[br] 逻辑回归模型的数学形式已经确定，即 [math]p\left(Y=1\mid^{ }x\right)=\frac{1}{_{1+e^{-\left(\omega^Tx+B\right)}}}[/math]，接下来就是如何求解模型中的参数，即公式中的 [math]\omega[/math] 值和 [math]b[/math] 值。在统计学中，常常使用极大似然估计法来求解，即找到一组参数，使得在这组参数下，数据的似然度（概率）最大。[br][br] 极大似然估计法是对独立样本（各样本均是独立事件）开展的参数估计方法，所以应首先对概率中的独立事件作出严谨的说明。[br][br] 定义：对于事件[math]E[/math]和事件[math]F[/math]，如果满足公式：[math]P(EF)=P\left(E\right)P\left(F\right)[/math]，那么称它们是独立的。若两个事件 [math]E[/math]和[math]F[/math]不独立，则称它们是相依的，或者相互不独立。[br][br] 如果从条件概率的角度来理解，即[math]P(E|F)=\frac{P\left(EF\right)}{P\left(F\right)},P\left(F\right)>0[/math]，可导出：[math]P(E|F)=P(E)[/math]（可理解为在 [math]F[/math] 事件发生的条件下 [math]E[/math] 事件发生的概率与 [math]E[/math] 事件自然发生的概率是一致的，即[math]E[/math] 事件的发生与 [math]F[/math]事件无关），公式的抽象性难以进一步理解独立事件的本质属性，可以用维恩图形象地剖析独立事件的内涵。条件概率的维恩图如图 2-6-10 所示。[br][center][img]https://s21.ax1x.com/2025/02/16/pEK2xkd.jpg[/img][br]图 2-6-10 条件概率的维恩图[/center]

[br] 两个独立事件[math]P(E|F)=P(E)[/math] ，如果用面积占比来表示， [math]P\left(E\mid F\right)=\frac{P\left(EF\right)}{P\left(F\right)}=\frac{S_{red}}{S_F}[/math]而 [math]P\left(E\right)=\frac{S_e}{S_a}[/math]，即 [math]\frac{S_{red}}{S_F}=\frac{S_E}{S_A}[/math]，这也就说明了事件[math]F[/math] 的样本空间对事件 [math]E[/math] 样本空间的切割后这部分（即形成维恩图中红色部分空间，即中间交叉部分）在 [math]F[/math] 中的比例和事件 E 在原来总体样本空间[math]A[/math] 中的比例是一致的，实际上这种“同比例切割”的特性，是确定 [math]F[/math] 与 [math]E[/math] 是否独立的一个标志，如果 [math]F[/math] 事件样本空间同比例切割 [math]E[/math] 事件空间，那么 [math]E[/math] 和 [math]F[/math] 就是独立的。这样的描述和传统意义上的描述“F 事件的发生并不影响 [math]E[/math] 发生的概率，那么 [math]E[/math]和 [math]F[/math] 就是独立的”好像是不相一致的，但事实上用“同比例切割”有时候更容易判断两个事件是否是独立的。相反的，不能同比例切割的话，那可以判断 [math]E[/math]和 [math]F[/math]是不独立的。[br][br] 如果再做进一步思考，观察另一幅维恩图，如图 2-6-11 所示。[br][center][img]https://s21.ax1x.com/2025/02/16/pEKRC1P.jpg[/img][br]图 2-6-11 维恩图[/center]

图中 [math]E[/math] 和 [math]F[/math] 没有相交，按照“同比例切割”的观点，[math]E[/math] 事件和 [math]F[/math]事件是“不独立”的。这个图告诉我们，两个不相交的事件，反而是“相互不独立”的。除了一种情况，事件[math]E[/math] 不可能出现，也就是 [math]P(E)=0[/math]。[br][br] 这给我们一种新的认识：世界上两个没有任何交集的人，却相互不独立。造成这种错觉的原因是，讨论问题的角度不一样，相交讨论的是两个事件的集合，而“独立性”与否讨论的是比例（也就是概率）的问题。另外，概率论中的“独立”都是特别针对概率值的影响，而人的独立性讨论的是人格特征。概率论中只是借用了“独立”这个词，概念上被赋予了严格的数学意义。

