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We consider a reinforcement learning setting introduced in (Maillard et al., NIPS 2011) where the learner does not have explicit access to the states of the underlying Markov decision process (MDP). Instead, she has access to several models…

Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…

We consider the problem of simulating diffusion bridges, which are diffusion processes that are conditioned to initialize and terminate at two given states. The simulation of diffusion bridges has applications in diverse scientific fields…

We describe an exact approach for calculating transition probabilities and waiting times in finite-state discrete-time Markov processes. All the states and the rules for transitions between them must be known in advance. We can then…

We study the limit behaviour of upper and lower bounds on expected time averages in imprecise Markov chains; a generalised type of Markov chain where the local dynamics, traditionally characterised by transition probabilities, are now…

Reinforcement learning with function approximation has recently achieved tremendous results in applications with large state spaces. This empirical success has motivated a growing body of theoretical work proposing necessary and sufficient…

We present a new method for inferring hidden Markov models from noisy time sequences without the necessity of assuming a model architecture, thus allowing for the detection of degenerate states. This is based on the statistical prediction…

The task of state estimation in active distribution systems faces a major challenge due to the integration of different measurements with multiple reporting rates. As a result, distribution systems are essentially unobservable in real time,…

Diffusion models have recently achieved great success in the synthesis of high-quality images and videos. However, the existing denoising techniques in diffusion models are commonly based on step-by-step noise predictions, which suffers…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

Recently, denoising diffusion models have led to significant breakthroughs in the generation of images, audio and text. However, it is still an open question on how to adapt their strong modeling ability to model time series. In this paper,…

Generating continuous-time, continuous-space stochastic processes (e.g., videos, weather forecasts) conditioned on partial observations (e.g., first and last frames) is a fundamental challenge. Existing approaches, (e.g., diffusion models),…

Denoising diffusion probabilistic models (DDPMs) have recently achieved leading performances in many generative tasks. However, the inherited iterative sampling process costs hinder their applications to text-to-speech deployment. Through…

Markov processes are widely used mathematical models for describing dynamic systems in various fields. However, accurately simulating large-scale systems at long time scales is computationally expensive due to the short time steps required…

Denoising Diffusion Probabilistic Models (DDPMs) are a very popular class of deep generative model that have been successfully applied to a diverse range of problems including image and video generation, protein and material synthesis,…

Piecewise Diffusion Markov Processes (PDifMPs) are valuable for modelling systems where continuous dynamics are interrupted by sudden shifts and/or changes in drift and diffusion. The first-passage time (FPT) in such models plays a central…

Motivated by the increasing importance of providing delay-guaranteed services in general computing and communication systems, and the recent wide adoption of learning and prediction in network control, in this work, we consider a general…

Systems of interacting continuous-time Markov chains are a powerful model class, but inference is typically intractable in high dimensional settings. Auxiliary information, such as noisy observations, is typically only available at discrete…

We propose a new algorithm for inferring the state of hidden spins and reconstructing the connections in a synchronous kinetic Ising model, given the observed history. Focusing on the case in which the hidden spins are conditionally…

We prove upper bounds on the rate, called "mixing rate", at which the von Neumann entropy of the expected density operator of a given ensemble of states changes under non-local unitary evolution. For an ensemble consisting of two states,…