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Sequential Modelling and Inference of High-frequency Limit Order Book with State-space Models and Monte Carlo Algorithms
The high-frequency limit order book (LOB) market has recently attracted increasing research attention from both the industry and the academia as a result of expanding algorithmic trading. However, the massive data throughput and the inherent complexity of high-frequency market dynamics also present challenges to some classic statistical modelling approaches. By adopting powerful state-space models from the field of signal processing as well as a number of Bayesian inference algorithms such as particle filtering, Markov chain Monte Carlo and variational inference algorithms, this thesis presents my extensive research into the high-frequency limit order book covering a wide scope of topics.
Chapter 2 presents a novel construction of the non-homogeneous Poisson process to allow online intensity inference of limit order transactions arriving at a central exchange as point data. Chapter 3 extends a baseline jump diffusion model for market fair-price process to include three additional model features taken from real-world market intuitions. In Chapter 4, another price model is developed to account for both long-term and short-term diffusion behaviours of the price process. This is achieved by incorporating multiple jump-diffusion processes each exhibiting a unique characteristic. Chapter 5 observes the multi-regime nature of price diffusion processes as well as the non-Markovian switching behaviour between regimes. As such, a novel model is proposed which combines the continuous-time state-space model, the hidden semi-Markov switching model and the non-parametric Dirichlet process model. Additionally, building upon the general structure of the particle Markov chain Monte Carlo algorithm, I further propose an algorithm which achieves sequential state inference, regime identification and regime parameters learning requiring minimal prior assumptions. Chapter 6 focuses on the development of efficient parameter-learning algorithms for state-space models and presents three algorithms each demonstrating promising results in comparison to some well-established methods.
The models and algorithms proposed in this thesis not only are practical tools for analysing high-frequency LOB markets, but can also be applied in various areas and disciplines beyond finance
Kalman-gain aided particle PHD filter for multi-target tracking
We propose an efficient SMC-PHD filter which employs the Kalman-gain approach during weight update to correct predicted particle states by minimizing the mean square error (MSE) between the estimated measurement and the actual measurement received at a given time in order to arrive at a more accurate posterior. This technique identifies and selects those particles belonging to a particular target from a given PHD for state correction during weight computation. Besides the improved tracking accuracy, fewer particles are required in the proposed approach. Simulation results confirm the improved tracking performance when evaluated with different measures
An evolving ensemble model of multi-stream convolutional neural networks for human action recognition in still images
Still image human action recognition (HAR) is a challenging problem owing to limited sources of information and large intra-class and small inter-class variations which requires highly discriminative features. Transfer learning offers the necessary capabilities in producing such features by preserving prior knowledge while learning new representations. However, optimally identifying dynamic numbers of re-trainable layers in the transfer learning process poses a challenge. In this study, we aim to automate the process of optimal configuration identification. Specifically, we propose a novel particle swarm optimisation (PSO) variant, denoted as EnvPSO, for optimal hyper-parameter selection in the transfer learning process with respect to HAR tasks with still images. It incorporates Gaussian fitness surface prediction and exponential search coefficients to overcome stagnation. It optimises the learning rate, batch size, and number of re-trained layers of a pre-trained convolutional neural network (CNN). To overcome bias of single optimised networks, an ensemble model with three optimised CNN streams is introduced. The first and second streams employ raw images and segmentation masks yielded by mask R-CNN as inputs, while the third stream fuses a pair of networks with raw image and saliency maps as inputs, respectively. The final prediction results are obtained by computing the average of class predictions from all three streams. By leveraging differences between learned representations within optimised streams, our ensemble model outperforms counterparts devised by PSO and other state-of-the-art methods for HAR. In addition, evaluated using diverse artificial landscape functions, EnvPSO performs better than other search methods with statistically significant difference in performance
Towards an Interactive Humanoid Companion with Visual Tracking Modalities
The idea of robots acting as human companions is not a particularly new or original one. Since the notion of “robot ” was created, the idea of robots replacing humans in dangerous, dirty and dull activities has been inseparably tied with the fantasy of human-like robots being friends and existing side by side with humans. In 1989, Engelberger (Engelberger
Advanced signal processing techniques for multi-target tracking
The multi-target tracking problem essentially involves the recursive joint estimation of the state of unknown and time-varying number of targets present in a tracking scene, given a series of observations. This problem becomes more challenging because the sequence of observations is noisy and can become corrupted due to miss-detections and false alarms/clutter. Additionally, the detected observations are indistinguishable from clutter. Furthermore, whether the target(s) of interest are point or extended (in terms of spatial extent) poses even more technical challenges.
