Page wikipedia of a Multiclass classification
this strategy involves training a single classifier per class in our case with have 4 class / houses / classifier
our dataset is compose of a 2 layer matrix
j = column / lectures
i = index / line
x = Values associate with > i and j
m = i max
y represent if our the validity ?
y = 1 >> the element is of the class
y = 0 >> the element is not of the class
J(θ) = (−1/m) m ∑ i=1 yi log( hθ(xi)) + (1 − yi) log(1 − hθ(xi))
we have 2 part in this equation if y = 1 it activate this part of the equation
yi log( hθ(xi))
and if y = 0
(1 − yi) log(1 − hθ(xi))
this is the hypothesis function for the input x it calculate the probability that the input data x belongs to the class
x = input data
h = hypothesis
theta = θ = this is the parameter we are tweaking during training >
hθ(x) = g(θT x)
probably of this form : θ0 * x0 + θ1 * x1 + θn * xn
Page wikipedia of a sigmoide function
this is a sigmoide function
L = Limit
g(z) = L/(1 + e^−z)
this is our activating function the activation function is usually an abstraction representing the probability/(activation) of a single neuron it will normalize our data between 0 and 1 Page wikipedia of a Logistic function this is a logistique function, its a sigmoide with L = 1
g(z) = 1/(1 + e^−z)
∂/∂θj J(θ) = 1/m m∑ i=1 (hθ(xi) − yi)xij
∂/∂θj J(θ) : This expression represents the partial derivative of the cost function J(θ) with respect to the j-th parameter θj.
i eme element of the j eme feature xij
this is the difference between our model prediction and the actual target
i being an index
it is the difference between the hypothesis hθ(xi) and the actual target yi
diff = (hθ(xi) − yi)
our goal is to make the sum of all the element(prediction * i do not know) in our dataset
m∑ i=1
rapporter au nombre d'element dans notre dataset
1/m
tweaking thetas during training to produce weight
takes as parameters the weight of the previous model create a houses.csv
we test houses.csv with the scikit-learn lib accuracy score wiki python scikit function accuracy