38,513 research outputs found
Ancestral Causal Inference
Constraint-based causal discovery from limited data is a notoriously
difficult challenge due to the many borderline independence test decisions.
Several approaches to improve the reliability of the predictions by exploiting
redundancy in the independence information have been proposed recently. Though
promising, existing approaches can still be greatly improved in terms of
accuracy and scalability. We present a novel method that reduces the
combinatorial explosion of the search space by using a more coarse-grained
representation of causal information, drastically reducing computation time.
Additionally, we propose a method to score causal predictions based on their
confidence. Crucially, our implementation also allows one to easily combine
observational and interventional data and to incorporate various types of
available background knowledge. We prove soundness and asymptotic consistency
of our method and demonstrate that it can outperform the state-of-the-art on
synthetic data, achieving a speedup of several orders of magnitude. We
illustrate its practical feasibility by applying it on a challenging protein
data set.Comment: In Proceedings of Advances in Neural Information Processing Systems
29 (NIPS 2016
On Sound Relative Error Bounds for Floating-Point Arithmetic
State-of-the-art static analysis tools for verifying finite-precision code
compute worst-case absolute error bounds on numerical errors. These are,
however, often not a good estimate of accuracy as they do not take into account
the magnitude of the computed values. Relative errors, which compute errors
relative to the value's magnitude, are thus preferable. While today's tools do
report relative error bounds, these are merely computed via absolute errors and
thus not necessarily tight or more informative. Furthermore, whenever the
computed value is close to zero on part of the domain, the tools do not report
any relative error estimate at all. Surprisingly, the quality of relative error
bounds computed by today's tools has not been systematically studied or
reported to date. In this paper, we investigate how state-of-the-art static
techniques for computing sound absolute error bounds can be used, extended and
combined for the computation of relative errors. Our experiments on a standard
benchmark set show that computing relative errors directly, as opposed to via
absolute errors, is often beneficial and can provide error estimates up to six
orders of magnitude tighter, i.e. more accurate. We also show that interval
subdivision, another commonly used technique to reduce over-approximations, has
less benefit when computing relative errors directly, but it can help to
alleviate the effects of the inherent issue of relative error estimates close
to zero
Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data
Constraint Programming (CP) has proved an effective paradigm to model and
solve difficult combinatorial satisfaction and optimisation problems from
disparate domains. Many such problems arising from the commercial world are
permeated by data uncertainty. Existing CP approaches that accommodate
uncertainty are less suited to uncertainty arising due to incomplete and
erroneous data, because they do not build reliable models and solutions
guaranteed to address the user's genuine problem as she perceives it. Other
fields such as reliable computation offer combinations of models and associated
methods to handle these types of uncertain data, but lack an expressive
framework characterising the resolution methodology independently of the model.
We present a unifying framework that extends the CP formalism in both model
and solutions, to tackle ill-defined combinatorial problems with incomplete or
erroneous data. The certainty closure framework brings together modelling and
solving methodologies from different fields into the CP paradigm to provide
reliable and efficient approches for uncertain constraint problems. We
demonstrate the applicability of the framework on a case study in network
diagnosis. We define resolution forms that give generic templates, and their
associated operational semantics, to derive practical solution methods for
reliable solutions.Comment: Revised versio
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