Related papers: Random Euler Complex-Valued Nonlinear Filters
Low-cost cross-modal representation learning is crucial for deriving semantic representations across diverse modalities such as text, audio, images, and video. Traditional approaches typically depend on large specialized models trained from…
Complex-valued neural networks (CVNNs) have been shown to be powerful nonlinear approximators when the input data can be properly modeled in the complex domain. One of the major challenges in scaling up CVNNs in practice is the design of…
This paper investigates an approximation scheme of the optimal nonlinear Bayesian filter based on the Gaussian mixture representation of the state probability distribution function. The resulting filter is similar to the particle filter,…
Recurrent Neural Networks (RNNs) are among the most successful machine learning models for sequence modelling, but tend to suffer from an exponential increase in the number of parameters when dealing with large multidimensional data. To…
Counter-adversarial system design problems have lately motivated the development of inverse Bayesian filters. For example, inverse Kalman filter (I-KF) has been recently formulated to estimate the adversary's Kalman-filter-tracked estimates…
Recent advancements in neural networks, supported by foundational theoretical insights, emphasize the superior representational power of complex numbers. However, their adoption in randomized neural networks (RNNs) has been limited due to…
In this article we present new results on neural networks with linear threshold activation functions. We precisely characterize the class of functions that are representable by such neural networks and show that 2 hidden layers are…
Likelihood-free approaches are appealing for performing inference on complex dependence models, either because it is not possible to formulate a likelihood function, or its evaluation is very computationally costly. This is the case for…
Non-stationary signals are ubiquitous in real life. Many techniques have been proposed in the last decades which allow decomposing multi-component signals into simple oscillatory mono-components, like the groundbreaking Empirical Mode…
Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…
In the last years, the success of kernel-based regularisation techniques in solving impulse response modelling tasks has revived the interest on linear system identification. In this work, an alternative perspective on the same problem is…
In this paper we develop a method for learning nonlinear systems with multiple outputs and inputs. We begin by modelling the errors of a nominal predictor of the system using a latent variable framework. Then using the maximum likelihood…
In non-linear filtering, it is traditional to compare non-linear architectures such as neural networks to the standard linear Kalman Filter (KF). We observe that this mixes the evaluation of two separate components: the non-linear…
We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems with superior accuracy. A major drawback of existing filtering methods, e.g., particle filters or ensemble Kalman filters, is the low…
Convolutional Neural Network (CNN)-based filters have achieved significant performance in video artifacts reduction. However, the high complexity of existing methods makes it difficult to be applied in real usage. In this paper, a CNN-based…
A complex-valued convolutional network (convnet) implements the repeated application of the following composition of three operations, recursively applying the composition to an input vector of nonnegative real numbers: (1) convolution with…
This paper presents a seamless algorithm for the application of the multilevel Monte Carlo (MLMC) method to the ensemble transform particle filter (ETPF). The algorithm uses a combination of optimal coupling transformations between coarse…
Rapid development in numerical modelling of materials and the complexity of new models increases quickly together with their computational demands. Despite the growing performance of modern computers and clusters, calibration of such models…
Random Fourier Features (RFF) is among the most popular and broadly applicable approaches for scaling up kernel methods. In essence, RFF allows the user to avoid costly computations on a large kernel matrix via a fast randomized…
Linear minimum mean square error (LMMSE) estimation is often ill-conditioned, suggesting that unconstrained minimization of the mean square error is an inadequate approach to filter design. To address this, we first develop a unifying…