arXiv subjects

Christopher Hawthorne

Publications and source records attributed to Christopher Hawthorne.

4 recordsLinked to original sources

arXiv2022

Multi-Task Dynamical Systems

Time series datasets are often composed of a variety of sequences from the same domain, but from different entities, such as individuals, products, or organizations. We are interested in how time series models can be specialized to individual sequences (capturing the specific characteristics) while still retaining statistical power by sharing commonalities across the sequences. This paper describes the multi-task dynamical system (MTDS); a general methodology for extending multi-task learning (MTL) to time series models. Our approach endows dynamical systems with a set of hierarchical latent variables which can modulate all model parameters. To our knowledge, this is a novel development of MTL, and applies to time series both with and without control inputs. We apply the MTDS to motion-capture data of people walking in various styles using a multi-task recurrent neural network (RNN), and to patient drug-response data using a multi-task pharmacodynamic model.

cs.LG↗

arXiv2020

Contributions to the theory of $F$-automatic sets

Fix an abelian group $\Gamma$ and an injective endomorphism $F \colon \Gamma \to \Gamma$. Improving on the results of Bell and Moosa, new characterizations are here obtained for the existence of spanning sets, $F$-automaticity, and $F$-sparsity. The model theoretic status of these sets is also investigated, culminating with a combinatorial description of the $F$-sparse sets that are stable in $(\Gamma, +)$, and a proof that the expansion of $(\Gamma, +)$ by any $F$-sparse set is NIP. These methods are also used to show for prime $p\ge 7$ that the expansion of $(\mathbb{F}_p[t], +)$ by multiplication restricted to $t^\mathbb{N}$ is NIP.

math.LO↗

arXiv2019

Multi-Task Time Series Analysis applied to Drug Response Modelling

Time series models such as dynamical systems are frequently fitted to a cohort of data, ignoring variation between individual entities such as patients. In this paper we show how these models can be personalised to an individual level while retaining statistical power, via use of multi-task learning (MTL). To our knowledge this is a novel development of MTL which applies to time series both with and without control inputs. The modelling framework is demonstrated on a physiological drug response problem which results in improved predictive accuracy and uncertainty estimation over existing state-of-the-art models.

cs.LG↗

arXiv2016

Input-Output Non-Linear Dynamical Systems applied to Physiological Condition Monitoring

We present a non-linear dynamical system for modelling the effect of drug infusions on the vital signs of patients admitted in Intensive Care Units (ICUs). More specifically we are interested in modelling the effect of a widely used anaesthetic drug (Propofol) on a patient's monitored depth of anaesthesia and haemodynamics. We compare our approach with one from the Pharmacokinetics/Pharmacodynamics (PK/PD) literature and show that we can provide significant improvements in performance without requiring the incorporation of expert physiological knowledge in our system.

cs.LG↗