Particle filters (PFs) are often combined with swarm intelligence (SI) algorithms, such as Chicken Swarm Optimization (CSO), for particle rejuvenation. Separately, Kullback--Leibler divergence (KLD) sampling is a common strategy for adaptively sizing the particle set. However, the theoretical interaction between SI-based rejuvenation kernels and KLD-based adaptive sampling is not yet fully understood. This paper investigates this specific interaction. We analyze, under a simplified modeling framework, the effect of the CSO rejuvenation step on the particle set distribution. We propose that the fitness-driven updates inherent in CSO can be approximated as a form of mean-square contraction. This contraction tends to produce a particle distribution that is more concentrated than that of a baseline PF, or in mathematical terms, a distribution that is plausibly more ``peaked'' in a majorization sense. By applying Karamata's inequality to the concave function that governs the expected bin occupancy in KLD-sampling, our analysis suggests a connection: under the stated assumptions, the CSO-enhanced PF (CPF) is expected to require a lower \emph{expected} particle count than the standard PF to satisfy the same statistical error bound. The goal of this study is not to provide a fully general proof, but rather to offer a tractable theoretical framework that helps to interpret the computational efficiency empirically observed when combining these techniques, and to provide a starting point for designing more efficient adaptive filters.

Filtering-based graph neural networks (GNNs) constitute a distinct class of GNNs that employ graph filters to handle graph-structured data, achieving notable success in various graph-related tasks. Conventional methods adopt a graph-wise filtering paradigm, imposing a uniform filter across all nodes, yet recent findings suggest that this rigid paradigm struggles with heterophilic graphs. To overcome this, recent works have introduced node-wise filtering, which assigns distinct filters to individual nodes, offering enhanced adaptability. However, a fundamental gap remains: a comprehensive framework unifying these two strategies is still absent, limiting theoretical insights into the filtering paradigms. Moreover, through the lens of Contextual Stochastic Block Model, we reveal that a synthesis of graph-wise and node-wise filtering provides a sufficient solution for classification on graphs exhibiting both homophily and heterophily, suggesting the risk of excessive parameterization and potential overfitting with node-wise filtering. To address the limitations, this paper introduces Coarsening-guided Partition-wise Filtering (CPF). CPF innovates by performing filtering on node partitions. The method begins with structure-aware partition-wise filtering, which filters node partitions obtained via graph coarsening algorithms, and then performs feature-aware partition-wise filtering, refining node embeddings via filtering on clusters produced by $k$-means clustering over features. In-depth analysis is conducted for each phase of CPF, showing its superiority over other paradigms. Finally, benchmark node classification experiments, along with a real-world graph anomaly detection application, validate CPF's efficacy and practical utility.

Knowledge Tracing (KT) aims to trace changes in students' knowledge states throughout their entire learning process by analyzing their historical learning data and predicting their future learning performance. Existing forgetting curve theory based knowledge tracing models only consider the general forgetting caused by time intervals, ignoring the individualization of students and the causal relationship of the forgetting process. To address these problems, we propose a Concept-driven Personalized Forgetting knowledge tracing model (CPF) which integrates hierarchical relationships between knowledge concepts and incorporates students' personalized cognitive abilities. First, we integrate the students' personalized capabilities into both the learning and forgetting processes to explicitly distinguish students' individual learning gains and forgetting rates according to their cognitive abilities. Second, we take into account the hierarchical relationships between knowledge points and design a precursor-successor knowledge concept matrix to simulate the causal relationship in the forgetting process, while also integrating the potential impact of forgetting prior knowledge points on subsequent ones. The proposed personalized forgetting mechanism can not only be applied to the learning of specifc knowledge concepts but also the life-long learning process. Extensive experimental results on three public datasets show that our CPF outperforms current forgetting curve theory based methods in predicting student performance, demonstrating CPF can better simulate changes in students' knowledge status through the personalized forgetting mechanism.

