lasso 的软阈值法和循环坐标
    英文回答：
    Lasso with Soft Thresholding and Iterative Coordinate Descent.
    Lasso (least absolute shrinkage and selection operator) is a regression method that performs both variable selection and regularization. It adds a penalty term to the loss function that is proportional to the absolute value of the coefficients, which encourages sparsity in the estimated model.
    Soft thresholding is a technique used in lasso to shrink the coefficients towards zero. It is applied to the estimated coefficients after each iteration of the optimization algorithm. The soft thresholding operator is defined as follows:
    soft_thresholding(x, lambda) = sign(x)  max(|x| lambda, 0)。
    where:
    x is the coefficient to be shrunk.
    lambda is the threshold value.
    Iterative coordinate descent (ICD) is an optimization algorithm that can be used to solve the lasso problem. ICD works by iteratively updating each coefficient while keeping all other coefficients fixed. The update for the jth coefficient is given by:
    beta_j = soft_thresholding(sum_i(x_i  beta_i) x_j  beta_j + y_j, lambda)。
    where:
    beta_j is the jth coefficient.
    x_i and y_i are the i-th features and response variable, respectively.
    lambda is the threshold value.
    The ICD algorithm is guaranteed to converge to a local minimum of the lasso objective function.
正则化坐标    中文回答：
    套索（Lasso）软阈值法与循环坐标下降法。
    套索（Lasso，最小绝对收缩和选择算子）是一种回归方法，它执行变量选择和正则化。它在损失函数中添加一个与系数的绝对值成正比的惩罚项，这会鼓励估计模型的稀疏性。
    软阈值法是 LASSO 中用于将系数收缩为零的技术。它在优化算法的每次迭代后应用于估计的系数。软阈值算子定义如下：
    soft_thresholding(x, lambda) = sign(x)  max(|x| lambda, 0)。
    其中：
    x 是要收缩的系数。
    lambda 是阈值。
    循环坐标下降 (ICD) 是一种优化算法，可用于解决 LASSO 问题。ICD 通过在固定所有其他系数的同时迭代更新每个系数来工作。第 j 个系数的更新由以下公式给出：
    beta_j = soft_thresholding(sum_i(x_i  beta_i) x_j  beta_j + y_j, lambda)。
    其中：
    beta_j 是第 j 个系数。
    x_i 和 y_i 分别是第 i 个特征和响应变量。
    lambda 是阈值。
    可以保证 ICD 算法收敛于 LASSO 目标函数的局部最小值。

版权声明：本站内容均来自互联网，仅供演示用，请勿用于商业和其他非法用途。如果侵犯了您的权益请与我们联系QQ:729038198，我们将在24小时内删除。