WEBVTT 00:00:00.000 --> 00:00:09.169 音乐 00:00:09.869 --> 00:00:13.099 本片由斯坦福 00:00:13.099 --> 00:00:14.979 学术发展中心提供 00:00:23.299 --> 00:00:26.800 早上好，欢迎回来。今天我们要讲第三课。 00:00:26.800 --> 00:00:30.619 这节课 00:00:30.619 --> 00:00:33.360 我会涉及这些内容， 00:00:33.360 --> 00:00:34.320 当中有些 00:00:34.320 --> 00:00:37.920 我今天涉及的内容，可能感觉有点跳， 00:00:37.920 --> 00:00:44.440 我的意思是话题和话题之间有点跳跃。但是，这都是依照这节课的教学大纲走的，并且保证了逻辑的连续性。 00:00:44.440 --> 00:00:45.370 上节课，我们谈到， 00:00:45.370 --> 00:00:48.240 线性回归，今天我要谈谈 00:00:48.240 --> 00:00:52.500 一种叫做局部权重回归的适应算法。这是一种非常强大的 00:00:52.500 --> 00:00:57.120 算法，也可能是我前一任导师最喜爱的 00:00:57.120 --> 00:00:59.360 机器学习算法。随后我们会 00:00:59.360 --> 00:01:02.800 讨论一种线性回归的概率解释， 00:01:02.800 --> 00:01:07.650 并且用其展开我们的第一个 00:01:07.650 --> 00:01:08.910 逻辑回归的分类算法；课程中 00:01:08.910 --> 00:01:12.630 会有一段小插曲来略微谈谈感知算法， 00:01:12.630 --> 00:01:15.990 详细的内容会在之后的课程中展开； 00:01:15.990 --> 00:01:17.170 如果 00:01:17.170 --> 00:01:21.070 时间允许，我希望可以讲讲牛顿法，一种用于 00:01:21.070 --> 00:01:23.119 Logistic插值回归法的算法。 00:01:24.490 --> 00:01:30.510 好了，先让我们回忆下上节课的内容， 00:01:30.510 --> 00:01:33.790 回一下我定义的符号， 00:01:33.790 --> 00:01:35.090 我用 00:01:35.090 --> 00:01:37.620 X^i， 00:01:37.620 --> 00:01:40.960 Y^i来表达第i个训练样本。 00:01:46.730 --> 00:01:48.210 当 00:01:49.150 --> 00:01:51.790 我们谈及线性回归 00:01:52.900 --> 00:01:54.080 或者一般最小二乘时， 00:01:54.080 --> 00:01:56.140 我们用这个去表示 00:01:56.140 --> 00:01:58.179 我假定的H， 00:01:58.179 --> 00:02:00.830 在输入值为X^i 00:02:00.830 --> 00:02:02.420 时的预测值。 00:02:02.420 --> 00:02:04.070 我假定的公式， 00:02:04.070 --> 00:02:06.160 系数由向量 00:02:06.160 --> 00:02:08.399 系数𝛳表示， 00:02:08.399 --> 00:02:13.809 这就等于对j求和的theta_j*x_j 00:02:13.809 --> 00:02:15.549 00:02:15.549 --> 00:02:19.870 00:02:19.870 --> 00:02:22.409 写作theta转置乘以X 00:02:22.409 --> 00:02:25.079 我们按习惯约定X_0等于1 00:02:25.079 --> 00:02:29.409 对应我们线性回归模型里的 00:02:29.409 --> 00:02:30.919 截距项 00:02:30.919 --> 00:02:32.799 这里的小写n 00:02:32.799 --> 00:02:36.780 是我用的一个记号 00:02:36.780 --> 00:02:40.209 来表示训练集合中特征的数量 00:02:40.209 --> 00:02:43.689 所以在我们预测房屋售价的例子中， 00:02:43.689 --> 00:02:45.939 00:02:45.939 --> 00:02:50.559 00:02:50.559 --> 00:02:51.989 00:02:51.989 --> 00:02:54.709 00:02:54.709 --> 00:02:57.079 00:02:57.079 --> 00:03:01.260 00:03:01.260 --> 00:03:05.510 00:03:05.510 --> 00:03:07.209 00:03:07.209 --> 00:03:10.379 00:03:10.379 --> 00:03:12.439 00:03:12.439 --> 00:03:16.819 00:03:16.819 --> 00:03:17.769 00:03:17.769 --> 00:03:21.129 00:03:21.129 --> 00:03:23.059 00:03:23.059 --> 00:03:25.400 00:03:25.400 --> 00:03:26.809 00:03:26.809 --> 00:03:30.840 00:03:30.840 --> 00:03:32.349 00:03:32.349 --> 00:03:35.369 00:03:35.369 --> 00:03:38.889 00:03:38.889 --> 00:03:42.409 00:03:42.409 --> 00:03:46.419 00:03:46.419 --> 00:03:50.609 00:03:50.609 --> 00:03:55.099 00:03:55.099 --> 00:04:02.099 00:04:04.709 --> 00:04:07.690 00:04:07.690 --> 00:04:10.440 00:04:10.440 --> 00:04:14.279 00:04:14.279 --> 00:04:18.449 00:04:18.449 --> 00:04:22.059 00:04:22.059 --> 00:04:23.060 00:04:23.060 --> 00:04:28.210 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