An approach known as random finite sets provides an elegant and rigorous framework for the handling of the multi-target tracking problem. With a random finite sets formulation, both the multi-target states and multi-target observations are modelled as finite set valued random variables, that is, random variables which are random in both the number of elements and the values of the elements themselves. Furthermore, compared to other approaches, the random finite sets approach possesses a desirable characteristic of being free of explicit data association prior to tracking. In addition, a framework is available for dealing with random finite sets and is known as finite sets statistics. In this thesis, advanced signal processing techniques are employed to provide enhancements to and develop new random finite sets based multi-target tracking algorithms for the tracking of both point and extended targets with the aim to improve tracking performance in cluttered
environments.
To this end, firstly, a new and efficient Kalman-gain aided sequential Monte Carlo probability hypothesis density (KG-SMC-PHD) filter and a cardinalised particle probability hypothesis density (KG-SMC-CPHD) filter are proposed. These filters employ the Kalman-
gain approach during weight update to correct predicted particle states by minimising
the mean square error between the estimated measurement and the actual measurement received at a given time in order to arrive at a more accurate posterior. This technique identifies and selects those particles belonging to a particular target from a given PHD for state correction during weight computation. The proposed SMC-CPHD filter provides a better estimate of the number of targets. Besides the improved tracking accuracy, fewer particles are required in the proposed approach. Simulation results confirm the improved tracking performance when evaluated with different measures.
Secondly, the KG-SMC-(C)PHD filters are particle filter (PF) based and as with PFs, they require a process known as resampling to avoid the problem of degeneracy. This thesis proposes a new resampling scheme to address a problem with the systematic resampling method which causes a high tendency of resampling very low weight particles especially when a large number of resampled particles are required; which in turn affect state estimation.
Thirdly, the KG-SMC-(C)PHD filters proposed in this thesis perform filtering and not tracking , that is, they provide only point estimates of target states but do not provide connected estimates of target trajectories from one time step to the next. A new post processing step using game theory as a solution to this filtering - tracking problem is proposed. This approach was named the GTDA method. This method was employed in the KG-SMC-(C)PHD filter as a post processing technique and was evaluated using both simulated and real data obtained using the NI-USRP software defined radio platform in a passive bi-static radar system.
Lastly, a new technique for the joint tracking and labelling of multiple extended targets is proposed. To achieve multiple extended target tracking using this technique, models for the target measurement rate, kinematic component and target extension are defined and jointly propagated in time under the generalised labelled multi-Bernoulli (GLMB) filter framework. The GLMB filter is a random finite sets-based filter. In particular, a Poisson mixture variational Bayesian (PMVB) model is developed to simultaneously estimate the measurement rate of multiple extended targets and extended target extension was modelled using B-splines. The proposed method was evaluated with various performance metrics in order to demonstrate its effectiveness in tracking multiple extended targets
Towards Bayesian System Identification: With Application to SHM of Offshore Structures
Within the offshore industry Structural Health Monitoring remains a growing area of interest. The oil and gas sectors are faced with ageing infrastructure and are driven by the desire for reliable lifetime extension, whereas the wind energy sector is investing heavily in a large number of structures. This leads to a number of distinct challenges for Structural Health Monitoring which are brought together by one unifying theme --- uncertainty. The offshore environment is highly uncertain, existing structures have not been monitored from construction and the loading and operational conditions they have experienced (among other factors) are not known. For the wind energy sector, high numbers of structures make traditional inspection methods costly and in some cases dangerous due to the inaccessibility of many wind farms. Structural Health Monitoring attempts to address these issues by providing tools to allow automated online assessment of the condition of structures to aid decision making.
The work of this thesis presents a number of Bayesian methods which allow system identification, for Structural Health Monitoring, under uncertainty. The Bayesian approach explicitly incorporates prior knowledge that is available and combines this with evidence from observed data to allow the formation of updated beliefs. This is a natural way to approach Structural Health Monitoring, or indeed, many engineering problems. It is reasonable to assume that there is some knowledge available to the engineer before attempting to detect, locate, classify, or model damage on a structure. Having a framework where this knowledge can be exploited, and the uncertainty in that knowledge can be handled rigorously, is a powerful methodology. The problem being that the actual computation of Bayesian results can pose a significant challenge both computationally and in terms of specifying appropriate models. This thesis aims to present a number of Bayesian tools, each of which leverages the power of the Bayesian paradigm to address a different Structural Health Monitoring challenge.
Within this work the use of Gaussian Process models is presented as a flexible nonparametric Bayesian approach to regression, which is extended to handle dynamic models within the Gaussian Process NARX framework. The challenge in training Gaussian Process models is seldom discussed and the work shown here aims to offer a quantitative assessment of different learning techniques including discussions on the choice of cost function for optimisation of hyperparameters and the choice of the optimisation algorithm itself. Although rarely considered, the effects of these choices are demonstrated to be important and to inform the use of a Gaussian Process NARX model for wave load identification on offshore structures.