[b] 引例 1：[/b]从一副洗好的 52 张扑克牌里随机抽取一张牌，令 E 表示事件“抽取的牌为一张A”，令 F 表示事件“抽取的牌为一张黑桃”，那么 [math]E[/math] 和 [math]F[/math] 就是独立的。[br] [br] 因为[math]P(EF)=1/52[/math] ，而[math]P(E)=4/52[/math] ， [math]P(F)=13/52[/math] ，符合 [math]P(EF)=P(E)P(F)[/math] 对独立事件的判断定义。[br][br] 这个例子也可以用“同比例分割”的方法来判断。原始样本空间大小为 52，事件 [math]E[/math] 空间大小有 4（因为有 4 张牌 A），因此事件 [math]E[/math]在原来空间中的分割比例是 4/52。相交事件 [math]EF[/math] 样本空间（既是牌 A 又是黑桃）1，事件 [math]F[/math] 的样本空间很明显是 13（因为有 13 张黑桃），因此，[math]EF[/math] 在 [math]F[/math]中的分割比例为 1/13。4/52=1/13，因此是独立的。

[b]引例 2：[/b]掷两枚均匀的骰子，令 [math]E_1[/math] 表示事件“骰子点数和为 6”，令 [math]F[/math]表示事件“第一枚骰子点数为 4”，那么[math]P\left(E_1F\right)=P\left(4,2\right)=\frac{1}{36}[/math]。因为总的样本空间组合是 36 个，而“骰子点数和为 6”并且“第一枚骰子点数为 4”的组合只有 1 个。而 [math]P\left(E_1\right)P\left(F\right)=\frac{5}{36}\times\frac{1}{6}=\frac{5}{216}[/math][br][br]因此，[math]E_1[/math]和 [math]F[/math] 不独立。也可以用“同比例分割”法来判断，[math]E_1F[/math] 相交事件在 [math]F[/math] 中分割的比例[br][br]为 1/6，而 [math]E_1[/math] 事件在原来空间的比例是 5/36。

[b]（一）极大似然估计[/b][br][br] 首先引入经典贝叶斯公式：[br] [br] [math]p\left(w\mid x\right)=\frac{p\left(x\mid w\right)p\left(w\right)}{p\left(x\right)}[/math][br] [b]【知识点引入】[/b]全概率公式。[br] 设随机试验[math]E[/math] 共有 [math]n[/math] 种可能的结果 [math]A_1,A_2,...,A_n[/math] ，这些结果两两不可能同时出现，即两两相互独立，那么，任一随机事件[math]B[/math]的概率满足：[br][br] [math]p\left(B\right)=p\left(B\mid A_1\right)p\left(A_1\right)+p\left(B\mid A_2\right)p\left(A_2\right)+...+p\left(B\mid A_n\right)p\left(A_n\right)[/math][br][br] 以上解题过程看起来非常明晰，但在解决实际问题时并不简单，因为先验概率 [math]p(w_{\text{i}})[/math]和类条件概率（各类的总体分布） [math]p(x\mid w_i)[/math] 都是未知的。我们能获得的数据可能只有有限数目的样本数据，根据仅有的样本数据进行分类时，一种可行的办法是需要先对先验概率和类条件概率进行估计，然后再套用贝叶斯分类器。[br][br] 先验概率的估计较简单：① 每个样本所属的自然状态都是已知的（有监督学习）；② 依靠经验进行判断，比如德尔菲法，也称专家调查法；③ 用训练样本中各类出现的频率估计，比如公园里的男女比例。[br][br] 类条件概率的估计就非常困难了，原因包括：① 概率密度函数包含了一个随机变量的全部信息；② 概率密度函数可以是满足下面条件的任何函数 [math]p\left(x\right)\ge0,[/math][math]\int p\left(x\right)dx=1[/math] ；③ 在很多情况下，已有的训练样本数总是太少；④ 当用于表示特征的向量[math]x[/math] 的维数较大时，就会产生严重的计算复杂度问题（算法的执行时间、系统资源开销等）。总之要直接估计类条件概率的密度函数很难。

