Conformal prediction (CP) is an Uncertainty Representation technique that delivers finite-sample calibrated prediction regions for any underlying Machine Learning model. Its status as an Uncertainty Quantification (UQ) tool, though, has remained conceptually opaque: While Conformal Prediction Regions (CPRs) give an ordinal representation of uncertainty (larger regions typically indicate higher uncertainty), they lack the capability to cardinally quantify it (twice as large regions do not imply twice the uncertainty). We adopt a category-theoretic approach to CP -- framing it as a morphism, embedded in a commuting diagram, of two newly-defined categories -- that brings us three joys. First, we show that -- under minimal assumptions -- CP is intrinsically a UQ mechanism, that is, its cardinal UQ capabilities are a structural feature of the method. Second, we demonstrate that CP bridges (and perhaps subsumes) the Bayesian, frequentist, and imprecise probabilistic approaches to predictive statistical reasoning. Finally, we show that a CPR is the image of a covariant functor. This observation is relevant to AI privacy: It implies that privacy noise added locally does not break the global coverage guarantee.

Regularized linear discriminant analysis (RLDA) is a widely used tool for classification and dimensionality reduction, but its performance in high-dimensional scenarios is inconsistent. Existing theoretical analyses of RLDA often lack clear insight into how data structure affects classification performance. To address this issue, we derive a non-asymptotic approximation of the misclassification rate and thus analyze the structural effect and structural adjustment strategies of RLDA. Based on this, we propose the Spectral Enhanced Discriminant Analysis (SEDA) algorithm, which optimizes the data structure by adjusting the spiked eigenvalues of the population covariance matrix. By developing a new theoretical result on eigenvectors in random matrix theory, we derive an asymptotic approximation on the misclassification rate of SEDA. The bias correction algorithm and parameter selection strategy are then obtained. Experiments on synthetic and real datasets show that SEDA achieves higher classification accuracy and dimensionality reduction compared to existing LDA methods.

This thesis advances the computational understanding and manipulation of text styles through three interconnected pillars: (1) Text Style Transfer (TST), which alters stylistic properties (e.g., sentiment, formality) while preserving content; (2)Authorship Attribution (AA), identifying the author of a text via stylistic fingerprints; and (3) Authorship V erification (A V), determining whether two texts share the same authorship. We address critical challenges in these areas by leveraging parameter-efficient adaptation of large language models (LLMs), contrastive disentanglement of stylistic features, and instruction-based fine-tuning for explainable verification. First, for TST, we conduct a comprehensive survey and reproducibility study of 19 state-of-the-art algorithms, establishing benchmarks across diverse datasets. Building on these insights, we introduce LLM-Adapters, a unified framework for parameter-efficient fine-tuning (PEFT) that enables cost-effective adaptation of LLMs for style-centric tasks. This culminates in Adapter-TST, a novel architecture that models multiple stylistic attributes (e.g., sentiment, tense) using lightweight neural adapters. Adapter-TST achieves superior performance in multi-attribute transfer and compositional editing while reducing computational costs by 80% compared to full fine-tuning. For AA, we propose ContrastDistAA, a contrastive learning framework that disentangles content and style features to address performance degradation under topic shifts. Our method advances both individual-level attribution and regional linguistic analysis, achieving state-of-the-art accuracy by isolating culturally influenced stylistic patterns.

This study evaluated the probability and uncertainty forecasts of five recently proposed Bayesian deep learning methods relative to a deterministic residual neural network (ResNet) baseline for 0-1 h convective initiation (CI) nowcasting using GOES-16 satellite infrared observations. Uncertainty was assessed by how well probabilistic forecasts were calibrated and how well uncertainty separated forecasts with large and small errors. Most of the Bayesian deep learning methods produced probabilistic forecasts that outperformed the deterministic ResNet, with one, the initial-weights ensemble + Monte Carlo (MC) dropout, an ensemble of deterministic ResNets with different initial weights to start training and dropout activated during inference, producing the most skillful and well-calibrated forecasts. The initial-weights ensemble + MC dropout benefited from generating multiple solutions that more thoroughly sampled the hypothesis space. The Bayesian ResNet ensemble was the only one that performed worse than the deterministic ResNet at longer lead times, likely due to the challenge of optimizing a larger number of parameters. To address this issue, the Bayesian-MOPED (MOdel Priors with Empirical Bayes using Deep neural network) ResNet ensemble was adopted, and it enhanced forecast skill by constraining the hypothesis search near the deterministic ResNet hypothesis. All Bayesian methods demonstrated well-calibrated uncertainty and effectively separated cases with large and small errors. In case studies, the initial-weights ensemble + MC dropout demonstrated better forecast skill than the Bayesian-MOPED ensemble and the deterministic ResNet on selected CI events in clear-sky regions. However, the initial-weights ensemble + MC dropout exhibited poorer generalization in clear-sky and anvil cloud regions without CI occurrence compared to the deterministic ResNet and Bayesian-MOPED ensemble.

