从零和使用mxnet实现线性回归

1.线性回归从零实现

from mxnet import ndarray as nd
import matplotlib.pyplot as plt
import numpy as np
import time

num_inputs = 2num_examples = 1000w = [2,-3.4]b = 4.2x = nd.random.normal(scale=1,shape=(num_examples,num_inputs))y = nd.dot(x,nd.array(w).T) + by += nd.random.normal(scale=0.01,shape=y.shape)print(y.shape)

(1000,)

plt.scatter(x[:,1].asnumpy(),y.asnumpy())plt.show()

class LinearRegressor:    def __init__(self,input_shape,output_shape):        self.input_shape = input_shape        self.output_shape = output_shape        self.weight = nd.random.normal(scale=0.01,shape=(input_shape,1))        self.bias = nd.zeros(shape=(1))    def fit(self,x,y,learning_rate,epoches,batch_size):        start = time.time()        for epoch in range(epoches):            for batch_data in self.batches(x,y,batch_size):                x_batch,y_batch = batch_data[0],batch_data[1]                y_hat = self.forward(x_batch)                loss = self.mse(y_batch,y_hat)                error = y_hat - y_batch.reshape(y_hat.shape)                self.optimizer(x_batch,error,learning_rate)            print('epoch:{},loss:{:.4f}'.format(epoch+1,self.mse(y,self.forward(x)).asscalar()))        print('weight:',self.weight)        print('bias:',self.bias)        print('time interval:{:.2f}'.format(time.time() - start))            def forward(self,x):        return nd.dot(x,self.weight) + self.bias        def mse(self,y,y_hat):        m = len(y)        mean_square = nd.sum((y - y_hat.reshape(y.shape)) ** 2) / (2 * m)        return mean_square        def optimizer(self,x,error,learning_rate):        gradient = 1/len(x) * nd.dot(x.T,error)        self.weight = self.weight - learning_rate * gradient        self.bias = self.bias - learning_rate * error[0]            def batches(self,x,y,batch_size):        nSamples = len(x)        nBatches = nSamples // batch_size         indexes = np.random.permutation(nSamples)        for i in range(nBatches):            yield (x[indexes[i*batch_size:(i+1)*batch_size]], y[indexes[i*batch_size:(i+1)*batch_size]])        

lr = LinearRegressor(input_shape=2,output_shape=1)lr.fit(x,y,learning_rate=0.1,epoches=20,batch_size=200)

epoch:1,loss:5.7996epoch:2,loss:2.1903epoch:3,loss:0.9078epoch:4,loss:0.3178epoch:5,loss:0.0795epoch:6,loss:0.0204epoch:7,loss:0.0156epoch:8,loss:0.0068epoch:9,loss:0.0022epoch:10,loss:0.0009epoch:11,loss:0.0003epoch:12,loss:0.0001epoch:13,loss:0.0001epoch:14,loss:0.0001epoch:15,loss:0.0000epoch:16,loss:0.0000epoch:17,loss:0.0000epoch:18,loss:0.0001epoch:19,loss:0.0001epoch:20,loss:0.0001weight: [[ 1.999662] [-3.400079]]<NDArray 2x1 @cpu(0)>bias: [4.2030163]<NDArray 1 @cpu(0)>time interval:0.22

2.线性回归简洁实现

from mxnet import gluonfrom mxnet.gluon import loss as glossfrom mxnet.gluon import data as gdatafrom mxnet.gluon import nnfrom mxnet import init,autograd# 定义模型net = nn.Sequential()net.add(nn.Dense(1))# 初始化模型参数net.initialize(init.Normal(sigma=0.01))# 定义损失函数loss = gloss.L2Loss()# 定义优化算法optimizer = gluon.Trainer(net.collect_params(), 'sgd',{'learning_rate':0.1})epoches = 20batch_size = 200# 获取批量数据dataset = gdata.ArrayDataset(x,y)data_iter = gdata.DataLoader(dataset,batch_size,shuffle=True)# 训练模型start = time.time()for epoch in range(epoches):    for batch_x,batch_y in data_iter:        with autograd.record():            l = loss(net(batch_x),batch_y)        l.backward()        optimizer.step(batch_size)    l = loss(net(x),y)    print('epoch:{},loss:{:.4f}'.format(epoch+1,l.mean().asscalar()))print('weight:',net[0].weight.data())print('weight:',net[0].bias.data())print('time interval:{:.2f}'.format(time.time() - start))

epoch:1,loss:5.7794epoch:2,loss:1.9934epoch:3,loss:0.6884epoch:4,loss:0.2381epoch:5,loss:0.0825epoch:6,loss:0.0286epoch:7,loss:0.0100epoch:8,loss:0.0035epoch:9,loss:0.0012epoch:10,loss:0.0005epoch:11,loss:0.0002epoch:12,loss:0.0001epoch:13,loss:0.0001epoch:14,loss:0.0001epoch:15,loss:0.0001epoch:16,loss:0.0000epoch:17,loss:0.0000epoch:18,loss:0.0000epoch:19,loss:0.0000epoch:20,loss:0.0000weight: [[ 1.9996439 -3.400059 ]]<NDArray 1x2 @cpu(0)>weight: [4.2002025]<NDArray 1 @cpu(0)>time interval:0.86

3. 附:mxnet中的损失函数核初始化方法

• 损失函数

  all = ['Loss', 'L2Loss', 'L1Loss',
  'SigmoidBinaryCrossEntropyLoss', 'SigmoidBCELoss',
  'SoftmaxCrossEntropyLoss', 'SoftmaxCELoss',
  'KLDivLoss', 'CTCLoss', 'HuberLoss', 'HingeLoss',
  'SquaredHingeLoss', 'LogisticLoss', 'TripletLoss', 'PoissonNLLLoss', 'CosineEmbeddingLoss']

• 初始化方法

  ['Zero', 'One', 'Constant', 'Uniform', 'Normal', 'Orthogonal','Xavier','MSRAPrelu','Bilinear','LSTMBias','DusedRNN']