Dynamic factorial graphical models for dynamic networks

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Abstract

Dynamic networks models describe a growing number of important scientific processes, from cell biology and epidemiology to sociology and finance. Estimating dynamic networks from noisy time series data is a difficult task since the number of components involved in the system is very large. As a result, the number of parameters to be estimated is typically larger than the number of observations. However, a characteristic of many real life networks is that they are sparse. For example, the molec- ular structure of genes make interactions with other components a highly-structured and, therefore, a sparse process. Penalized Gaussian graphical models have been used to estimate sparse networks. However, the literature has focussed on static networks, which lack specific temporal interpretations.We propose a flexible collection of ANOVA-like dynamic network models, where the user can select specific time dynamics, known presence or absence of links and a particular autoregressive structure. We use undirected graphical models with block equality constraints on the parameters. This reduces the number of parameters, increases the accuracy of the estimates and makes interpretation of the results more relevant. We show that the constrained likelihood optimization problem can be solved by taking advantage of an efficient solver, LogdetPPA, developed in convex optimization. Model selection strategies can be used to select a particular model. We illustrate the flexibility of the method on both synthetic and real data.
Lingua originaleEnglish
Numero di pagine23
RivistaNetwork Science
Volume00
Stato di pubblicazionePublished - 2014

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Sociology
Molecular Structure
Cell Biology
Analysis of Variance
Epidemiology
Cytology
interpretation
Convex optimization
Finance
Analysis of variance (ANOVA)
epidemiology
Molecular structure
Genes
time series
biology
Time series
equality
finance
sociology
flexibility

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title = "Dynamic factorial graphical models for dynamic networks",
abstract = "Dynamic networks models describe a growing number of important scientific processes, from cell biology and epidemiology to sociology and finance. Estimating dynamic networks from noisy time series data is a difficult task since the number of components involved in the system is very large. As a result, the number of parameters to be estimated is typically larger than the number of observations. However, a characteristic of many real life networks is that they are sparse. For example, the molec- ular structure of genes make interactions with other components a highly-structured and, therefore, a sparse process. Penalized Gaussian graphical models have been used to estimate sparse networks. However, the literature has focussed on static networks, which lack specific temporal interpretations.We propose a flexible collection of ANOVA-like dynamic network models, where the user can select specific time dynamics, known presence or absence of links and a particular autoregressive structure. We use undirected graphical models with block equality constraints on the parameters. This reduces the number of parameters, increases the accuracy of the estimates and makes interpretation of the results more relevant. We show that the constrained likelihood optimization problem can be solved by taking advantage of an efficient solver, LogdetPPA, developed in convex optimization. Model selection strategies can be used to select a particular model. We illustrate the flexibility of the method on both synthetic and real data.",
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T1 - Dynamic factorial graphical models for dynamic networks

AU - Abbruzzo, Antonino

PY - 2014

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N2 - Dynamic networks models describe a growing number of important scientific processes, from cell biology and epidemiology to sociology and finance. Estimating dynamic networks from noisy time series data is a difficult task since the number of components involved in the system is very large. As a result, the number of parameters to be estimated is typically larger than the number of observations. However, a characteristic of many real life networks is that they are sparse. For example, the molec- ular structure of genes make interactions with other components a highly-structured and, therefore, a sparse process. Penalized Gaussian graphical models have been used to estimate sparse networks. However, the literature has focussed on static networks, which lack specific temporal interpretations.We propose a flexible collection of ANOVA-like dynamic network models, where the user can select specific time dynamics, known presence or absence of links and a particular autoregressive structure. We use undirected graphical models with block equality constraints on the parameters. This reduces the number of parameters, increases the accuracy of the estimates and makes interpretation of the results more relevant. We show that the constrained likelihood optimization problem can be solved by taking advantage of an efficient solver, LogdetPPA, developed in convex optimization. Model selection strategies can be used to select a particular model. We illustrate the flexibility of the method on both synthetic and real data.

AB - Dynamic networks models describe a growing number of important scientific processes, from cell biology and epidemiology to sociology and finance. Estimating dynamic networks from noisy time series data is a difficult task since the number of components involved in the system is very large. As a result, the number of parameters to be estimated is typically larger than the number of observations. However, a characteristic of many real life networks is that they are sparse. For example, the molec- ular structure of genes make interactions with other components a highly-structured and, therefore, a sparse process. Penalized Gaussian graphical models have been used to estimate sparse networks. However, the literature has focussed on static networks, which lack specific temporal interpretations.We propose a flexible collection of ANOVA-like dynamic network models, where the user can select specific time dynamics, known presence or absence of links and a particular autoregressive structure. We use undirected graphical models with block equality constraints on the parameters. This reduces the number of parameters, increases the accuracy of the estimates and makes interpretation of the results more relevant. We show that the constrained likelihood optimization problem can be solved by taking advantage of an efficient solver, LogdetPPA, developed in convex optimization. Model selection strategies can be used to select a particular model. We illustrate the flexibility of the method on both synthetic and real data.

UR - http://hdl.handle.net/10447/101426

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JO - Network Science

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