如是我闻： 面试的是一家在加拿大的初创公司，我想他们是需要清纯质朴的廉价劳动力干点杂活，非常符合我目前的情况。祝我成功吧。以下是他们的面试作业题（take home questions），主要考察了一些基础知识，分享给各位同修做参考。

Question 1

1. Explain the principle of the gradient descent algorithm.

Answer

Question 2

2.Given the target function:
$$\hat{y}(w_0,w_1)=w_0+w_1{x}_i$$
And Error Function
$$E=(y_i-\hat{y}(w_0,w_1){)}^2$$
Assuming that a set of training examples $N$ is provided, where each training example $n\in N$ is associated with the target output $y_n$.

Find the cost function, $J$, and derive $\frac{\partial J}{\partial w_0}$ and $\frac{\partial J}{\partial w_1}$

Answer

Question3

How would you design a Neural Network model to classify the diamonds from the crosses with as few as nodes and layers as possible.

Answer

Question4

Given the simple logistic regression:
$${\hat{y}}^{(n)}=\frac{1}{1+exp(-x^{(n)}\hat{w})}$$

Where: $\hat{w}=-log4$

Given input features $x=\left[\begin{array}{c}1\\ 0\\ 1\end{array}\right]$ and Ground Truth $y=\left[\begin{array}{c}0\\ 0\\ 1\end{array}\right]$

Using thresholds t ∈ { 0 , 0.25 , 1 } t\in \{0,0.25,1\} t∈{0,0.25,1}, draw the ROC curve.

Answer

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