解决的办法就是，把估计完全未知的概率密度转化为估计参数。这里就将概率密度估计问题转化为参数估计问题，极大似然估计就是一种参数估计方法。概率密度函数的选取很重要，模型正确，在样本区域无穷时，会得到较准确的估计值，如果模型是错误的，那么参数估计是毫无意义的。[br][br] 参数估计的重要前提是：训练样本的分布能代表样本的真实分布。每个样本集中的样本都是所谓独立同分布的随机变量，即满足独立同分布条件（IID 条件），且有充分的训练样本。[br][br] [b]【知识点引入】[/b]IID 即独立同分布（Independent and Identically Distributed）。[br][br] 在概率统计理论中，IID 指随机过程中，任何时刻的取值都为随机变量，如果这些随机变量服从同一分布，并且互相独立，那么这些随机变量是独立同分布。如果随机变量[math]x_1[/math] 和 [math]x_2[/math]独立，是指 [math]x_1[/math] 的取值不影响 [math]x_2[/math] 的取值， [math]x_2[/math] 的取值也不影响[math]x_1[/math] 的取值且随机变量[math]x_1[/math]和 [math]x_2[/math] 服从同一分布，这意味着 [math]x_1[/math] 和 [math]x_2[/math] 具有相同的分布形状和相同的分布参数，对离散随机变量具有相同的分布律，对连续随机变量具有相同的概率密度函数，有着相同的分布函数，相同的期望、方差。如试验条件保持不变，一系列的抛硬币的正反面结果是独立同分布。[br][br] 极大似然估计原理：极大似然估计提供了一种给定观察数据来评估模型参数的方法，即“模型已定，参数未知”。通过若干次试验，观察其结果，利用试验结果得到某个参数值能够使样本出现的概率为最大，则称为极大似然估计。[br][br] 由于样本集中的样本都是独立同分布，可以只考虑一类样本集 [math]D[/math]，来估计参数向量[math]\theta[/math]，已知的样本集为 [math]D=\left\{x_1,x_2,...,x_N\right\}[/math] 。

似然函数（likelihood function）：联合概率密度函数[math]p\left(D\mid\theta\right)[/math] 称为相对于[math]\left\{x_1,x_2,...,x_N\right\}[/math] 的[math]\theta[/math]的[br]似然函数。[br] [math]l\left(\theta\right)=P\left(D\mid\theta\right)=P\left(x_1,x_2,...,x_N\mid\theta\right)=\prod^N_{i=1}p\left(x_i\mid\theta\right)[/math][br] [br] 这里可以将样本集 D 看作在以 为参数的某种概率函数模型的不同取值，或者在同一条件下试验 [math]N[/math]次，第一次取得 [math]x_1[/math] 值，第二次取得 [math]x_2[/math] 值，直至第 [math]N[/math] 次取得 [math]x_N[/math] 值的概率。

最大似然估计（Maximum Likelihood Estimation，MLE）求解：如果[math]\theta[/math]是参数空间中能使似然函数 [math]l(\theta)[/math] 最大的[math]\theta[/math]值，则[math]\theta[/math]应该是“最可能”的参数值，那么[math]\theta[/math]就是[math]\theta[/math] 的极大似然估计量。它是样本集的函数，记作：[math]\theta=d\left(x_1,x_2,...,x_N\right)=d\left(D\right)[/math]，则 [math]\theta\left(x_1,x_2,..,x_N\right)[/math] 称为极大似然估计值。[br][br] [math]\theta=argmaxl\left(\theta\right)=argmax\prod^N_{i=1}p\left(x_i\mid\theta\right)[/math]

[b]【知识点引入】[/b]数学符号 arg 的全称为 argument of the maximum/minimum。[br] arg max [math]f(x)[/math] ：当 [math]f(x)[/math]取最大值时，[math]x[/math] 的取值。[br] [br] arg min [math]f\left(x\right)[/math] ：当[math]f(x)[/math] 取最小值时，[math]x[/math]的取值。[br][br] 实际上为了便于分析，定义了对数似然函数：[br][br] [math]H\left(\theta\right)=lnl\left(\theta\right)[/math][br] [br] [math]\theta=argmaxH\left(\theta\right)=argmaxlnl\left(\theta\right)=argmax\prod^N_{i=1}lnp\left(x_i\mid\theta\right)[/math]

第一种情况：未知参数只有一个（[math]\theta[/math]为标量）。[br][br] 在似然函数满足连续、可微的正则条件下，极大似然估计量是下面微分方程的解：[br] [math]\frac{dl\left(\theta\right)}{d\theta}=0[/math]或者等价于[math]\frac{dH\left(\theta\right)}{d\theta}=\frac{dlnl\left(\theta\right)}{d\theta}=0[/math]

