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Restricted kernel machines (RKMs) have demonstrated a significant impact in enhancing generalization ability in the field of machine learning. Recent studies have introduced various methods within the RKM framework, combining kernel…
This paper provides a unifying view of optimal kernel hypothesis testing across the MMD two-sample, HSIC independence, and KSD goodness-of-fit frameworks. Minimax optimal separation rates in the kernel and $L^2$ metrics are presented, with…
Among various quantum machine learning (QML) algorithms, the quantum kernel method has especially attracted attention due to its compatibility with noisy intermediate-scale quantum devices and its potential to achieve quantum advantage.…
Quantum learning from state samples is often benchmarked in a fixed-budget paradigm, relating error to a prescribed number of copies. We instead adopt a stopping-time viewpoint: in minimal-feedback learning, the learning completion can be…
In this paper, we propose new specification tests for regression models with measurement errors in the explanatory variables. Inspired by the integrated conditional moment (ICM) approach, we use a deconvoluted residual-marked empirical…
We propose and study kernel conjugate gradient methods (KCGM) with random projections for least-squares regression over a separable Hilbert space. Considering two types of random projections generated by randomized sketches and Nystr\"{o}m…
Quantum Machine Learning (QML) has gathered significant attention through approaches like Quantum Kernel Machines. While these methods hold considerable promise, their quantum nature presents inherent challenges. One major challenge is the…
Error mitigation techniques, while instrumental in extending the capabilities of near-term quantum computers, often suffer from exponential resource scaling with noise levels. To address this limitation, we introduce a novel approach,…
We present simple, user-friendly bounds for the expected operator norm of a random kernel matrix under general conditions on the kernel function $k(\cdot,\cdot)$. Our approach uses decoupling results for U-statistics and the non-commutative…
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…
We characterize the asymptotic performance of nonparametric goodness of fit testing. The exponential decay rate of the type-II error probability is used as the asymptotic performance metric, and a test is optimal if it achieves the maximum…
We obtain for the Kempner series (i.e. harmonic series where certain digits are excluded from all denominators, for example the digit 9 in base 10) new representations as geometrically convergent series. The coefficients for these…
In this paper, we propose a test for the equality of multiple distributions based on kernel mean embeddings. Our framework provides a flexible way to handle multivariate or even high-dimensional data by virtue of kernel methods and allows…
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, distances between…
Score-based kernelised Stein discrepancy (KSD) tests have emerged as a powerful tool for the goodness of fit tests, especially in high dimensions; however, the test performance may depend on the choice of kernels in an underlying…
The quantum circuit Born machine (QCBM) is a quantum physics inspired implicit generative model naturally suitable for learning binary images, with a potential advantage of modeling discrete distributions that are hard to simulate…
Memory consistency models (MCMs) are at the heart of concurrent programming. They represent the behaviour of concurrent programs at the chip level. To test these models small program snippets called litmus test are generated, which show…
Model-free time-to-event regression under confounding presents challenges due to biases introduced by causal and censoring sampling mechanisms. This phenomenology poses problems for classical non-parametric estimators like Beran's or the…
We introduce kernel integrated $R^2$, a new measure of statistical dependence that combines the local normalization principle of the recently introduced integrated $R^2$ with the flexibility of reproducing kernel Hilbert spaces (RKHSs). The…
Particle collisions at accelerators such as the Large Hadron Collider, recorded and analyzed by experiments such as ATLAS and CMS, enable exquisite measurements of the Standard Model and searches for new phenomena. Simulations of collision…