We propose semantic anchoring, a unified account of how large language models turn pretrained capacity into goal-directed behavior: external structure (in-context examples, retrieval, or light tuning) binds the model's latent patterns to desired targets. Unified Contextual Control Theory (UCCT) formalizes this via anchoring strength $S = ρ_d - d_r - \log k$, where $ρ_d$ measures target cohesion in representation space, $d_r$ measures mismatch from prior knowledge, and $k$ is the anchor budget. UCCT predicts threshold-like performance flips and strictly generalizes in-context learning, reading retrieval and fine-tuning as anchoring variants. Three controlled studies provide evidence. Experiment 1 demonstrates cross-domain anchoring rebinding strong priors in text and vision. Experiment 2 varies representational familiarity via numeral bases (base-10/8/9) at fixed complexity, yielding ordered thresholds and transfer patterns tracking $ρ_d$, $d_r$, and $S$. Experiment 3 establishes a geometry-to-behavior correlate: layer-wise peak anchoring and trajectory area predict few-shot thresholds $θ_{50}$. UCCT offers testable theory and practical metrics for optimizing prompts, retrieval, and tuning.

Machine learning models perform well across domains such as diagnostics, weather forecasting, NLP, and autonomous driving, but their limited uncertainty handling restricts use in safety-critical settings. Traditional neural networks often fail to detect out-of-domain (OOD) data and may output confident yet incorrect predictions. Bayesian neural networks (BNNs) address this by providing probabilistic estimates, but incur high computational cost because predictions require sampling weight distributions and multiple forward passes. The Probabilistic Forward Pass (PFP) offers a highly efficient approximation to Stochastic Variational Inference (SVI) by assuming Gaussian-distributed weights and activations, enabling fully analytic uncertainty propagation and replacing sampling with a single deterministic forward pass. We present an end-to-end pipeline for training, compiling, optimizing, and deploying PFP-based BNNs on embedded ARM CPUs. Using the TVM deep learning compiler, we implement a dedicated library of Gaussian-propagating operators for multilayer perceptrons and convolutional neural networks, combined with manual and automated tuning strategies. Ablation studies show that PFP consistently outperforms SVI in computational efficiency, achieving speedups of up to 4200x for small mini-batches. PFP-BNNs match SVI-BNNs on Dirty-MNIST in accuracy, uncertainty estimation, and OOD detection while greatly reducing compute cost. These results highlight the potential of combining Bayesian approximations with code generation to enable efficient BNN deployment on resource-constrained systems.

Bayesian computational strategies for inference can be inefficient in approximating the posterior distribution in models that exhibit some form of periodicity. This is because the probability mass of the marginal posterior distribution of the parameter representing the period is usually highly concentrated in a very small region of the parameter space. Therefore, it is necessary to provide as much information as possible to the inference method through the parameter prior distribution. We intend to show that it is possible to construct a prior distribution from the data by fitting a Gaussian process (GP) with a periodic kernel. More specifically, we want to show that it is possible to approximate the marginal posterior distribution of the hyperparameter corresponding to the period in the kernel. Subsequently, this distribution can be used as a prior distribution for the inference method. We use an adaptive importance sampling method to approximate the posterior distribution of the hyperparameters of the GP. Then, we use the marginal posterior distribution of the hyperparameter related to the periodicity in order to construct a prior distribution for the period of the parametric model. This workflow is empirical Bayes, implemented as a modular (cut) transfer of a GP posterior for the period to the parametric model. We applied the proposed methodology to both synthetic and real data. We approximated the posterior distribution of the period of the GP kernel and then passed it forward as a posterior-as-prior with no feedback. Finally, we analyzed its impact on the marginal posterior distribution.

Support vector machines are widely used in machine learning classification tasks, but traditional SVM models suffer from sensitivity to outliers and instability in resampling, which limits their performance in practical applications. To address these issues, this paper proposes a novel rescaled Huberized pinball loss function with asymmetric, non-convex, and smooth properties. Based on this loss function, we develop a corresponding SVM model called RHPSVM (Rescaled Huberized Pinball Loss Support Vector Machine). Theoretical analyses demonstrate that RHPSVM conforms to Bayesian rules, has a strict generalization error bound, a bounded influence function, and controllable optimality conditions, ensuring excellent classification accuracy, outlier insensitivity, and resampling stability. Additionally, RHPSVM can be extended to various advanced SVM variants by adjusting parameters, enhancing its flexibility. We transform the non-convex optimization problem of RHPSVM into a series of convex subproblems using the concave-convex procedure (CCCP) and solve it with the ClipDCD algorithm, which is proven to be convergent. Experimental results on simulated data, UCI datasets, and small-sample crop leaf image classification tasks show that RHPSVM outperforms existing SVM models in both noisy and noise-free scenarios, especially in handling high-dimensional small-sample data.

Uncertainty quantification is vital for decision-making and risk assessment in machine learning. Mean-variance regression models, which predict both a mean and residual noise for each data point, provide a simple approach to uncertainty quantification. However, overparameterized mean-variance models struggle with signal-to-noise ambiguity, deciding whether prediction targets should be attributed to signal (mean) or noise (variance). At one extreme, models fit all training targets perfectly with zero residual noise, while at the other, they provide constant, uninformative predictions and explain the targets as noise. We observe a sharp phase transition between these extremes, driven by model regularization. Empirical studies with varying regularization levels illustrate this transition, revealing substantial variability across repeated runs. To explain this behavior, we develop a statistical field theory framework, which captures the observed phase transition in alignment with experimental results. This analysis reduces the regularization hyperparameter search space from two dimensions to one, significantly lowering computational costs. Experiments on UCI datasets and the large-scale ClimSim dataset demonstrate robust calibration performance, effectively quantifying predictive uncertainty.

