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Modeling dynamical systems plays a crucial role in capturing and understanding complex physical phenomena. When physical models are not sufficiently accurate or hardly describable by analytical formulas, one can use generic function…

Estimating mutual information accurately is pivotal across diverse applications, from machine learning to communications and biology, enabling us to gain insights into the inner mechanisms of complex systems. Yet, dealing with…

We prove that a denoising diffusion sampler equipped with a sequential bias across the batch dimension is exactly an Euler-Maruyama integrator for overdamped Langevin dynamics. Each reverse denoising step, with its associated spring…

Pairwise learning focuses on learning tasks with pairwise loss functions, depends on pairs of training instances, and naturally fits for modeling relationships between pairs of samples. In this paper, we focus on the privacy of pairwise…

Stochastic discriminative EM (sdEM) is an online-EM-type algorithm for discriminative training of probabilistic generative models belonging to the exponential family. In this work, we introduce and justify this algorithm as a stochastic…

Calibration of large-scale differential equation models to observational or experimental data is a widespread challenge throughout applied sciences and engineering. A crucial bottleneck in state-of-the art calibration methods is the…

A molecule traveling in a realistic propagation environment can experience stochastic interactions with other molecules and the environment boundary. The statistical behavior of some isolated phenomena, such as dilute unbounded molecular…

Learning models for dynamical systems in continuous time is significant for understanding complex phenomena and making accurate predictions. This study presents a novel approach utilizing differential neural networks (DNNs) to model…

We propose a new multi-scale molecular dynamics simulation method which can achieve high accuracy and high sampling efficiency simultaneously without aforehand knowledge of the coarse grained (CG) potential and test it for a biomolecular…

Our study focuses on fractional order compartment models derived from underlying physical stochastic processes, providing a more physically grounded approach compared to models that use the dynamical system approach by simply replacing…

In many supervised learning applications, the response consists of both continuous and binary outcomes. Studies have shown that jointly modeling such mixed-type responses can substantially improve predictive performance compared to separate…

Stochastic models are often used to help understand the behavior of intracellular biochemical processes. The most common such models are continuous time Markov chains (CTMCs). Parametric sensitivities, which are derivatives of expectations…

Stochastic differential equations (SDEs) are one of the most important representations of dynamical systems. They are notable for the ability to include a deterministic component of the system and a stochastic one to represent random…

Reinforcement Learning from Human Feedback (RLHF) is increasingly used to fine-tune diffusion models, but a key challenge arises from the mismatch between stochastic samplers used during training and deterministic samplers used during…

Motion sensing and tracking with IMU data is essential for spatial intelligence, which however is challenging due to the presence of time-varying stochastic bias. IMU bias is affected by various factors such as temperature and vibration,…

A computationally efficient method for online joint state inference and dynamical model learning is presented. The dynamical model combines an a priori known, physically derived, state-space model with a radial basis function expansion…

The performance of data fusion and tracking algorithms often depends on parameters that not only describe the sensor system, but can also be task-specific. While for the sensor system tuning these variables is time-consuming and mostly…

The task of learning a diffusion-based neural sampler for drawing samples from an unnormalized target distribution can be viewed as a stochastic optimal control problem on path measures. However, the training of neural samplers can be…

We introduce Compartmentalized Diffusion Models (CDM), a method to train different diffusion models (or prompts) on distinct data sources and arbitrarily compose them at inference time. The individual models can be trained in isolation, at…

Robust Bayesian inference using density power divergence (DPD) has emerged as a promising approach for handling outliers in statistical estimation. Although the DPD-based posterior offers theoretical guarantees of robustness, its practical…