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Quantum kernel methods have been widely recognized as one of promising quantum machine learning algorithms that have potential to achieve quantum advantages. In this paper, we theoretically characterize the power of noisy quantum kernels…

The Gaussian process is a powerful and flexible technique for interpolating spatiotemporal data, especially with its ability to capture complex trends and uncertainty from the input signal. This chapter describes Gaussian processes as an…

Despite recent advances in automated machine learning, model selection is still a complex and computationally intensive process. For Gaussian processes (GPs), selecting the kernel is a crucial task, often done manually by the expert.…

Bayesian inference is used to estimate continuous parameter values given measured data in many fields of science. The method relies on conditional probability densities to describe information about both data and parameters, yet the notion…

Studies of hadron resonances and their properties are limited by the accuracy and consistency of measured datasets, which can originate from many different experiments. We have used Gaussian Processes (GP) to build interpolated datasets,…

Multipath time-delay estimation is commonly encountered in radar and sonar signal processing. In some real-life environments, impulse noise is ubiquitous and significantly degrades estimation performance. Here, we propose a Bayesian…

In this work we review the application of the theory of Gaussian processes to the modeling of noise in pulsar-timing data analysis, and we derive various useful and optimized representations for the likelihood expressions that are needed in…

Traditional interpolation techniques for particle tracking include binning and convolutional formulas that use pre-determined (i.e., closed-form, parameteric) kernels. In many instances, the particles are introduced as point sources in time…

We present a Bayesian approach to identify optimal transformations that map model input points to low dimensional latent variables. The "projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to…

Among the various approaches for producing point distributions with blue noise spectrum, we argue for an optimization framework using Gaussian kernels. We show that with a wise selection of optimization parameters, this approach attains…

Probabilistic neural networks are typically modeled with independent weight priors, which do not capture weight correlations in the prior and do not provide a parsimonious interface to express properties in function space. A desirable class…

We seek to achieve the Holy Grail of Bayesian inference for gravitational-wave astronomy: using deep-learning techniques to instantly produce the posterior $p(\theta|D)$ for the source parameters $\theta$, given the detector data $D$. To do…

Sensor noise sources cause differences in the signal recorded across pixels in a single image and across multiple images. This paper presents a Bayesian approach to decomposing and characterizing the sensor noise sources involved in imaging…

Kernel random matrices have attracted a lot of interest in recent years, from both practical and theoretical standpoints. Most of the theoretical work so far has focused on the case were the data is sampled from a low-dimensional structure.…

Bayesian learning using Gaussian processes provides a foundational framework for making decisions in a manner that balances what is known with what could be learned by gathering data. In this dissertation, we develop techniques for…

Spherical radial-basis-based kernel interpolation abounds in image sciences including geophysical image reconstruction, climate trends description and image rendering due to its excellent spatial localization property and perfect…

We provide a geometric interpretation to Bayesian inference that allows us to introduce a natural measure of the level of agreement between priors, likelihoods, and posteriors. The starting point for the construction of our geometry is the…

Nested sampling provides an estimate of the evidence of a Bayesian inference problem via probing the likelihood as a function of the enclosed prior volume. However, the lack of precise values of the enclosed prior mass of the samples…

In statistical applications, it is common to encounter parameters supported on a varying or unknown dimensional space. Examples include the fused lasso regression, the matrix recovery under an unknown low rank, etc. Despite the ease of…

Structural kernels are a flexible learning paradigm that has been widely used in Natural Language Processing. However, the problem of model selection in kernel-based methods is usually overlooked. Previous approaches mostly rely on setting…