Unlike traditional statistical models depending on hand-specified priors, neural processes (NPs) have recently emerged as a class of powerful neural statistical models that combine the strengths of neural networks and stochastic processes. NPs can define a flexible class of stochastic processes well suited for highly non-trivial functions by encoding contextual knowledge into the function space. However, noisy context points introduce challenges to the algorithmic stability that small changes in training data may significantly change the models and yield lower generalization performance. In this paper, we provide theoretical guidelines for deriving stable solutions with high generalization by introducing the notion of algorithmic stability into NPs, which can be flexible to work with various NPs and achieves less biased approximation with theoretical guarantees. To illustrate the superiority of the proposed model, we perform experiments on both synthetic and real-world data, and the results demonstrate that our approach not only helps to achieve more accurate performance but also improves model robustness.

Amortized Bayesian inference (ABI) offers fast, scalable approximations to posterior densities by training neural surrogates on data simulated from the statistical model. However, ABI methods are highly sensitive to model misspecification: when observed data fall outside the training distribution (generative scope of the statistical models), neural surrogates can behave unpredictably. This makes it a challenge in a model comparison setting, where multiple statistical models are considered, of which at least some are misspecified. Recent work on self-consistency (SC) provides a promising remedy to this issue, accessible even for empirical data (without ground-truth labels). In this work, we investigate how SC can improve amortized model comparison conceptualized in four different ways. Across two synthetic and two real-world case studies, we find that approaches for model comparison that estimate marginal likelihoods through approximate parameter posteriors consistently outperform methods that directly approximate model evidence or posterior model probabilities. SC training improves robustness when the likelihood is available, even under severe model misspecification. The benefits of SC for methods without access of analytic likelihoods are more limited and inconsistent. Our results suggest practical guidance for reliable amortized Bayesian model comparison: prefer parameter posterior-based methods and augment them with SC training on empirical datasets to mitigate extrapolation bias under model misspecification.

This manuscript has been submitted for peer review and possible publication in an IEEE journal. The content herein represents the version prepared by the authors and may be subject to further revision during the review. Abstract--Accurately mapping the radio environment (e.g., identifying wireless signal strength at specific frequency bands and geographic locations) is crucial for efficient spectrum sharing, enabling Secondary Users (SUs) to access underutilized spectrum bands while protecting Primary Users (PUs). While existing models have made progress, they often degrade in performance when multiple transmitters coexist, due to the compounded effects of shadowing, interference from adjacent transmitters. T o address this challenge, we extend our prior work on Physics-Informed Neural Networks (PINNs) for single-transmitter mapping to derive a new multi-transmitter Partial Differential Equation (PDE) formulation of the Received Signal Strength Indicator (RSSI). We then propose ReV eal-MT (Re-constructor and Visualizer of Spectrum Landscape for Multiple Transmitters), a novel PINN which integrates the multi-source PDE residual into a neural network loss function, enabling accurate spectrum landscape reconstruction from sparse RF sensor measurements. ReV eal-MT is validated using real-world measurements from the ARA wireless living lab across rural and suburban environments, and benchmarked against 3GPP and ITU-R channel models and a baseline PINN model for a single transmitter use-case. Results show that ReV eal-MT achieves substantial accuracy gains in multi-transmitter scenarios, e.g., achieving an RMSE of only 2.66 dB with as few as 45 samples over a 370-square-kilometer region, while maintaining low computational complexity. These findings demonstrate that ReV eal-MT significantly advances radio environment mapping under realistic multi-transmitter conditions, with strong potential for enabling fine-grained spectrum management and precise coexistence between PUs and SUs. I. INTRODUCTION Existing spectrum sharing frameworks, such as those implemented in the TV White Space (TVWS) database and Citizens Broadband Radio Service (CBRS) Spectrum Access System (SAS), rely heavily on traditional statistical models. However, such models struggle to accurately capture the real-world spectrum occupancy and do not generalize well enough to capture shadowing and fading caused by different kinds of terrain and environmental conditions, leading to conservative approaches that over-protect the primary users (PUs) and cause discrepancies in channel availability for spectrum re-use [1]- [3].

In multi-step learning, where a final learning task is accomplished via a sequence of intermediate learning tasks, the intuition is that successive steps or levels transform the initial data into representations more and more ``suited to the final learning task. A related principle arises in transfer-learning where Baxter (2000) proposed a theoretical framework to study how learning multiple tasks transforms the inductive bias of a learner. The most widespread multi-step learning approach is semi-supervised learning with two steps: unsupervised, then supervised. Several authors (Castelli-Cover, 1996; Balcan-Blum, 2005; Niyogi, 2008; Ben-David et al, 2008; Urner et al, 2011) have analyzed SSL, with Balcan-Blum (2005) proposing a version of the PAC learning framework augmented by a ``compatibility function to link concept class and unlabeled data distribution. We propose to analyze SSL and other multi-step learning approaches, much in the spirit of Baxter's framework, by defining a learning problem generatively as a joint statistical model on $X \times Y$.

Bayesian optimization (BO) is a popular way to tackle optimization problems with expensive objective function evaluations, but has mostly been applied to unconstrained problems.

In this paper, we present a learning algorithm that explicitly considers safety, defined in terms of stability guarantees.

The most widespread multi-step learning approach is semi-supervised learning with two steps: unsupervised, then supervised.

We propose a novel class of network models for temporal dyadic interaction data.

Natural images take up only a tiny fraction of the space of possible images.

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.