Breast cancer is considered the most critical and frequently diagnosed cancer in women worldwide, leading to an increase in cancer-related mortality. Early and accurate detection is crucial as it can help mitigate possible threats while improving survival rates. In terms of prediction, conventional diagnostic methods are often limited by variability, cost, and, most importantly, risk of misdiagnosis. To address these challenges, machine learning (ML) has emerged as a powerful tool for computer-aided diagnosis, with feature selection playing a vital role in improving model performance and interpretability. This research study proposes an integrated framework that incorporates customized Particle Swarm Optimization (PSO) for feature selection. This framework has been evaluated on a comprehensive set of 29 different models, spanning classical classifiers, ensemble techniques, neural networks, probabilistic algorithms, and instance-based algorithms. To ensure interpretability and clinical relevance, the study uses cross-validation in conjunction with explainable AI methods. Experimental evaluation showed that the proposed approach achieved a superior score of 99.1\% across all performance metrics, including accuracy and precision, while effectively reducing dimensionality and providing transparent, model-agnostic explanations. The results highlight the potential of combining swarm intelligence with explainable ML for robust, trustworthy, and clinically meaningful breast cancer diagnosis.

Reward model (RM) plays a pivotal role in reinforcement learning with human feedback (RLHF) for aligning large language models (LLMs). However, classical RMs trained on human preferences are vulnerable to reward hacking and generalize poorly to out-of-distribution (OOD) inputs. By contrast, strong LLM judges equipped with reasoning capabilities demonstrate superior generalization, even without additional training, but incur significantly higher inference costs, limiting their applicability in online RLHF. In this work, we propose an uncertainty-based routing framework that efficiently complements a fast RM with a strong but costly LLM judge. Our approach formulates advantage estimation in policy gradient (PG) methods as pairwise preference classification, enabling principled uncertainty quantification to guide routing. Uncertain pairs are forwarded to the LLM judge, while confident ones are evaluated by the RM. Experiments on RM benchmarks demonstrate that our uncertainty-based routing strategy significantly outperforms random judge calling at the same cost, and downstream alignment results showcase its effectiveness in improving online RLHF.

Federated Learning (FL) aims to train a global inference model from remotely distributed clients, gaining popularity due to its benefit of improving data privacy. However, traditional FL often faces challenges in practical applications, including model overfitting and divergent local models due to limited and non-IID data among clients. To address these issues, we introduce a novel Bayesian meta-learning approach called meta-variational dropout (MetaVD). MetaVD learns to predict client-dependent dropout rates via a shared hypernetwork, enabling effective model personalization of FL algorithms in limited non-IID data settings. We also emphasize the posterior adaptation view of meta-learning and the posterior aggregation view of Bayesian FL via the conditional dropout posterior. We conducted extensive experiments on various sparse and non-IID FL datasets. MetaVD demonstrated excellent classification accuracy and uncertainty calibration performance, especially for out-of-distribution (OOD) clients. MetaVD compresses the local model parameters needed for each client, mitigating model overfitting and reducing communication costs. Code is available at https://github.com/insujeon/MetaVD.

Causal discovery remains a central challenge in machine learning, yet existing methods face a fundamental gap: algorithms like GES and GraN-DAG achieve strong empirical performance but lack finite-sample guarantees, while theoretically principled approaches fail to scale. We close this gap by introducing a game-theoretic reinforcement learning framework for causal discovery, where a DDQN agent directly competes against a strong baseline (GES or GraN-DAG), always warm-starting from the opponent's solution. This design yields three provable guarantees: the learned graph is never worse than the opponent, warm-starting strictly accelerates convergence, and most importantly, with high probability the algorithm selects the true best candidate graph. To the best of our knowledge, our result makes a first-of-its-kind progress in explaining such finite-sample guarantees in causal discovery: on synthetic SEMs (30 nodes), the observed error probability decays with n, tightly matching theory. On real-world benchmarks including Sachs, Asia, Alarm, Child, Hepar2, Dream, and Andes, our method consistently improves upon GES and GraN-DAG while remaining theoretically safe. Remarkably, it scales to large graphs such as Hepar2 (70 nodes), Dream (100 nodes), and Andes (220 nodes). Together, these results establish a new class of RL-based causal discovery algorithms that are simultaneously provably consistent, sample-efficient, and practically scalable, marking a decisive step toward unifying empirical performance with rigorous finite-sample theory.

The VC-dimension is a well-studied and fundamental complexity measure of a set system (or hypergraph) that is central to many areas of machine learning. We establish several new results on the complexity of computing the VC-dimension. In particular, given a hypergraph $\mathcal{H}=(\mathcal{V},\mathcal{E})$, we prove that the naive $2^{\mathcal{O}(|\mathcal{V}|)}$-time algorithm is asymptotically tight under the Exponential Time Hypothesis (ETH). We then prove that the problem admits a $1$-additive fixed-parameter approximation algorithm when parameterized by the maximum degree of $\mathcal{H}$ and a fixed-parameter algorithm when parameterized by its dimension, and that these are essentially the only such exploitable structural parameters. Lastly, we consider a generalization of the problem, formulated using graphs, which captures the VC-dimension of both set systems and graphs. We design a $2^{\mathcal{O}(\rm{tw}\cdot \log \rm{tw})}\cdot |V|$-time algorithm for any graph $G=(V,E)$ of treewidth $\rm{tw}$ (which, for a set system, applies to the treewidth of its incidence graph). This is in contrast with closely related problems that require a double-exponential dependency on the treewidth (assuming the ETH).

