arXiv subjects

Lawrence Fulton

Publications and source records attributed to Lawrence Fulton.

4 recordsLinked to original sources

arXiv2026

CORAL: Constrained Oblique Rotation with Anchored Loadings for Fidelity-Constrained Decorrelation

Decorrelating a multivariate system need not destroy source-variable identity. We introduce Constrained Oblique Rotation with Anchored Loadings (CORAL), which minimizes residual cross-correlation while guaranteeing a declared minimum correlation between each transformed variable and its designated source. For a p-variable correlation matrix $R$, we show that every exact decorrelator can be written as $R^{-1/2}Q$ for some orthogonal matrix $Q$, and define $\rho_\star(R)$ as the maximum common source fidelity compatible with exact decorrelation. Constructive lower bounds and rigorous analytical upper bounds tightly bracket $\rho_\star$ at [0.972,0.976], [0.959,0.962], and [0.949,0.950] in simulations with p={6,18,50}, respectively, compared with PCA's largest achievable minimum correlation between distinct principal components and matched source variables of 0.358, 0.329, and 0.172. Corresponding intervals are [0.751,0.758] for World Development Indicators and [0.826,0.835] for wine chemistry data sets. Thus, loss of source-variable identity is not inherent to exact decorrelation but depends on the decorrelator selected. CORAL uses constrained Riemannian optimization and extends to exact support restrictions.

stat.ME↗

arXiv2026

Classical $\mathrm{SU}(2)$ Models Match or Exceed Shallow Variational Quantum Circuits on Vision Benchmarks

Quaternion-valued neural networks and variational quantum circuits (VQCs) both derive local transformations from $\mathrm{SU}(2)$ geometry, yet their performance on classical supervised learning remains poorly understood. We compare real-valued, quaternion-valued, and quantum classification heads on identical frozen features across MNIST, FashionMNIST, and CIFAR-10. CIFAR-10 uses a learned 16-dimensional bottleneck and frozen ImageNet-pretrained ResNet18 features to separate architecture from representation quality. Quaternion classifiers match or approach real-valued baselines while outperforming shallow VQCs. On MNIST and FashionMNIST, quaternion networks nearly equal real-valued MLPs, whereas product-state VQCs show lower accuracy and higher cost. On CIFAR-10, quaternion networks retain 94--97% of real-valued performance and remain stable under a 32-fold increase in dimensionality. Product-state circuits underperform quaternion classifiers, while entanglement gives modest grayscale gains but reverses under pretrained CNN features (9.25 pp degradation vs.\ product-state). Fubini--Study/QFI natural gradients improve geometric alignment but not short-horizon loss reduction vs.\ Adam. A Friedman test on five-seed MNIST detects model differences ($\chi^2=12.796$, $p=0.0051$, $n=5$), with Wilcoxon tests yielding large effect sizes ($d>5$) for QuatNet vs.\ quantum comparisons. For FashionMNIST and CIFAR-10, large effects ($d>2.0$) are the primary statistic given $n=3$. These results indicate that quaternion networks provide efficient, stable $\mathrm{SU}(2)$ alternatives to shallow VQCs on tasks lacking intrinsic quantum structure. Shared local $\mathrm{SU}(2)$ geometry and shallow entanglement are insufficient, within the regime studied, to confer practical quantum advantage. Conclusions are limited to shallow, measurement-limited circuits on such tasks.

cs.PF↗

arXiv2026

Retrospective Orthogonal Design: Response-Surface Reconstruction from Observational Data

Regression estimates from observational data can depend on specification under multicollinearity, while sequential sums of squares (SS) depend on term order. We introduce Retrospective Orthogonal Design (ROD), which reconstructs conditional mean surfaces on a probability-balanced lattice. ROD preserves observed cell means, completes unsupported cells, applies weighted tensor-product contrasts, and evaluates the reconstructed surface through piecewise-affine interpolation over Freudenthal polyhedra. Resolution and completion are selected jointly by validation among rank-admissible candidates, followed by refitting and evaluation on an untouched test set. For an admissible lattice, $\mathbf{X}^{\top}\mathbf{W}\mathbf{X}=c\mathbf{I}$, yielding specification-invariant contrast effects and unique, order-independent SS within the retained contrast space. Response-free projection calibration maps the fixed reconstruction onto a declared scientific basis and corrects finite-resolution recovery loss. Across 6,480 simulation conditions spanning nine data-generating processes, ROD matched or exceeded polynomial regression in five processes and performed strongest on threshold, sign-interaction, and localized surfaces. For the quadratic-interaction process, mean out-of-sample $R^2$ differed by only $0.0001$, while calibrated coefficient bias remained small across prespecified targets. A Rao-based information adjustment provides dependence-aware sample-size guidance for ROD planning. In a weighted Mincer application, ROD produced the highest out-of-sample $R^2$ point estimate, with substantial interval overlap with polynomial regression, and provided exhaustive SS allocations invariant to term-entry order.

stat.ME↗

arXiv2020

Social Media Information Sharing for Natural Disaster Response

Social media has become an essential channel for posting disaster-related information, which provide governments and relief agencies real-time data for better disaster management. However, research in this field has not received sufficient attention and extracting useful information is still challenging. This paper aims to improve disaster relief efficiency via mining and analyzing social media data like public attitudes towards disaster response and public demands for targeted relief supplies during different types of disasters. We focus on different natural disasters based on properties such as types, durations, and damages, which contains a total of 41,993 tweets. In this paper, public perception is assessed qualitatively by manually classified tweets, which contain information like the demand for targeted relief supplies, satisfactions of disaster response, and public fear. Public attitudes to natural disasters are studied via a quantitative analysis using eight machine learning models. To better provide decision-makers with the appropriate model, the comparison of machine learning models based on computational time and prediction accuracy is conducted. The change of public opinion during different natural disasters and the evolution of people's behavior of using social media for disaster relief in the face of the identical type of natural disasters as Twitter continues to evolve are studied. The results in this paper demonstrate the feasibility and validation of the proposed research approach and provide relief agencies with insights into better disaster management.

cs.SI↗