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| @@ -8,6 +8,8 @@ Consider the case of a single variable of interest y and a single predictor vari | |||||
| We have some data $D=\{x{\tiny i},y{\tiny i}\}$ and we assume a simple linear model of this dataset with Gaussian noise: | We have some data $D=\{x{\tiny i},y{\tiny i}\}$ and we assume a simple linear model of this dataset with Gaussian noise: | ||||
| 线性回归是一种线性建模方法，这种方法用来描述自变量与一个或多个因变量的之间的关系。在只有一个因变量y和一个自变量的情况下。自变量还有以下几种叫法：协变量，输入，特征；因变量通常被叫做响应变量，输出，输出结果。 | |||||
| 假如我们有数据$D=\{x{\tiny i},y{\tiny i}\}$，并且假设这个数据集是满足高斯分布的线性模型： | |||||
| ```csharp | ```csharp | ||||
| // Prepare training Data | // Prepare training Data | ||||
| var train_X = np.array(3.3f, 4.4f, 5.5f, 6.71f, 6.93f, 4.168f, 9.779f, 6.182f, 7.59f, 2.167f, 7.042f, 10.791f, 5.313f, 7.997f, 5.654f, 9.27f, 3.1f); | var train_X = np.array(3.3f, 4.4f, 5.5f, 6.71f, 6.93f, 4.168f, 9.779f, 6.182f, 7.59f, 2.167f, 7.042f, 10.791f, 5.313f, 7.997f, 5.654f, 9.27f, 3.1f); | ||||
| @@ -18,6 +20,8 @@ var n_samples = train_X.shape[0]; | |||||
| Based on the given data points, we try to plot a line that models the points the best. The red line can be modelled based on the linear equation: $y = wx + b$. The motive of the linear regression algorithm is to find the best values for $w$ and $b$. Before moving on to the algorithm, le's have a look at two important concepts you must know to better understand linear regression. | Based on the given data points, we try to plot a line that models the points the best. The red line can be modelled based on the linear equation: $y = wx + b$. The motive of the linear regression algorithm is to find the best values for $w$ and $b$. Before moving on to the algorithm, le's have a look at two important concepts you must know to better understand linear regression. | ||||
| 按照上图根据数据描述的数据点，在这些数据点之间画出一条线，这条线能达到最好模拟点的分布的效果。红色的线能够通过下面呢线性等式来描述：$y = wx + b$。线性回归算法的目标就是找到这条线对应的最好的参数$w$和$b$。在介绍线性回归算法之前，我们先看两个重要的概念，这两个概念有助于你理解线性回归算法。 | |||||
| ### Cost Function | ### Cost Function | ||||
| The cost function helps us to figure out the best possible values for $w$ and $b$ which would provide the best fit line for the data points. Since we want the best values for $w$ and $b$, we convert this search problem into a minimization problem where we would like to minimize the error between the predicted value and the actual value. | The cost function helps us to figure out the best possible values for $w$ and $b$ which would provide the best fit line for the data points. Since we want the best values for $w$ and $b$, we convert this search problem into a minimization problem where we would like to minimize the error between the predicted value and the actual value. | ||||
| @@ -65,4 +69,4 @@ When we visualize the graph in TensorBoard: | |||||
|  |  | ||||
| The full example is [here](https://github.com/SciSharp/TensorFlow.NET/blob/master/test/TensorFlowNET.Examples/LinearRegression.cs). | |||||
| The full example is [here](https://github.com/SciSharp/TensorFlow.NET/blob/master/test/TensorFlowNET.Examples/LinearRegression.cs). | |||||