L2 · Jounery2Stellar

L2

 - DataSet
 - Model
 - Training
 - Inferring

Training methis

Supppose that students would get y points in final exams . if they spent x hours in paper

x	y
1	2
2	4
3	6
4	?
4 hours -> model ->?points

Input                 Prediction

supervised Learning:Test Set用于测试泛化能力前3行Training Set 第4行Test Set

kaggle

训练 $(x,y)$ $D(x,y)$ 为 $x,y$ 的联合分布采样set 是否能够达到 $D(x,y)$ 的目标

大数定律维度的诅咒即便数据量很大依旧难以表示真实的分布

真实的场景和训练存在差异 **训练集过好 —> 过拟合但我们希望我们的模型能够有较好的泛化能力因而常常我们将训练集分为 Train和Dev两部分。Dev开发集对模型泛化能力进行评估

Model Design

What would be the best model for the data **Linear Model? 最初我们会选择LInear作为实验若效果不好则换模型 $f(x)=w*x+b$ To simplify the model $\hat y=x*w$ 值得注意的是 $\hat y$ 加上标的y一般表示预测的结果 The machine starts with a random guess w=random value Evalvate Model

Training Loss

$loss=(\hat y-y)^2=(x*w-y)^2$ $\hat y$ 预测值 y 真实值 **Mean Square Error $\text{cost} = \frac{1}{N} \sum_{n=1}^{N} \left( \hat{y}_n - y_n \right)^2$ 平均平方误差 : MSE

穷举 穷举w的所有取值，观察MSE曲线找到最优权重

import numpy as np
import matplotlib.pyplot as plt

x_data=[1.0,2.0,3.0]
y_data=[2.0,4.0,6.0]

def forward(x):
	return x*w
def loss(x,y):
	y_pred = forward(x)
	return (y_pred-y)*(y_pred-y)
w_list=[]
mse_list=[]
for w in np.arrange(0.0,4.1,0.1)
	printf('w=',w)
	l_sum=0
	for x_val,y_val in zip(x_data,y_data)
		y_pred_val=forward(x_val)
		loss_val=loss(x_val,y_val)
		l_sum+=loss_val
		print('\t',x_val,y_val,y_pred_val,loss_val)
	print('MSE=',l_sum/3)
	w_list.append(w)
	mse_list.append(l_sum/3)

plt.plot(w_list,mse_list)
plt.ylabel('Loss')
plt.xlabel('w')
plt.show()

常常我们需要话这种plot表格但是横坐标一般是Epot轮数观察最佳轮数收敛点考虑模型训练过程中的存盘和持久化 Visdom

Test: **Try to use the model in right-side and draw the cost graph $\hat y=x*w+b$

**Tips: read the material of how to darw 3d graph Function np.meshgrid is very popular for drawing 3d graph