Related papers: Markov kernels in Mathlib's probability library
Uncertainty quantification for full-waveform inversion provides a probabilistic characterization of the ill-conditioning of the problem, comprising the sensitivity of the solution with respect to the starting model and data noise. This…
We find the transition kernels for four Markovian interacting particle systems on the line, by proving that each of these kernels is intertwined with a Karlin-McGregor type kernel. The resulting kernels all inherit the determinantal…
Behavioural metrics have been shown to be an effective mechanism for constructing representations in reinforcement learning. We present a novel perspective on behavioural metrics for Markov decision processes via the use of positive…
This paper considers the speed of convergence (mixing) of a finite Markov kernel $P$ with respect to the Kullback-Leibler divergence (entropy). Given a Markov kernel one defines either a discrete-time Markov chain (with the $n$-step…
Kernel mean embeddings have recently attracted the attention of the machine learning community. They map measures $\mu$ from some set $M$ to functions in a reproducing kernel Hilbert space (RKHS) with kernel $k$. The RKHS distance of two…
Similarity-sensitive entropy measures the uncertainty of a probability law relative to a similarity kernel that encodes the distinguishability between states. We develop a measure-theoretic treatment covering both finite similarity matrices…
We propose a framework for hypothesis testing on conditional probability distributions, which we then use to construct statistical tests of functionals of conditional distributions. These tests identify the inputs where the functionals…
We develop kernel criteria for the likelihood-ratio, hazard-rate, usual stochastic, and relative log-concavity orders in parametric families of univariate probability laws with densities. The score is the derivative of the log density with…
We study a category of probability spaces and measure-preserving Markov kernels up to almost sure equality. This category contains, among its isomorphisms, mod-zero isomorphisms of probability spaces. It also gives an isomorphism between…
Since its inception the Metropolis-Hastings kernel has been applied in sophisticated ways to address ever more challenging and diverse sampling problems. Its success stems from the flexibility brought by the fact that its verification and…
We report an exact likelihood computation for Linear Gaussian Markov processes that is more scalable than existing algorithms for complex models and sparsely sampled signals. Better scaling is achieved through elimination of repeated…
Kernel mean embeddings are a popular tool that consists in representing probability measures by their infinite-dimensional mean embeddings in a reproducing kernel Hilbert space. When the kernel is characteristic, mean embeddings can be used…
We extend the class of semimartingales in a natural way. This allows us to incorporate processes having paths that leave the state space R^d. In particular Markov processes related to sub-Markovian kernels, but also non-Markovian processes…
Mixture distributions provide a versatile and widely used framework for modeling random phenomena, and are particularly well-suited to the analysis of geoscientific processes and their attendant risks to society. For continuous mixtures of…
Composition of low-dimensional distributions, whose foundations were laid in the papaer published in the Proceeding of UAI'97 (Jirousek 1997), appeared to be an alternative apparatus to describe multidimensional probabilistic models. In…
Regularized empirical risk minimization using kernels and their corresponding reproducing kernel Hilbert spaces (RKHSs) plays an important role in machine learning. However, the actually used kernel often depends on one or on a few…
We consider the problem of learning a set from random samples. We show how relevant geometric and topological properties of a set can be studied analytically using concepts from the theory of reproducing kernel Hilbert spaces. A new kind of…
We introduce from an analytic perspective Christoffel-Darboux kernels associated to bounded, tracial noncommutative distributions. We show that properly normalized traces, respectively norms, of evaluations of such kernels on finite…
We investigate sampling laws for particle algorithms and the influence of these laws on the efficiency of particle approximations of marginal likelihoods in hidden Markov models. Among a broad class of candidates we characterize the…
The problem of estimating an unknown discrete distribution from its samples is a fundamental tenet of statistical learning. Over the past decade, it attracted significant research effort and has been solved for a variety of divergence…