We present a method for learning Bayesian networks from data sets containingthousands of variables without the need for structure constraints. Our approachis made of two parts. The first is a novel algorithm that effectively explores thespace of possible parent sets of a node.

Multi-output Gaussian processes provide a convenient framework for multi-task problems. An illustrative and motivating example of a multi-task problem is multi-region electrophysiological time-series data, where experimentalists are interested in both power and phase coherence between channels. Recently, Wilson and Adams (2013) proposed the spectral mixture (SM) kernel to model the spectral density of a single task in a Gaussian process framework. In this paper, we develop a novel covariance kernel for multiple outputs, called the cross-spectral mixture (CSM) kernel. This new, flexible kernel represents both the power and phase relationship between multiple observation channels. We demonstrate the expressive capabilities of the CSM kernel through implementation of a Bayesian hidden Markov model, where the emission distribution is a multi-output Gaussian process with a CSM covariance kernel. Results are presented for measured multi-region electrophysiological data.

We consider the problem of binary classification when the covariates conditioned on the each of the response values follow multivariate Gaussian distributions. We focus on the setting where the covariance matrices for the two conditional distributions are the same. The corresponding generative model classifier, derived via the Bayes rule, also called Linear Discriminant Analysis, has been shown to behave poorly in high-dimensional settings. We present a novel analysis of the classification error of any linear discriminant approach given conditional Gaussian models. This allows us to compare the generative model classifier, other recently proposed discriminative approaches that directly learn the discriminant function, and then finally logistic regression which is another classical discriminative model classifier. As we show, under a natural sparsity assumption, and letting $s$ denote the sparsity of the Bayes classifier, $p$ the number of covariates, and $n$ the number of samples, the simple ($\ell_1$-regularized) logistic regression classifier achieves the fast misclassification error rates of $O\left(\frac{s \log p}{n}\right)$, which is much better than the other approaches, which are either inconsistent under high-dimensional settings, or achieve a slower rate of $O\left(\sqrt{\frac{s \log p}{n}}\right)$.

Restricted Boltzmann machines are undirected neural networks which have been shown tobe effective in many applications, including serving as initializations fortraining deep multi-layer neural networks. One of the main reasons for their success is theexistence of efficient and practical stochastic algorithms, such as contrastive divergence,for unsupervised training. We propose an alternative deterministic iterative procedure based on an improved mean field method from statistical physics known as the Thouless-Anderson-Palmer approach. We demonstrate that our algorithm provides performance equal to, and sometimes superior to, persistent contrastive divergence, while also providing a clear and easy to evaluate objective function. We believe that this strategycan be easily generalized to other models as well as to more accurate higher-order approximations, paving the way for systematic improvements in training Boltzmann machineswith hidden units.

We propose an exploratory approach to statistical model criticism using maximum mean discrepancy (MMD) two sample tests. Typical approaches to model criticism require a practitioner to select a statistic by which to measure discrepancies between data and a statistical model. MMD two sample tests are instead constructed as an analytic maximisation over a large space of possible statistics and therefore automatically select the statistic which most shows any discrepancy. We demonstrate on synthetic data that the selected statistic, called the witness function, can be used to identify where a statistical model most misrepresents the data it was trained on. We then apply the procedure to real data where the models being assessed are restricted Boltzmann machines, deep belief networks and Gaussian process regression and demonstrate the ways in which these models fail to capture the properties of the data they are trained on.

Machine learning (ML) systems are increasingly deployed in high-stakes domains where reliability is paramount. This thesis investigates how uncertainty estimation can enhance the safety and trustworthiness of ML, focusing on selective prediction -- where models abstain when confidence is low. We first show that a model's training trajectory contains rich uncertainty signals that can be exploited without altering its architecture or loss. By ensembling predictions from intermediate checkpoints, we propose a lightweight, post-hoc abstention method that works across tasks, avoids the cost of deep ensembles, and achieves state-of-the-art selective prediction performance. Crucially, this approach is fully compatible with differential privacy (DP), allowing us to study how privacy noise affects uncertainty quality. We find that while many methods degrade under DP, our trajectory-based approach remains robust, and we introduce a framework for isolating the privacy-uncertainty trade-off. Next, we then develop a finite-sample decomposition of the selective classification gap -- the deviation from the oracle accuracy-coverage curve -- identifying five interpretable error sources and clarifying which interventions can close the gap. This explains why calibration alone cannot fix ranking errors, motivating methods that improve uncertainty ordering. Finally, we show that uncertainty signals can be adversarially manipulated to hide errors or deny service while maintaining high accuracy, and we design defenses combining calibration audits with verifiable inference. Together, these contributions advance reliable ML by improving, evaluating, and safeguarding uncertainty estimation, enabling models that not only make accurate predictions -- but also know when to say "I do not know".

