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Image processing researchers commonly assert that "median filtering is better than linear filtering for removing noise in the presence of edges." Using a straightforward large-$n$ decision-theory framework, this folk-theorem is seen to be…
This paper presents a tractable sufficient condition for the consistency of maximum likelihood estimators (MLEs) in partially observed diffusion models, stated in terms of stationary distribution of the associated fully observed diffusion,…
Monte Carlo simulations of diffusion processes often introduce bias in the final result, due to time discretization. Using an auxiliary Poisson process, it is possible to run simulations which are unbiased. In this article, we propose such…
Missing values in multivariate time series data can harm machine learning performance and introduce bias. These gaps arise from sensor malfunctions, blackouts, and human error and are typically addressed by data imputation. Previous work…
The research described herewith investigates detecting change points of means and of variances in a sequence of observations. The number of change points can be divergent at certain rate as the sample size goes to infinity. We define a…
Building on recent advances in image generation, we present a fully data-driven approach to rendering markup into images. The approach is based on diffusion models, which parameterize the distribution of data using a sequence of denoising…
In this paper, we learn a diffusion model to generate 3D data on a scene-scale. Specifically, our model crafts a 3D scene consisting of multiple objects, while recent diffusion research has focused on a single object. To realize our goal,…
Watermarking has emerged as a promising technique to track AI-generated content and differentiate it from authentic human creations. While prior work extensively studies watermarking for autoregressive large language models (LLMs) and image…
While diffusion-based generative models have made significant strides in visual content creation, conventional approaches face computational challenges, especially for high-resolution images, as they denoise the entire image from noisy…
We present a parameter-decoupled superresolution framework for estimating sub-wavelength separations of passive two-point sources without requiring prior knowledge or control of the source. Our theoretical foundation circumvents the need to…
We investigate the use of possibly the simplest scheme for the parallelisation of the standard particle filter, that consists in splitting the computational budget into $M$ fully independent particle filters with $N$ particles each, and…
In this technical report we analyse the performance of diffusion strategies applied to the Least-Mean-Square adaptive filter. We configure a network of cooperative agents running adaptive filters and discuss their behaviour when compared…
Sequential Monte Carlo (SMC), or particle filtering, is widely used in nonlinear state-space systems, but its performance often suffers from poorly approximated proposal and state-transition distributions. This work introduces a…
Recent research works on distributed adaptive networks have intensively studied the case where the nodes estimate a common parameter vector collaboratively. However, there are many applications that are multitask-oriented in the sense that…
Accurate estimation of the states of a nonlinear dynamical system is crucial for their design, synthesis, and analysis. Particle filters are estimators constructed by simulating trajectories from a sampling distribution and averaging them…
In this article we consider Bayesian parameter inference associated to partially-observed stochastic processes that start from a set B0 and are stopped or killed at the first hitting time of a known set A. Such processes occur naturally…
Kinetic equations model distributions of particles in position-velocity phase space. Often, one is interested in studying the long-time behavior of particles in high-collisional regimes in which an approximate (advection)-diffusion model…
We model filtration of a feed solution, containing both small and large foulant particles, by a membrane filter. The membrane interior is modeled as a network of pores, allowing for the simultaneous adsorption of small particles and sieving…
Object pose estimation plays a vital role in embodied AI and computer vision, enabling intelligent agents to comprehend and interact with their surroundings. Despite the practicality of category-level pose estimation, current approaches…
Diffusion models have gained attention for their ability to represent complex distributions and incorporate uncertainty, making them ideal for robust predictions in the presence of noisy or incomplete data. In this study, we develop and…