![Explore Boston housing datasetexploringthe Boston housing dataset](img/image1_069.jpg)
*n* 是样本数, *x* *<sub>i</sub>* 和 *y* *<sub>i</sub>* 是要累加的各个样本,![Explore Boston housing datasetexploringthe Boston housing dataset](img/X_1_1.jpg)和![Explore Boston housing datasetexploringthe Boston housing dataset](img/Y_1_1.jpg)是每组的平均值。
`n`是样本数,`x`*<sub>i</sub>* 和`y`*<sub>i</sub>* 是要累加的各个样本,![Explore Boston housing datasetexploringthe Boston housing dataset](img/X_1_1.jpg)和![Explore Boston housing datasetexploringthe Boston housing dataset](img/Y_1_1.jpg)是每组的平均值。
在前面的示例中,我们正在创建一个 x 值列表,以使用`arange`函数绘制介于-3 和 3 之间的值,并在它们之间以 0.001 为增量。 因此,这些是图形上的 x 值,我们将使用这些值绘制*x* 轴。 *y*轴将成为正态函数`norm.pdf`,即在这些 x 值上正态分布的概率密度函数。 我们最终得到以下输出:
在前面的示例中,我们正在创建一个 x 值列表,以使用`arange`函数绘制介于-3 和 3 之间的值,并在它们之间以 0.001 为增量。 因此,这些是图形上的 x 值,我们将使用这些值绘制`x`轴。`y`轴将成为正态函数`norm.pdf`,即在这些 x 值上正态分布的概率密度函数。 我们最终得到以下输出:
前面的公式将皮尔逊相关性定义为*X* 和 *Y* 之间的协方差,除以 *X* 和 *Y*的标准偏差。 ,或者也可以将其定义为随机变量相对于均值的差值之和的期望均值除以 X 和 Y 的标准偏差。让我们以一个示例来理解。 让我们看一下各种汽车的行驶里程和马力,看看两者之间是否有关系。 这可以使用 SciPy 包中的`pearsonr`函数来实现:
前面的公式将皮尔逊相关性定义为`X`和`Y`之间的协方差,除以`X`和`Y`的标准偏差。 ,或者也可以将其定义为随机变量相对于均值的差值之和的期望均值除以 X 和 Y 的标准偏差。让我们以一个示例来理解。 让我们看一下各种汽车的行驶里程和马力,看看两者之间是否有关系。 这可以使用 SciPy 包中的`pearsonr`函数来实现:
![Time series forecasting using the ARIMA model](img/00185.jpeg)
其中![Time series forecasting using the ARIMA model](img/00186.jpeg)是从先前观察值和![Time series forecasting using the ARIMA model](img/00187.jpeg)中获知的模型的权重,是观察值 *t* 的残差。
其中![Time series forecasting using the ARIMA model](img/00186.jpeg)是从先前观察值和![Time series forecasting using the ARIMA model](img/00187.jpeg)中获知的模型的权重,是观察值`t`的残差。
![Time series forecasting using the ARIMA model](img/00189.jpeg)
***I**: Stands for **integrated**. For the ARIMA model to work, it is assumed that the time series is stationary or can be made stationary. A series is said to be stationary ([https://en.wikipedia.org/wiki/Stationary_process](https://en.wikipedia.org/wiki/Stationary_process)) if its mean and variance doesn't change over time.
*`I`: Stands for **integrated**. For the ARIMA model to work, it is assumed that the time series is stationary or can be made stationary. A series is said to be stationary ([https://en.wikipedia.org/wiki/Stationary_process](https://en.wikipedia.org/wiki/Stationary_process)) if its mean and variance doesn't change over time.
![Time series forecasting using the ARIMA model](img/00190.jpeg)和![Time series forecasting using the ARIMA model](img/00191.jpeg)对于任何 *t* , *m* 和 *k,*都是相同的,其中 *F* 是联合概率分布 。
![Time series forecasting using the ARIMA model](img/00190.jpeg)和![Time series forecasting using the ARIMA model](img/00191.jpeg)对于任何`t`,`m`和 *k,*都是相同的,其中`F`是联合概率分布 。
是时间序列的平均值,![Time series forecasting using the ARIMA model](img/00187.jpeg)是序列中的残差,![Time series forecasting using the ARIMA model](img/00195.jpeg)是滞后残差的权重。
***Adjacency matrix**: Represents the graph using an*n* by *n* matrix (we'll call it *A*), where *n* is the number of vertices in the graph. The vertices are indexed using 1 to *n* integers. We use ![Graph representations](img/00214.jpeg) to denote that an edge exists between vertex *i* and vertex *j* and ![Graph representations](img/00215.jpeg) to denote that no edge exists between vertex *i* and vertex *j*. In the case of undirected graphs, we would always have ![Graph representations](img/00216.jpeg)![Graph representations](img/00217.jpeg) because the order doesn't matter. However, in the case of digraphs where order matters, *A**<sub class="calibre29">i,j</sub>* may be different from *A**<sub class="calibre29">j,i</sub>*. The following example shows how to represent a sample graph in an adjacency matrix both directed and undirected:
***Adjacency matrix**: Represents the graph using an`n`by`n`matrix (we'll call it `A`), where`n`is the number of vertices in the graph. The vertices are indexed using 1 to`n`integers. We use ![Graph representations](img/00214.jpeg) to denote that an edge exists between vertex`i`and vertex`j`and ![Graph representations](img/00215.jpeg) to denote that no edge exists between vertex`i`and vertex`j`. In the case of undirected graphs, we would always have ![Graph representations](img/00216.jpeg)![Graph representations](img/00217.jpeg) because the order doesn't matter. However, in the case of digraphs where order matters,`A`<subclass="calibre29">i,j</sub>* may be different from`A`<sub class="calibre29">j,i</sub>*. The following example shows how to represent a sample graph in an adjacency matrix both directed and undirected:
* **Shortest path betweenness**: Measure based on how many times the given vertex is part of the shortest path between any two nodes. The intuition is that the more a vertex contributes to shortest paths, the more important it is. The mathematical equation for shortest path betweenness is provided here: