相关论文: High-resolution product quantization for Gaussian …
Using the generic chaining method, we derive upper bounds for the \(L^q\) process of sub-Gaussian classes when \(1 \le q \le 2\), thereby resolving an open problem posed by Al-Ghattas, Chen, and Sanz-Alonso in arXiv:2502.16916. Combined…
Tomographic reconstruction, despite its revolutionary impact on a wide range of applications, suffers from its ill-posed nature in that there is no unique solution because of limited and noisy measurements. Therefore, in the absence of…
We investigate what happens when an entire sample path of a smooth Gaussian process on a compact interval lies above a high level. Specifically, we determine the precise asymptotic probability of such an event, the extent to which the high…
By combining the Minkowski inequality and the quantum Chernoff bound, we derive easy-to-compute upper bounds for the error probability affecting the optimal discrimination of Gaussian states. In particular, these bounds are useful when the…
We present results on the estimation and evaluation of success probabilities for ordinal optimisation over uncountable sets (such as subsets of $\mathbb{R}^{d}$). Our formulation invokes an assumption of a Gaussian copula model, and we show…
We address the estimation of the loss parameter of a bosonic channel probed by Gaussian signals. We derive the ultimate quantum bound on precision and show that no improvement may be obtained by having access to the environment degrees of…
Signal processing in non-Gaussian noise environment is addressed in this paper. For many real-life situations, the additive noise process present in the system is found to be dominantly non-Gaussian. The problem of detection and estimation…
We study quantum process tomography given the prior information that the map is a unitary or close to a unitary process. We show that a unitary map on a $d$-level system is completely characterized by a minimal set of $d^2{+}d$ elements…
We prove new lower bounds for the upper tail probabilities of suprema of Gaussian processes. Unlike many existing bounds, our results are not asymptotic, but supply strong information when one is only a little into the upper tail. We…
We consider a problem of approximation of $d$-variate functions defined on $\mathbb{R}^d$ which belong to the Hilbert space with tensor product-type reproducing Gaussian kernel with constant shape parameter. Within worst case setting, we…
Product Quantization, a dictionary based hashing method, is one of the leading unsupervised hashing techniques. While it ignores the labels, it harnesses the features to construct look up tables that can approximate the feature space. In…
We study the spherical cap packing problem with a probabilistic approach. Such probabilistic considerations result in an asymptotic sharp universal uniform bound on the maximal inner product between any set of unit vectors and a…
This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical…
Enhancing quantum illumination with highly entangled probes remains an active area of research. In this context, non-Gaussian operations provide an effective route for engineering probe states that can surpass the standard two-mode squeezed…
In order to improve the performance of Bayesian optimisation, we develop a modified Gaussian process upper confidence bound (GP-UCB) acquisition function. This is done by sampling the exploration-exploitation trade-off parameter from a…
In this paper, the optimal sampling strategies (uniform or nonuniform) and distortion tradeoffs for Gaussian bandlimited periodic signals with additive white Gaussian noise are studied. Our emphasis is on characterizing the optimal sampling…
Gaussian processes (GPs) are widely used in nonparametric regression, classification and spatio-temporal modeling, motivated in part by a rich literature on theoretical properties. However, a well known drawback of GPs that limits their use…
Gaussian boson sampling, a computational model that is widely believed to admit quantum supremacy, has already been experimentally demonstrated and is claimed to surpass the classical simulation capabilities of even the most powerful…
By enabling constraint-aware online model adaptation, model predictive control using Gaussian process (GP) regression has exhibited impressive performance in real-world applications and received considerable attention in the learning-based…
The purpose of this paper is to estimate the limiting variance of asymptotically stationary Gaussian processes observed at high frequency, using the second moment estimator (SME). We study rates of convergence of the central limit theorem…