Related papers: Analysis of error propagation in particle filters …
Bootstrap particle filter (BPF) is the corner stone of many popular algorithms used for solving inference problems involving time series that are observed through noisy measurements in a non-linear and non-Gaussian context. The long term…
We propose a new sampling-based approach for approximate inference in filtering problems. Instead of approximating conditional distributions with a finite set of states, as done in particle filters, our approach approximates the…
The typical particle filtering approximation error is exponentially dependent on the dimension of the model. Therefore, to control this error, an enormous number of particles are required, which means a heavy computational burden that is…
We introduce the lcm-filtration and stepwise filtration, comparing their performance across various scenarios in terms of computational complexity, efficiency, and redundancy. The lcm-filtration often involves identical steps or ideals,…
We consider the problem of approximating optimal in the Minimum Mean Squared Error (MMSE) sense nonlinear filters in a discrete time setting, exploiting properties of stochastically convergent state process approximations. More…
Coherent lower previsions are general probabilistic models allowing incompletely specified probability distributions. However, for complete description of a coherent lower prevision -- even on finite underlying sample spaces -- an infinite…
Inference for partially observed Markov process models has been a longstanding methodological challenge with many scientific and engineering applications. Iterated filtering algorithms maximize the likelihood function for partially observed…
With the rapid development of large language models (LLMs) and the growing demand for personalized content, recommendation systems have become critical in enhancing user experience and driving engagement. Collaborative filtering algorithms,…
Error bounds have been studied for more than seventy years, beginning with the seminal result of Hoffman (1952) [{\it J. Res. Natl. Bur. Standards}, 49 (1952), 263--265], which establishes an upper bound for the distance from an arbitrary…
Propagation of linear constraints has become a crucial sub-routine in modern Mixed-Integer Programming (MIP) solvers. In practice, iterative algorithms with tolerance-based stopping criteria are used to avoid problems with slow or infinite…
The implicit particle filter is a sequential Monte Carlo method for data assimilation that guides the particles to the high-probability regions via a sequence of steps that includes minimizations. We present a new and more general…
This paper focuses on the estimation of partially observed branching processes. First, the estimators from a frequentist perspective proposed in the literature are reviewed. The main objective of this paper is to present computational tools…
Reducing the impact of seismic activity on the motion of suspended optics is essential for the operation of ground-based gravitational wave detectors. During periods of increased seismic activity, low-frequency ground translation and tilt…
For particle filters and ensemble Kalman filters it is of practical importance to understand how and why data assimilation methods can be effective when used with a fixed small number of particles, since for many large-scale applications it…
The aim of this paper is twofold: In the first part, we leverage recent results on scenario design to develop randomized algorithmsfor approximating the image set of a nonlinear mapping, that is, a (possibly noisy) mapping of a set via a…
We present recent results on the existence of a continuous time limit for Ensemble Kalman Filter algorithms. In the setting of continuous signal and observation processes, we apply the original Ensemble Kalman Filter algorithm proposed by…
Amplitude filtering is concerned with identifying basis-states in a superposition whose amplitudes are greater than a specified threshold; probability filtering is defined analogously for probabilities. Given the scarcity of qubits, the…
We address the problem of distributing approximation errors in large-scale quantum programs. It has been known for some time that when compiling quantum algorithms for a fault-tolerant architecture, some operations must be approximated as…
Large-Eddy Simulations (LES) of two-phase turbulent flows exhibit quantitative differences in particle statistics if compared to Direct Numerical Simulations (DNS) which, in the context of the present study, is considered the exact…
State estimation in non-linear models is performed by tracking the posterior distribution recursively. A plethora of algorithms have been proposed for this task. Among them, the Gaussian particle filter uses a weighted set of particles to…