Factorized Binary Search: change point detection in the network structure of multivariate high-dimensional time series

Functional magnetic resonance imaging (fMRI) time series data presents a unique opportunity to understand temporal brain connectivity, and models that uncover the complex dynamic workings of this organ are of keen interest in neuroscience. Change point models can capture and reflect the dynamic nature of brain connectivity, however methods that translate well into a high-dimensional context (where $p>>n$) are scarce. To this end, we introduce $\textit{factorized binary search}$ (FaBiSearch), a novel change point detection method in the network structure of multivariate high-dimensional time series. FaBiSearch uses non-negative matrix factorization, an unsupervised dimension reduction technique, and a new binary search algorithm to identify multiple change points. In addition, we propose a new method for network estimation for data between change points. We show that FaBiSearch outperforms another state-of-the-art method on simulated data sets and we apply FaBiSearch to a resting-state and to a task-based fMRI data set. In particular, for the task-based data set, we explore network dynamics during the reading of Chapter 9 in $\textit{Harry Potter and the Sorcerer's Stone}$ and find that change points across subjects coincide with key plot twists. Further, we find that the density of networks was positively related to the frequency of speech between characters in the story. Finally, we make all the methods discussed available in the R package $\textbf{fabisearch}$ on CRAN

Lake Volume Data Analyses: A Deep Look into the Shrinking and Expansion Patterns of Lakes Azuei and Enriquillo, Hispaniola

This paper presents the development of an evenly spaced volume time series for Lakes Azuei and Enriquillo both located on the Caribbean island of Hispaniola. The time series is derived from an unevenly spaced Landsat imagery data set which is then exposed to several imputation methods to construct the gap filled uniformly‐spaced time series so it can be subjected to statistical analyses methods. The volume time series features both gradual and sudden changes the latter of which is attributed to North Atlantic cyclone activity. Relevant cyclone activity is defined as an event passing within 80 km and having regional monthly rainfall averages higher than a threshold value of 87 mm causing discontinuities in the lake responses. Discontinuities are accounted for in the imputation algorithm by dividing the time series into two sub‐sections: Before/after the event. Using leave‐p‐out cross‐validation and computing the NRMSE index the Stineman interpolation proves to be the best algorithm among 15 different imputation alternatives that were tested. The final time series features 16‐day intervals which is subsequently resampled into one with monthly time steps. Data analyses of the monthly volume change time series show Lake Enriquillo’s seasonal periodicity in its behavior and also its sensitivity due to the occurrence of storm events. Response times feature a growth pattern lasting for one to two years after an extreme event, followed by a shrinking pattern lasting 5–7 years returning the lake to its original state. While both lakes show a remarkable long term increase in size starting in 2005, Lake Azuei is different in that it is much less sensitive to storm events and instead shows a stronger response to just changing seasonal rainfall patterns

Desarrollo de una Toolbox para medir la respuesta positiva de un sistema hacia estímulos externos

El objetivo de este proyecto es desarrollar una metodología que permita la detección de respuestas de un sistema ante un estímulo específico en condiciones de incertidumbre. En muchos casos, la actividad continua inherente a un sistema, la reverberación de la información, la latencia en el tiempo de respuesta y otros problemas complican la detección de respuestas con fiabilidad. Este es el caso de los experimentos llevados a cabo en neurociencia sobre las neuronas que componen el sistema nervioso. En el campo de la neurociencia, no existe un consenso sobre qué protocolos deben seguirse a la hora de analizar los datos procedentes de mediciones sobre neuronas y, como consecuencia de esto, no siempre se aplican métodos robustos y estandarizados de detección de respuestas, así como tampoco existen formatos universales de representación y etiquetado de experimentos. Teniendo en cuenta lo anterior, en este proyecto se implementa una metodología robusta de detección de respuestas basada en un método bayesiano propuesto por el GNB de la UAM y se desarrollan las herramientas software necesarias para que pueda aplicarse de forma fácil y automática a datos procedentes de diferentes experimentos, definiendo para ello un formato estándar de representación de los mismos. La metodología implementada es validada mediante su aplicación a datos generados de forma artificial mediante un modelo matématico sencillo para después ser aplicado sobre datos procedentes de experimentos reales llevados a cabo sobre las neuronas del lóbulo antenal y el cuerpo fungiforme del sistema olfativo de la langosta con diferentes estímulos. Los resultados son analizados y las conclusiones extraídas gracias a la aplicación de la metodología son coherentes con lo que se sabe sobre el funcionamiento de dicho sistema.The main goal of this project is to develope a methodology which allows the detection of responses to a specific stimulus in a system under uncertainty. Most of the times, the continous inherent activy of a system, information reverberation, latency in response time and other problems make it difficult to detect responses with reliability. This is the case of the experiments carried out in Neuroscience on neurons that compose the nervous system. In Neuroscience, there is no consensus about which protocols must be followed during the analysis of the data collected from measurements on neurons and, as a result of this, robust and standardized methods for response detection are not always applied, nor are there universal formats for the representation and labeled of experiments. Given the above, this project implements a robust methodology for response detection based on a bayesian method proposed by the GNB and developes the software tool necessary to apply it easily and automatically to analyze data from different experiments, defining for this purpose a standard format of representation. The methodology developed is then validated through applying it to data that is artificially generated by a simple mathematical model. Then, it is applied to real data from experiments carried out on neurons located in the antennal lobe and the mushroom body in the locust olfactory system. The results obtained are analyzed and the conclusions drawn from them are consistent with what it is known about how this system works

Non-parametric change point detection for spike trains

Mosqueiro T, Strube-Bloss M, Tuma R, Pinto R, Smith BH, Huerta R. Non-parametric change point detection for spike trains. In: 2016 Annual Conference on Information Science and Systems (CISS). Piscataway, NJ: IEEE; 2016