In addition to accurate scene understanding through precise semantic segmentation of LiDAR point clouds, detecting out-of-distribution (OOD) objects, instances not encountered during training, is essential to prevent the incorrect assignment of unknown objects to known classes. While supervised OOD detection methods depend on auxiliary OOD datasets, unsupervised methods avoid this requirement but typically rely on predictive entropy, the entropy of the predictive distribution obtained by averaging over an ensemble or multiple posterior weight samples. However, these methods often conflate epistemic (model) and aleatoric (data) uncertainties, misclassifying ambiguous in distribution regions as OOD. To address this issue, we present an unsupervised OOD detection approach that employs epistemic uncertainty derived from hierarchical Bayesian modeling of Gaussian Mixture Model (GMM) parameters in the feature space of a deep neural network. Without requiring auxiliary data or additional training stages, our approach outperforms existing uncertainty-based methods on the SemanticKITTI dataset, achieving an 18\% improvement in AUROC, 22\% increase in AUPRC, and 36\% reduction in FPR95 (from 76\% to 40\%), compared to the predictive entropy approach used in prior works.

Phylogenetic trees elucidate evolutionary relationships among species, but phylogenetic inference remains challenging due to the complexity of combining continuous (branch lengths) and discrete parameters (tree topology).

Differentiable structure learning is a novel line of causal discovery research that transforms the combinatorial optimization of structural models into a continuous optimization problem. However, the field has lacked feasible methods to integrate partial order constraints, a critical prior information typically used in real-world scenarios, into the differentiable structure learning framework. The main difficulty lies in adapting these constraints, typically suited for the space of total orderings, to the continuous optimization context of structure learning in the graph space. To bridge this gap, this paper formalizes a set of equivalent constraints that map partial orders onto graph spaces and introduces a plug-and-play module for their efficient application. This module preserves the equivalent effect of partial order constraints in the graph space, backed by theoretical validations of correctness and completeness. It significantly enhances the quality of recovered structures while maintaining good efficiency, which learns better structures using 90% fewer samples than the data-based method on a real-world dataset. This result, together with a comprehensive evaluation on synthetic cases, demonstrates our method's ability to effectively improve differentiable structure learning with partial orders.

Causal discovery is essential for understanding relationships among variables of interest in many scientific domains. In this paper, we focus on permutation-based methods for learning causal graphs in Linear Gaussian Acyclic Models (LiGAMs), where the permutation encodes a causal ordering of the variables. Existing methods in this setting do not scale due to their high computational complexity.

ML models call for an equitable model valuation method to price them. In particular, we investigate the black-box access setting which allows querying a model (to observe predictions) without disclosing model-specific information (e.g., architecture and parameters). By exploiting a Dirichlet abstraction of a model's predictions, we propose a novel and equitable model valuation method called

Probabilistic principal component analysis (PPCA) is currently one of the most used statistical tools to reduce the ambient dimension of the data.