pytorch集智-2单车预测器

完整代码在个人主页简介链接pytorch路径下可找到

1 单车预测器1.0

1.1 人工神经元

对于sigmoid函数来说，w控制函数曲线的方向，b控制曲线水平方向位移，w'控制曲线在y方向的幅度

1.2 多个人工神经元

模型如下

数学上可证，有限神经元绘制的曲线可以逼近任意有限区间内的曲线（闭区间连续函数有界）

1.3 模型与代码

通过训练可得到逼近真实曲线的神经网络参数

通过梯度下降法寻找局部最优（如何寻找全局最优后面考虑）

思考 n个峰需在一个隐层要多少隐单元？材料说3个峰10个单元就够了，理论上算，最少需要5个，可能保险起见，加其他一些不平滑处，就弄了10个

初次代码如下

python 复制代码

from os import path
import numpy as np
import pandas as pd
import torch
import torch.optim as optim
import matplotlib.pyplot as plot

DATA_PATH = path.realpath('pytorch/jizhi/bike/data/hour.csv')

class Bike():
    def exec(self):
        self.prepare_data_and_params()
        self.train()
        
    def prepare_data_and_params(self):
        self.data = pd.read_csv(DATA_PATH)
        
        counts = self.data['cnt'][:50]
        self.x = torch.FloatTensor(np.arange(len(counts)))
        self.y = torch.FloatTensor(np.array(counts, dtype=float))
        self.size = 10
        self.weights = torch.randn((1, self.size), requires_grad=True)
        self.biases = torch.randn((self.size), requires_grad=True)
        self.weights2 = torch.randn((self.size, 1), requires_grad=True)

    def train(self):
        rate = 0.001
        losses = []
        x, y = self.x.view(50, -1), self.y.view(50, -1) # reshape
        for num in range(30000):
            hidden = x * self.weights + self.biases
            hidden = torch.sigmoid(hidden)
            predictions = hidden.mm(self.weights2)
            loss = torch.mean((predictions - y) ** 2)
            losses.append(loss.data.numpy())
            if num % 3000 == 0:
                print(f'loss: {loss}')
            loss.backward()
            
            self.weights.data.add_(- rate * self.weights.grad.data)
            self.biases.data.add_(- rate * self.biases.grad.data)
            self.weights2.data.add_(- rate * self.weights2.grad.data)
            
            self.weights.grad.data.zero_()
            self.biases.grad.data.zero_()
            self.weights2.grad.data.zero_()
        
        # plot loss
        #plot.plot(losses)
        #plot.xlabel('epoch')
        #plot.ylabel('loss')
        #plot.show()
        
        # plot predict
        x_data = x.data.numpy()
        plot.figure(figsize=(10, 7))
        xplot, = plot.plot(x_data, y.data.numpy(), 'o')
        yplot, = plot.plot(x_data, predictions.data.numpy())
        plot.xlabel('x')
        plot.ylabel('y')
        plot.legend([xplot, yplot], ['Data', 'prediction with 30000 epoch'])
        plot.show()

def main():
    Bike().exec()

if __name__ == '__main__':
    main()

拟合有问题，原因是拟合次数不够，为啥不够？从sklearn学习了解到，神经网络对输入参数敏感，一般来说需要对数据做标准化处理。具体来说，第一个隐层输出范围变成-50-50，0.0001学习率情况下100000次也不够，可以对数据做预处理，减小x跨度，变为0-1，可加快训练速度，进行如下改动再次训练

python 复制代码

self.x = torch.FloatTensor(np.arange(len(counts))) / len(counts)

正确了，再取50个点预测一下

python 复制代码

    def predict_and_plot(self):
        counts_predict = self.data['cnt'][50:100]
        x = torch.FloatTensor((np.arange(len(counts_predict), dtype=float) + 50) / 100)
        y = torch.FloatTensor(np.array(counts_predict, dtype=float))
        
        # num multiply replace matrix multiply
        hidden = x.expand(self.size, len(x)).t() * self.weights.expand(len(x), self.size)
        hidden = torch.sigmoid(hidden)
        predictions = hidden.mm(self.weights2)
        loss = torch.mean((predictions - y) ** 2)
        print(f'loss: {loss}')
        
        x_data = x.data.numpy()
        plot.figure(figsize=(10, 7))
        xplot, = plot.plot(x_data, y.data.numpy(), 'o')
        yplot, = plot.plot(x_data, predictions.data.numpy())
        plot.xlabel('x')
        plot.ylabel('y')
        plot.legend([xplot, yplot], ['data', 'prediction'])
        plot.show()