第二种情况：未知参数有多个（[math]\theta[/math] 为向量）。[br][br] 则[math]\theta[/math]可表示为具有[math]s[/math]个分量的未知向量：[br][br] [math]\theta=\left[\theta_1,\theta_2,...,\theta_s\right]^T[/math][br][br] 记梯度算子：[br] [math]\nabla_{\theta}=\left[\frac{\partial}{\partial\theta_1},\frac{\partial}{\partial\theta_2},...,\frac{\partial}{\partial\theta_s}\right]^T[/math][br][br] 若似然函数满足连续可导的条件，则最大似然估计量就是如下方程的解。[br][br] [math]\nabla_{\theta}H\left(\theta\right)=\nabla_{\theta}lnl\left(\theta\right)=\sum^N_{i=1}\nabla_{\theta}lnp\left(x_i\mid\theta\right)=0[/math][br][br] 方程的解只是一个估计值，只有在样本数趋于无限多的时候，它才会接近于真实值。

[b]引例一：[/b]设样本服从正态分布 [math]N(\mu,\sigma^2)[/math]，则似然函数为[br][br] [math]L\left(\mu,\sigma^2\right)=\prod^N_{i=1}\frac{1}{\sqrt{2\pi\sigma}}e^{-\frac{\left(x_i-\mu\right)^2}{2\sigma^2}}=\left(2\pi\sigma^2\right)^{\frac{n}{2}}e^{\frac{1}{2\sigma^2}\sum^n_{i=1}\left(x_i-\mu\right)^2}[/math][br][br] 它的对数：[br] [math]lnl\left(\mu,\sigma^2\right)=-\frac{n}{2}ln\left(2\pi\right)-\frac{n}{2}ln\left(\sigma^2\right)-\frac{1}{2\sigma^2}\sum^n_{i=1}\left(x_i-\mu\right)^2[/math][br] [br] [br] 求导，得方程组（这里将[math]\sigma^2[/math]作为一个整体变量对待）：[br] [br] [math]\frac{\partial lnL\left(\mu,\sigma^2\right)}{\partial\mu}=\frac{1}{\sigma^2}\sum^n_{i=1}\left(x_i-\mu\right)=0[/math][br] [math]\frac{\partial lnL\left(\mu,\sigma^2\right)}{\partial\sigma^2}=-\frac{n}{2\sigma^2}+\frac{1}{2\sigma^4}\sum^2_{i=1}\left(x_i-\mu\right)^2=0[/math][br] [br] 联合解得[br] [br] [math]\mu^{\cdot}=x_{avg}=\frac{1}{n}\sum^n_{i=1}x_i[/math][br] [math]\sigma^{\cdot2}=\frac{1}{n}\sum^n_{i=1}\left(x_i-x_{avg}\right)^2[/math]

似然函数有唯一解[math]\left(\mu^{\cdot},\sigma^{\cdot2}\right)[/math]，而且它一定是最大值点，因为[math]\mid\mu\mid\longrightarrow\infty[/math]或[math]\sigma^2\longrightarrow\infty[/math]或0 时，非负函数 [math]L(\mu,\sigma^2)\longrightarrow0[/math] ，是连续函数。由此 [math]\mu[/math] 和[math]\sigma^2[/math] 的极大似然估计值是[math]\left(\mu^{\cdot}，\sigma^{\cdot2}\right)[/math]。[br][br] 下面我们以模型的方式动态演示正态分布的极大似然估计，模型首先设定一个正态分布函数并呈现其图像，然后给出不同样本总量下正态分布模拟数，并按照上述公式求解其极大似然估计值 [math]\mu*[/math]和 [math]\sigma^{*2}[/math] ，然后描绘极大似然估计值为参数的正态分布图像，可以清晰呈现其与设定的正态分布曲线的贴合变化，并能给出具体的参数差额量。模型展现的一般趋势是，随着样本量的不断增加，其差额不断缩减，与原正态分布曲线的贴合度更高。如图 2-6-12所示高斯分布极大似然估计对比图。

