Towards Efficient Maximum Likelihood Estimation of LPV-SS Models

How to efficiently identify multiple-input multiple-output (MIMO) linear parameter-varying (LPV) discrete-time state-space (SS) models with affine dependence on the scheduling variable still remains an open question, as identification methods proposed in the literature suffer heavily from the curse of dimensionality and/or depend on over-restrictive approximations of the measured signal behaviors. However, obtaining an SS model of the targeted system is crucial for many LPV control synthesis methods, as these synthesis tools are almost exclusively formulated for the aforementioned representation of the system dynamics. Therefore, in this paper, we tackle the problem by combining state-of-the-art LPV input-output (IO) identification methods with an LPV-IO to LPV-SS realization scheme and a maximum likelihood refinement step. The resulting modular LPV-SS identification approach achieves statical efficiency with a relatively low computational load. The method contains the following three steps: 1) estimation of the Markov coefficient sequence of the underlying system using correlation analysis or Bayesian impulse response estimation, then 2) LPV-SS realization of the estimated coefficients by using a basis reduced Ho-Kalman method, and 3) refinement of the LPV-SS model estimate from a maximum-likelihood point of view by a gradient-based or an expectation-maximization optimization methodology. The effectiveness of the full identification scheme is demonstrated by a Monte Carlo study where our proposed method is compared to existing schemes for identifying a MIMO LPV system

Benelux meeting on systems and control, 23rd, March 17-19, 2004, Helvoirt, The Netherlands

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Dynamic models of brain imaging data and their Bayesian inversion

This work is about understanding the dynamics of neuronal systems, in particular with respect to brain connectivity. It addresses complex neuronal systems by looking at neuronal interactions and their causal relations. These systems are characterized using a generic approach to dynamical system analysis of brain signals - dynamic causal modelling (DCM). DCM is a technique for inferring directed connectivity among brain regions, which distinguishes between a neuronal and an observation level. DCM is a natural extension of the convolution models used in the standard analysis of neuroimaging data. This thesis develops biologically constrained and plausible models, informed by anatomic and physiological principles. Within this framework, it uses mathematical formalisms of neural mass, mean-field and ensemble dynamic causal models as generative models for observed neuronal activity. These models allow for the evaluation of intrinsic neuronal connections and high-order statistics of neuronal states, using Bayesian estimation and inference. Critically it employs Bayesian model selection (BMS) to discover the best among several equally plausible models. In the first part of this thesis, a two-state DCM for functional magnetic resonance imaging (fMRI) is described, where each region can model selective changes in both extrinsic and intrinsic connectivity. The second part is concerned with how the sigmoid activation function of neural-mass models (NMM) can be understood in terms of the variance or dispersion of neuronal states. The third part presents a mean-field model (MFM) for neuronal dynamics as observed with magneto- and electroencephalographic data (M/EEG). In the final part, the MFM is used as a generative model in a DCM for M/EEG and compared to the NMM using Bayesian model selection

Structure-Preserving Model Reduction of Physical Network Systems

This paper considers physical network systems where the energy storage is naturally associated to the nodes of the graph, while the edges of the graph correspond to static couplings. The first sections deal with the linear case, covering examples such as mass-damper and hydraulic systems, which have a structure that is similar to symmetric consensus dynamics. The last section is concerned with a specific class of nonlinear physical network systems; namely detailed-balanced chemical reaction networks governed by mass action kinetics. In both cases, linear and nonlinear, the structure of the dynamics is similar, and is based on a weighted Laplacian matrix, together with an energy function capturing the energy storage at the nodes. We discuss two methods for structure-preserving model reduction. The first one is clustering; aggregating the nodes of the underlying graph to obtain a reduced graph. The second approach is based on neglecting the energy storage at some of the nodes, and subsequently eliminating those nodes (called Kron reduction).</p

Enhanced clustering analysis pipeline for performance analysis of parallel applications