The work is not restricted to only Gaussian Process models, but Bayesian state-space models are also used. The novel use of Particle Gibbs for identification of nonlinear oscillators is shown and modifications to this algorithm are applied to handle its specific use in Structural Health Monitoring. Alongside this, the Bayesian state-space model is used to perform joint input-state-parameter inference for Operational Modal Analysis where the use of priors over the parameters and the forcing function (in the form of a Gaussian Process transformed into a state-space representation) provides a methodology for this output-only identification under parameter uncertainty. Interestingly, this method is shown to recover the parameter distributions of the model without compromising the recovery of the loading time-series signal when compared to the case where the parameters are known.
Finally, a novel use of an online Bayesian clustering method is presented for performing Structural Health Monitoring in the absence of any available training data. This online method does not require a pre-collected training dataset, nor a model of the structure, and is capable of detecting and classifying a range of operational and damage conditions while in service. This leaves the reader with a toolbox of methods which can be applied, where appropriate, to identification of dynamic systems with a view to Structural Health Monitoring problems within the offshore industry and across engineering
Industrial applications of hybrid modelling techniques
Eng. D ThesisIn the present study, the application of hybrid modelling techniques is applied to industrial
applications. Many of the studies currently known to the literature for the fields under
examination are either purely model-based, theory-based or lab/pilot scale empirical
studies. In this work, we present a hybrid approach whereby empirical data is used to
form statistical models for relationships where no clear fundamental relationship can be
described mathematically. Equally, first-principles models are employed where no suitable
data can be gathered empirically. Finally, the process understanding, heuristics and
recollections of plant operators, engineers and maintenance personnel can be integrated
formally into the decision-making process of process design/optimisation.
The first half of this work is concerned with process development of a proprietary modular Gas-to-Liquids process, briefly comprised of a packed bed plate-fin ’mini-channel’
Fischer-Tropsch reactor. Currently, little can be predicted about the flow or temperature
performance of a complex reactor geometry in the design phase. Data-driven models
provide a simplistic approximation with no added understanding. At commercially relevant
scales, the parameters of interest are both costly and hazardous to iterate through empirical
trial and improvement. By integrating offline analysis, online data and a novel temperature
sensing scheme, we increase the spaciotemporal resolution of data while adding process
understanding.
The second theme of this work is related to flue gas filtration in large-scale Biomass
and Energy-from-Waste Power Generation plants. Flue gas filtration is overlooked as an
opportunity for process improvement. We argue that a filtration system designed on the
basis of lowest CAPEX, and operated at the lowest maintenance cost will not provide the
lowest total cost of ownership. By integrating industrial historic data, maintenance records,
commercial data and multivariate modelling methods, we produce a set of recommendations
for improved operation. Commercially available solutions are benchmarked in predictive
hybrid models on a ROI basisEngineering and Physical Sciences Research Council for part funding this work. Innovate UK for part funding this wor
Multiple-objective sensor management and optimisation
One of the key challenges associated with exploiting modern Autonomous Vehicle technology for military surveillance tasks is the development of Sensor Management strategies which maximise the performance of the on-board Data-Fusion systems. The focus of this thesis is the development of Sensor Management algorithms which aim to optimise target tracking processes. Three principal theoretical and analytical contributions are presented which are related to the manner in which such problems are formulated and subsequently solved.Firstly, the trade-offs between optimising target tracking and other system-level objectives relating to expected operating lifetime are explored in an autonomous ground sensor scenario. This is achieved by modelling the observer trajectory control design as a probabilistic, information-theoretic, multiple-objective optimisation problem. This novel approach explores the relationships between the changes in sensor-target geometry that are induced by tracking performance measures and those relating to power consumption. This culminates in a novel observer trajectory control algorithm based onthe minimax approach.The second contribution is an analysis of the propagation of error through a limited-lookahead sensor control feedback loop. In the last decade, it has been shown that the use of such non-myopic (multiple-step) planning strategies can lead to superior performance in many Sensor Management scenarios. However, relatively little is known about the performance of strategies which use different horizon lengths. It is shown that, in the general case, planning performance is a function of the length of the horizon over which the optimisation is performed. While increasing the horizon maximises the chances of achieving global optimality, by revealing information about the substructureof the decision space, it also increases the impact of any prediction error, approximations, or unforeseen risk present within the scenario. These competing mechanisms aredemonstrated using an example tracking problem. This provides the motivation for a novel sensor control methodology that employs an adaptive length optimisation horizon. A route to selecting the optimal horizon size is proposed, based on a new non-myopic risk equilibrium which identifies the point where the two competing mechanisms are balanced.The third area of contribution concerns the development of a number of novel optimisation algorithms aimed at solving the resulting sequential decision making problems. These problems are typically solved using stochastic search methods such as Genetic Algorithms or Simulated Annealing. The techniques presented in this thesis are extensions of the recently proposed Repeated Weighted Boosting Search algorithm. In its originalform, it is only applicable to continuous, single-objective, ptimisation problems. The extensions facilitate application to mixed search spaces and Pareto multiple-objective problems. The resulting algorithms have performance comparable with Genetic Algorithm variants, and offer a number of advantages such as ease of implementation and limited tuning requirements
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