1,417 research outputs found
Takeuchi's Information Criteria as a form of Regularization
Takeuchi's Information Criteria (TIC) is a linearization of maximum
likelihood estimator bias which shrinks the model parameters towards the
maximum entropy distribution, even when the model is mis-specified. In
statistical machine learning, regularization (a.k.a. ridge regression)
also introduces a parameterized bias term with the goal of minimizing
out-of-sample entropy, but generally requires a numerical solver to find the
regularization parameter. This paper presents a novel regularization approach
based on TIC; the approach does not assume a data generation process and
results in a higher entropy distribution through more efficient sample noise
suppression. The resulting objective function can be directly minimized to
estimate and select the best model, without the need to select a regularization
parameter, as in ridge regression. Numerical results applied to a synthetic
high dimensional dataset generated from a logistic regression model demonstrate
superior model performance when using the TIC based regularization over a
and a penalty term
1-loop matching and NNLL resummation for all partonic 2 to 2 processes in QCD
The Wilson Coefficients for all 4-parton operators which arise in matching
QCD to Soft-Collinear Effective Theory (SCET) are computed at 1-loop. Any dijet
observable calculated in SCET beyond leading order will require these results.
The Wilson coefficients are separated by spin and color, although most
applications will involve only the spin-averaged hard functions. The anomalous
dimensions for the Wilson coefficients are given to 2-loop order, and the
renormalization group equations are solved explicitly. This will allow for
analytical resummation of dijet observables to next-to-next-to-leading
logarithmic accuracy. For each channel, there is a natural basis in which the
evolution is diagonal in color space. The same basis also diagonalizes the
color evolution for the soft function. Even though soft functions required for
SCET calculations are observable dependent, it is shown that their
renormalization group evolution is almost completely determined by a universal
structure. With these results, it will be possible to calculate hadronic event
shapes or other dijet observables to next-to-leading order with
next-to-next-to-leading log resummation.Comment: 28 pages, 5 tables; v2: typo corrected in Eq. (56
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