographic groups, the notion of 'fairness' has recently drawn much attention from the community, thereby motivating the study of fairness in graph clustering. Fair graph clustering aims to partition the set of nodes in a graph into $k$ disjoint clusters such that the proportion of each protected group within each cluster is consistent with the proportion of that group in the entire dataset. It is, however, computationally challenging to incorporate fairness constraints into existing graph clustering algorithms, particularly for large graphs. To address this problem, we propose FairAD, a computationally efficient fair graph clustering method. It first constructs a new affinity matrix based on the notion of algebraic distance such that fairness constraints are imposed. A graph coarsening process is then performed on this affinity matrix to find representative nodes that correspond to $k$ clusters. Finally, a constrained minimization problem is solved to obtain the solution of fair clustering. Experiment results on the modified stochastic block model and six public datasets show that FairAD can achieve fair clustering while being up to 40 times faster compared to state-of-the-art fair graph clustering algorithms.

Given two algorithms for the same problem, can we determine whether they are meaningfully different? In full generality, the question is uncomputable, and empirically it is muddied by competing notions of similarity. Yet, in many applications (such as clone detection or program synthesis) a pragmatic and consistent similarity metric is necessary. We review existing equivalence and similarity notions and introduce EMOC: An Evaluation-Memory-Operations-Complexity framework that embeds algorithm implementations into a feature space suitable for downstream tasks. We compile PACD, a curated dataset of verified Python implementations across three problems, and show that EMOC features support clustering and classification of algorithm types, detection of near-duplicates, and quantification of diversity in LLM-generated programs. Code, data, and utilities for computing EMOC embeddings are released to facilitate reproducibility and future work on algorithm similarity.

The connection between texts is referred to as intertextuality in literary theory, which served as an important theoretical basis in many digital humanities studies. Over the past decade, advancements in natural language processing have ushered intertextuality studies into the quantitative age. Large-scale intertextuality research based on cutting-edge methods has continuously emerged. This paper provides a roadmap for quantitative intertextuality studies, summarizing their data, methods, and applications. Drawing on data from multiple languages and topics, this survey reviews methods from statistics to deep learning. It also summarizes their applications in humanities and social sciences research and the associated platform tools. Driven by advances in computer technology, more precise, diverse, and large-scale intertext studies can be anticipated. Intertextuality holds promise for broader application in interdisciplinary research bridging AI and the humanities.

This paper presents a novel approach to sentiment classification using the application of Combinatorial Fusion Analysis (CFA) to integrate an ensemble of diverse machine learning models, achieving state-of-the-art accuracy on the IMDB sentiment analysis dataset of 97.072\%. CFA leverages the concept of cognitive diversity, which utilizes rank-score characteristic functions to quantify the dissimilarity between models and strategically combine their predictions. This is in contrast to the common process of scaling the size of individual models, and thus is comparatively efficient in computing resource use. Experimental results also indicate that CFA outperforms traditional ensemble methods by effectively computing and employing model diversity. The approach in this paper implements the combination of a transformer-based model of the RoBERTa architecture with traditional machine learning models, including Random Forest, SVM, and XGBoost.