Reinforcement Learning (RL) Sutton and Barto [2018] and Probabilistic planning Puterman [2014] are two research branches that address stochastic problems, often under the Markov assumption for state dynamics. The planning approach requires a given model, while the learning approach improves through repeated interaction with an environment, which can be viewed as a black box. Thus, the tools and the benchmarks for these two branches have grown apart. Learning agents do not require to be able to simulate model-based transitions, and thus frameworks such as OpenAI Gym Brockman et al. [2016] have become a standard, serving also as an interface for third-party benchmarks such as Todorov et al. [2012], Bellemare et al. [2013] and more. As the model is not necessary for solving the learning problem, the environments are hard-coded in a programming language. This has several downsides; if one does wish to see the model describing the environment, it has to be reverse-engineered from the environment framework, complex problems can result in a significant development period, code bugs may make their way into the environment and finally, there is no clean way to verify the model or reuse it directly. Thus, the creation of a verified acceptable benchmark is a challenging task. Planning agents on the other hand can interact with an environment Sanner [2010a], but in many cases simulate the model within the planning agent in order to solve the problem Keller and Eyerich [2012]. The planning community has also come up with formal description languages for various types of problems; these include the Planning Domain Definition Language (PDDL) Aeronautiques et al. [1998] for classical planning problems, PDDL2.1 Fox and Long [2003] for problems involving time and continuous variables, PPDDL Bryce and Buet [2008] for classical planning problems with action probabilistic effects and rewards, and Relational Dynamic Influence Diagram Language (RDDL)

In this work we consider a new family of algorithms for sequential prediction, Hierarchical Partitioning Forecasters (HPFs). Our goal is to provide appealing theoretical - regret guarantees on a powerful model class - and practical - empirical performance comparable to deep networks - properties at the same time. We built upon three principles: hierarchically partitioning the feature space into sub-spaces, blending forecasters specialized to each sub-space and learning HPFs via local online learning applied to these individual forecasters. Following these principles allows us to obtain regret guarantees, where Constant Partitioning Forecasters (CPFs) serve as competitor. A CPF partitions the feature space into sub-spaces and predicts with a fixed forecaster per sub-space. Fixing a hierarchical partition $\mathcal H$ and considering any CPF with a partition that can be constructed using elements of $\mathcal H$ we provide two guarantees: first, a generic one that unveils how local online learning determines regret of learning the entire HPF online; second, a concrete instance that considers HPF with linear forecasters (LHPF) and exp-concave losses where we obtain $O(k \log T)$ regret for sequences of length $T$ where $k$ is a measure of complexity for the competing CPF. Finally, we provide experiments that compare LHPF to various baselines, including state of the art deep learning models, in precipitation nowcasting. Our results indicate that LHPF is competitive in various settings.

Tredence, the Data Science and AI Solutions company, announced it has raised USD 175 million in Series B funding from Advent International (Advent) to accelerate data-fueled growth and AI value realization for industries. Advent is one of the largest and most experienced global private equity investors. The full financial terms of the agreement have not been disclosed. Advent will acquire a minority stake in Tredence with the $175 million investment. Advent has significant investment experience in the technology services and software sectors.

Node classification on graph data is a major problem, and various graph neural networks (GNNs) have been proposed. Variants of GNNs such as H2GCN and CPF outperform graph convolutional networks (GCNs) by improving on the weaknesses of the traditional GNN. However, there are some graph data which these GNN variants fail to perform well than other GNNs in the node classification task. This is because H2GCN has a feature thinning on graph data with high average degree, and CPF gives rise to a problem about label-propagation suitability. Accordingly, we propose a hierarchical model selection framework (HMSF) that selects an appropriate GNN model by analyzing the indicators of each graph data. In the experiment, we show that the model selected by our HMSF achieves high performance on node classification for various types of graph data.

In this article, we propose a new variational approach to learn private and/or fair representations. This approach is based on the Lagrangians of a new formulation of the privacy and fairness optimization problems that we propose. In this formulation, we aim at generating representations of the data that keep a prescribed level of the relevant information that is not shared by the private or sensitive data, while minimizing the remaining information they keep. The proposed approach (i) exhibits the similarities of the privacy and fairness problems, (ii) allows us to control the trade-off between utility and privacy or fairness through the Lagrange multiplier parameter, and (iii) can be comfortably incorporated to common representation learning algorithms such as the VAE, the $\beta$-VAE, the VIB, or the nonlinear IB.

Solving cooperative path finding (CPF) by translating it to propositional satisfiability represents a viable option in highly constrained situations. The task in CPF is to relocate agents from their initial positions to given goals in a collision free manner. In this paper, we propose a reduced time expansion that is focused on makespan sub-optimal solving. The suggested reduced time expansion is especially beneficial in conjunction with a goal decomposition where agents are relocated one by one.

Solving cooperative path finding (CPF) by translating it to propositional satisfiability represents a viable option in highly constrained situations. The task in CPF is to relocate agents from their initial positions to given goals in a collision free manner. In this paper, we propose a reduced time expansion that is focused on makespan sub-optimal solving of the problem. The suggested reduced time expansion is especially beneficial in conjunction with a goal decomposition where agents are relocated one by one.