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We consider parametric inference for an ergodic and stationary diffusion process, when the data are high-frequency observations of the integral of the diffusion process. Such data are obtained via certain measurement devices, or if…
Targeting to understand the underlying explainable factors behind observations and modeling the conditional generation process on these factors, we connect disentangled representation learning to Diffusion Probabilistic Models (DPMs) to…
The Voronoi tessellation is the partition of space for a given seeds pattern and the result of the partition depends completely on the type of given pattern "random", Poisson-Voronoi tessellations (PVT), or "non-random", Non Poisson-Voronoi…
We study Dirichlet process-based models for sets of predictor-dependent probability distributions, where the domain and predictor space are general Polish spaces. We generalize the definition of dependent Dirichlet processes, originally…
This work studies the variation in Kullback-Leibler divergence between random draws from some popular nonparametric processes and their baseline measure. In particular we focus on the Dirichlet process, the P\'olya tree and the frequentist…
Marked point process data arise when events occur in a space with event-level marks. We study clustering of replicated marked Poisson point processes and introduce Dirichlet process mixtures of marked Poisson point processes, a Bayesian…
The assumption that data samples are independent and identically distributed (iid) is standard in many areas of statistics and machine learning. Nevertheless, in some settings, such as social networks, infectious disease modeling, and…
This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form…
In recent years, conditional copulas, that allow dependence between variables to vary according to the values of one or more covariates, have attracted increasing attention. In high dimension, vine copulas offer greater flexibility compared…
Diffusion models have recently emerged as powerful stochastic frameworks for high-dimensional inference and generation. However, existing applications to partial differential equations (PDEs) predominantly rely on physics-informed training…
We propose a framework for probabilistic forecasting of dynamical systems based on generative modeling. Given observations of the system state over time, we formulate the forecasting problem as sampling from the conditional distribution of…
P{\'o}lya urns are urns where at each unit of time a ball is drawn and is replaced with some other balls according to its colour. We introduce a more general model: The replacement rule depends on the colour of the drawn ball and the value…
In this article, we consider a non-parametric Bayesian approach to multivariate quantile regression. The collection of related conditional distributions of a response vector Y given a univariate covariate X is modeled using a Dependent…
The fractional advection-dispersion equation (FADE) has attracted increased attention from researchers as it provides an accurate description for challenging phenomenas with long-range time memory and spatial interactions, such as the…
Predictive modeling is the key factor for saving time and resources with respect to manufacturing processes such as fermentation processes arising e.g.\ in food and chemical manufacturing processes. According to Zhang et al. (2002), the…
Assume we have potential "causes" $z\in Z$, which produce "events" $w$ with known probabilities $\beta(w|z)$. We observe $w_1,w_2,...,w_n$, what can we say about the distribution of the causes? A Bayesian estimate will assume a prior on…
Positional reasoning is the process of ordering unsorted parts contained in a set into a consistent structure. We present Positional Diffusion, a plug-and-play graph formulation with Diffusion Probabilistic Models to address positional…
Analysis of competing risks data plays an important role in the lifetime data analysis. Recently Feizjavadian and Hashemi (Computational Statistics and Data Analysis, vol. 82, 19-34, 2015) provided a classical inference of a competing risks…
We construct a stationary Markov process corresponding to the evolution of masses and distances of subtrees along the spine from the root to a branch point in a conjectured stationary, continuum random tree-valued diffusion that was…
Predictive statistical mechanics is a form of inference from available data, without additional assumptions, for predicting reproducible phenomena. By applying it to systems with Hamiltonian dynamics, a problem of predicting the macroscopic…