On the Goodness-of-Fit Tests for Some Continuous Time Processes

We present a review of several results concerning the construction of the Cramer-von Mises and Kolmogorov-Smirnov type goodness-of-fit tests for continuous time processes. As the models we take a stochastic differential equation with small noise, ergodic diffusion process, Poisson process and self-exciting point processes. For every model we propose the tests which provide the asymptotic size $\alpha$ and discuss the behaviour of the power function under local alternatives. The results of numerical simulations of the tests are presented.Comment: 22 pages, 2 figure

Magnetic Resonance Imaging of the Codman Microsensor Transducer Used for Intraspinal Pressure Monitoring: Findings from the Injured Spinal Cord Pressure Evaluation study.

STUDY DESIGN: Laboratory and human study. OBJECTIVE: 1) To test the Codman Microsensor Transducer (CMT) in a cervical gel phantom. 2) To test the CMT inserted to monitor intraspinal pressure in a patient with spinal cord injury. SUMMARY OF BACKGROUND DATA: We recently introduced the technique of intraspinal pressure monitoring using the CMT to guide management of traumatic spinal cord injury [Werndle et al. Crit Care Med 2014;42:646]. This is analogous to intracranial pressure monitoring to guide management of patients with traumatic brain injury. It is unclear whether MRI of patients with spinal cord injury is safe with the intraspinal pressure CMT in situ. METHODS: We measured the heating produced by the CMT placed in a gel phantom in various configurations. A 3 T MRI system was used with the body transmit coil and the spine array receive coil. A CMT was then inserted subdurally at the injury site in a patient who had traumatic spinal cord injury and MRI was performed at 1.5 T. RESULTS: In the gel phantom, heating of up to 5 °C occurred with the transducer wire placed straight through the magnet bore. The heating was abolished when the CMT wire was coiled and passed away from the bore. We then tested the CMT in a patient with an American Spinal Injuries Association grade C cervical cord injury. The CMT wire was placed in the configuration that abolished heating in the gel phantom. Good quality T1 and T2 images of the cord were obtained without neurological deterioration. The transducer remained functional after the MRI. CONCLUSION: Our data suggest that the CMT is MR conditional when used in the spinal configuration in humans. Data from a large patient group are required to confirm these findings. LEVEL OF EVIDENCE: N/A

A Recurrent Neural Network Survival Model: Predicting Web User Return Time

The size of a website's active user base directly affects its value. Thus, it is important to monitor and influence a user's likelihood to return to a site. Essential to this is predicting when a user will return. Current state of the art approaches to solve this problem come in two flavors: (1) Recurrent Neural Network (RNN) based solutions and (2) survival analysis methods. We observe that both techniques are severely limited when applied to this problem. Survival models can only incorporate aggregate representations of users instead of automatically learning a representation directly from a raw time series of user actions. RNNs can automatically learn features, but can not be directly trained with examples of non-returning users who have no target value for their return time. We develop a novel RNN survival model that removes the limitations of the state of the art methods. We demonstrate that this model can successfully be applied to return time prediction on a large e-commerce dataset with a superior ability to discriminate between returning and non-returning users than either method applied in isolation.Comment: Accepted into ECML PKDD 2018; 8 figures and 1 tabl

Modelling informative time points: an evolutionary process approach

Real time series sometimes exhibit various types of "irregularities": missing observations, observations collected not regularly over time for practical reasons, observation times driven by the series itself, or outlying observations. However, the vast majority of methods of time series analysis are designed for regular time series only. A particular case of irregularly spaced time series is that in which the sampling procedure over time depends also on the observed values. In such situations, there is stochastic dependence between the process being modelled and the times of the observations. In this work, we propose a model in which the sampling design depends on all past history of the observed processes. Taking into account the natural temporal order underlying available data represented by a time series, then a modelling approach based on evolutionary processes seems a natural choice. We consider maximum likelihood estimation of the model parameters. Numerical studies with simulated and real data sets are performed to illustrate the benefits of this model-based approach.- The authors acknowledge Foundation FCT (FundacAo para a Ciencia e Tecnologia) as members of the research project PTDC/MAT-STA/28243/2017 and Center for Research & Development in Mathematics and Applications of Aveiro University within project UID/MAT/04106/2019

Personalized Sentiment Analysis and a Framework with Attention-Based Hawkes Process Model

People use different words when expressing their opinions. Sentiment analysis as a way to automatically detect and categorize people’s opinions in text, needs to reflect this diversity and individuality. One possible approach to analyze such traits is to take a person’s past opinions into consideration. In practice, such a model can suffer from the data sparsity issue, thus it is difficult to develop. In this article, we take texts from social platforms and propose a preliminary model for evaluating the effectiveness of including user information from the past, and offer a solution for the data sparsity. Furthermore, we present a finer-designed, enhanced model that focuses on frequent users and offers to capture the decay of past opinions using various gaps between the creation time of the text. An attention-based Hawkes process on top of a recurrent neural network is applied for this purpose, and the performance of the model is evaluated with Twitter data. With the proposed framework, positive results are shown which opens up new perspectives for future research

How Structure Determines Correlations in Neuronal Networks

Networks are becoming a ubiquitous metaphor for the understanding of complex biological systems, spanning the range between molecular signalling pathways, neural networks in the brain, and interacting species in a food web. In many models, we face an intricate interplay between the topology of the network and the dynamics of the system, which is generally very hard to disentangle. A dynamical feature that has been subject of intense research in various fields are correlations between the noisy activity of nodes in a network. We consider a class of systems, where discrete signals are sent along the links of the network. Such systems are of particular relevance in neuroscience, because they provide models for networks of neurons that use action potentials for communication. We study correlations in dynamic networks with arbitrary topology, assuming linear pulse coupling. With our novel approach, we are able to understand in detail how specific structural motifs affect pairwise correlations. Based on a power series decomposition of the covariance matrix, we describe the conditions under which very indirect interactions will have a pronounced effect on correlations and population dynamics. In random networks, we find that indirect interactions may lead to a broad distribution of activation levels with low average but highly variable correlations. This phenomenon is even more pronounced in networks with distance dependent connectivity. In contrast, networks with highly connected hubs or patchy connections often exhibit strong average correlations. Our results are particularly relevant in view of new experimental techniques that enable the parallel recording of spiking activity from a large number of neurons, an appropriate interpretation of which is hampered by the currently limited understanding of structure-dynamics relations in complex networks