48,138 research outputs found
Graphical continuous Lyapunov models
The linear Lyapunov equation of a covariance matrix parametrizes the
equilibrium covariance matrix of a stochastic process. This parametrization can
be interpreted as a new graphical model class, and we show how the model class
behaves under marginalization and introduce a method for structure learning via
-penalized loss minimization. Our proposed method is demonstrated to
outperform alternative structure learning algorithms in a simulation study, and
we illustrate its application for protein phosphorylation network
reconstruction.Comment: 10 pages, 5 figure
Learning Large-Scale Bayesian Networks with the sparsebn Package
Learning graphical models from data is an important problem with wide
applications, ranging from genomics to the social sciences. Nowadays datasets
often have upwards of thousands---sometimes tens or hundreds of thousands---of
variables and far fewer samples. To meet this challenge, we have developed a
new R package called sparsebn for learning the structure of large, sparse
graphical models with a focus on Bayesian networks. While there are many
existing software packages for this task, this package focuses on the unique
setting of learning large networks from high-dimensional data, possibly with
interventions. As such, the methods provided place a premium on scalability and
consistency in a high-dimensional setting. Furthermore, in the presence of
interventions, the methods implemented here achieve the goal of learning a
causal network from data. Additionally, the sparsebn package is fully
compatible with existing software packages for network analysis.Comment: To appear in the Journal of Statistical Software, 39 pages, 7 figure
Learning the dynamics and time-recursive boundary detection of deformable objects
We propose a principled framework for recursively segmenting deformable objects across a sequence
of frames. We demonstrate the usefulness of this method on left ventricular segmentation across a cardiac
cycle. The approach involves a technique for learning the system dynamics together with methods of
particle-based smoothing as well as non-parametric belief propagation on a loopy graphical model capturing
the temporal periodicity of the heart. The dynamic system state is a low-dimensional representation
of the boundary, and the boundary estimation involves incorporating curve evolution into recursive state
estimation. By formulating the problem as one of state estimation, the segmentation at each particular
time is based not only on the data observed at that instant, but also on predictions based on past and future
boundary estimates. Although the paper focuses on left ventricle segmentation, the method generalizes
to temporally segmenting any deformable object
Modeling cumulative biological phenomena with Suppes-Bayes Causal Networks
Several diseases related to cell proliferation are characterized by the
accumulation of somatic DNA changes, with respect to wildtype conditions.
Cancer and HIV are two common examples of such diseases, where the mutational
load in the cancerous/viral population increases over time. In these cases,
selective pressures are often observed along with competition, cooperation and
parasitism among distinct cellular clones. Recently, we presented a
mathematical framework to model these phenomena, based on a combination of
Bayesian inference and Suppes' theory of probabilistic causation, depicted in
graphical structures dubbed Suppes-Bayes Causal Networks (SBCNs). SBCNs are
generative probabilistic graphical models that recapitulate the potential
ordering of accumulation of such DNA changes during the progression of the
disease. Such models can be inferred from data by exploiting likelihood-based
model-selection strategies with regularization. In this paper we discuss the
theoretical foundations of our approach and we investigate in depth the
influence on the model-selection task of: (i) the poset based on Suppes' theory
and (ii) different regularization strategies. Furthermore, we provide an
example of application of our framework to HIV genetic data highlighting the
valuable insights provided by the inferred
Observational-Interventional Priors for Dose-Response Learning
Controlled interventions provide the most direct source of information for
learning causal effects. In particular, a dose-response curve can be learned by
varying the treatment level and observing the corresponding outcomes. However,
interventions can be expensive and time-consuming. Observational data, where
the treatment is not controlled by a known mechanism, is sometimes available.
Under some strong assumptions, observational data allows for the estimation of
dose-response curves. Estimating such curves nonparametrically is hard: sample
sizes for controlled interventions may be small, while in the observational
case a large number of measured confounders may need to be marginalized. In
this paper, we introduce a hierarchical Gaussian process prior that constructs
a distribution over the dose-response curve by learning from observational
data, and reshapes the distribution with a nonparametric affine transform
learned from controlled interventions. This function composition from different
sources is shown to speed-up learning, which we demonstrate with a thorough
sensitivity analysis and an application to modeling the effect of therapy on
cognitive skills of premature infants
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