In many applications, observations are naturally grouped into different classes.

We establish a new theoretical framework for learning under multi-class, instance-dependent label noise. This framework casts learning with label noise as a form of domain adaptation, in particular, domain adaptation under posterior drift.

Recently, Sur and Candès [2019] showed that these issues can be corrected by applying a new approximation of the MLE's sampling distribution in this highdimensional regime. Unfortunately, these corrections are difficult to implement in practice, because they require an estimate of thesignal strength, which is a function of the underlying parametersβ of the logistic regression.

Partial Least Squares (PLS) learns shared structure from paired data via the top singular vectors of the empirical cross-covariance (PLS-SVD), but multimodal datasets often have missing entries in both views. We study PLS-SVD under independent entry-wise missing-completely-at-random masking in a proportional high-dimensional spiked model. After appropriate normalization, the masked cross-covariance behaves like a spiked rectangular random matrix whose effective signal strength is attenuated by $\sqrtρ$, where $ρ$ is the joint entry retention probability. As a result, PLS-SVD exhibits a sharp BBP-type phase transition: below a critical signal-to-noise threshold the leading singular vectors are asymptotically uninformative, while above it they achieve nontrivial alignment with the latent shared directions, with closed-form asymptotic overlap formulas. Simulations and semi-synthetic multimodal experiments corroborate the predicted phase diagram and recovery curves across aspect ratios, signal strengths, and missingness levels.

Logistic regression remains one of the most widely used tools in applied statistics, machine learning and data science. However, in moderately high-dimensional problems, where the number of features $d$ is a non-negligible fraction of the sample size $n$, the logistic regression maximum likelihood estimator (MLE), and statistical procedures based the large-sample approximation of its distribution, behave poorly. Recently, Sur and Candès (2019) showed that these issues can be corrected by applying a new approximation of the MLE's sampling distribution in this high-dimensional regime. Unfortunately, these corrections are difficult to implement in practice, because they require an estimate of the \emph{signal strength}, which is a function of the underlying parameters $\beta$ of the logistic regression. To address this issue, we propose SLOE, a fast and straightforward approach to estimate the signal strength in logistic regression. The key insight of SLOE is that the Sur and Candès (2019) correction can be reparameterized in terms of the corrupted signal strength, which is only a function of the estimated parameters $\widehat \beta$. We propose an estimator for this quantity, prove that it is consistent in the relevant high-dimensional regime, and show that dimensionality correction using SLOE is accurate in finite samples. Compared to the existing ProbeFrontier heuristic, SLOE is conceptually simpler and orders of magnitude faster, making it suitable for routine use. We demonstrate the importance of routine dimensionality correction in the Heart Disease dataset from the UCI repository, and a genomics application using data from the UK Biobank.

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 millimeter wave (mmWave) communications, beam alignment and tracking are crucial to combat the significant path loss. As scanning the entire directional space is inefficient, designing an efficient and robust method to identify the optimal beam directions is essential. Since traditional bandit algorithms require a long time horizon to converge under large beam spaces, many existing works propose efficient bandit algorithms for beam alignment by relying on unimodality or multimodality assumptions on the reward function's structure. However, such assumptions often do not hold (or cannot be strictly satisfied) in practice, which causes such algorithms to converge to choosing suboptimal beams. In this work, we propose two physics-informed bandit algorithms \textit{pretc} and \textit{prgreedy} that exploit the sparse multipath property of mmWave channels - a generic but realistic assumption - which is connected to the Phase Retrieval Bandit problem. Our algorithms treat the parameters of each path as black boxes and maintain optimal estimates of them based on sampled historical rewards. \textit{pretc} starts with a random exploration phase and then commits to the optimal beam under the estimated reward function. \textit{prgreedy} performs such estimation in an online manner and chooses the best beam under current estimates. Our algorithms can also be easily adapted to beam tracking in the mobile setting. Through experiments using both the synthetic DeepMIMO dataset and the real-world DeepSense6G dataset, we demonstrate that both algorithms outperform existing approaches in a wide range of scenarios across diverse channel environments, showing their generalizability and robustness.

We establish a new theoretical framework for learning under multi-class, instance-dependent label noise. This framework casts learning with label noise as a form of domain adaptation, in particular, domain adaptation under posterior drift.