25,045 research outputs found
Bayesian nonparametric sparse VAR models
High dimensional vector autoregressive (VAR) models require a large number of
parameters to be estimated and may suffer of inferential problems. We propose a
new Bayesian nonparametric (BNP) Lasso prior (BNP-Lasso) for high-dimensional
VAR models that can improve estimation efficiency and prediction accuracy. Our
hierarchical prior overcomes overparametrization and overfitting issues by
clustering the VAR coefficients into groups and by shrinking the coefficients
of each group toward a common location. Clustering and shrinking effects
induced by the BNP-Lasso prior are well suited for the extraction of causal
networks from time series, since they account for some stylized facts in
real-world networks, which are sparsity, communities structures and
heterogeneity in the edges intensity. In order to fully capture the richness of
the data and to achieve a better understanding of financial and macroeconomic
risk, it is therefore crucial that the model used to extract network accounts
for these stylized facts.Comment: Forthcoming in "Journal of Econometrics" ---- Revised Version of the
paper "Bayesian nonparametric Seemingly Unrelated Regression Models" ----
Supplementary Material available on reques
The Infinite Degree Corrected Stochastic Block Model
In Stochastic blockmodels, which are among the most prominent statistical
models for cluster analysis of complex networks, clusters are defined as groups
of nodes with statistically similar link probabilities within and between
groups. A recent extension by Karrer and Newman incorporates a node degree
correction to model degree heterogeneity within each group. Although this
demonstrably leads to better performance on several networks it is not obvious
whether modelling node degree is always appropriate or necessary. We formulate
the degree corrected stochastic blockmodel as a non-parametric Bayesian model,
incorporating a parameter to control the amount of degree correction which can
then be inferred from data. Additionally, our formulation yields principled
ways of inferring the number of groups as well as predicting missing links in
the network which can be used to quantify the model's predictive performance.
On synthetic data we demonstrate that including the degree correction yields
better performance both on recovering the true group structure and predicting
missing links when degree heterogeneity is present, whereas performance is on
par for data with no degree heterogeneity within clusters. On seven real
networks (with no ground truth group structure available) we show that
predictive performance is about equal whether or not degree correction is
included; however, for some networks significantly fewer clusters are
discovered when correcting for degree indicating that the data can be more
compactly explained by clusters of heterogenous degree nodes.Comment: Originally presented at the Complex Networks workshop NIPS 201
Loan maturity aggregation in interbank lending networks obscures mesoscale structure and economic functions
Since the 2007-2009 financial crisis, substantial academic effort has been dedicated to improving our understanding of interbank lending networks (ILNs). Because of data limitations or by choice, the literature largely lacks multiple loan maturities. We employ a complete interbank loan contract dataset to investigate whether maturity details are informative of the network structure. Applying the layered stochastic block model of Peixoto (2015) and other tools from network science on a time series of bilateral loans with multiple maturity layers in the Russian ILN, we find that collapsing all such layers consistently obscures mesoscale structure. The optimal maturity granularity lies between completely collapsing and completely separating the maturity layers and depends on the development phase of the interbank market, with a more developed market requiring more layers for optimal description. Closer inspection of the inferred maturity bins associated with the optimal maturity granularity reveals specific economic functions, from liquidity intermediation to financing. Collapsing a network with multiple underlying maturity layers or extracting one such layer, common in economic research, is therefore not only an incomplete representation of the ILN's mesoscale structure, but also conceals existing economic functions. This holds important insights and opportunities for theoretical and empirical studies on interbank market functioning, contagion, stability, and on the desirable level of regulatory data disclosure
Topological Feature Based Classification
There has been a lot of interest in developing algorithms to extract clusters
or communities from networks. This work proposes a method, based on
blockmodelling, for leveraging communities and other topological features for
use in a predictive classification task. Motivated by the issues faced by the
field of community detection and inspired by recent advances in Bayesian topic
modelling, the presented model automatically discovers topological features
relevant to a given classification task. In this way, rather than attempting to
identify some universal best set of clusters for an undefined goal, the aim is
to find the best set of clusters for a particular purpose.
Using this method, topological features can be validated and assessed within
a given context by their predictive performance.
The proposed model differs from other relational and semi-supervised learning
models as it identifies topological features to explain the classification
decision. In a demonstration on a number of real networks the predictive
capability of the topological features are shown to rival the performance of
content based relational learners. Additionally, the model is shown to
outperform graph-based semi-supervised methods on directed and approximately
bipartite networks.Comment: Awarded 3rd Best Student Paper at 14th International Conference on
Information Fusion 201
Latent space models for multidimensional network data
Network data are any relational data recorded among a group of individuals, the nodes. When multiple relations are recorded among the same set of nodes, a more complex object arises, which we refer to as “multidimensional network”, or
“multiplex”, where different relations corresponding to different networks. In the past, statistical analysis of networks has mainly focused on single-relation network data, referring to a single relation of interest. Only in recent years statistical
models specifically tailored for multiplex data begun to be developed. In this context, only a few works have been introduced in the literature with the aim at extending the latent space modeling framework to multiplex data. Such framework postulates
that nodes may be characterized by latent positions in a p-dimensional Euclidean space and that the presence/absence of an edge between any two nodes depends on such positions. When considering multidimensional network data, latent space
models can help capture the associations between the nodes and summarize the observed structure in the different networks composing a multiplex. This dissertation discusses some latent space models for multidimensional network
data, to account for different features that observed multiplex data may present. A first proposal allows to jointly represent the different networks into a single latent space, so that average similarities between the nodes may be captured as
proximities in such space. A second work introduces a class of latent space models with node-specific effects, in order to deal with different degrees of heterogeneity within and between networks in multiplex data, corresponding to different types
of node-specific behaviours. A third work addresses the issue of clustering of the nodes in the latent space, a frequently observed feature in many real world network and multidimensional network data. Here, clusters of nodes in the latent space
correspond to communities of nodes in the multiplex. The proposed models are illustrated both via simulation studies and real world applications, to study their perfomances and abilities
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