Related papers: Learning Transfer Operators by Kernel Density Esti…

We consider Markov models of stochastic processes where the next-step conditional distribution is defined by a kernel density estimator (KDE), similar to Markov forecast densities and certain time-series bootstrap schemes. The KDE Markov…

Despite the remarkable empirical performance of Transformers, their theoretical understanding remains elusive. Here, we consider a deep multi-head self-attention network, that is closely related to Transformers yet analytically tractable.…

Kernel density estimation (KDE) stands out as a challenging task in machine learning. The problem is defined in the following way: given a kernel function $f(x,y)$ and a set of points $\{x_1, x_2, \cdots, x_n \} \subset \mathbb{R}^d$, we…

This paper focuses on data-driven fault detection, identification, and recovery (FDIR) for nonlinear control-affine systems under actuator faults. We create a unified framework in the space of probability densities, rather than on…

While robust parameter estimation has been well studied in parametric density estimation, there has been little investigation into robust density estimation in the nonparametric setting. We present a robust version of the popular kernel…

Anomalous behavior is ubiquitous in subsurface solute transport due to the presence of high degrees of heterogeneity at different scales in the media. Although fractional models have been extensively used to describe the anomalous transport…

The filtering problems are derived from a sequential minimization of a quadratic function representing a compromise between model and data. In this paper, we use the Perron-Frobenius operator in stochastic process to develop a…

Density level sets can be estimated using plug-in methods, excess mass algorithms or a hybrid of the two previous methodologies. The plug-in algorithms are based on replacing the unknown density by some nonparametric estimator, usually the…

This paper introduces two transfer learning methodologies for estimating nonparametric Bayesian networks under scarce data. We propose two algorithms, a constraint-based structure learning method, called PC-stable-transfer learning…

We propose a \textbf{uni}fied \textbf{f}ramework for \textbf{i}mplicit \textbf{ge}nerative \textbf{m}odeling (UnifiGem) with theoretical guarantees by integrating approaches from optimal transport, numerical ODE, density-ratio…

Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…

A kernel method is proposed to estimate the condensed density of the generalized eigenvalues of pencils of Hankel matrices whose elements have a joint noncentral Gaussian distribution with nonidentical covariance. These pencils arise when…

We consider a class of statistical inverse problems involving the estimation of a regression operator from a Polish space to a separable Hilbert space, where the target lies in a vector-valued reproducing kernel Hilbert space induced by an…

We address the problem of upsampling a low-resolution (LR) depth map using a registered high-resolution (HR) color image of the same scene. Previous methods based on convolutional neural networks (CNNs) combine nonlinear activations of…

Although generative diffusion models (GDMs) are widely used in practice, their theoretical foundations remain limited, especially concerning the impact of different discretization schemes applied to the underlying stochastic differential…

Machine learning models are increasingly used to predict material properties and accelerate atomistic simulations, but the reliability of their predictions depends on the representativeness of the training data. We present a scalable,…

We propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density estimator (KDE) with ideas from classical…

This paper develops a transfer operator framework for stochastic hybrid systems with guard-induced resets, encompassing both the Koopman and Frobenius--Perron operators. Exploiting their duality, we derive a unified formulation in which…

The prediction of thermo-mechanical behaviour of heterogeneous materials such as heat and moisture transport is strongly influenced by the uncertainty in parameters. Such materials occur e.g. in historic buildings, and the durability…

Robust estimation under Huber's $\epsilon$-contamination model has become an important topic in statistics and theoretical computer science. Statistically optimal procedures such as Tukey's median and other estimators based on depth…