[b]引例二：[/b]设样本服从均匀分布 [math]\left[a,b\right][/math]，则 [math]x[/math] 的概率密度函数为[br] [br] [math]f\left(x\right)=\frac{1}{b-a},a\le x\le b;0,其他[/math][br] [br] 对于样本 [math]D=\left\{x_1,x_2,...,x_n\right\},L\left(a,b\right)=\frac{1}{\left(b-a\right)^n},a\le x_i\le b,i=1,2,...,n;0,其他[/math]

很显然， [math]l\left(a,b\right)[/math]作为 [math]a[/math] 和 [math]b[/math] 的二元函数是不连续的，这时不能用导数来求解，而必须从极大似然估计的定义出发求 [math]L(a,b)[/math] 的最大值，为使 [math]L(a,b)[/math]达到最大，[math]b-a[/math]应该尽可能地小，但[math]b[/math]又不能小于 [math]Max(x_1,x_2,...,x_n)[/math]，否则 [math]L(aba,b)=0[/math]。类似地 [math]a[/math]不能大过 [math]Min\left(x_1,x_2,...,x_n\right)[/math]，因此，[br][br] a 和 b 的极大似然估计：[br] [br] [math]a^{\ast}=Min\left(x_1,x_2,...,x_n\right)[/math][br] [br] [math]b^{\ast}=Min\left(x_1,x_2,...,x_n\right)[/math]

[b]引例三：[/b]伯努利分布的极大似然函数公式推导。首先要说明的是，伯努利分布是一个离散型随机变量分布。如将随机变量 X  1表示抛硬币正面朝上，设正面朝上的概率为 p ，那么随机变量 X 的概率密度函数（Probability Density Function，PDF）为[br] [br] [math]p\left(x\right)=[/math]{[math]p\left(x\right)=p,x=1;1-p,x=0[/math]

需要说明的是，我们一般用大写字母[math]P[/math] 或 [math]F[/math] 来表示概率质量函数，而用小写字母[math]p[/math] 或者[math]f[/math]来表示概率密度函数。[br][br] 如逻辑分布（连续型随机变量分布）：[br][br] 分布函数:[math]F\left(x\right)=P\left(X\le x\right)=\frac{1}{1+e^{-\left(x-\mu\right)\slash\gamma}}[/math][br][br] 密度函数：[math]f\left(x\right)=F'\left(X\le x\right)=\frac{e^{-\left(x-\mu\right)\slash\gamma}}{\gamma\left(1+e^{-\left(x-\mu\right)\slash\lambda}\right)^2}[/math][br][br] 再如正态分布（也叫高斯分布，连续型随机变量分布）：[br][br] 分布函数：[math]F\left(x\right)=\frac{1}{\sqrt{2\pi}\sigma}\int^x_{-\propto}e^{-\frac{\left(x-\mu\right)^2}{2\sigma^2}}dx,-\propto[/math][br] 密度函数：[math]f\left(x\right)=\frac{1}{\sqrt{2\pi}\sigma}e^{\frac{\left(x-\mu\right)^2}{2\sigma^2}},-\propto[/math]

