Causal discovery combines data with knowledge provided by experts to learn the DAG representing the causal relationships between a given set of variables. When data are scarce, bagging is used to measure our confidence in an average DAG obtained by aggregating bootstrapped DAGs. However, the aggregation step has received little attention from the specialized literature: the average DAG is constructed using only the confidence in the individual edges of the bootstrapped DAGs, thus disregarding complex higher-order edge structures. In this paper, we introduce a novel theoretical framework based on higher-order structures and describe a new DAG aggregation algorithm. We perform a simulation study, discussing the advantages and limitations of the proposed approach. Our proposal is both computationally efficient and effective, outperforming state-of-the-art solutions, especially in low sample size regimes and under high dimensionality settings.

Small and medium-sized enterprises (SMEs) represent 99.9% of U.S. businesses yet remain systematically excluded from AI due to a mismatch between their operational scale and modern machine learning's data requirements. This paper introduces SmallML, a Bayesian transfer learning framework achieving enterprise-level prediction accuracy with datasets as small as 50-200 observations. We develop a three-layer architecture integrating transfer learning, hierarchical Bayesian modeling, and conformal prediction. Layer 1 extracts informative priors from 22,673 public records using a SHAP-based procedure transferring knowledge from gradient boosting to logistic regression. Layer 2 implements hierarchical pooling across J=5-50 SMEs with adaptive shrinkage, balancing population patterns with entity-specific characteristics. Layer 3 provides conformal sets with finite-sample coverage guarantees P(y in C(x)) >= 1-alpha for distribution-free uncertainty quantification. Validation on customer churn data demonstrates 96.7% +/- 4.2% AUC with 100 observations per business -- a +24.2 point improvement over independent logistic regression (72.5% +/- 8.1%), with p < 0.000001. Conformal prediction achieves 92% empirical coverage at 90% target. Training completes in 33 minutes on standard CPU hardware. By enabling enterprise-grade predictions for 33 million U.S. SMEs previously excluded from machine learning, SmallML addresses a critical gap in AI democratization. Keywords: Bayesian transfer learning, hierarchical models, conformal prediction, small-data analytics, SME machine learning

Bridging continuous perceptual signals and discrete symbolic reasoning is a fundamental challenge in AI systems that must operate under uncertainty. We present a neuro-symbolic framework that explicitly models and propagates uncertainty from perception to planning, providing a principled connection between these two abstraction levels. Our approach couples a transformer-based perceptual front-end with graph neural network (GNN) relational reasoning to extract probabilistic symbolic states from visual observations, and an uncertainty-aware symbolic planner that actively gathers information when confidence is low. We demonstrate the framework's effectiveness on tabletop robotic manipulation as a concrete application: the translator processes 10,047 PyBullet-generated scenes (3--10 objects) and outputs probabilistic predicates with calibrated confidences (overall F1=0.68). When embedded in the planner, the system achieves 94\%/90\%/88\% success on Simple Stack, Deep Stack, and Clear+Stack benchmarks (90.7\% average), exceeding the strongest POMDP baseline by 10--14 points while planning within 15\,ms. A probabilistic graphical-model analysis establishes a quantitative link between calibrated uncertainty and planning convergence, providing theoretical guarantees that are validated empirically. The framework is general-purpose and can be applied to any domain requiring uncertainty-aware reasoning from perceptual input to symbolic planning.

Online ratings influence customer decision-making, yet standard aggregation methods, such as the sample mean, fail to adapt to quality changes over time and ignore review heterogeneity (e.g., review sentiment, a review's helpfulness). To address these challenges, we demonstrate the value of using the Gaussian process (GP) framework for rating aggregation. Specifically, we present a tailored GP model that captures the dynamics of ratings over time while additionally accounting for review heterogeneity. Based on 121,123 ratings from Yelp, we compare the predictive power of different rating aggregation methods in predicting future ratings, thereby finding that the GP model is considerably more accurate and reduces the mean absolute error by 10.2% compared to the sample mean. Our findings have important implications for marketing practitioners and customers. By moving beyond means, designers of online reputation systems can display more informative and adaptive aggregated rating scores that are accurate signals of expected customer satisfaction.

Like visual processing, language processing is susceptible to illusions in which people systematically misperceive stimuli. In one such case--the comparative illusion (CI), e.g., More students have been to Russia than I have--comprehenders tend to judge the sentence as acceptable despite its underlying nonsensical comparison. Prior research has argued that this phenomenon can be explained as Bayesian inference over a noisy channel: the posterior probability of an interpretation of a sentence is proportional to both the prior probability of that interpretation and the likelihood of corruption into the observed (CI) sentence. Initial behavioral work has supported this claim by evaluating a narrow set of alternative interpretations of CI sentences and showing that comprehenders favor interpretations that are more likely to have been corrupted into the illusory sentence. In this study, we replicate and go substantially beyond this earlier work by directly predicting the strength of illusion with a quantitative model of the posterior probability of plausible interpretations, which we derive through a novel synthesis of statistical language models with human behavioral data. Our model explains not only the fine gradations in the strength of CI effects, but also a previously unexplained effect caused by pronominal vs. full noun phrase than-clause subjects. These findings support a noisy-channel theory of sentence comprehension by demonstrating that the theory makes novel predictions about the comparative illusion that bear out empirically. This outcome joins related evidence of noisy channel processing in both illusory and non-illusory contexts to support noisy channel inference as a unified computational-level theory of diverse language processing phenomena.

