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.

Large language models (LLMs) are increasingly applied to sequential decision-making through in-context learning (ICL), yet their effectiveness is highly sensitive to prompt quality. Effective prompts should meet three principles: focus on decision-critical information, provide step-level granularity, and minimize reliance on expert annotations through label efficiency. However, existing ICL methods often fail to satisfy all three criteria simultaneously. Motivated by these challenges, we introduce SkillGen, a skill-based ICL framework for structured sequential reasoning. It constructs an action-centric, domain-level graph from sampled trajectories, identifies high-utility actions via temporal-difference credit assignment, and retrieves step-wise skills to generate fine-grained, context-aware prompts. We further present a theoretical analysis showing that focusing on high-utility segments supports task identifiability and informs more effective ICL prompt design. Experiments on ALFWorld, BabyAI, and ScienceWorld, using both open-source and proprietary LLMs, show that SkillGen achieves consistent gains, improving progress rate by 5.9%-16.5% on average across models.

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.

Robust humanoid locomotion requires accurate and globally consistent perception of the surrounding 3D environment. However, existing perception modules, mainly based on depth images or elevation maps, offer only partial and locally flattened views of the environment, failing to capture the full 3D structure. This paper presents Gallant, a voxel-grid-based framework for humanoid locomotion and local navigation in 3D constrained terrains. It leverages voxelized LiDAR data as a lightweight and structured perceptual representation, and employs a z-grouped 2D CNN to map this representation to the control policy, enabling fully end-to-end optimization. A high-fidelity LiDAR simulation that dynamically generates realistic observations is developed to support scalable, LiDAR-based training and ensure sim-to-real consistency. Experimental results show that Gallant's broader perceptual coverage facilitates the use of a single policy that goes beyond the limitations of previous methods confined to ground-level obstacles, extending to lateral clutter, overhead constraints, multi-level structures, and narrow passages. Gallant also firstly achieves near-100% success rates in challenging scenarios such as stair climbing and stepping onto elevated platforms through improved end-to-end optimization.

Learning the parameters of Partially Observable Markov Decision Processes (POMDPs) from limited data is a significant challenge. We introduce the Fuzzy MAP EM algorithm, a novel approach that incorporates expert knowledge into the parameter estimation process by enriching the Expectation Maximization (EM) framework with fuzzy pseudo-counts derived from an expert-defined fuzzy model. This integration naturally reformulates the problem as a Maximum A Posteriori (MAP) estimation, effectively guiding learning in environments with limited data. In synthetic medical simulations, our method consistently outperforms the standard EM algorithm under both low-data and high-noise conditions. Furthermore, a case study on Myasthenia Gravis illustrates the ability of the Fuzzy MAP EM algorithm to recover a clinically coherent POMDP, demonstrating its potential as a practical tool for data-efficient modeling in healthcare.

Effective contact-rich manipulation requires robots to synergistically leverage vision, force, and proprioception. However, Reinforcement Learning agents struggle to learn in such multisensory settings, especially amidst sensory noise and dynamic changes. We propose MultiSensory Dynamic Pretraining (MSDP), a novel framework for learning expressive multisensory representations tailored for task-oriented policy learning. MSDP is based on masked autoencoding and trains a transformer-based encoder by reconstructing multisensory observations from only a subset of sensor embeddings, leading to cross-modal prediction and sensor fusion. For downstream policy learning, we introduce a novel asymmetric architecture, where a cross-attention mechanism allows the critic to extract dynamic, task-specific features from the frozen embeddings, while the actor receives a stable pooled representation to guide its actions. Our method demonstrates accelerated learning and robust performance under diverse perturbations, including sensor noise, and changes in object dynamics. Evaluations in multiple challenging, contact-rich robot manipulation tasks in simulation and the real world showcase the effectiveness of MSDP. Our approach exhibits strong robustness to perturbations and achieves high success rates on the real robot with as few as 6,000 online interactions, offering a simple yet powerful solution for complex multisensory robotic control.

Classifier-Free Guidance (CFG) has become a mainstream approach for simultaneously improving prompt fidelity and generation quality in conditional generative models. During training, CFG stochastically alternates between conditional and null prompts to enable both conditional and unconditional generation. However, during sampling, CFG outputs both null and conditional prompts simultaneously, leading to inconsistent noise estimates between the training and sampling processes. To reduce this error, we propose CFG-EC, a versatile correction scheme augmentable to any CFG-based method by refining the unconditional noise predictions. CFG-EC actively realigns the unconditional noise error component to be orthogonal to the conditional error component. This corrective maneuver prevents interference between the two guidance components, thereby constraining the sampling error's upper bound and establishing more reliable guidance trajectories for high-fidelity image generation. Our numerical experiments show that CFG-EC handles the unconditional component more effectively than CFG and CFG++, delivering a marked performance increase in the low guidance sampling regime and consistently higher prompt alignment across the board.