Multi-class wine classification presents fundamental trade-offs between model accuracy, feature dimensionality, and interpretability - critical factors for production deployment in analytical chemistry. This paper presents a comprehensive empirical study of One-vs-Rest logistic regression on the UCI Wine dataset (178 samples, 3 cultivars, 13 chemical features), comparing from-scratch gradient descent implementation against scikit-learn's optimized solvers and quantifying L1 regularization effects on feature sparsity. Manual gradient descent achieves 92.59 percent mean test accuracy with smooth convergence, validating theoretical foundations, though scikit-learn provides 24x training speedup and 98.15 percent accuracy. Class-specific analysis reveals distinct chemical signatures with heterogeneous patterns where color intensity varies dramatically (0.31 to 16.50) across cultivars. L1 regularization produces 54-69 percent feature reduction with only 4.63 percent accuracy decrease, demonstrating favorable interpretability-performance trade-offs. We propose an optimal 5-feature subset achieving 62 percent complexity reduction with estimated 92-94 percent accuracy, enabling cost-effective deployment with 80 dollars savings per sample and 56 percent time reduction. Statistical validation confirms robust generalization with sub-2ms prediction latency suitable for real-time quality control. Our findings provide actionable guidelines for practitioners balancing comprehensive chemical analysis against targeted feature measurement in resource-constrained environments.

Although quantum systems are generally described by quantum state vectors, we show that in certain cases their measurement processes can be reformulated as probabilistic equations expressed in terms of probabilistic state vectors. These probabilistic representations can, in turn, be approximated by the neural network dynamics of the Tensor Brain (TB) model. The Tensor Brain is a recently proposed framework for modeling perception and memory in the brain, providing a biologically inspired mechanism for efficiently integrating generated symbolic representations into reasoning processes.

Learning to infer the conditional posterior model is a key step for robust meta-learning. This paper presents a new Bayesian meta-learning approach called Neural Variational Dropout Processes (NVDPs). NVDPs model the conditional posterior distribution based on a task-specific dropout; a low-rank product of Bernoulli experts meta-model is utilized for a memory-efficient mapping of dropout rates from a few observed contexts. It allows for a quick reconfiguration of a globally learned and shared neural network for new tasks in multi-task few-shot learning. In addition, NVDPs utilize a novel prior conditioned on the whole task data to optimize the conditional \textit{dropout} posterior in the amortized variational inference. Surprisingly, this enables the robust approximation of task-specific dropout rates that can deal with a wide range of functional ambiguities and uncertainties. We compared the proposed method with other meta-learning approaches in the few-shot learning tasks such as 1D stochastic regression, image inpainting, and classification. The results show the excellent performance of NVDPs.

The growing interest in ocean discovery imposes a need for inspection and intervention in confined and demanding environments. Eely's slender shape, in addition to its ability to change its body configurations, makes articulated underwater robots an adequate option for such environments. However, operation of Eely in such environments imposes demanding requirements on the system, as it must deal with uncertain and unstructured environments, extreme environmental conditions, and reduced navigational capabilities. This paper proposes a Bayesian approach to assess the risks of losing Eely during two mission scenarios. The goal of this work is to improve Eely's performance and the likelihood of mission success. Sensitivity analysis results are presented in order to demonstrate the causes having the highest impact on losing Eely.

The rapid ascent of artificial intelligence (AI) is often portrayed as a revolution born from computer science and engineering. This narrative, however, obscures a fundamental truth: the theoretical and methodological core of AI is, and has always been, statistical. This paper systematically argues that the field of statistics provides the indispensable foundation for machine learning and modern AI. We deconstruct AI into nine foundational pillars-Inference, Density Estimation, Sequential Learning, Generalization, Representation Learning, Interpretability, Causality, Optimization, and Unification-demonstrating that each is built upon century-old statistical principles. From the inferential frameworks of hypothesis testing and estimation that underpin model evaluation, to the density estimation roots of clustering and generative AI; from the time-series analysis inspiring recurrent networks to the causal models that promise true understanding, we trace an unbroken statistical lineage. While celebrating the computational engines that power modern AI, we contend that statistics provides the brain-the theoretical frameworks, uncertainty quantification, and inferential goals-while computer science provides the brawn-the scalable algorithms and hardware. Recognizing this statistical backbone is not merely an academic exercise, but a necessary step for developing more robust, interpretable, and trustworthy intelligent systems. We issue a call to action for education, research, and practice to re-embrace this statistical foundation. Ignoring these roots risks building a fragile future; embracing them is the path to truly intelligent machines. There is no machine learning without statistical learning; no artificial intelligence without statistical thought.