预测失败，可能是过拟合

2 单车预测器2.0

2.1 数据预处理

通过上节学习和之前写的sklearn博客发现，神经网络训练前需要预处理数据，主要有1数值型变量需要范围标准化2数值型类型变量需处理为onehot。标准化可用sklearn的scaler，也可手动标准化，类型变量可用pd.get_dummies操作。直接开始操作

python 复制代码

    def prepare_data_and_params_2(self):
        # type columns to dummy
        self.data = pd.read_csv(DATA_PATH)
        dummy_fields = ['season', 'weathersit', 'mnth', 'hr', 'weekday']
        for each in dummy_fields:
            dummies = pd.get_dummies(self.data[each], prefix=each, drop_first=False)
            self.data = pd.concat([self.data], dummies)
        drop_fields = ['season', 'weathersit', 'mnth', 'hr', 'weekday', 'instant', 'dteday', 'workingday', 'atemp']
        self.data = self.data.drop(drop_fields, axis=1)
        
        # decimal columns to scaler
        quant_features = ['cnt', 'temp', 'hum', 'windspeed']
        scaled_features = {}
        for each in quant_features:
            mean, std = self.data[each].mean(), self.data[each].std()
            scaled_features[each] = [mean, std]
            self.data.loc[:, each] = (self.data[each] - mean) / std
            
        self.tr, self.te = self.data[:-21 * 24], self.data[-21 * 24:]
        target_fields = ['cnt', 'casual', 'registered']
        self.xtr, self.ytr = self.tr.drop(self.tr.drop[target_fields], axis=1), self.tr[target_fields]
        self.xte, self.yte = self.te.drop(self.te.drop[target_fields], axis=1), self.te[target_fields]
        self.x = self.xtr.values
        y = self.ytr.values.astype(float)
        self.y = np.reshape(y, [len(y), 1])        
        self.loss = []

2.2 构造神经网络

python 复制代码

    def train_and_plot2(self):
        input_size = self.xtr.shape[1]
        hidden_size=10
        output_size=1
        batch_size=128
        neu = torch.nn.Sequential(
            torch.nn.Linear(input_size, hidden_size),
            torch.nn.Sigmoid(),
            torch.nn.Linear(hidden_size, output_size)
        )
        cost = torch.nn.MSELoss()
        optimizer = torch.optim.SGD(neu.parameters(), lr=0.01)

2.3 数据批处理

为啥要批处理？如果数据太多，每个iter直接处理所有数据会比较慢

python 复制代码

        for i in range(1000):
            batch_loss = []
            for start in range(0, len(self.x), batch_size):
                end = start + batch_size if start + batch_size < len(self.x) else len(self.x)
                xx = torch.FloatTensor(self.x[start:end])
                yy = torch.FloatTensor(self.y[start:end])
                predictions = neu(xx)
                loss = cost(predictions, yy)
                optimizer.zero_grad()
                loss.backward()
                optimizer.step()
                batch_loss.append(loss.data.numpy())
            if i % 100 == 0:
                self.loss.append(np.mean(batch_loss))
                print(i, np.mean(batch_loss))
        plot.plot(np.arange(len(self.loss)) * 100, self.loss)
        plot.xlabel('epoch')
        plot.ylabel('MSE')
        plot.show()

2.4 测试神经网络

原始数据是从2011-2012两个完整年，按教材，取2012最后21天作测试集预测

python 复制代码

    def predict_and_plot2(self):
        targets = self.yte['cnt']
        targets = targets.values.reshape([len(targets), 1]).astype(float)
        x = torch.FloatTensor(self.xte.values.astype(float))
        y = torch.FloatTensor(targets)
        predict = self.neu(x)
        predict = predict.data.numpy()
        
        fig, ax = plot.subplots(figsize=(10, 7))
        mean, std = self.scaled_features['cnt']
        ax.plot(predict * std + mean, label='prediction')
        ax.plot(targets * std + mean, label='data')
        ax.legend()
        ax.set_xlabel('date-time')
        ax.set_ylabel('counts')
        dates = pd.to_datetime(self.rides.loc[self.te.index]['dteday'])
        dates = dates.apply(lambda d: d.strftime('%b %d'))
        ax.set_xticks(np.arange(len(dates))[12::24])
        ax.set_xticklabels(dates[12::24], rotation=45)
        plot.show()

发现2012最后21天前半段还行，后半段有差异，看日历发现临近圣诞节，可能不能用正常日程预测

2.5 改进与分析（重要）

这节有啥用？上节圣诞节预测不准，为啥？这节可以通过分析神经网络回答这个问题

怎么分析？本节主要通过分析神经网络参数来在底层寻找原因，帮助分析问题

在异常处将多个神经源绘制独自的曲线，绘制其图像，分析找原因，比如趋势相同，趋势相反这种曲线，重点分析对象。适用于神经元较少，可以一个一个神经元看，多了就不行了