2,599 research outputs found
Weighted-Lasso for Structured Network Inference from Time Course Data
We present a weighted-Lasso method to infer the parameters of a first-order
vector auto-regressive model that describes time course expression data
generated by directed gene-to-gene regulation networks. These networks are
assumed to own a prior internal structure of connectivity which drives the
inference method. This prior structure can be either derived from prior
biological knowledge or inferred by the method itself. We illustrate the
performance of this structure-based penalization both on synthetic data and on
two canonical regulatory networks, first yeast cell cycle regulation network by
analyzing Spellman et al's dataset and second E. coli S.O.S. DNA repair network
by analysing U. Alon's lab data
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
High-Dimensional Joint Estimation of Multiple Directed Gaussian Graphical Models
We consider the problem of jointly estimating multiple related directed
acyclic graph (DAG) models based on high-dimensional data from each graph. This
problem is motivated by the task of learning gene regulatory networks based on
gene expression data from different tissues, developmental stages or disease
states. We prove that under certain regularity conditions, the proposed
-penalized maximum likelihood estimator converges in Frobenius norm to
the adjacency matrices consistent with the data-generating distributions and
has the correct sparsity. In particular, we show that this joint estimation
procedure leads to a faster convergence rate than estimating each DAG model
separately. As a corollary, we also obtain high-dimensional consistency results
for causal inference from a mix of observational and interventional data. For
practical purposes, we propose \emph{jointGES} consisting of Greedy Equivalence
Search (GES) to estimate the union of all DAG models followed by variable
selection using lasso to obtain the different DAGs, and we analyze its
consistency guarantees. The proposed method is illustrated through an analysis
of simulated data as well as epithelial ovarian cancer gene expression data
Foundational principles for large scale inference: Illustrations through correlation mining
When can reliable inference be drawn in the "Big Data" context? This paper
presents a framework for answering this fundamental question in the context of
correlation mining, with implications for general large scale inference. In
large scale data applications like genomics, connectomics, and eco-informatics
the dataset is often variable-rich but sample-starved: a regime where the
number of acquired samples (statistical replicates) is far fewer than the
number of observed variables (genes, neurons, voxels, or chemical
constituents). Much of recent work has focused on understanding the
computational complexity of proposed methods for "Big Data." Sample complexity
however has received relatively less attention, especially in the setting when
the sample size is fixed, and the dimension grows without bound. To
address this gap, we develop a unified statistical framework that explicitly
quantifies the sample complexity of various inferential tasks. Sampling regimes
can be divided into several categories: 1) the classical asymptotic regime
where the variable dimension is fixed and the sample size goes to infinity; 2)
the mixed asymptotic regime where both variable dimension and sample size go to
infinity at comparable rates; 3) the purely high dimensional asymptotic regime
where the variable dimension goes to infinity and the sample size is fixed.
Each regime has its niche but only the latter regime applies to exa-scale data
dimension. We illustrate this high dimensional framework for the problem of
correlation mining, where it is the matrix of pairwise and partial correlations
among the variables that are of interest. We demonstrate various regimes of
correlation mining based on the unifying perspective of high dimensional
learning rates and sample complexity for different structured covariance models
and different inference tasks
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