以上公式表达是一个二阶式，不利于算法推演，所以伯努利分布的概率密度函数也可写成[math]p\left(x\right)=p^x\left(1-p\right)^{1-x}[/math] 。当然，根据伯努利分布的计算方式，完全可以将其表达式写成[math]p\left(x\right)=px+\left(1-p\right)\left(1-x\right)[/math]，但这样的表达方式完全不能保证与二项分布特性的统一，也无法揭示与二项分布的本质关联，所以，一般都将伯努利分布的概率密度函数表达为[math]p\left(x\right)=p^x\left(1-p\right)^{1-x}[/math] 。[br][br] 从本质来讲，极大似然估计的过程是：通过若干次试验，观察结果并记录，利用试验的结果来推测某个参数，使得样本出现的概率（这里体现为似然函数）为最大，则称为极大似然估计。简单来讲，即“模型已定，参数未知”，接下来就需要求解伯努利分布的极大似然估计值。需要注意的是，伯努利极大似然估计函数的求解参数是 p 值。[br][br] 这里假设进行了 n 次伯努利试验，得到的样本集为[br][br] [math]D=\left\{x_1,x_2,...,x_n\right\}[/math][br][br] [br] 例如,[math]n=10,D_{n=10}\left\{0,1,0,1,1,1,0,1,0,0\right\}[/math]，由于每次试验是独立的，也就是说这些样本是独立同分布的，那么这些样本在同参数的伯努利试验中按序出现的概率就是这些样本单独出现的概率的乘积，这就是伯努利分布的似然函数（Likelihood Function）。[br] [br] [math]L\left(p\mid x_1,x_2,...,x_n\right)=\prod^n_{i=1}p\left(x_i\mid p\right)=\prod^n_{i=1}p^{^{_{x_i}}}\left(1-p\right)^{1-x_i}[/math][br] [br] 为便于求偏导计算极值，一般列出对数似然函数：[br][br] [math]L=ln\prod^n_{i=1}p\left(x_i\mid p\right)=\sum^n_{i=1}lnp\left(_{x_i}\mid p\right)=\sum^n_{i=1}\left[x_ilnp+\left(1-x_i\right)ln\left(1-p\right)\right][/math][br][br] 根据极限求导理论，要想使这一函数取最大值，就需要求出导函数等于 0 时的 [math]p[/math] 值，即函数取最大值时的参数值。[br][br] [math]p=arg_{_{p_{ }}}maxL\left(p\mid X\right)=arg_{_{_p}}max\sum^n_{i=1}\left[x_ilnp+\left(1-x_i\right)ln\left(1-p\right)\right][/math][br][br] [math]\frac{\partial L}{\partial p}=\sum^n_{i=1}\left(\frac{x_i}{p}+\frac{1-x_i}{p-1}\right)=\sum^n_{i=1}\frac{p-x_i}{p\left(p-1\right)}=0[/math][br] [br] 由上式可得[br] [br] [math]\sum^n_{i=1}\left(p-x_i\right)=0\Longrightarrow p=\frac{1}{n}\sum^n_{i=1}x_i[/math]

上式 [math]p[/math] 的精度与样本总量的大小密切相关，显然，一般来说，样本总量越大， [math]p[/math]值越接近设定的模型参数值。为形象地表示这一趋势性，以模型的方式动态演示。模型中，先设定一个伯努利分布，然后用不同数量的伯努利随机数计算最大似然估计的参数[math]p_{MLE}[/math]值，其差额[math]margin_p=\mid p-p_{MLE}\mid[/math] 。可以明显看出，随着样本总量的增加，其差额的一般趋势是逐渐缩减的，如图 2-6-13 所示伯努利分布极大似然估计对比图。

总结，求最大似然估计量[math]\theta[/math]的一般步骤：[br][br] （1）写出似然函数；[br][br] （2）对似然函数取对数，并整理；[br][br] （3）求导数；[br][br] （4）解似然方程。[br][br] 最大似然估计的特点：[br][br] ① 比其他估计方法更加简单；[br][br] ② 收敛性：无偏或者渐近无偏，当样本数目增加时，收敛性质会更好；[br][br] ③ 如果假设的类条件概率模型正确，则通常能获得较好的结果。但如果假设模型出现偏差，将导致非常差的估计结果。[br] [br] 再次回到对逻辑回归函数的极大似然估计的求解问题，其数学模型公式为[math]p\left(Y=1\mid x\right)=\frac{1}{1+e^{-\left(\omega^{Tx+b}\right)}}[/math]，因为逻辑回归从本质上来讲是解决二分类问题的数学模型，其分类要么是 0，要么是 1，与伯努利分布极大似然估计的求解思路有一致性。因此，设：[br] [br] [math]P\left(Y=1\mid x\right)=p\left(x\right)[/math][br] [br] [math]P\left(Y=0\mid x\right)=1-p\left(x\right)[/math][br][br] 则其似然函数为（请借鉴伯努利分布的极大似然估计函数的求解过程)[br][br] [math]L\left(\omega^T,b\right)=\sum\left[y_ilnp\left(x_i\right)+\left(1-y_i\right)ln\left(1-p\left(x_i\right)\right)\right][/math][br][br] [math]=\sum\left[y_ilnp\left(x_i\right)+ln\left(1-p\left(x_i\right)\right)\right]-y_iln\left[1-p\left(x_i\right)\right][/math][br] [br] [math]=\sum\left[y_iln\frac{p\left(x_i\right)}{1-p\left(x_i\right)}+ln\left(1-p\left(x_i\right)\right)\right][/math][br][br] 将[math]p\left(x_i\right)=\frac{1}{1+e^{-\left(\omega^Tx_i+b\right)}}[/math],即[math]p\left(x_i\right)=\frac{e^{\left(\omega^Tx_i+b\right)}}{1+e^{\left(\omega^Tx_i+b\right)}}[/math]代入上式，可得 [br][br] [math]L\left(\omega^T,b\right)=\sum\left[y_i\left(\omega^Tx_i+b\right)-ln\left(1+e^{\left(\omega^Tx_i+b\right)}\right)\right][/math]

