64,576 research outputs found
MSSM Forecast for the LHC
We perform a forecast of the MSSM with universal soft terms (CMSSM) for the
LHC, based on an improved Bayesian analysis. We do not incorporate ad hoc
measures of the fine-tuning to penalize unnatural possibilities: such
penalization arises from the Bayesian analysis itself when the experimental
value of is considered. This allows to scan the whole parameter space,
allowing arbitrarily large soft terms. Still the low-energy region is
statistically favoured (even before including dark matter or g-2 constraints).
Contrary to other studies, the results are almost unaffected by changing the
upper limits taken for the soft terms. The results are also remarkable stable
when using flat or logarithmic priors, a fact that arises from the larger
statistical weight of the low-energy region in both cases. Then we incorporate
all the important experimental constrains to the analysis, obtaining a map of
the probability density of the MSSM parameter space, i.e. the forecast of the
MSSM. Since not all the experimental information is equally robust, we perform
separate analyses depending on the group of observables used. When only the
most robust ones are used, the favoured region of the parameter space contains
a significant portion outside the LHC reach. This effect gets reinforced if the
Higgs mass is not close to its present experimental limit and persits when dark
matter constraints are included. Only when the g-2 constraint (based on
data) is considered, the preferred region (for ) is well inside
the LHC scope. We also perform a Bayesian comparison of the positive- and
negative- possibilities.Comment: 42 pages: added figures and reference
Data complexity in machine learning
We investigate the role of data complexity in the context of binary classification problems. The universal data complexity is defined for a data set as the Kolmogorov complexity of the mapping enforced by the data set. It is closely related to several existing principles used in machine learning such as Occam's razor, the minimum description length, and the Bayesian approach. The data complexity can also be defined based on a learning model, which is more realistic for applications. We demonstrate the application of the data complexity in two learning problems, data decomposition and data pruning. In data decomposition, we illustrate that a data set is best approximated by its principal subsets which are Pareto optimal with respect to the complexity and the set size. In data pruning, we show that outliers usually have high complexity contributions, and propose methods for estimating the complexity contribution. Since in practice we have to approximate the ideal data complexity measures, we also discuss the impact of such approximations
Optimality of Universal Bayesian Sequence Prediction for General Loss and Alphabet
Various optimality properties of universal sequence predictors based on
Bayes-mixtures in general, and Solomonoff's prediction scheme in particular,
will be studied. The probability of observing at time , given past
observations can be computed with the chain rule if the true
generating distribution of the sequences is known. If
is unknown, but known to belong to a countable or continuous class \M
one can base ones prediction on the Bayes-mixture defined as a
-weighted sum or integral of distributions \nu\in\M. The cumulative
expected loss of the Bayes-optimal universal prediction scheme based on
is shown to be close to the loss of the Bayes-optimal, but infeasible
prediction scheme based on . We show that the bounds are tight and that no
other predictor can lead to significantly smaller bounds. Furthermore, for
various performance measures, we show Pareto-optimality of and give an
Occam's razor argument that the choice for the weights
is optimal, where is the length of the shortest program describing
. The results are applied to games of chance, defined as a sequence of
bets, observations, and rewards. The prediction schemes (and bounds) are
compared to the popular predictors based on expert advice. Extensions to
infinite alphabets, partial, delayed and probabilistic prediction,
classification, and more active systems are briefly discussed.Comment: 34 page
On Universal Prediction and Bayesian Confirmation
The Bayesian framework is a well-studied and successful framework for
inductive reasoning, which includes hypothesis testing and confirmation,
parameter estimation, sequence prediction, classification, and regression. But
standard statistical guidelines for choosing the model class and prior are not
always available or fail, in particular in complex situations. Solomonoff
completed the Bayesian framework by providing a rigorous, unique, formal, and
universal choice for the model class and the prior. We discuss in breadth how
and in which sense universal (non-i.i.d.) sequence prediction solves various
(philosophical) problems of traditional Bayesian sequence prediction. We show
that Solomonoff's model possesses many desirable properties: Strong total and
weak instantaneous bounds, and in contrast to most classical continuous prior
densities has no zero p(oste)rior problem, i.e. can confirm universal
hypotheses, is reparametrization and regrouping invariant, and avoids the
old-evidence and updating problem. It even performs well (actually better) in
non-computable environments.Comment: 24 page
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