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We study the geometry of the algebraic set of tuples of composable matrices which multiply to a fixed matrix, using tools from the theory of quiver representations. In particular, we determine its codimension $C$ and the number $\theta$ of its top-di
Externí odkaz:
http://arxiv.org/abs/2411.19920
We introduce a novel class of Bayesian mixtures for normal linear regression models which incorporates a further Gaussian random component for the distribution of the predictor variables. The proposed cluster-weighted model aims to encompass potentia
Externí odkaz:
http://arxiv.org/abs/2411.18957
The problem of incorporating information from observations received serially in time is widespread in the field of uncertainty quantification. Within a probabilistic framework, such problems can be addressed using standard filtering techniques. Howev
Externí odkaz:
http://arxiv.org/abs/2411.18864
Autor:
Pathiraja, Sahani, Wacker, Philipp
It has long been posited that there is a connection between the dynamical equations describing evolutionary processes in biology and sequential Bayesian learning methods. This manuscript describes new research in which this precise connection is rigo
Externí odkaz:
http://arxiv.org/abs/2411.16366
Piecewise deterministic Markov processes provide scalable methods for sampling from the posterior distributions in big data settings by admitting principled sub-sampling strategies that do not bias the output. An important example is the Zig-Zag proc
Externí odkaz:
http://arxiv.org/abs/2411.14983
Inverse problems of partial differential equations are ubiquitous across various scientific disciplines and can be formulated as statistical inference problems using Bayes' theorem. To address large-scale problems, it is crucial to develop discretiza
Externí odkaz:
http://arxiv.org/abs/2411.13277
Autor:
Aksenov, Vitalii, Eigel, Martin
The possibility of using the Eulerian discretization for the problem of modelling high-dimensional distributions and sampling, is studied. The problem is posed as a minimization problem over the space of probability measures with respect to the Wasse
Externí odkaz:
http://arxiv.org/abs/2411.12430
Autor:
Chak, Martin
Existing guarantees for algorithms sampling from nonlogconcave measures on $\mathbb{R}^d$ are generally inexplicit or unscalable. Even for the class of measures with logdensities that have bounded Hessians and are strongly concave outside a Euclidean
Externí odkaz:
http://arxiv.org/abs/2411.07776
We consider goal-oriented optimal design of experiments for infinite-dimensional Bayesian linear inverse problems governed by partial differential equations (PDEs). Specifically, we seek sensor placements that minimize the posterior variance of a pre
Externí odkaz:
http://arxiv.org/abs/2411.07532
This work studies the inverse problem of photoacoustic tomography (more precisely, the acoustic subproblem) as the identification of a space-dependent source parameter. The model consists of a wave equation involving a time-fractional damping term to
Externí odkaz:
http://arxiv.org/abs/2411.06609