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The purpose of this paper is to adapt the empirical characteristic function (ECF) method to stable, but possibly not inverse stable linear stochastic system driven by the increments of a Levy-process. A remarkable property of the ECF method…

This paper presents a regularized recursive identification algorithm with simultaneous on-line estimation of both the model parameters and the algorithms hyperparameters. A new kernel is proposed to facilitate the algorithm development. The…

L\'evy processes are widely used in financial mathematics to model return data. Price processes are then defined as a corresponding geometric L\'evy process, implying the fact that returns are independent. In this paper we propose an…

A novel procedure for the online identification of a class of discrete-time switched linear systems, which simultaneously estimates the parameters and switching manifolds of the systems, is proposed in this paper. Firstly, to estimate the…

This paper presents a novel online identification algorithm for nonlinear regression models. The online identification problem is challenging due to the presence of nonlinear structure in the models. Previous works usually ignore the…

Online system identification algorithms are widely used for monitoring, diagnostics and control by continuously adapting to time-varying dynamics. Typically, these algorithms consider a model structure that lacks parsimony and offers…

Conditional Random Fields (CRFs) are undirected graphical models, a special case of which correspond to conditionally-trained finite state machines. A key advantage of these models is their great flexibility to include a wide array of…

Levy processes are widely used in financial mathematics, telecommunication, economics, queueing theory and natural sciences for modelling. A typical model is obtained by considering finite dimensional linear stochastic SISO systems driven…

Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…

The classical sparse parameter identification methods are usually based on the iterative basis selection such as greedy algorithms, or the numerical optimization of regularized cost functions such as LASSO and Bayesian posterior probability…

Markov processes are used in a wide range of disciplines, including finance. The transition densities of these processes are often unknown. However, the conditional characteristic functions are more likely to be available, especially for…

An efficient structural identifiability analysis algorithm is developed in this study for a broad range of network structures. The proposed method adopts the Wright's path coefficient method to generate identifiability equations in forms of…

This paper studies the problem of online parameter estimation for cyber-physical systems with binary outputs that may be subject to adversarial data tampering. Existing methods are primarily offline and unsuitable for real-time learning. To…

We present an algorithm that can efficiently compute a broad class of inferences for discrete-time imprecise Markov chains, a generalised type of Markov chains that allows one to take into account partially specified probabilities and other…

Linear dependent types allow to precisely capture both the extensional behaviour and the time complexity of lambda terms, when the latter are evaluated by Krivine's abstract machine. In this work, we show that the same paradigm can be…

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…

In this paper we propose a recursive online algorithm for estimating the parameters of a time-varying ARCH process. The estimation is done by updating the estimator at time point $t-1$ with observations about the time point $t$ to yield an…

This paper develops an incremental learning algorithm based on quadratic inference function (QIF) to analyze streaming datasets with correlated outcomes such as longitudinal data and clustered data. We propose a renewable QIF (RenewQIF)…

Dynamical systems, for instance in model predictive control, often contain unknown parameters, which must be determined during system operation. Online or on-the-fly parameter identification methods are therefore necessary. The challenge of…

Linear causal models are important tools for modeling causal dependencies and yet in practice, only a subset of the variables can be observed. In this paper, we examine the parameter identifiability of these models by investigating whether…