Related papers: Rethinking the Mathematical Framework and Optimali…

In this paper, we focus on the distributed set-membership filtering (SMFing) problem for a multi-agent system with absolute (taken from agents themselves) and relative (taken from neighbors) measurements. In the literature, the relative…

This paper considers the state estimation problem for nonlinear dynamic systems with unknown but bounded noises. Set membership filter (SMF) is a popular algorithm to solve this problem. In the set membership setting, we investigate the…

This article studies the Set-Membership Smoothing (SMSing) problem for non-stochastic Hidden Markov Models. By adopting the mathematical concept of uncertain variables, an optimal SMSing framework is established for the first time. This…

The issue of filter stability with respect to (w.r.t.) the initial condition refers to the unreliable filtering process caused by improper prior information of the initial state. This paper focuses on analyzing and resolving the stability…

The invariant filtering theory based on the group theory has been successful in statistical filtering methods. However, there exists a class of state estimation problems with unknown statistical properties of noise disturbances, and it is…

In this technical note, a recursive set-membership filtering algorithm for discrete-time nonlinear dynamical systems subject to unknown but bounded process and measurement noises is proposed. The nonlinear dynamics is represented in a…

In this paper, we derive a novel procedure for set-membership estimation of dynamical systems affected by stochastic noise with unbounded support. Employing a bound on the sample covariance matrix, we are able to provide a finite- sample…

Set-membership estimation is usually formulated in the context of set-valued calculus and no probabilistic calculations are necessary. In this paper, we show that set-membership estimation can be equivalently formulated in the probabilistic…

In this paper, a new filter model called set-membership Kalman filter for nonlinear state estimation problems was designed, where both random and unknown but bounded uncertainties were considered simultaneously in the discrete-time system.…

Matched filters are widely used to localise signal patterns due to their high efficiency and interpretability. However, their effectiveness deteriorates for low signal-to-noise ratio (SNR) signals, such as those recorded on edge devices,…

Asymptotic boundedness is a crucial property of Distributed Set-Membership Filtering (DSMFing) that prevents the unbounded growth of the set estimates caused by the wrapping effect. However, this important property remains…

Supervised matrix factorization (SMF) is a classical machine learning method that simultaneously seeks feature extraction and classification tasks, which are not necessarily a priori aligned objectives. Our goal is to use SMF to learn…

The problem of finding overlapping communities in networks has gained much attention recently. Optimization-based approaches use non-negative matrix factorization (NMF) or variants, but the global optimum cannot be provably attained in…

Nonnegative Matrix Factorization (NMF) is a versatile and powerful tool for discovering latent structures in data matrices, with many variations proposed in the literature. Recently, Leplat et al.\@ (2019) introduced a minimum-volume NMF…

This work introduces the Supervised Expectation-Maximization Framework (SEMF), a versatile and model-agnostic approach for generating prediction intervals with any ML model. SEMF extends the Expectation-Maximization algorithm, traditionally…

Spatio-Temporal Multivariate time series Forecast (STMF) uses the time series of $n$ spatially distributed variables in a period of recent past to forecast their values in a period of near future. It has important applications in…

An important objective of the classical processing of stationary random sequences under nonparametric uncertainty is the problem of filtering in case when the distribution of the underlying signal is unknown. In this paper it is assumed…

State Space Models (SSMs), particularly recent selective variants like Mamba, have emerged as a leading architecture for sequence modeling, challenging the dominance of Transformers. However, the success of these state-of-the-art models…

We consider the problem of learning a sparse rule model, a prediction model in the form of a sparse linear combination of rules, where a rule is an indicator function defined over a hyper-rectangle in the input space. Since the number of…

This paper presents the machine learning-based ensemble conditional mean filter (ML-EnCMF) -- a filtering method based on the conditional mean filter (CMF) previously introduced in the literature. The updated mean of the CMF matches that of…