These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing kernel Hilbert spaces (RKHS), and Hilbert-Schmidt operators, emphasizing their role in statistical estimation and representation of probability measures. Classical concepts such as covariance, regression, and information measures are revisited through the lens of Hilbert space geometry. We also introduce kernel density estimation, kernel embeddings of distributions, and the Maximum Mean Discrepancy (MMD). The exposition is designed to serve as a foundation for more advanced topics, including Gaussian processes, kernel Bayesian inference, and functional analytic approaches to modern machine learning.

Model-based reinforcement learning (RL) methods that leverage search are responsible for many milestone breakthroughs in RL. Sequential Monte Carlo (SMC) recently emerged as an alternative to the Monte Carlo Tree Search (MCTS) algorithm which drove these breakthroughs. SMC is easier to parallelize and more suitable to GPU acceleration. However, it also suffers from large variance and path degeneracy which prevent it from scaling well with increased search depth, i.e., increased sequential compute. To address these problems, we introduce Twice Sequential Monte Carlo Tree Search (TSMCTS). Across discrete and continuous environments TSMCTS outperforms the SMC baseline as well as a popular modern version of MCTS. Through variance reduction and mitigation of path degeneracy, TSMCTS scales favorably with sequential compute while retaining the properties that make SMC natural to parallelize.

This paper presents a BIM-discrepancy-driven active sensing framework for cooperative navigation between unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) in dynamic construction environments. Traditional navigation approaches rely on static Building Information Modeling (BIM) priors or limited onboard perception. In contrast, our framework continuously fuses real-time LiDAR data from aerial and ground robots with BIM priors to maintain an evolving 2D occupancy map. We quantify navigation safety through a unified corridor-risk metric integrating occupancy uncertainty, BIM-map discrepancy, and clearance. When risk exceeds safety thresholds, the UAV autonomously re-scans affected regions to reduce uncertainty and enable safe replanning. Compared to frontier-based exploration, our approach achieves similar uncertainty reduction in half the mission time. These results demonstrate that integrating BIM priors with risk-adaptive aerial sensing enables scalable, uncertainty-aware autonomy for construction robotics. Introduction Construction sites are among the most dynamic, unstructured, and safety-critical environments for autonomous robots. Unlike factory floors or structured indoor spaces, these environments are marked by continual change. New buildings are erected, materials are relocated, and the movement of heavy machinery and workers can be unpredictable. Such conditions make autonomous navigation particularly challenging. Construction 4.0 [1], emphasizing automation and digitalization, is moving robotics from trial phases to regular use on construction sites.

Bayesian networks (BNs) are a widely used class of probabilistic graphical models employed in numerous application domains. However, inferring the network's graphical structure from data remains challenging. Bayesian structure learners approach this problem by inferring a posterior distribution over the possible directed acyclic graphs underlying the BN. The inference process often requires marginalizing over probability distributions, which is typically done using dynamic programming methods that restrict the set of possible parents for each node. Instead, we present a novel method that utilizes tractable probabilistic circuits to circumvent this restriction. This method utilizes a new learning routine that trains these circuits on both the original distribution and marginal queries. The architecture of probabilistic circuits then inherently allows for fast and exact marginalization on the learned distribution. We then show empirically that utilizing our method to answer marginals allows Bayesian structure learners to improve their performance compared to current methods.

Recently, Bjøru et al. proposed a novel divide-and-conquer algorithm for bounding counterfactual probabilities in structural causal models (SCMs). They assumed that the SCMs were learned from purely observational data, leading to an imprecise characterization of the marginal distributions of exogenous variables. Their method leveraged the canonical representation of structural equations to decompose a general SCM with high-cardinality exogenous variables into a set of sub-models with low-cardinality exogenous variables. These sub-models had precise marginals over the exogenous variables and therefore admitted efficient exact inference. The aggregated results were used to bound counterfactual probabilities in the original model. The approach was developed for Markovian models, where each exogenous variable affects only a single endogenous variable. In this paper, we investigate extending the methodology to \textit{semi-Markovian} SCMs, where exogenous variables may influence multiple endogenous variables. Such models are capable of representing confounding relationships that Markovian models cannot. We illustrate the challenges of this extension using a minimal example, which motivates a set of alternative solution strategies. These strategies are evaluated both theoretically and through a computational study.