相关论文: High-resolution product quantization for Gaussian …

Gaussian Processes are used in many applications to model spatial phenomena. Within this context, a key issue is to decide the set of locations where to take measurements so as to obtain a better approximation of the underlying function.…

We consider finite dimensional rough differential equations driven by centered Gaussian processes. Combining Malliavin calculus, rough paths techniques and interpolation inequalities, we establish upper bounds on the density of the…

Bayesian optimisation has gained great popularity as a tool for optimising the parameters of machine learning algorithms and models. Somewhat ironically, setting up the hyper-parameters of Bayesian optimisation methods is notoriously hard.…

We consider a generalization of the Bauer maximum principle. We work with tensorial products of convex measures sets, that are non necessarily compact but generated by their extreme points. We show that the maximum of a quasi-convex lower…

Brown-Resnick processes are max-stable processes that are associated to Gaussian processes. Their simulation is often based on the corresponding spectral representation which is not unique. We study to what extent simulation accuracy and…

Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters…

In this paper, we consider an inference problem for an Ornstein-Uhlenbeck process driven by a general one-dimensional centered Gaussian process $(G_t)_{t\ge 0}$. The second order mixed partial derivative of the covariance function $ R(t,\,…

Non-conservative uncertainty bounds are essential for making reliable predictions about latent functions from noisy data, and thus, a key enabler for safe learning-based control. In this domain, kernel methods such as Gaussian process…

The paper deals with the expected maxima of continuous Gaussian processes $X = (X_t)_{t\ge 0}$ that are H\"older continuous in $L_2$-norm and/or satisfy the opposite inequality for the $L_2$-norms of their increments. Examples of such…

Nonparametric modeling approaches show very promising results in the area of system identification and control. A naturally provided model confidence is highly relevant for system-theoretical considerations to provide guarantees for…

Bayesian optimization is a class of global optimization techniques. In Bayesian optimization, the underlying objective function is modeled as a realization of a Gaussian process. Although the Gaussian process assumption implies a random…

We present a class of Gauss-Markov processes which can be represented as space-time scaled stationary Ornstein-Uhlenbeck processes defined on the real line. We give several explicit examples of the representation for certain Gauss bridge…

In Chen and Zhou 2021, they consider an inference problem for an Ornstein-Uhlenbeck process driven by a general one-dimensional centered Gaussian process $(G_t)_{t\ge 0}$. The second order mixed partial derivative of the covariance function…

Many functions have approximately-known upper and/or lower bounds, potentially aiding the modeling of such functions. In this paper, we introduce Gaussian process models for functions where such bounds are (approximately) known. More…

This paper considers extreme values attained by a centered, multidimensional Gaussian process $X(t)= (X_1(t),\ldots,X_n(t))$ minus drift $d(t)=(d_1(t),\ldots,d_n(t))$, on an arbitrary set $T$. Under mild regularity conditions, we establish…

We provide a stochastic interpretation of non-commutative Dirichlet forms in the context of quantum filtering. For stochastic processes motivated by quantum optics experiments, we derive an optimal finite time deviation bound expressed in…

We provide a general approach to obtain upper bounds for small deviations $ \mathbb{P}(\Vert y \Vert \le \epsilon)$ in different norms, namely the supremum and $\beta$- H\"older norms. The large class of processes $y$ under consideration…

Using quantum systems as sensors or probes has been shown to greatly improve the precision of parameter estimation by exploiting unique quantum features such as entanglement. A major task in quantum sensing is to design the optimal…

The seminal papers of Pickands [1,2] paved the way for a systematic study of high exceedance probabilities of both stationary and non-stationary Gaussian processes. Yet, in the vector-valued setting, due to the lack of key tools including…

We investigate analytically and numerically the role of quantum fluctuations in reconstruction of optical objects from diffraction-limited images. Taking as example of an input object two closely spaced Gaussian peaks we demonstrate that…