26,614 research outputs found
Discovering Cyclic Causal Models with Latent Variables: A General SAT-Based Procedure
We present a very general approach to learning the structure of causal models
based on d-separation constraints, obtained from any given set of overlapping
passive observational or experimental data sets. The procedure allows for both
directed cycles (feedback loops) and the presence of latent variables. Our
approach is based on a logical representation of causal pathways, which permits
the integration of quite general background knowledge, and inference is
performed using a Boolean satisfiability (SAT) solver. The procedure is
complete in that it exhausts the available information on whether any given
edge can be determined to be present or absent, and returns "unknown"
otherwise. Many existing constraint-based causal discovery algorithms can be
seen as special cases, tailored to circumstances in which one or more
restricting assumptions apply. Simulations illustrate the effect of these
assumptions on discovery and how the present algorithm scales.Comment: Appears in Proceedings of the Twenty-Ninth Conference on Uncertainty
in Artificial Intelligence (UAI2013
Approximate parameter inference in systems biology using gradient matching: a comparative evaluation
Background: A challenging problem in current systems biology is that of
parameter inference in biological pathways expressed as coupled ordinary
differential equations (ODEs). Conventional methods that repeatedly numerically
solve the ODEs have large associated computational costs. Aimed at reducing this
cost, new concepts using gradient matching have been proposed, which bypass
the need for numerical integration. This paper presents a recently established
adaptive gradient matching approach, using Gaussian processes, combined with a
parallel tempering scheme, and conducts a comparative evaluation with current
state of the art methods used for parameter inference in ODEs. Among these
contemporary methods is a technique based on reproducing kernel Hilbert spaces
(RKHS). This has previously shown promising results for parameter estimation,
but under lax experimental settings. We look at a range of scenarios to test the
robustness of this method. We also change the approach of inferring the penalty
parameter from AIC to cross validation to improve the stability of the method.
Methodology: Methodology for the recently proposed adaptive gradient
matching method using Gaussian processes, upon which we build our new
method, is provided. Details of a competing method using reproducing kernel
Hilbert spaces are also described here.
Results: We conduct a comparative analysis for the methods described in this
paper, using two benchmark ODE systems. The analyses are repeated under
different experimental settings, to observe the sensitivity of the techniques.
Conclusions: Our study reveals that for known noise variance, our proposed
method based on Gaussian processes and parallel tempering achieves overall the
best performance. When the noise variance is unknown, the RKHS method
proves to be more robust
Gradient matching methods for computational inference in mechanistic models for systems biology: a review and comparative analysis
Parameter inference in mathematical models of biological pathways, expressed as coupled ordinary differential equations (ODEs), is a challenging problem in contemporary systems biology. Conventional methods involve repeatedly solving the ODEs by numerical integration, which is computationally onerous and does not scale up to complex systems. Aimed at reducing the computational costs, new concepts based on gradient matching have recently been proposed in the computational statistics and machine learning literature. In a preliminary smoothing step, the time series data are interpolated; then, in a second step, the parameters of the ODEs are optimised so as to minimise some metric measuring the difference between the slopes of the tangents to the interpolants, and the time derivatives from the ODEs. In this way, the ODEs never have to be solved explicitly. This review provides a concise methodological overview of the current state-of-the-art methods for gradient matching in ODEs, followed by an empirical comparative evaluation based on a set of widely used and representative benchmark data
Penalized Likelihood Methods for Estimation of Sparse High Dimensional Directed Acyclic Graphs
Directed acyclic graphs (DAGs) are commonly used to represent causal
relationships among random variables in graphical models. Applications of these
models arise in the study of physical, as well as biological systems, where
directed edges between nodes represent the influence of components of the
system on each other. The general problem of estimating DAGs from observed data
is computationally NP-hard, Moreover two directed graphs may be observationally
equivalent. When the nodes exhibit a natural ordering, the problem of
estimating directed graphs reduces to the problem of estimating the structure
of the network. In this paper, we propose a penalized likelihood approach that
directly estimates the adjacency matrix of DAGs. Both lasso and adaptive lasso
penalties are considered and an efficient algorithm is proposed for estimation
of high dimensional DAGs. We study variable selection consistency of the two
penalties when the number of variables grows to infinity with the sample size.
We show that although lasso can only consistently estimate the true network
under stringent assumptions, adaptive lasso achieves this task under mild
regularity conditions. The performance of the proposed methods is compared to
alternative methods in simulated, as well as real, data examples.Comment: 19 pages, 8 figure
Computational inference in systems biology
Parameter inference in mathematical models of biological pathways, expressed as coupled ordinary differential equations (ODEs), is a challenging problem. The computational costs associated with repeatedly solving the ODEs are often high. Aimed at reducing this cost, new concepts using gradient matching have been proposed. This paper combines current adaptive gradient matching approaches, using Gaussian processes, with a parallel tempering scheme, and conducts a comparative evaluation with current methods used for parameter inference in ODEs
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