Related papers: A Stochastic Multivariate Latent Variable Model Fo…
We provide a comprehensive overview of latent Markov (LM) models for the analysis of longitudinal categorical data. The main assumption behind these models is that the response variables are conditionally independent given a latent process…
Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…
In this paper we provide a conceptual overview of latent variable models within a probabilistic modeling framework, an overview that emphasizes the compositional nature and the interconnectedness of the seemingly disparate models commonly…
Multivariate categorical data occur in many applications of machine learning. One of the main difficulties with these vectors of categorical variables is sparsity. The number of possible observations grows exponentially with vector length,…
The present paper aims to demonstrate the usage of Convolutional Neural Networks as a generative model for stochastic processes, enabling researchers from a wide range of fields (such as quantitative finance and physics) to develop a…
After collecting data from observations or experiments, the next step is to build an appropriate mathematical or stochastic model to describe the data so that further studies can be done with the help of the models. In this article, the…
Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…
We address the problem of estimating unknown model parameters and state variables in stochastic reaction processes when only sparse and noisy measurements are available. Using an asymptotic system size expansion for the backward equation we…
We introduce Latent Gaussian Process Regression which is a latent variable extension allowing modelling of non-stationary multi-modal processes using GPs. The approach is built on extending the input space of a regression problem with a…
In this paper we focus on the parameter estimation of dynamic load models with stochastic terms, in particular, load models where protection settings are uncertain, such as in aggregated air conditioning units. We show how the uncertainty…
Multivariate regression model is a natural generalization of the classical univari- ate regression model for fitting multiple responses. In this paper, we propose a high- dimensional multivariate conditional regression model for…
Recent innovations in diffusion probabilistic models have paved the way for significant progress in image, text and audio generation, leading to their applications in generative time series forecasting. However, leveraging such abilities to…
We consider a hidden Markov model, where the signal process, given by a diffusion, is only indirectly observed through some noisy measurements. The article develops a variational method for approximating the hidden states of the signal…
Stochastic processes find applications in modelling systems in a variety of disciplines. A large number of stochastic models considered are Markovian in nature. It is often observed that higher order Markov processes can model the data…
We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
In this paper, we provide a multiscale perspective on the problem of maximum marginal likelihood estimation. We consider and analyse a diffusion-based maximum marginal likelihood estimation scheme using ideas from multiscale dynamics. Our…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…
High-dimensional multivariate longitudinal data, which arise when many outcome variables are measured repeatedly over time, are becoming increasingly common in social, behavioral and health sciences. We propose a latent variable model for…