Related papers: Kernelized Normalizing Constant Estimation: Bridgi…
We introduce kernel-QA, a black-box optimization (BBO) method that constructs surrogate models analytically using low-order polynomial kernels within a quadratic unconstrained binary optimization (QUBO) framework, enabling efficient…
We review the method of stochastic quantization for a scalar field theory. We first give a brief survey for the case of self-interacting scalar fields, implementing the stochastic perturbation theory up to the one-loop level. The…
Despite their many appealing properties, kernel methods are heavily affected by the curse of dimensionality. For instance, in the case of inner product kernels in $\mathbb{R}^d$, the Reproducing Kernel Hilbert Space (RKHS) norm is often…
Bayesian optimisation has proven to be a powerful tool for expensive global black-box optimisation problems. In this paper, we propose new Bayesian optimisation variants of the popular Knowledge Gradient acquisition functions for problems…
Many real-world optimisation problems such as hyperparameter tuning in machine learning or simulation-based optimisation can be formulated as expensive-to-evaluate black-box functions. A popular approach to tackle such problems is Bayesian…
Normalization of polynomials plays a vital role in the approximate basis computation of vanishing ideals. Coefficient normalization, which normalizes a polynomial with its coefficient norm, is the most common method in computer algebra.…
For the kernel estimator of the quantile density function (the derivative of the quantile function), I show how to perform the boundary bias correction, establish the rate of strong uniform consistency of the bias-corrected estimator, and…
We study in this paper a smoothness regularization method for functional linear regression and provide a unified treatment for both the prediction and estimation problems. By developing a tool on simultaneous diagonalization of two positive…
Let $X$ be a complete, simply connected harmonic manifold of purely exponential volume growth. This class contains all non-flat harmonic manifolds of non-positive curvature and, in particular all known examples of harmonic manifolds except…
Bayesian optimization (BO) is a sample-efficient method and has been widely used for optimizing expensive black-box functions. Recently, there has been a considerable interest in BO literature in optimizing functions that are affected by…
Blind inverse problems arise in many experimental settings where both the signal of interest and the forward operator are (partially) unknown. In this context, methods developed for the non-blind case cannot be adapted in a straightforward…
This study targets the mixed-integer black-box optimization (MI-BBO) problem where continuous and integer variables should be optimized simultaneously. The CMA-ES, our focus in this study, is a population-based stochastic search method that…
Parallel black box optimization consists in estimating the optimum of a function using $\lambda$ parallel evaluations of $f$. Averaging the $\mu$ best individuals among the $\lambda$ evaluations is known to provide better estimates of the…
Gradient descent algorithms on Riemannian manifolds have been used recently for the optimization of quantum channels. In this contribution, we investigate the influence of various regularization terms added to the cost function of these…
Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its…
Nonparametric estimation using uniform-width binning is a standard approach for evaluating the calibration performance of machine learning models. However, existing theoretical analyses of the bias induced by binning are limited to binary…
The quantum phase estimation (QPE) is one of the fundamental algorithms based on the quantum Fourier transform. It has applications in order-finding, factoring, and finding the eigenvalues of unitary operators. The major challenge in…
Parameter-space regularization in neural network optimization is a fundamental tool for improving generalization. However, standard parameter-space regularization methods make it challenging to encode explicit preferences about desired…
Probably the simplest and most frequently used way to illustrate the power of quantum computing is to solve the so-called {\it Deutsch's problem}. Consider a Boolean function $f: \{0,1\} \to \{0,1\}$ and suppose that we have a (classical)…
We are concerned with structured $\ell_0$-norms regularization problems, with a twice continuously differentiable loss function and a box constraint. This class of problems have a wide range of applications in statistics, machine learning…