英文回答:
Ridgeback is a return technique that addresses multiple co—linear problems。 The existence of multiple co—linears in themon minimum two—fold method leads to model instability, and parameters are estimated to be vulnerable to minor data changes。 To address this problem, the retreat reduced the variance in the estimation of parameters by punishing the coefficient size。 The penalty is achieved by adding a regularization item to the minimum two—fold loss function, which is the square of the coefficient and the product of the hyperparametric alpha specified by the user。 The increase in alpha increases the importance of the penalty item in the process of optimization and encourages the model to choose simpler parameters。 The loss function of a ridge return can be written as L(b) = ||Y — Xbeta…2 + αbeta…2, where Y is the observed target variable, X is the observed self—variant and beta is the desired parameter vector。 The estimated value of beta is obtained by minimizing this loss function。
岭回归是一种用于解决多重共线性问题的回归技术。在普通最小二乘法中,存在多重共线性会
导致模型不稳定,参数估计容易受到微小数据变动的影响。为解决这一问题,岭回归通过对系数大小施加惩罚,减少了参数估计的方差。这种惩罚是通过在最小二乘损失函数中添加一个正则化项实现的,该正则化项为系数的平方和与用户指定的超参数α的乘积。增大α会使得惩罚项在优化过程中变得更加重要,鼓励模型选择更简单的参数解。岭回归的损失函数可以写成 L(β) = ||Y - Xβ||^2 + α||β||^2,其中Y为观测到的目标变量,X为观测到的自变量,β为需要估计的参数向量。通过最小化这个损失函数来得到β的估计值。
An important feature of the return is that it can steadily estimate highly relevant characteristics。 Since the ridge return penalizes the coefficient size, even if there is a strong correlation between the characteristics, the ridge return can give a reasonable estimate of the parameters。 As a result, the Ridge Return is more reliable in processing co—linear data than themon minimum two—folder。 Ridge return also prevents over—sizing, especially when processing high—dimensional data sets。 Reconciles the value of the α for the retrospect parameter to find a suitable model that is neither over or under。 Quest return also allows for characterization because it reduces the coefficients of some characteristics to zero in the model。
正则化最小二乘问题
岭回归的一个重要特点是它可以稳健地估计高度相关的特征。因为岭回归对系数大小施加了惩罚,所以就算特征之间有很强的相关性,岭回归也能给出合理的参数估计。这样一来,岭回归在处理有共线性的数据时比普通最小二乘法更可靠。岭回归还可以防止过拟合,特别是在处理高维数据集时。调节正则化参数α的值,就可以到一个既不过拟合又不欠拟合的合适模型。岭回归还可以进行特征选择,因为它会压缩一些特征的系数,使得它们在模型中变成零。
In addition to these advantages, there are a number of issues that require attention。 Users need to specify the value of the regular parameter alpha manually, which requires a certain level of knowledge or experience in the field, otherwise it is difficult to find a suitable alpha value。 It is moreplex to calculate the return, especially in high—dimensional data sets。 For large—scale datasets, calculation time may be a problem。 Ridge regression is sensitive to abnormal values and therefore requires rigorous pre—processing of data prior to use。 Ridgeback is an effective tool for dealing with the issues of multi—colineality and ovepatibility, yet in practical applications special attention needs to be paid to the selection of parameters and the calculation ofplexity。
岭回归除了具有上述优点之外,还存在一些需要引起注意的问题。用户需要手动指定正则化参数α的值,这要求具备一定的领域知识或调参经验,否则很难到合适的α值。岭回归的计算复杂度较高,尤其是在高维数据集上。对于大规模数据集,计算时间可能会成为一个问题。岭回归对异常值敏感,因此在使用前需要对数据进行严格的预处理。岭回归是一种有效处理多重共线性和过拟合问题的工具,然而在实际应用中需要特别注意参数的选择和计算复杂度的问题。
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