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The robustness of the kernel recursive least square (KRLS) algorithm has recently been improved by combining them with more robust information-theoretic learning criteria, such as minimum error entropy (MEE) and generalized MEE (GMEE),…

The kernel ridge regression (KRR) approach is extended to include the odd-even effects in nuclear mass predictions by remodulating the kernel function without introducing new weight parameters and inputs in the training network. By taking…

The prediction of spectral properties via linear response (LR) theory is an important tool in quantum chemistry for understanding photo-induced processes in molecular systems. With the advances of quantum computing, we recently adapted this…

Exact calculation of electronic properties of molecules is a fundamental step for intelligent and rational compounds and materials design. The intrinsically graph-like and non-vectorial nature of molecular data generates a unique and…

Atomistic simulations are a powerful tool for studying the dynamics of molecules, proteins, and materials on wide time and length scales. Their reliability and predictiveness, however, depend directly on the accuracy of the underlying…

We investigate the basis-set convergence of electronic correlation energies calculated using coupled cluster theory and a recently proposed finite basis-set correction technique. The correction is applied to atomic and molecular systems and…

One of the most fundamental aspects of any machine learning algorithm is the training data used by the algorithm. We introduce the novel concept of $\epsilon$-approximation of datasets, obtaining datasets which are much smaller than or are…

This paper carries out a large dimensional analysis of a variation of kernel ridge regression that we call \emph{centered kernel ridge regression} (CKRR), also known in the literature as kernel ridge regression with offset. This modified…

Reinforcement learning (RL) provides a principled framework for decision-making in partially observable environments, which can be modeled as Markov decision processes and compactly represented through dynamic decision Bayesian networks.…

The electron density of a molecule or material has recently received major attention as a target quantity of machine-learning models. A natural choice to construct a model that yields transferable and linear-scaling predictions is to…

Quantum computing can empower machine learning models by enabling kernel machines to leverage quantum kernels for representing similarity measures between data. Quantum kernels are able to capture relationships in the data that are not…

Chemical compound space (CCS), the set of all theoretically conceivable combinations of chemical elements and (meta-)stable geometries that make up matter, is colossal. The first principles based virtual sampling of this space, for example…

Similar to other electron correlation methods, many-body perturbation theory methods based on Green functions, such as the so-called $GW$ approximation, suffer from the usual slow convergence of energetic properties with respect to the size…

The effective contact area in rough surface contact plays a critical role in multi-physics phenomena such as wear, sealing, and thermal or electrical conduction. Although accurate numerical methods, like the Boundary Element Method (BEM),…

We propose a novel adaptive kernel based regression method for complex-valued signals: the generalized complex-valued kernel least-mean-square (gCKLMS). We borrow from the new results on widely linear reproducing kernel Hilbert space…

Classification is at the core of data-driven prediction and decision-making, representing a fundamental task in supervised machine learning. Recently, several quantum machine learning algorithms that use quantum kernels as a measure of…

We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train…

Compositional disorder is common in crystal compounds. In these compounds, some atoms are randomly distributed at some crystallographic sites. For such compounds, randomness forms many non-identical independent structures. Thus, calculating…

The random feature (RF) approach is a well-established and efficient tool for scalable kernel methods, but existing literature has primarily focused on kernel ridge regression with random features (KRR-RF), which has limitations in handling…

A computationally efficient protocol for machine learning in chemical space using Boltzmann ensembles of conformers as input is proposed; the method is based on rewriting Kernel Ridge Regression expressions in terms of Structured Orthogonal…