[b] （二）梯度下降[/b][br][br] 一般来说，关于求解函数的最优解（极大值和极小值），在数学中一般会对函数求导，然后让导数等于 0，获得方程，最后通过解方程直接得到结果。但是在机器学习中，函数常常是多维高阶的，得到导数为 0 的方程后很难直接求解（有些时候甚至不能求解），逻辑回归的最大似然估计函数就属于无法求解的情况，所以就需要通过其他方法来获得函数的极值，而[br]梯度下降就是其中一种方法。[br][br] 关于梯度下降，先从一个简单的二次函数来举例，比如 [math]y=x^2[/math] 函数， [math]y[/math] 的一阶导数为[math]y'=2x[/math] ，令[math]y'=2x=0[/math] ，即可求得该函数的最小极值点为 (0, 0) 。[br][br] 这里不采用导数求解法，用梯度下降的方法来模拟其求解的迭代过程。先给出梯度下降的一般公式：[br][br] 设有函数 [math]J\left(\omega_i\right)[/math]，对 [math]\omega_i^j[/math]求偏导，得 [math]g_i^j=\frac{\partial J\left(\omega_i\right)}{\partial\omega_i^j}，[/math]将 [math]g^j_i[/math]作为 [math]\omega_j[/math]的下降方向，其下降幅度为[br][math]\omega_i^{k+1}=\omega_i^k-\alpha g_i[/math] ，其中 [math]k[/math] 为迭代次数， [math]\alpha[/math]为步长值，每次更新参数后，可以通过比较[math][/math][math]\parallel J\left(\omega^{k+1}\right)-J\left(\omega^k\right)\parallel[/math]小于阈值或者到达最大迭代次数来停止迭代。[br][br] 对于简单二次函数，将初始值选为[math]x=-8[/math] ，步长值[math]\alpha=0.1[/math] ，以迭代 16 次为停止标志。需要说明的是，这里只是作为简单案例来演示梯度下降的数学原理，在实际运算中，即使迭代值要小得多，但迭代次数也会达到几百上千次，因此必须要按照算法编程，用计算机运算来实现。[br][br] 表 2-6-2 为每次迭代的计算结果，同时以图示的方式显示。[br][br] 表 2-6-2 二次函数梯度下降表[br][img]data:image/png;base64,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[/img]

以上案例中，将步长设置为 0.1，看上去是逐步收敛的，但是不同的 [math]\alpha[/math] 值的收敛程度是不一样的，如果将[math]\alpha[/math] 值设置过大，甚至会造成不收敛。仍以该二次函数举例，不同的 [math]\alpha[/math] 值其y 值的梯度降幅呈现不同的形态，如图 2-6-14 所示。[br][center][img]https://s21.ax1x.com/2025/02/16/pEKW4R1.png[/img][br] 图 2-6-14 不同 [math]\alpha[/math] 值 [math]y[/math] 的梯度降幅[/center]

由图 2-6-14 可见，选择相对正确的值对极大似然估计函数的收敛相当重要。梯度下降的学习率不能太大，理论上学习率越小越好[br] [br] 关于梯度下降的学习率，这里有必要做进一步的说明。如图 2-6-15 所示，一个简单的二次函数，如果学习率选择不当，就会造成梯度下降无法达到效果的情况。图 2-6-15（a）学习率为 0.1，是正常梯度下降的效果，图 2-6-15（b）学习率为 0.9，其梯度下降就产生震荡效应，梯度下降就无法得到满意效果。在实际应用中，梯度下降的学习率一般取千分之一精度，才有可能取得满意的迭代效应。[br][table][tr][td][img]https://s21.ax1x.com/2025/02/16/pEKWoM6.png[/img][br] （a）图[/td][td][/td][td][img]https://s21.ax1x.com/2025/02/16/pEKWbZD.png[/img][br] （b）图[/td][/tr][/table][br] 图 2-6-15 梯度下降学习率示意

为动态展示梯度下降不同学习率的变化状态，请在下图操作。