4,510 research outputs found
Information-theoretic inference of common ancestors
A directed acyclic graph (DAG) partially represents the conditional
independence structure among observations of a system if the local Markov
condition holds, that is, if every variable is independent of its
non-descendants given its parents. In general, there is a whole class of DAGs
that represents a given set of conditional independence relations. We are
interested in properties of this class that can be derived from observations of
a subsystem only. To this end, we prove an information theoretic inequality
that allows for the inference of common ancestors of observed parts in any DAG
representing some unknown larger system. More explicitly, we show that a large
amount of dependence in terms of mutual information among the observations
implies the existence of a common ancestor that distributes this information.
Within the causal interpretation of DAGs our result can be seen as a
quantitative extension of Reichenbach's Principle of Common Cause to more than
two variables. Our conclusions are valid also for non-probabilistic
observations such as binary strings, since we state the proof for an
axiomatized notion of mutual information that includes the stochastic as well
as the algorithmic version.Comment: 18 pages, 4 figure
Identifying interactions in the time and frequency domains in local and global networks : a Granger causality approach
Background
Reverse-engineering approaches such as Bayesian network inference, ordinary differential equations (ODEs) and information theory are widely applied to deriving causal relationships among different elements such as genes, proteins, metabolites, neurons, brain areas and so on, based upon multi-dimensional spatial and temporal data. There are several well-established reverse-engineering approaches to explore causal relationships in a dynamic network, such as ordinary differential equations (ODE), Bayesian networks, information theory and Granger Causality.
Results
Here we focused on Granger causality both in the time and frequency domain and in local and global networks, and applied our approach to experimental data (genes and proteins). For a small gene network, Granger causality outperformed all the other three approaches mentioned above. A global protein network of 812 proteins was reconstructed, using a novel approach. The obtained results fitted well with known experimental findings and predicted many experimentally testable results. In addition to interactions in the time domain, interactions in the frequency domain were also recovered.
Conclusions
The results on the proteomic data and gene data confirm that Granger causality is a simple and accurate approach to recover the network structure. Our approach is general and can be easily applied to other types of temporal data
Gentzen-Prawitz Natural Deduction as a Teaching Tool
We report a four-years experiment in teaching reasoning to undergraduate
students, ranging from weak to gifted, using Gentzen-Prawitz's style natural
deduction. We argue that this pedagogical approach is a good alternative to the
use of Boolean algebra for teaching reasoning, especially for computer
scientists and formal methods practionners
Identifying the consequences of dynamic treatment strategies: A decision-theoretic overview
We consider the problem of learning about and comparing the consequences of
dynamic treatment strategies on the basis of observational data. We formulate
this within a probabilistic decision-theoretic framework. Our approach is
compared with related work by Robins and others: in particular, we show how
Robins's 'G-computation' algorithm arises naturally from this
decision-theoretic perspective. Careful attention is paid to the mathematical
and substantive conditions required to justify the use of this formula. These
conditions revolve around a property we term stability, which relates the
probabilistic behaviours of observational and interventional regimes. We show
how an assumption of 'sequential randomization' (or 'no unmeasured
confounders'), or an alternative assumption of 'sequential irrelevance', can be
used to infer stability. Probabilistic influence diagrams are used to simplify
manipulations, and their power and limitations are discussed. We compare our
approach with alternative formulations based on causal DAGs or potential
response models. We aim to show that formulating the problem of assessing
dynamic treatment strategies as a problem of decision analysis brings clarity,
simplicity and generality.Comment: 49 pages, 15 figure
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