Label shift, a prevalent challenge in supervised learning, arises when the class prior distribution of test data differs from that of training data, leading to significant degradation in classifier performance. To accurately estimate the test priors and enhance classification accuracy, we propose a Bayesian framework for label shift estimation, termed Full Maximum A Posterior Label Shift (FMAPLS), along with its online version, online-FMAPLS. Leveraging batch and online Expectation-Maximization (EM) algorithms, these methods jointly and dynamically optimize Dirichlet hyperparameters $\boldsymbolα$ and class priors $\boldsymbolπ$, thereby overcoming the rigid constraints of the existing Maximum A Posterior Label Shift (MAPLS) approach. Moreover, we introduce a linear surrogate function (LSF) to replace gradient-based hyperparameter updates, yielding closed-form solutions that reduce computational complexity while retaining asymptotic equivalence. The online variant substitutes the batch E-step with a stochastic approximation, enabling real-time adaptation to streaming data. Furthermore, our theoretical analysis reveals a fundamental trade-off between online convergence rate and estimation accuracy. Extensive experiments on CIFAR100 and ImageNet datasets under shuffled long-tail and Dirichlet test priors demonstrate that FMAPLS and online-FMAPLS respectively achieve up to 40% and 12% lower KL divergence and substantial improvements in post-shift accuracy over state-of-the-art baselines, particularly under severe class imbalance and distributional uncertainty. These results confirm the robustness, scalability, and suitability of the proposed methods for large-scale and dynamic learning scenarios.

This study develops a hierarchical Bayesian framework that integrates expert domain knowledge to quantify player-specific effects in expected goals (xG) estimation, addressing a limitation of standard models that treat all players as identical finishers. Using 9,970 shots from StatsBomb's 2015-16 data and Football Manager 2017 ratings, we combine Bayesian logistic regression with informed priors to stabilise player-level estimates, especially for players with few shots. The hierarchical model reduces posterior uncertainty relative to weak priors and achieves strong external validity: hierarchical and baseline predictions correlate at R2 = 0.75, while an XGBoost benchmark validated against StatsBomb xG reaches R2 = 0.833. The model uncovers interpretable specialisation profiles, including one-on-one finishing (Aguero, Suarez, Belotti, Immobile, Martial), long-range shooting (Pogba), and first-touch execution (Insigne, Salah, Gameiro). It also identifies latent ability in underperforming players such as Immobile and Belotti. The framework supports counterfactual "what-if" analysis by reallocating shots between players under identical contexts. Case studies show that Sansone would generate +2.2 xG from Berardi's chances, driven largely by high-pressure situations, while Vardy-Giroud substitutions reveal strong asymmetry: replacing Vardy with Giroud results in a large decline (about -7 xG), whereas the reverse substitution has only a small effect (about -1 xG). This work provides an uncertainty-aware tool for player evaluation, recruitment, and tactical planning, and offers a general approach for domains where individual skill and contextual factors jointly shape performance.

Every day we share our personal information through digital systems which are constantly exposed to threats. For this reason, security-oriented disciplines of signal processing have received increasing attention in the last decades: multimedia forensics, digital watermarking, biometrics, network monitoring, steganography and steganalysis are just a few examples. Even though each of these fields has its own peculiarities, they all have to deal with a common problem: the presence of one or more adversaries aiming at making the system fail. Adversarial Signal Processing lays the basis of a general theory that takes into account the impact that the presence of an adversary has on the design of effective signal processing tools. By focusing on the application side of Adversarial Signal Processing, namely adversarial information fusion in distributed sensor networks, and adopting a game-theoretic approach, this thesis contributes to the above mission by addressing four issues. First, we address decision fusion in distributed sensor networks by developing a novel soft isolation defense scheme that protect the network from adversaries, specifically, Byzantines. Second, we develop an optimum decision fusion strategy in the presence of Byzantines. In the next step, we propose a technique to reduce the complexity of the optimum fusion by relying on a novel near-optimum message passing algorithm based on factor graphs. Finally, we introduce a defense mechanism to protect decentralized networks running consensus algorithm against data falsification attacks.

Reliable positioning in GNSS-challenged environments remains a critical challenge for navigation systems. Tightly coupled GNSS/IMU fusion improves robustness but remains vulnerable to non-Gaussian noise and outliers. We present a robust and adaptive factor graph-based fusion framework that directly integrates GNSS pseudorange measurements with IMU preintegration factors and incorporates the Barron loss, a general robust loss function that unifies several m-estimators through a single tunable parameter. By adaptively down weighting unreliable GNSS measurements, our approach improves resilience positioning. The method is implemented in an extended GTSAM framework and evaluated on the UrbanNav dataset. The proposed solution reduces positioning errors by up to 41% relative to standard FGO, and achieves even larger improvements over extended Kalman filter (EKF) baselines in urban canyon environments. These results highlight the benefits of Barron loss in enhancing the resilience of GNSS/IMU-based navigation in urban and signal-compromised environments.

Methods for probability updating, of which Bayesian conditionalization is the most well-known and widely used, are modeling tools that aim to represent the process of modifying an initial epistemic state, typically represented by a prior probability function P, which is adjusted in light of new information. Notably, updating methods and conditional sentences seem to intuitively share a deep connection, as is evident in the case of conditionalization. The present work contributes to this line of research and aims at shedding new light on the relationship between updating methods and conditional connectives. Departing from previous literature that often focused on a specific type of conditional or a particular updating method, our goal is to prove general results concerning the connection between conditionals and their probabilities. This will allow us to characterize the probabilities of certain conditional connectives and to understand what class of updating procedures can be represented using specific conditional connectives. Broadly, we adopt a general perspective that encompasses a large class of conditionals and a wide range of updating methods, enabling us to prove some general results concerning their interrelation.