其中 slow convergence rate: 其中O_p(·)代表p\geq n \rightarrow \infty。(2.21)的含义是:当||\beta^0||_1 \ll \sqrt{n/log(p)},可以实现预测的一致性(consistency for prediction) fast convergence rate: oracle optimality改进了(2.21),实现了(2.22)式中更快的收敛速度以及L1,L2估计误差的边界: ...
Under the normality or sub-Gaussian assumption, the rate can be improved to nearly $s/\\sqrt{n}$ for certain design matrices. We further outline a general partitioning technique that helps to derive sharper convergence rate for the Lasso. The result is applicable to many covariance matrices ...
In this paper, we investigate the rate of convergence of the ALASSO estimator to the oracle distribution when the dimension of the regression parameters may grow to infinity with the sample size. It is shown that the rate critically depends on the choices of the penalty parameter and the ...
求导后: }repeat until convergence:{θj:=θj−α1m∑i=1m(hθ(x(i))−y(i))⋅x(i)jfor j := 0...n 即: }repeat until convergence:{θ0:=θ0−α1m∑i=1m(hθ(x(i))−y(i))⋅x(i)0θ1:=θ1−α1m∑i=1m(hθ(x(i))−y(i))⋅x(i)1θ2:=θ2−α1m...
Sconvergencerate.Inthisthesis,weprovetheconvergencerateofaninexactacceleratedforward—backwardsplittingmethodproposedbySalzo[20]andshowitseffectivenessbypreliminaryexper-iment.WeconsideravariantofLassoproblem.Itsobjectivefunctionisdifferentiable.Thisproblemcanbesolvedbynonlinearconjugategradientmethod.Weshowtheeffec—ti...
sum(error) # Update weights and bias weights -= learning_rate * grad_w bias -= learning_rate * grad_b # Check for convergence if np.linalg.norm(grad_w, ord=1) < tol: break return weights, bias 经过前几题的拷打,代码基本能直接读懂了,其中注意grad_w和grad_b的表达式,就是对Lasso回归...
We develop a PAC-Bayesian bound for the convergence rate of a Bayesian variant of Mul-tiple Kernel Learning (MKL) that is an estimation method for the sparse additive model. Standard analyses for MKL require a strong condition on the des... T Suzuki - 《Journal of Machine Learning Research...
which imply that the rates of convergence of LASSO are different from those in the familiar cross sectional case. In practical applications given a mixture of stationary, nonstationary, and cointegrated predictors, LASSO preserves asymptotic guarantee if the predictors are scale-standardized, and the ...
By exploiting the structure of the non-smooth "fusion penalty", our method achieves a faster convergence rate than the standard first-order method, sub-gradient method, and is significantly more scalable than the widely adopted second-order cone-programming and quadratic-programming formulations. In ...
Furthermore, a rate of convergence result is obtained on the l(2) error with an appropriate choice of the smoothing parameter. The rate is shown to be optimal under the condition of bounded maximal and minimal sparse eigenvalues. Our results imply that, with high probability, all important ...