Ask Ghassem - Recent questions tagged ml-midterm

How to calculate feed-forward (forward-propagation) in neural network for classification?

Wed, 02 Oct 2024 14:47:26 +0000

For the following neural network, calculate accuracy of classification, given these settings

How to calculate the residual errors, (MSE),(MAE), and (RMSE)?

Fri, 27 Jan 2023 04:09:28 +0000

Given the following sample dataset with 5 samples and 2 features:

Sample	Feature 1	Feature 2	Actual Value	Predicted Value
1	2	3	4	6
2	3	4	5	6
3	4	5	6	7
4	5	6	7	8
5	6	7	8	9

Calculate the residual errors, mean squared error (MSE), mean absolute error (MAE), and root mean squared error (RMSE) using a sample model.

How to calculate residual errors for linear regression and interpret regression metrics?

Tue, 18 Feb 2020 18:30:51 +0000

Assuming we have a linear regression equation and some data points (sample), how can we calculate residual error for each data point, and total cost based on the metrics such as MAE, MSE, RMSE, MAPE, or MPE if we have their formula?

How to calculate the probability and accuracy of a Logistic Regression classifier?

Mon, 03 Feb 2020 20:31:49 +0000

How to solve this problem?

https://i.imgur.com/8urywpf.jpg

Q1) Complete the ? sections

Q2) Accuracy of system if threshold = 0.5?

Q3) Accuracy of system if threshold = 0.95?

How to calculate Accuracy, Precision, Recall or F1?

Mon, 27 Jan 2020 19:22:26 +0000

In the following example, calculate Accuracy, Precision, Recall or F1?

https://i.imgur.com/OezFpqC.png

How to perform a classification or regression using k-NN?

Thu, 27 Jun 2019 02:54:42 +0000

Suppose, you have given the following dataset where x and y are the 2 features and color Red or Blue is the target variable.

a) A new data point $x=1$ and $y=1$ is given. Using Euclidean distance in 3-NN, what you predict as the color for this data point?

Dataset
x	y	Color
-1	1	Red
0	1	Blue
0	2	Red
1	-1	Red
1	0	Blue
1	2	Blue
2	2	Red
2	3	Blue

b) Now assume we have the following dataset and the target value is the price. A new data point $x=1$ and $y=1$ is given. Using Euclidean distance in 3-NN. What would be the estimated price?

Dataset
x	y	Price
-1	1	$100
0	1	$50
0	2	$20
1	-1	$40
1	0	$30
1	2	$40
2	2	$70
2	3	$30

How to calculate k-means clustering with a numerical example?

Thu, 27 Jun 2019 02:16:32 +0000

Use the k-means algorithm and Euclidean distance to cluster the following 8 examples into 3 clusters:

$A1=(2,10), A2=(2,5), A3=(8,4), A4=(5,8), A5=(7,5), A6=(6,4), A7=(1,2), A8=(4,9)$.

Suppose that the initial seeds (centers of each cluster) are $A1$, $A4$ and $A7$. Run the k-means algorithm for 1 epoch only. At the end of this epoch show:

a) The new clusters (i.e. the examples belonging to each cluster)

b) The centers of the new clusters

c) Draw a 10 by 10 space with all the 8 points and show the clusters after the first epoch and the new centroids.

d) How many more iterations are needed to converge? Draw the result for each epoch

How to calculate Softmax Regression probabilities in this example?

Thu, 04 Apr 2019 18:20:53 +0000

1) What will be the probability of an iris with petal length = 4.6 and petal width = 1.7 to be classified as Virginica?

2) What will be the probability of Virginica, if we use all features petal length = 4.6 and petal width = 1.7, sepal length = 5.5 and sepal width = 3.0 with the same weight initialization?

How to calculate feed-forward (forward-propagation) in neural network?

Thu, 04 Apr 2019 15:54:17 +0000

In the figure below, a neural network is shown. Calculate the following:

1) How many neurons do we have in the input layer and the output layer?

2) How many hidden layers do we have?

3) If all the weights initialized with 1 ($w1=w2=w3=...=w19=1$), what is the output of this network after feed-forward for the sample shown in the figure (X = (x1,x2,x3) = (2,5,3) and y=10)? What is the error of the network ($\text { Error }=\frac{1}{2}(\hat{y}-y)^{2}$)? Assume activation functions for all neurons except the output neuron is $f(z)=z$.

4) If we change the activation function of all the neurons in the second hidden layer to Sigmoid ($S(x)=\frac{1}{1+e^{-x}}=\frac{e^{x}}{e^{x}+1}$), what would be the output of the network after this change? Calculate the error as well.

https://i.imgur.com/rtqPiRa.jpg

How to calculate Softmax Regression probabilities?

Thu, 21 Mar 2019 16:11:09 +0000

The scatter plot of Iris Dataset is shown in the figure below. Assume Softmax Regression is used to classify Iris to Setosa, Versicolor, or Viriginica using just petal length and petal width. If all the weights required for Softmax Regression initialized to 0.5 and the network includes bias nodes:

1) Write the weight vectors and equations for calculating the class probabilities.

2) We have a new iris and we have measured petal length = 4.5 and petal width = 1.6. Using the above initial model, what would be the result of classification?

3) If we change all the weights related to the class blue to 1 and keep all other weights 0.5, what will be the predicted class?

How to calculate LogLoss in logistic regression?

Mon, 18 Mar 2019 20:34:40 +0000

The dataset of pass/fail in an exam for 5 students is given in the table below. If we use Logistic Regression as the classifier and assume the model suggested by the optimizer will become the following for Odds of passing a course:

$\log_e(Odds) = -64 + 2 \times hours$

1) How to calculate the loss of model for the student who studied 33 hours?

2) What is the total loss of the model given in equation below?

$Logloss = -\frac{1}{N} \sum_{i=1}^N(y_i\log_e(p_i) + (1 - y_i)\log_e(1 - p_i))$

How to calculate probability in Logistic Regression?

Mon, 18 Mar 2019 20:22:35 +0000

$\log (Odds) = -64 + 2 \times hours$

1) How to calculate the probability of Pass for the student who studied 33 hours?

2) At least how many hours the student should study that makes sure will pass the course with the probability of more than 95%?