如何在感知器的批量训练期间计算偏差

Question

I am in the process of implementing batch training on a single node perceptron but cant figure out how to update my bias.

I am updating the weight as follow:

For each batch I am running the following temporary weight update during a single batch

# update weight_update where y[i] is the actual label and o1 is the predicted output and x[i] is the input
weight_update = weight_update + (self.weights + self.learning_rate * (y[i] - o1)*x[i])

then one a complete batch is completed I update the main weight in my class

# update main weights (self.weights) where len(x) is the number of samples
self.weights = self.weights + (weight_update / len(x))

Answer 1

I assume (y[i] - o1)*x[i]) is the partial derivative of loss function wrt weight, I am not sure what you used, but just assume you used -1/2 * (y[i] - o1)^2

now let o1 = wx + b, where w is weight matrix and b is bias vector, 
also let, L = -1/2 * (y[i] - o1)^2
you have already calculated dLdw = dLd(o1) * d(o1)dw = (y[i] - o1) * x

In a summilar way calculate dLdb, 
dLdb = dLd(o1) * d(o1)db
dLd(o1) = (y[i] - o1)
d(o1)db = d/db (wx + b) = 0 + 1 = 1
so dLdb = (y[i] - o1) * 1

Now this line,

weight_update = weight_update + (self.weights + self.learning_rate * (y[i] - o1)*x[i])  

There's no need to add the weights at this point, just add the gradients

weight_update += self.learning_rate * dLdw
# similarily
bias_update += self.learning_rate * dLdb  

When one batch is completed, just do

# update main weights (self.weights) and biases (self.biases)
# where len(x) is the number of samples
self.weights += (weight_update / len(x))
self.biases+= (bias_update / len(x)) 

# dont forget to set the values of weight_update, bias_update  to 0 

This is something I wrote a few days back (1 hidden layered network for the MNIST example) you might find this useful