Related papers: Gauss-Newton Filtering incorporating Levenberg-Mar…
This paper presents a compact, recursive, non-linear, filter, derived from the Gauss-Newton (GNF), which is an algorithm that is based on weighted least squares and the Newton method of local linearisation. The recursive form (RGNF), which…
We explore the usage of the Levenberg-Marquardt (LM) algorithm for regression (non-linear least squares) and classification (generalized Gauss-Newton methods) tasks in neural networks. We compare the performance of the LM method with other…
In this paper we revisit a non-linear filter for {\em non-Gaussian} noises that was introduced in [1]. Goggin proved that transforming the observations by the score function and then applying the Kalman Filter (KF) to the transformed…
For numerous parameter and state estimation problems, assimilating new data as they become available can help produce accurate and fast inference of unknown quantities. While most existing algorithms for solving those kind of ill-posed…
This paper proposes an efficient implementation of the generalized labeled multi-Bernoulli (GLMB) filter by combining the prediction and update into a single step. In contrast to the original approach which involves separate truncations in…
Graph Neural Networks (GNNs) are powerful learning methods for recommender systems owing to their robustness in handling complicated user-item interactions. Recently, the integration of contrastive learning with GNNs has demonstrated…
Graph neural networks (GNNs) are currently one of the most performant collaborative filtering methods. Meanwhile, owing to the use of an embedding table to represent each user/item as a distinct vector, GNN-based recommenders have inherited…
Graph Neural Networks (GNNs) have achieved impressive performance in collaborative filtering. However, GNNs tend to yield inferior performance when the distributions of training and test data are not aligned well. Also, training GNNs…
Reduced rank nonlinear filters are increasingly utilized in data assimilation of geophysical flows, but often require a set of ensemble forward simulations to estimate forecast covariance. On the other hand, predictor-corrector type nudging…
The expressive power of a Gaussian process (GP) model comes at a cost of poor scalability in the data size. To improve its scalability, this paper presents a low-rank-cum-Markov approximation (LMA) of the GP model that is novel in…
This paper proposes an efficient implementation of the generalized labeled multi-Bernoulli (GLMB) filter by combining the prediction and update into a single step. In contrast to an earlier implementation that involves separate truncations…
We present practical Levenberg-Marquardt variants of Gauss-Newton and natural gradient methods for solving non-convex optimization problems that arise in training deep neural networks involving enormous numbers of variables and huge data…
The Kalman filter provides an optimal estimation for a linear system with Gaussian noise. However when the noises are non-Gaussian in nature, its performance deteriorates rapidly. For non-Gaussian noises, maximum correntropy Kalman filter…
In this manuscript we introduce numerical Gaussian process Kalman filtering (GPKF). Numerical Gaussian processes have recently been developed to simulate spatiotemporal models. The contribution of this paper is to embed numerical Gaussian…
This paper exploits Geometric (Clifford) Algebra (GA) theory in order to devise and introduce a new adaptive filtering strategy. From a least-squares cost function, the gradient is calculated following results from Geometric Calculus (GC),…
In this paper, we develop a variant of the well-known Gauss-Newton (GN) method to solve a class of nonconvex optimization problems involving low-rank matrix variables. As opposed to the standard GN method, our algorithm allows one to handle…
We present a novel Kalman filter for spatiotemporal systems called the numerical Gaussian process Kalman filter (GPKF). Numerical Gaussian processes have recently been introduced as a physics informed machine learning method for simulating…
We consider the nonlinear Kalman filtering problem using Kullback-Leibler (KL) and $\alpha$-divergence measures as optimization criteria. Unlike linear Kalman filters, nonlinear Kalman filters do not have closed form Gaussian posteriors…
Neural fields have emerged as a powerful framework for representing continuous multidimensional signals such as images and videos, 3D and 4D objects and scenes, and radiance fields. While efficient, achieving high-quality representation…
Non-negative matrix factorization (NMF) has become a popular machine learning approach to many problems in text mining, speech and image processing, bio-informatics and seismic data analysis to name a few. In NMF, a matrix of non-negative…