We prove that all standard subregular language classes are linearly separable when represented by their deciding predicates. This establishes finite observability and guarantees learnability with simple linear models. Synthetic experiments confirm perfect separability under noise-free conditions, while real-data experiments on English morphology show that learned features align with well-known linguistic constraints. These results demonstrate that the subregular hierarchy provides a rigorous and interpretable foundation for modeling natural language structure. Our code used in real-data experiments is available at https://github.com/UTokyo-HayashiLab/subregular.

Whenever data-based systems are employed in engineering applications, defining an optimal statistical representation is subject to the problem of model selection. This paper focusses on how well models can generalise in Structural Health Monitoring (SHM). Although statistical model validation in this field is often performed heuristically, it is possible to estimate generalisation more rigorously using the bounds provided by Statistical Learning Theory (SLT). Therefore, this paper explores the selection process of a kernel smoother for modelling the impulse response of a linear oscillator from the perspective of SLT. It is demonstrated that incorporating domain knowledge into the regression problem yields a lower guaranteed risk, thereby enhancing generalisation.

Based on limited observations, machine learning discerns a dependence which is expected to hold in the future. What makes it possible? Statistical learning theory imagines indefinitely increasing training sample to justify its approach. In reality, there is no infinite time or even infinite general population for learning. Here I argue that practical machine learning is based on an implicit assumption that underlying dependence is relatively ``smooth" : likely, there are no abrupt differences in feedback between cases with close data points. From this point of view learning shall involve selection of the hypothesis ``smoothly" approximating the training set. I formalize this as Practical learning paradigm. The paradigm includes terminology and rules for description of learners. Popular learners (local smoothing, k-NN, decision trees, Naive Bayes, SVM for classification and for regression) are shown here to be implementations of this paradigm.

Mathematical equivalence between statistical mechanics and machine learning theory has been known since the 20th century, and researches based on such equivalence have provided novel methodology in both theoretical physics and statistical learning theory. For example, algebraic approach in statistical mechanics such as operator algebra enables us to analyze phase transition phenomena mathematically. In this paper, for theoretical physicists who are interested in artificial intelligence, we review and prospect algebraic researches in machine learning theory. If a learning machine has hierarchical structure or latent variables, then the random Hamiltonian cannot be expressed by any quadratic perturbation because it has singularities. To study an equilibrium state defined by such a singular random Hamiltonian, algebraic approach is necessary to derive asymptotic form of the free energy and the generalization error. We also introduce the most recent advance, in fact, theoretical foundation for alignment of artificial intelligence is now being constructed based on algebraic learning theory. This paper is devoted to the memory of Professor Huzihiro Araki who is a pioneer founder of algebraic research in both statistical mechanics and quantum field theory.

The purpose of this paper is to look into how central notions in statistical learning theory, such as realisability, generalise under the assumption that train and test distribution are issued from the same credal set, i.e., a convex set of probability distributions. This can be considered as a first step towards a more general treatment of statistical learning under epistemic uncertainty.

This paper considers the epistemic justification for a simplicity preference in inductive inference that may be obtained from the machine learning framework of statistical learning theory. Uniting elements from both earlier arguments suggesting and rejecting such a justification, the paper spells out a qualified means-ends and model-relative justificatory argument, built on statistical learning theory's central mathematical learning guarantee for the method of empirical risk minimization.

In many applications of machine learning, a large number of variables are considered. Motivated by machine learning of interacting particle systems, we consider the situation when the number of input variables goes to infinity. First, we continue the recent investigation of the mean field limit of kernels and their reproducing kernel Hilbert spaces, completing the existing theory. Next, we provide results relevant for approximation with such kernels in the mean field limit, including a representer theorem. Finally, we use these kernels in the context of statistical learning in the mean field limit, focusing on Support Vector Machines. In particular, we show mean field convergence of empirical and infinite-sample solutions as well as the convergence of the corresponding risks. On the one hand, our results establish rigorous mean field limits in the context of kernel methods, providing new theoretical tools and insights for large-scale problems. On the other hand, our setting corresponds to a new form of limit of learning problems, which seems to have not been investigated yet in the statistical learning theory literature.