There exist certain intrinsic relations between the ultraviolet divergent graphs and the convergent ones at the same loop order in renormalizable quantum field theories. Whereupon we may establish a new method, the intrinsic regularization method, to regularize those divergent graphs. In this paper, we apply this method to QCD at the one loop order. It turns out to be satisfactory: The gauge in...

Regularization involves a large family of the state-of-the-art techniques in classifier learning. However, since traditional regularization methods essentially derive from ill-posed multivariate functional fitting problems which can be viewed as a kind of regression, in classifier design, they usually give more concerns to the smoothness of the classifier, and do not sufficiently use the prior ...

We present a hybrid multivariate calibration method, constrained regularization (CR), and demonstrate its utility via numerical simulations and experimental Raman spectra. In this new method, multivariate calibration is treated as an inverse problem in which an optimal balance between model complexity and noise rejection is achieved with the inclusion of prior information in the form of a spect...

Linear models are often built to understand how a set of input data affects output data and predict its value. A linear regression model assumes that that regression function E(Y |X) is linear in the inputsX1, . . . ,Xp. The output is represented as a weighted sum of the input variables (or features), where the weights are called the regression coefficients. The regressions coefficients are asc...

We tackle the inverse problem of reconstructing an unknown finite measure μ from a noisy observation of a generalized moment of μ defined as the integral of a continuous and bounded operator Φ with respect to μ . When only a quadratic approximation Φm of the operator is known, we introduce the L2 approximate maximum entropy solution as a minimizer of a convex functional subject to a sequence of...