Related papers: Temporal and Spatial Data Mining with Second-Order…
Hidden Markov models (HMMs) and partially observable Markov decision processes (POMDPs) provide useful tools for modeling dynamical systems. They are particularly useful for representing the topology of environments such as road networks…
The ability to predict the future in a given domain can be acquired by discovering empirically from experience certain temporal patterns that tend to repeat unerringly. Previous works in time series analysis allow one to make quantitative…
We define a Hidden Markov Model (HMM) in which each hidden state has time-dependent $\textit{activity levels}$ that drive transitions and emissions, and show how to estimate its parameters. Our construction is motivated by the problem of…
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…
In this paper we concentrate on an alternative modeling strategy for positive data that exhibit spatial or spatio-temporal dependence. Specifically we propose to consider stochastic processes obtained trough a monotone transformation of…
Spatial documentation is exponentially increasing given the availability of Big IoT Data, enabled by the devices miniaturization and data storage capacity. Bayesian spatial statistics is a useful statistical tool to determine the dependence…
Recent years have seen a huge development in spatial modelling and prediction methodology, driven by the increased availability of remote-sensing data and the reduced cost of distributed-processing technology. It is well known that…
We propose new continuous-time formulations for first-order stochastic optimization algorithms such as mini-batch gradient descent and variance-reduced methods. We exploit these continuous-time models, together with simple Lyapunov analysis…
In this chapter we review stochastic modelling methods in climate science. First we provide a conceptual framework for stochastic modelling of deterministic dynamical systems based on the Mori-Zwanzig formalism. The Mori-Zwanzig equations…
The advent of deep learning and recurrent neural networks revolutionized the field of time-series processing. Therefore, recent research on spectrum prediction has focused on the use of these tools. However, spectrum prediction, which…
Short-term demand forecasting models commonly combine convolutional and recurrent layers to extract complex spatiotemporal patterns in data. Long-term histories are also used to consider periodicity and seasonality patterns as time series…
Brain can recognize different objects as ones that it has experienced before. The recognition accuracy and its processing time depend on task properties such as viewing condition, level of noise and etc. Recognition accuracy can be well…
With an ever-increasing number of sensors in modern society, spatio-temporal time series forecasting has become a de facto tool to make informed decisions about the future. Most spatio-temporal forecasting models typically comprise distinct…
Spatial transcriptomics (ST) provides essential spatial context by mapping gene expression within tissue, enabling detailed study of cellular heterogeneity and tissue organization. However, aligning ST data with histology images poses…
Deep learning applies hierarchical layers of hidden variables to construct nonlinear high dimensional predictors. Our goal is to develop and train deep learning architectures for spatio-temporal modeling. Training a deep architecture is…
In this article we focus on dynamic network data which describe interactions among a fixed population through time. We model this data using the latent space framework, in which the probability of a connection forming is expressed as a…
Nature, as far as we know, evolves continuously through space and time. Yet the ubiquitous hidden Markov model (HMM)--originally developed for discrete time and space analysis in natural language processing--remains a central tool in…
Modern approaches have proved the huge potential of addressing semantic segmentation as a mask classification task which is widely used in instance-level segmentation. This paradigm trains models by assigning part of object queries to…
Understanding the temporal dependence of precipitation is key to improving weather predictability and developing efficient stochastic rainfall models. We introduce an information-theoretic approach to quantify memory effects in discrete…
Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both…