Related papers: Constructing Generalized Sample Transition Probabi…

The existing literature on stochastic simulation of chemical reaction networks has a tendency to move as quickly as possible to the abstract formulation of the stochastic dynamics in terms of probabilities based on the concept of the…

Generalized linear mixed models (GLMM) are used for inference and prediction in a wide range of different applications providing a powerful scientific tool. An increasing number of sources of data are becoming available, introducing a…

In this paper, we consider a generalized birth-death process (GBDP) and examined its linear versions. Using its transition probabilities, we obtain the system of differential equations that governs its state probabilities. The distribution…

The health condition of components in civil infrastructures can be described by various discrete states according to their performance degradation. Inferring these states from measurable responses is typically an ill-posed inverse problem.…

Diffusion models can generate a variety of high-quality images by modeling complex data distributions. Trained diffusion models can also be very effective image priors for solving inverse problems. Most of the existing diffusion-based…

Score-based diffusion models demonstrate superior performance in generative tasks but encounter fundamental bottlenecks in inverse problems due to the analytical intractability of the time-dependent likelihood score. To bridge this gap, we…

Probabilistic models for sequential data are the basis for a variety of applications concerned with processing timely ordered information. The predominant approach in this domain is given by recurrent neural networks, implementing either an…

Discrete stochastic processes (DSP) are instrumental for modelling the dynamics of probabilistic systems and have a wide spectrum of applications in science and engineering. DSPs are usually analyzed via Monte Carlo methods since the number…

This paper presents an improved implicit sampling method for hierarchical Bayesian inverse problems. A widely used approach for sampling posterior distribution is based on Markov chain Monte Carlo (MCMC). However, the samples generated by…

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…

Gaussian Process (GP) models are a powerful tool in probabilistic machine learning with a solid theoretical foundation. Thanks to current advances, modeling complex data with GPs is becoming increasingly feasible, which makes them an…

We introduce a flexible and scalable class of Bayesian geostatistical models for discrete data, based on the class of nearest neighbor mixture transition distribution processes (NNMP), referred to as discrete NNMP. The proposed class…

Stochastic modeling of transcription is a classic yet long-standing problem in theoretical biophysics. The lack of unified results and a computationally efficient approach for a general, fine-grained transcription model has confined…

Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…

This work addresses the general problem of control synthesis for continuous-space, discrete-time stochastic systems with probabilistic guarantees via finite abstractions. While established methods exist, they often trade off accuracy for…

The exploration of transition state (TS) geometries is crucial for elucidating chemical reaction mechanisms and modeling their kinetics. Recently, machine learning (ML) models have shown remarkable performance for prediction of TS…

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

Molecular transitions -- such as protein folding, allostery, and membrane transport -- are central to biology yet remain notoriously difficult to simulate. Their intrinsic rarity pushes them beyond reach of standard molecular dynamics,…

Metastability is one of the major encountered obstacle when performing long molecular dynamics simulations, and many methods were developed to address this challenge. The "Parallel Replica" (ParRep) dynamics is known for allowing to…

Markov state models (MSMs) have been broadly adopted for analyzing molecular dynamics trajectories, but the approximate nature of the models that results from coarse-graining into discrete states is a long-known limitation. We show…