B £ŠãZ„ã@s`dZddlZGdd„deƒZGdd„deƒZGdd„deƒZGd d „d eƒZGd d „d eƒZdS) a A collection of smooth penalty functions. Penalties on vectors take a vector argument and return a scalar penalty. The gradient of the penalty is a vector with the same shape as the input value. Penalties on covariance matrices take two arguments: the matrix and its inverse, both in unpacked (square) form. The returned penalty is a scalar, and the gradient is returned as a vector that contains the gradient with respect to the free elements in the lower triangle of the covariance matrix. All penalties are subtracted from the log-likelihood, so greater penalty values correspond to a greater degree of penalization. The penaties should be smooth so that they can be subtracted from log likelihood functions and optimized using standard methods (i.e. L1 penalties do not belong here). éNc@s(eZdZdZdd„Zdd„Zdd„ZdS) ÚPenaltya) A class for representing a scalar-value penalty. Parameters ---------- wts : array-like A vector of weights that determines the weight of the penalty for each parameter. Notes ----- The class has a member called `alpha` that scales the weights. cCs||_d|_dS)Ngð?)ÚwtsÚalpha)Úselfr©rú:lib/python3.7/site-packages/statsmodels/base/_penalties.pyÚ__init__(szPenalty.__init__cCst‚dS)a A penalty function on a vector of parameters. Parameters ---------- params : array-like A vector of parameters. Returns ------- A scalar penaty value; greater values imply greater penalization. N)ÚNotImplementedError)rÚparamsrrrÚfunc,sz Penalty.funccCst‚dS)a The gradient of a penalty function. Parameters ---------- params : array-like A vector of parameters Returns ------- The gradient of the penalty with respect to each element in `params`. N)r )rr rrrÚgrad<sz Penalty.gradN)Ú__name__Ú __module__Ú __qualname__Ú__doc__rr r rrrrrsrc@s*eZdZdZd dd„Zdd„Zdd„ZdS) ÚL2z! The L2 (ridge) penalty. NcCs |dkrd|_n||_d|_dS)Ngð?)rr)rrrrrrRsz L2.__init__cCst |j|j|d¡S)Né)ÚnpÚsumrr)rr rrrr YszL2.funccCsd|j|j|S)Nr)rr)rr rrrr \szL2.grad)N)r rrrrr r rrrrrMs rc@s*eZdZdZd dd„Zdd„Zdd„ZdS) Ú PseudoHuberz# The pseudo-Huber penalty. NcCs&||_|dkrd|_n||_d|_dS)Ngð?)Údltrr)rrrrrrres zPseudoHuber.__init__cCsDt d||jd¡}|d8}||jd9}t |j|j|¡S)Nér)rÚsqrtrrrr)rr Úvrrrr mszPseudoHuber.funccCs,t d||jd¡}||j|j|S)Nrr)rrrrr)rr rrrrr sszPseudoHuber.grad)N)r rrrrr r rrrrr`s rc@s$eZdZdd„Zdd„Zdd„ZdS)ÚCovariancePenaltycCs ||_dS)N)Úwt)rrrrrrzszCovariancePenalty.__init__cCst‚dS)zõ Parameters ---------- mat : square matrix The matrix to be penalized. mat_inv : square matrix The inverse of `mat`. Returns ------- A scalar penalty value N)r )rÚmatÚmat_invrrrr }s zCovariancePenalty.funccCst‚dS)a[ Parameters ---------- mat : square matrix The matrix to be penalized. mat_inv : square matrix The inverse of `mat`. Returns ------- A vector containing the gradient of the penalty with respect to each element in the lower triangle of `mat`. N)r )rrrrrrr ŒszCovariancePenalty.gradN)r rrrr r rrrrrxsrc@s eZdZdZdd„Zdd„ZdS)ÚPSDzž A penalty that converges to +infinity as the argument matrix approaches the boundary of the domain of symmetric, positive definite matrices. cCsLytj |¡}Wntjjk r*tjSXd|jt t t |¡¡¡S)Néþÿÿÿ) rZlinalgZcholeskyZ LinAlgErrorÚinfrrÚlogÚdiag)rrrÚcyrrrr ¥s zPSD.funccCsH| ¡}d|t t |¡¡}t |jd¡\}}|j |||fS)Nrr)Úcopyrr"Z tril_indicesÚshaper)rrrr#ÚiÚjrrrr ¬szPSD.gradN)r rrrr r rrrrržsr) rZnumpyrÚobjectrrrrrrrrrÚs 5&