Using simulated data and text data, we investigate the properties of these estimators. Lastly, we also study a modified problem in which the observation stream consists of collections of tokens (i.e., documents) arising from a random measure drawn from a stable beta process,

Neural Information Processing Systems http://nips.cc/

The purpose of this work is to study the general properties of this quantity and to show how they can be leveraged in practice.

Neural Information Processing Systems http://nips.cc/

Data serves as the fundamental basis for advancing deep learning.

Conformal prediction (CP) constructs uncertainty sets for model outputs with finite-sample coverage guarantees. A candidate output is included in the prediction set if its non-conformity score is not considered extreme relative to the scores observed on a set of calibration examples. However, this procedure is only straightforward when scores are scalar-valued, which has limited CP to real-valued scores or ad-hoc reductions to one dimension. The problem of ordering vectors has been studied via optimal transport (OT), which provides a principled method for defining vector-ranks and multivariate quantile regions, though typically with only asymptotic coverage guarantees. We restore finite-sample, distribution-free coverage by conformalizing the vector-valued OT quantile region. Here, a candidate's rank is defined via a transport map computed for the calibration scores augmented with that candidate's score. This defines a continuum of OT problems for which we prove that the resulting optimal assignment is piecewise-constant across a fixed polyhedral partition of the score space. This allows us to characterize the entire prediction set tractably, and provides the machinery to address a deeper limitation of prediction sets: that they only indicate which outcomes are plausible, but not their relative likelihood. In one dimension, conformal predictive distributions (CPDs) fill this gap by producing a predictive distribution with finite-sample calibration. Extending CPDs beyond one dimension remained an open problem. We construct, to our knowledge, the first multivariate CPDs with finite-sample calibration, i.e., they define a valid multivariate distribution where any derived uncertainty region automatically has guaranteed coverage. We present both conservative and exact randomized versions, the latter resulting in a multivariate generalization of the classical Dempster-Hill procedure.

We present a class of algorithms for state estimation in nonlinear, non-Gaussian state-space models. Our approach is based on a variational Lagrangian formulation that casts Bayesian inference as a sequence of entropic trust-region updates subject to dynamic constraints. This framework gives rise to a family of forward-backward algorithms, whose structure is determined by the chosen factorization of the variational posterior. By focusing on Gauss--Markov approximations, we derive recursive schemes with favorable computational complexity. For general nonlinear, non-Gaussian models we close the recursions using generalized statistical linear regression and Fourier--Hermite moment matching.

Abstract--Conventional radio frequency (RF) passive components modeling based on machine learning requires extensive electromagnetic (EM) simulations to cover geometric and frequency design spaces, creating computational bottlenecks. In this paper, we introduce an uncertainty-aware Bayesian online learning framework for efficient parametric modeling of RF passive components, which includes: 1) a Bayesian neural network with reconfigurable heads for joint geometric-frequency domain modeling while quantifying uncertainty; 2) an adaptive sampling strategy that simultaneously optimizes training data sampling across geometric parameters and frequency domain using uncertainty guidance. V alidated on three RF passive components, the framework achieves accurate modeling while using only 2.86% EM simulation time compared to traditional ML-based flow, achieving a 35 speedup. Radio frequency integrated circuits (RFICs) form the cornerstone of modern communication systems, enabling critical technologies from 5G/6G networks to Internet-of-Things (IoT) devices [1]. As operational frequencies increase into millimeter-wave and terahertz regimes, traditional lumped-element circuit models become inadequate in mm-wave circuits.

Accurate prediction of project duration and cost remains one of the most challenging aspects of project management, particularly in resource-constrained and interdependent task networks. Traditional analytical techniques such as the Critical Path Method (CPM) and Program Evaluation and Review Technique (PERT) rely on simplified and often static assumptions regarding task interdependencies and resource performance. This study proposes a novel resource-based predictive framework that integrates network representations of project activities with graph neural networks (GNNs) to capture structural and contextual relationships among tasks, resources, and time-cost dynamics. The model represents the project as a heterogeneous activity-resource graph in which nodes denote activities and resources, and edges encode temporal and resource dependencies. We evaluate multiple learning paradigms, including GraphSAGE and Temporal Graph Networks, on both synthetic and benchmark project datasets. Experimental results show that the proposed GNN framework achieves an average 23 to 31 percent reduction in mean absolute error compared to traditional regression and tree-based methods, while improving the coefficient of determination R2 from approximately 0.78 to 0.91 for large and complex project networks. Furthermore, the learned embeddings provide interpretable insights into resource bottlenecks and critical dependencies, enabling more explainable and adaptive scheduling decisions.