45,625 research outputs found
Bayesian Causal Induction
Discovering causal relationships is a hard task, often hindered by the need
for intervention, and often requiring large amounts of data to resolve
statistical uncertainty. However, humans quickly arrive at useful causal
relationships. One possible reason is that humans extrapolate from past
experience to new, unseen situations: that is, they encode beliefs over causal
invariances, allowing for sound generalization from the observations they
obtain from directly acting in the world.
Here we outline a Bayesian model of causal induction where beliefs over
competing causal hypotheses are modeled using probability trees. Based on this
model, we illustrate why, in the general case, we need interventions plus
constraints on our causal hypotheses in order to extract causal information
from our experience.Comment: 4 pages, 4 figures; 2011 NIPS Workshop on Philosophy and Machine
Learnin
Tensor Analysis and Fusion of Multimodal Brain Images
Current high-throughput data acquisition technologies probe dynamical systems
with different imaging modalities, generating massive data sets at different
spatial and temporal resolutions posing challenging problems in multimodal data
fusion. A case in point is the attempt to parse out the brain structures and
networks that underpin human cognitive processes by analysis of different
neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the
multimodal, multi-scale nature of neuroimaging data is well reflected by a
multi-way (tensor) structure where the underlying processes can be summarized
by a relatively small number of components or "atoms". We introduce
Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network
notation in order to analyze these models. These diagrams not only clarify
matrix and tensor EEG and fMRI time/frequency analysis and inverse problems,
but also help understand multimodal fusion via Multiway Partial Least Squares
and Coupled Matrix-Tensor Factorization. We show here, for the first time, that
Granger causal analysis of brain networks is a tensor regression problem, thus
allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI
recordings shows the potential of the methods and suggests their use in other
scientific domains.Comment: 23 pages, 15 figures, submitted to Proceedings of the IEE
Precision Determination of the Top Quark Mass
The CDF and D0 collaborations have updated their measurements of the mass of
the top quark using proton-antiproton collisions at sqrt{s}=1.96TeV produced at
the Tevatron. The uncertainties in each of the of top-antitop decay channels
have been reduced. The new Tevatron average for the mass of the top quark based
on about 1/fb of data per experiment is 170.9+-1.8GeV/c^2.Comment: 14 pages, 4 figures; LaTeX2e, 8 .eps files, uses LaThuileFPSpro.sty
(included). To appear in the proceedings of the 21st Rencontres des Physique
de la Vallee d'Aoste, La Thuile, March 4-10, 200
Free Energy and the Generalized Optimality Equations for Sequential Decision Making
The free energy functional has recently been proposed as a variational
principle for bounded rational decision-making, since it instantiates a natural
trade-off between utility gains and information processing costs that can be
axiomatically derived. Here we apply the free energy principle to general
decision trees that include both adversarial and stochastic environments. We
derive generalized sequential optimality equations that not only include the
Bellman optimality equations as a limit case, but also lead to well-known
decision-rules such as Expectimax, Minimax and Expectiminimax. We show how
these decision-rules can be derived from a single free energy principle that
assigns a resource parameter to each node in the decision tree. These resource
parameters express a concrete computational cost that can be measured as the
amount of samples that are needed from the distribution that belongs to each
node. The free energy principle therefore provides the normative basis for
generalized optimality equations that account for both adversarial and
stochastic environments.Comment: 10 pages, 2 figure
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