26 accepted papers
The first order vector autoregression with a symmetric transition matrix (sym-VAR(1)) occurs widely in applications such as electrical networks, robotics and mechanical systems. However, there is so far almost no work on estimating a sym- VAR(1) from time series data that guarantees the estimated sy…
The Hawkes process has been applied successfully to model point process data in a number of application areas including seismology, neural coding, high-frequency finance, and genomics. But the Hawkes process does not accommodate inhibitory effects observed jointly with excitatory behavior, e.g., for…
Kernel ridge regression is widely used but the theory of its performance has never been fully developed. While there are results on convergence there are few on bias and variance. Here we find expressions for local bias and variance for the important case of the exponential quadratic kernel. Using t…
Subspace tracking has a long and still growing list of applications with recent interest stimulated by the advent of ’streaming’ data. Despite the considerable literature, all of it motivated by the desire to track time varying subspaces, there seems to be almost no analysis of that time varying pro…
While clustering in general is a heavily worked area, clustering of auto-correlated time series (CATS) has received relatively little attention. Here, we develop a convex clustering algorithm suited to auto-correlated time series and compare it with a state of the art method. We find the proposed al…
Point processes are finding increasing applications in neuroscience, genomics, and social media. But basic modelling properties are little studied. Here we consider a periodic time-varying Poisson model and develop the asymptotic Cramer-Rao bound. We also develop, for the first time, a maximum likel…
Attention has turned in recently to clustering of collections networks where each network is characterized by a sparse inverse covariance matrix. Here we consider a mixture model of sparse Gaussian graphical models and develop an exact EM algorithm that improves considerably on a previous approximat…
In a range of network system identification problems point processes are the nodal signals. In many of these applications a fundamental question involves characterizing the internodal dynamics. Here we address that question using mutual information flows and establish a connection with Granger causa…
Stochastic differential equations (SDEs) evolving in Stiefel manifold have numerous applications in Science and Engineering. While numerical schemes for ordinary differential equations (ODEs) in Stiefel manifolds are reasonably well established, much less has been done for numerical SDEs schemes in…
While there is now a significant literature on sparse inverse covariance estimation, all that literature, with only a couple of exceptions, has dealt only with univariate (or scalar) networks where each node carries a univariate signal. However in many, perhaps most, applications, each node may carr…
Time-series clustering involves grouping homogeneous time series together based on certain similarity measures. The mixture AR model (MxAR) has already been developed for time series clustering, as has an associated EM algorithm. However, this EM clustering algorithm fails to perform satisfactorily…
Many applications in science and engineering involve tracking the state of a stochastic differential equation (SDE) evolving in a Lie group. This has been tackled by particle filtering although some existing schemes fail to satisfy geometric constraints. Further the conventional particle filter suff…
We sketch some aspects of LMS particularly focussing on some puzzles, problems and potentials. We explain the 'independence heuristic' by means of averaging theory for which we give a simple expose'. We suggest an explanation for the 'urban myth' that white noise only performance formulae can be use…
Networks of interacting Hawkes processes have emerged as useful models in neuroscience, geophysics, high frequency finance, and social network analysis. The Hawkes process is of fundamental importance, being a point process analog of an autoregression. Here we develop a fixed gain adaptive (aka onli…
Increasingly in the `big data' era, point process network data is appearing e.g. in social media but also genomics, high frequency finance and neurosicence. And the most basic problem is that of identifying network structure. As with all network system identification problems this is enabled by the…
One of the main approaches to system identification of networks of time series or signals is conditional independence graphical (CIG) modeling. In the Gaussian case, the conditional dependence structure of the nodal time series is determined by the location of zeros in the precision matrix (inverse…
In many engineering applications the state of a dynamical system is modelled by a Stochastic Differential Equation (SDE) evolving in a “curved” (non-Euclidean) space such as the Stiefel manifold - the set of n × p real matrices with orthonormal columns, (n ≥ p). Due to the advances in computing powe…
In many important engineering applications the state dynamics of a system are modelled by Stochastic Differential Equations (SDEs) evolving in non-Euclidean spaces such as matrix Lie groups. Due to the advances in computing power, the problem of state estimation can be efficiently addressed by the p…
Non-negative matrix factorization (NMF) has found use in fields such as remote sensing and computer vision where the signals of interest are usually non-negative. Data dimensions in these applications can be huge and traditional algorithms break down due to unachievable memory demands. One is then c…
There has been significant interest in sparse inverse covariance estimation in areas such as statistics, machine learning, and signal processing. In this problem, the sparse inverse of a covariance matrix of a multivariate normal distribution is estimated. A Penalised Log-Likelihood (PLL) optimisati…
The Hawkes process is the workhorse of dynamic point process modelling - the point process version of the autoregression. It has been applied, for example, in high frequency finance, electricity price spike modelling and gene regulatory network modelling. But, in all these and other applications, it…
There is an achilles heel underlying the consensus literature. It has been known for some time that measurement noise causes the explosive growth of the consensus mode. Here we state the noise problem; characterise the behaviour of the noisy consensus system including its drift to ∞ critique the exi…
Recently, the availability of high-dimensional point process data in a growing number of application areas is driving the demand for analysis tools for such data. An extremely challenging yet important problem is the inference of causal relationships from network data or network topology identificat…
High dimensional data is often modeled as a linear combination of a sparse component, a low-rank component, and noise. An example is a video sequence of a busy scene where the background is the low-rank part and the foreground, e.g. moving pedestrians, is the sparse part. Sparse and low rank (SLR) m…
We consider estimation of the angular velocity of a satellite undergoing noisy process dynamics. Modelling the attitude as a diffusion process evolving in SO(3), we propose an offline nonparametric estimator of the angular velocity over an interval based on noise free observations of the attitude. T…
Three emerging applications are driving a renewed interest in vector point processes: neural coding, high frequency finance and genomics. This pressure has revealed a gross lack of models and system identification methods. In particular in at least the first two applications coincidences can occur i…