Related papers: RetroBridge: Modeling Retrosynthesis with Markov B…
Sampling from the conditional (or posterior) probability distribution of the latent states of a Hidden Markov Model, given the realization of the observed process, is a non-trivial problem in the context of Markov Chain Monte Carlo. To do…
Phenotype-based screening has attracted much attention for identifying cell-active compounds. Transcriptional and proteomic profiles of cell population or single cells are informative phenotypic measures of cellular responses to…
Time series generation is widely used in real-world applications such as simulation, data augmentation, and hypothesis testing. Recently, diffusion models have emerged as the de facto approach to time series generation, enabling diverse…
When statistical analyses consider multiple data sources, Markov melding provides a method for combining the source-specific Bayesian models. Markov melding joins together submodels that have a common quantity. One challenge is that the…
Transporting between arbitrary distributions is a fundamental goal in generative modeling. Recently proposed diffusion bridge models provide a potential solution, but they rely on a joint distribution that is difficult to obtain in…
We consider the problem of solving robust Markov decision process (MDP), which involves a set of discounted, finite state, finite action space MDPs with uncertain transition kernels. The goal of planning is to find a robust policy that…
The embedding problem for Markov chains is a famous problem in probability theory and only partial results are available up till now. In this paper, we propose a variant of the embedding problem called the reversible embedding problem which…
Model predictive path integral (MPPI) is a sampling-based method for solving complex model predictive control (MPC) problems, but its real-time implementation faces two key challenges: the computational cost and sample requirements grow…
Schr\"{o}dinger bridge is a diffusion process that steers a given distribution to another in a prescribed time while minimizing the effort to do so. It can be seen as the stochastic dynamical version of the optimal mass transport, and has…
This paper aims to conduct a comprehensive theoretical analysis of current diffusion models. We introduce a novel generative learning methodology utilizing the Schr{\"o}dinger bridge diffusion model in latent space as the framework for…
De novo design of bioactive drug molecules with potential to treat desired biological targets is a profound task in the drug discovery process. Existing approaches tend to leverage the pocket structure of the target protein to condition the…
We consider the inverse problem of reconstructing the posterior measure over the trajec- tories of a diffusion process from discrete time observations and continuous time constraints. We cast the problem in a Bayesian framework and derive…
Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure,…
This paper considers robust Markov decision processes under parametric transition distributions. We assume that the true transition distribution is uniquely specified by some parametric distribution, and explicitly enforce that the…
High-resolution structure determination by cryo-electron microscopy (cryo-EM) requires the accurate fitting of an atomic model into an experimental density map. Traditional refinement pipelines such as Phenix.real_space_refine and Rosetta…
Denoising diffusion probabilistic models and score-matching models have proven to be very powerful for generative tasks. While these approaches have also been applied to the generation of discrete graphs, they have, so far, relied on…
The diffusion-driven Turing instability is a potential mechanism for spatial pattern formation in numerous biological and chemical systems. However, engineering these patterns and demonstrating that they are produced by this mechanism is…
Markov decision processes can be viewed as transformers of probability distributions. While this view is useful from a practical standpoint to reason about trajectories of distributions, basic reachability and safety problems are known to…
Conventional diffusion models typically relies on a fixed forward process, which implicitly defines complex marginal distributions over latent variables. This can often complicate the reverse process' task in learning generative…
We investigate the parameter recovery of Markov-switching ordinary differential processes from discrete observations, where the differential equations are nonlinear additive models. This framework has been widely applied in biological…