ACTU PS5841 Data Science in Finance & Insurance – Autumn 2021 (Y. Wang) Assignment – 4
Assigned 10/19/21, Due 10/26/21
英国金融assignment代写 A plot of the fifinal 50 (or a reasonable number of) updates of the loss values vs the update number, in the following format
Problem 1. Gradient Descent 英国金融assignment代写
The file data.csv contains a small sample from the unobserved true data generating model,
y = 10 + 20x1 + 30x2 + s, s ∼ N (µ = 0, σ2 = 4)
You decide to use the data to fit a linear regression model, assuming homoscedasticity:
y = β0 + β1x1 + β2x2 + s 英国金融assignment代写
A.Usecode to calculate and report the theretical LSE value of β = (β0, β1, β2)T as well as the sum of squared residuals
B.Usea simple neural network with no hidden layers to perform the same regression involving the loss function
Please write your own code from scratch and refrain from using existing deep learning packages. 英国金融assignment代写
Use gradient descent or stochastic gradient descent, with the initial weights β(0) = (0.01, 0.01, 0.01)T as well as a fixed learning rate of your choice, to estimate the weights β = (β0, β1, β2)T of the neural network.
Report the following at convergence:
b1. The smallest loss your network is able to achieve b2. The corresponding learning rate
b2. The corresponding estimated ”optimal” weights 英国金融assignment代写
b3. The corresponding number of updates when your network reaches the ”optimal” estimates b4. A plot of the final 50 (or a reasonable number of) updates of the loss values vs the update number, in the following format
b4. A plot of the fifinal 50 (or a reasonable number of) updates of the loss values vs the update number, in the following format
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