2,200 research outputs found
Causal Discovery by Kernel Deviance Measures with Heterogeneous Transforms
The discovery of causal relationships in a set of random variables is a
fundamental objective of science and has also recently been argued as being an
essential component towards real machine intelligence. One class of causal
discovery techniques are founded based on the argument that there are inherent
structural asymmetries between the causal and anti-causal direction which could
be leveraged in determining the direction of causation. To go about capturing
these discrepancies between cause and effect remains to be a challenge and many
current state-of-the-art algorithms propose to compare the norms of the kernel
mean embeddings of the conditional distributions. In this work, we argue that
such approaches based on RKHS embeddings are insufficient in capturing
principal markers of cause-effect asymmetry involving higher-order structural
variabilities of the conditional distributions. We propose Kernel Intrinsic
Invariance Measure with Heterogeneous Transform (KIIM-HT) which introduces a
novel score measure based on heterogeneous transformation of RKHS embeddings to
extract relevant higher-order moments of the conditional densities for causal
discovery. Inference is made via comparing the score of each hypothetical
cause-effect direction. Tests and comparisons on a synthetic dataset, a
two-dimensional synthetic dataset and the real-world benchmark dataset
T\"ubingen Cause-Effect Pairs verify our approach. In addition, we conduct a
sensitivity analysis to the regularization parameter to faithfully compare
previous work to our method and an experiment with trials on varied
hyperparameter values to showcase the robustness of our algorithm
Massive Vector Mesons and Gauge Theory
We show that the requirements of renormalizability and physical consistency
imposed on perturbative interactions of massive vector mesons fix the theory
essentially uniquely. In particular physical consistency demands the presence
of at least one additional physical degree of freedom which was not part of the
originally required physical particle content. In its simplest realization
(probably the only one) these are scalar fields as envisaged by Higgs but in
the present formulation without the ``symmetry-breaking Higgs condensate''. The
final result agrees precisely with the usual quantization of a classical gauge
theory by means of the Higgs mechanism. Our method proves an old conjecture of
Cornwall, Levin and Tiktopoulos stating that the renormalization and
consistency requirements of spin=1 particles lead to the gauge theory structure
(i.e. a kind of inverse of 't Hooft's famous renormalizability proof in
quantized gauge theories) which was based on the on-shell unitarity of the
-matrix. We also speculate on a possible future ghostfree formulation which
avoids ''field coordinates'' altogether and is expected to reconcile the
on-shell S-matrix point of view with the off-shell field theory structure.Comment: 53 pages, version to appear in J. Phys.
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Foundations and New Horizons for Causal Inference
While causal inference is established in some disciplines such as econometrics and biostatistics, it is only starting to emerge as a
valuable tool in areas such as machine learning and artificial intelligence. The mathematical foundations of causal inference are fragmented at present.
The aim of the workshop "Foundations and new horizons for causal inference" was to
unify existing approaches and mathematical foundations as well as exchange ideas between different fields.
We regard this workshop as successful in that
it brought together researchers from different disciplines
who
were able to
learn from each other not only about
different formulations of related problems,
but also about solutions and methods that exist
in the different fields
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