We propose a joint learning framework for Byzantine-resilient spectrum sensing and secure intelligent reflecting surface (IRS)--assisted opportunistic access under channel state information (CSI) uncertainty. The sensing stage performs logit-domain Bayesian updates with trimmed aggregation and attention-weighted consensus, and the base station (BS) fuses network beliefs with a conservative minimum rule, preserving detection accuracy under a bounded number of Byzantine users. Conditioned on the sensing outcome, we pose downlink design as sum mean-squared error (MSE) minimization under transmit-power and signal-leakage constraints and jointly optimize the BS precoder, IRS phase shifts, and user equalizers. With partial (or known) CSI, we develop an augmented-Lagrangian alternating algorithm with projected updates and provide provable sublinear convergence, with accelerated rates under mild local curvature. With unknown CSI, we perform constrained Bayesian optimization (BO) in a geometry-aware low-dimensional latent space using Gaussian process (GP) surrogates; we prove regret bounds for a constrained upper confidence bound (UCB) variant of the BO module, and demonstrate strong empirical performance of the implemented procedure. Simulations across diverse network conditions show higher detection probability at fixed false-alarm rate under adversarial attacks, large reductions in sum MSE for honest users, strong suppression of eavesdropper signal power, and fast convergence. The framework offers a practical path to secure opportunistic communication that adapts to CSI availability while coherently coordinating sensing and transmission through joint learning.

In this work, we address the problem of training Reinforcement Learning (RL) agents over communication networks. The RL paradigm requires the agent to instantaneously perceive the state evolution to infer the effects of its actions on the environment. This is impossible if the agent receives state updates over lossy or delayed wireless systems and thus operates with partial and intermittent information. In recent years, numerous frameworks have been proposed to manage RL with imperfect feedback; however, they often offer specific solutions with a substantial computational burden. To address these limits, we propose a novel architecture, named Homomorphic Robust Remote Reinforcement Learning (HR3L), that enables the training of remote RL agents exchanging observations across a non-ideal wireless channel. HR3L considers two units: the transmitter, which encodes meaningful representations of the environment, and the receiver, which decodes these messages and performs actions to maximize a reward signal. Importantly, HR3L does not require the exchange of gradient information across the wireless channel, allowing for quicker training and a lower communication overhead than state-of-the-art solutions. Experimental results demonstrate that HR3L significantly outperforms baseline methods in terms of sample efficiency and adapts to different communication scenarios, including packet losses, delayed transmissions, and capacity limitations.

Large Language Models (LLMs) with inference-time scaling techniques show promise for code generation, yet face notable efficiency and scalability challenges. Construction-based tree-search methods suffer from rapid growth in tree size, high token consumption, and lack of anytime property. In contrast, improvement-based methods offer better performance but often struggle with uninformative reward signals and inefficient search strategies. In this work, we propose \textbf{ReLoc}, a unified local search framework which effectively performs step-by-step code revision. Specifically, ReLoc explores a series of local revisions through four key algorithmic components: initial code drafting, neighborhood code generation, candidate evaluation, and incumbent code updating, each of which can be instantiated with specific decision rules to realize different local search algorithms such as Hill Climbing (HC) or Genetic Algorithm (GA). Furthermore, we develop a specialized revision reward model that evaluates code quality based on revision distance to produce fine-grained preferences that guide the local search toward more promising candidates. Finally, our extensive experimental results demonstrate that our approach achieves superior performance across diverse code generation tasks, significantly outperforming both construction-based tree search as well as the state-of-the-art improvement-based code generation methods.

Proteins are essential macromolecules responsible for the structural and functional mechanisms of living things. Phage structural proteins are a subclass of the protein family corresponding to the bacteriophages, which are the most prevalent kind of biological creatures [1]. The PVPs are mainly associated with building structural constituents of the bacteriophage [2], such as the baseplate and head as shown in Figure 1, enabling efficient host-phage binding for genome transfer. The amino acid sequences, particularly those involved in structure synthesis, exhibit significant diversity among phages and their respective groups [3]. Consequently, characterizing these sequences becomes a challenging yet crucial task, as the shortage of annotations for phage proteins has emerged as a hindrance in numerous research studies focused on phage genomics [4]. With the advent of high-throughput sequencing technology, rapid additions of sequences are being observed in standard biological databases [6] as shown in Figure 1, giving rise to the need for proper annotation of the sequences. Enhancement of annotations for the phage family is vital for exploring effective anti-bacterial drug synthesis [7, 8], disease diagnosis [9], food production [10], bacterial genome remodeling [11], etc. Traditionally, mass spectrometry and protein array techniques [12, 13] were utilized for characterizing these proteins. However, these methods are associated with significant time, labor, and computational expenses [1]. Similarly, alignment-based methods do not always work well with PVP categorization due to the lack of collinearity [14] in viral genomes, resulting from factors such as horizontal gene transfer, high mutation rates, etc., leading to dissimilar sequences 2 Figure 1 Structural constituents of Phage