A common approach for handling missing values in data analysis pipelines is multiple imputation via software packages such as MICE (Van Buuren and Groothuis-Oudshoorn, 2011) and Amelia (Honaker et al., 2011). These packages typically assume the data are missing at random (MAR), and impose parametric or smoothing assumptions upon the imputing distributions in a way that allows imputation to proceed even if not all missingness patterns have support in the data. Such assumptions are unrealistic in practice, and induce model misspecification bias on any analysis performed after such imputation. In this paper, we provide a principled alternative. Specifically, we develop a new characterization for the full data law in graphical models of missing data. This characterization is constructive, is easily adapted for the calculation of imputation distributions for both MAR and MNAR (missing not at random) mechanisms, and is able to handle lack of support for certain patterns of missingness. We use this characterization to develop a new imputation algorithm -- Multivariate Imputation via Supported Pattern Recursion (MISPR) -- which uses Gibbs sampling, by analogy with the Multivariate Imputation with Chained Equations (MICE) algorithm, but which is consistent under both MAR and MNAR settings, and is able to handle missing data patterns with no support without imposing additional assumptions beyond those already imposed by the missing data model itself. In simulations, we show MISPR obtains comparable results to MICE when data are MAR, and superior, less biased results when data are MNAR. Our characterization and imputation algorithm based on it are a step towards making principled missing data methods more practical in applied settings, where the data are likely both MNAR and sufficiently high dimensional to yield missing data patterns with no support at available sample sizes.

Calibrating the confidence of neural network classifiers is essential for quantifying the reliability of their predictions during inference. However, conventional Gaussian Process (GP) calibration methods often fail to capture the internal hierarchical structure of deep neural networks, limiting both interpretability and effectiveness for assessing predictive reliability. We propose a Semantic-Aware Layer-wise Gaussian Process (SAL-GP) framework that mirrors the layered architecture of the target neural network. Instead of applying a single global GP correction, SAL-GP employs a multi-layer GP model, where each layer's feature representation is mapped to a local calibration correction. These layerwise GPs are coupled through a structured multi-layer kernel, enabling joint marginalization across all layers. This design allows SAL-GP to capture both local semantic dependencies and global calibration coherence, while consistently propagating predictive uncertainty through the network. The resulting framework enhances interpretability aligned with the network architecture and enables principled evaluation of confidence consistency and uncertainty quantification in deep models.

Despite the transformative potential of AI, the concept of neural networks that can produce other neural networks by generating model weights (hypernetworks) has been largely understudied. One of the possible reasons is the lack of available research resources that can be used for the purpose of hypernetwork research. Here we describe a dataset of neural networks, designed for the purpose of hypernetworks research. The dataset includes $10^4$ LeNet-5 neural networks trained for binary image classification separated into 10 classes, such that each class contains 1,000 different neural networks that can identify a certain ImageNette V2 class from all other classes. A computing cluster of over $10^4$ cores was used to generate the dataset. Basic classification results show that the neural networks can be classified with accuracy of 72.0%, indicating that the differences between the neural networks can be identified by supervised machine learning algorithms. The ultimate purpose of the dataset is to enable hypernetworks research. The dataset and the code that generates it are open and accessible to the public.

This paper addresses the critical need for high-quality evaluation datasets in low-resource languages to advance cross-lingual transfer. While cross-lingual transfer offers a key strategy for leveraging multilingual pretraining to expand language technologies to understudied and typologically diverse languages, its effectiveness is dependent on quality and suitable benchmarks. We release new sense-annotated datasets of sentences containing polysemous words, spanning ten low-resource languages across diverse language families and scripts. To facilitate dataset creation, the paper presents a demonstrably beneficial semi-automatic annotation method. The utility of the datasets is demonstrated through Word-in-Context (WiC) formatted experiments that evaluate transfer on these low-resource languages. Results highlight the importance of targeted dataset creation and evaluation for effective polysemy disambiguation in low-resource settings and transfer studies. The released datasets and code aim to support further research into fair, robust, and truly multilingual NLP.

Quantum sensing harnesses the unique properties of quantum systems to enable precision measurements of physical quantities such as time, magnetic and electric fields, acceleration, and gravitational gradients well beyond the limits of classical sensors. However, identifying suitable sensing probes and measurement schemes can be a classically intractable task, as it requires optimizing over Hilbert spaces of high dimension. In variational quantum sensing, a probe quantum system is generated via a parameterized quantum circuit (PQC), exposed to an unknown physical parameter through a quantum channel, and measured to collect classical data. PQCs and measurements are typically optimized using offline strategies based on frequentist learning criteria. This paper introduces an adaptive protocol that uses Bayesian inference to optimize the sensing policy via the maximization of the active information gain. The proposed variational methodology is tailored for non-asymptotic regimes where a single probe can be deployed in each time step, and is extended to support the fusion of estimates from multiple quantum sensing agents.

Human intelligence exhibits a remarkable capacity for rapid adaptation and effective problem-solving in novel and unfamiliar contexts. We argue that this profound adaptability is fundamentally linked to the efficient construction and refinement of internal representations of the environment, commonly referred to as world models, and we refer to this adaptation mechanism as world model induction . However, current understanding and evaluation of world models in artificial intelligence (AI) remains narrow, often focusing on static representations learned from training on massive corpora of data, instead of the efficiency and efficacy in learning these representations through interaction and exploration within a novel environment. In this Perspective, we provide a view of world model induction drawing on decades of research in cognitive science on how humans learn and adapt so efficiently; we then call for a new evaluation framework for assessing adaptive world models in AI. Concretely, we propose a new benchmarking paradigm based on suites of carefully designed games with genuine, deep and continually refreshing novelty in the underlying game structures -- we refer to this class of games as novel games . We detail key desiderata for constructing these games and propose appropriate metrics to explicitly challenge and evaluate the agent's ability for rapid world model induction. We hope that this new evaluation framework will inspire future evaluation efforts on world models in AI and provide a crucial step towards developing AI systems capable of human-like rapid adaptation and robust generalization -- a critical component of artificial general intelligence.