Clustering analysis is widely used to stratify data in the same cluster when they are similar according to the specific metrics. We can use the cluster analysis to group the CPU burst of a parallel application, and the regions on each process in-between communication calls or calls to the parallel runtime. The resulting clusters obtained are the different computational trends or phases that appear in the application. These clusters are useful to understand the behavior of the computation part of the application and focus the analyses on those that present performance issues. Although density-based clustering algorithms are a powerful and efficient tool to summarize this type of information, their traditional user-guided clustering methodology has many shortcomings and deficiencies in dealing with the complexity of data, the diversity of data structures, high-dimensionality of data, and the dramatic increase in the amount of data. Consequently, the majority of DBSCAN-like algorithms have weaknesses to handle high-dimensionality and/or Multi-density data, and they are sensitive to their hyper-parameter configuration. Furthermore, extracting insight from the obtained clusters is an intuitive and manual task. To mitigate these weaknesses, we have proposed a new unified approach to replace the user-guided clustering with an automated clustering analysis pipeline, called Enhanced Cluster Identification and Interpretation (ECII) pipeline. To build the pipeline, we propose novel techniques including Robust Independent Feature Selection, Feature Space Curvature Map, Organization Component Analysis, and hyper-parameters tuning to feature selection, density homogenization, cluster interpretation, and model selection which are the main components of our machine learning pipeline. This thesis contributes four new techniques to the Machine Learning field with a particular use case in Performance Analytics field. The first contribution is a novel unsupervised approach for feature selection on noisy data, called Robust Independent Feature Selection (RIFS). Specifically, we choose a feature subset that contains most of the underlying information, using the same criteria as the Independent component analysis. Simultaneously, the noise is separated as an independent component. The second contribution of the thesis is a parametric multilinear transformation method to homogenize cluster densities while preserving the topological structure of the dataset, called Feature Space Curvature Map (FSCM). We present a new Gravitational Self-organizing Map to model the feature space curvature by plugging the concepts of gravity and fabric of space into the Self-organizing Map algorithm to mathematically describe the density structure of the data. To homogenize the cluster density, we introduce a novel mapping mechanism to project the data from the non-Euclidean curved space to a new Euclidean flat space. The third contribution is a novel topological-based method to study potentially complex high-dimensional categorized data by quantifying their shapes and extracting fine-grain insights from them to interpret the clustering result. We introduce our Organization Component Analysis (OCA) method for the automatic arbitrary cluster-shape study without an assumption about the data distribution. Finally, to tune the DBSCAN hyper-parameters, we propose a new tuning mechanism by combining techniques from machine learning and optimization domains, and we embed it in the ECII pipeline. Using this cluster analysis pipeline with the CPU burst data of a parallel application, we provide the developer/analyst with a high-quality SPMD computation structure detection with the added value that reflects the fine grain of the computation regions.El análisis de conglomerados se usa ampliamente para estratificar datos en el mismo conglomerado cuando son similares según las métricas específicas. Nosotros puede usar el análisis de clúster para agrupar la ráfaga de CPU de una aplicación paralela y las regiones en cada proceso intermedio llamadas de comunicación o llamadas al tiempo de ejecución paralelo. Los clusters resultantes obtenidos son las diferentes tendencias computacionales o fases que aparecen en la solicitud. Estos clusters son útiles para entender el comportamiento de la parte de computación del aplicación y centrar los análisis en aquellos que presenten problemas de rendimiento. Aunque los algoritmos de agrupamiento basados en la densidad son una herramienta poderosa y eficiente para resumir este tipo de información, su La metodología tradicional de agrupación en clústeres guiada por el usuario tiene muchas deficiencias y deficiencias al tratar con la complejidad de los datos, la diversidad de estructuras de datos, la alta dimensionalidad de los datos y el aumento dramático en la cantidad de datos. En consecuencia, el La mayoría de los algoritmos similares a DBSCAN tienen debilidades para manejar datos de alta dimensionalidad y/o densidad múltiple, y son sensibles a su configuración de hiperparámetros. Además, extraer información de los clústeres obtenidos es una forma intuitiva y tarea manual Para mitigar estas debilidades, hemos propuesto un nuevo enfoque unificado para reemplazar el agrupamiento guiado por el usuario con un canalización de análisis de agrupamiento automatizado, llamada canalización de identificación e interpretación de clúster mejorada (ECII). para construir el tubería, proponemos técnicas novedosas que incluyen la selección robusta de características independientes, el mapa de curvatura del espacio de características, Análisis de componentes de la organización y ajuste de hiperparámetros para la selección de características, homogeneización de densidad, agrupación interpretación y selección de modelos, que son los componentes principales de nuestra canalización de aprendizaje automático. Esta tesis aporta cuatro nuevas técnicas al campo de Machine Learning con un caso de uso particular en el campo de Performance Analytics. La primera contribución es un enfoque novedoso no supervisado para la selección de características en datos ruidosos, llamado Robust Independent Feature. Selección (RIFS).Específicamente, elegimos un subconjunto de funciones que contiene la mayor parte de la información subyacente, utilizando el mismo criterios como el análisis de componentes independientes. Simultáneamente, el ruido se separa como un componente independiente. La segunda contribución de la tesis es un método de transformación multilineal paramétrica para homogeneizar densidades de clústeres mientras preservando la estructura topológica del conjunto de datos, llamado Mapa de Curvatura del Espacio de Características (FSCM). Presentamos un nuevo Gravitacional Mapa autoorganizado para modelar la curvatura del espacio característico conectando los conceptos de gravedad y estructura del espacio en el Algoritmo de mapa autoorganizado para describir matemáticamente la estructura de densidad de los datos. Para homogeneizar la densidad del racimo, introducimos un mecanismo de mapeo novedoso para proyectar los datos del espacio curvo no euclidiano a un nuevo plano euclidiano espacio. La tercera contribución es un nuevo método basado en topología para estudiar datos categorizados de alta dimensión potencialmente complejos mediante cuantificando sus formas y extrayendo información detallada de ellas para interpretar el resultado de la agrupación. presentamos nuestro Método de análisis de componentes de organización (OCA) para el estudio automático de forma arbitraria de conglomerados sin una suposición sobre el distribución de datos.Postprint (published version

Model Order Reduction

An increasing complexity of models used to predict real-world systems leads to the need for algorithms to replace complex models with far simpler ones, while preserving the accuracy of the predictions. This three-volume handbook covers methods as well as applications. This third volume focuses on applications in engineering, biomedical engineering, computational physics and computer science