Ask Ghassem - Recent questions tagged ai-final

How to use Genetic Algorithm to optimize a function?

Tue, 07 Dec 2021 23:53:51 +0000

Assume the function is defined as $f(x,y)=x^2+y^2-4xy$, and $1\leq x \leq 4,1\leq y \leq 4$. The Genetic Algorithm is selected to maximize the function. If the first population for pairs of $(x,y)$ is defined as $S=\{A=(1,2), B=(2,1), C=(2,2), D=(2,3), E=(3,1) \}$.

a) Calculate the fitness of each of individuals (A,B,C,D,E) in population if: $\text{fitness function}=f(x,y)$
b) Calculate the probability of each individual and sort them in descending order. Which individual has the maximum fitness (probability)? $p_{i}=\frac{f_{i}}{\sum_{j=1}^{N} f_{j}}$
c) Draw the roulette wheel and calculate the boundaries for each individual
d) If we use two individuals and their arithmetic mean for crossover each time, and for mutation, we add 0.1 to x and subtract 0.1 from y for each individual created after crossover, what will be the next population with five members?
For part (d), use the following random numbers in order whenever you need them in the selection process:
$\text{random numbers} = \{0.780,0.220,0.776,0.507,0.822,0.765,0.288,0.881,0.895,0.421\}$

How to create a Decision Tree using the ID3 algorithm?

Wed, 01 Dec 2021 11:26:02 +0000

NASA wants to be able to discriminate between Martians (M) and Humans (H) based on the
following characteristics: Green ∈{N, Y }, Legs ∈{2, 3}, Height ∈{S, T}, Smelly ∈{N, Y }.
Our available training data is as follows:

https://i.imgur.com/3bC391L.png

a) Greedily learn a decision tree using the ID3 algorithm and draw the tree.
b) Write the learned concept for Martian as a set of conjunctive rules (e.g., if (green=Y
and legs=2 and height=T and smelly=N), then Martian; else if ... then Martian; ...; else
Human).

How to calculate the class probabilities and classify using Naive Bayes classifier?

Mon, 10 Aug 2020 21:26:28 +0000

We have data on 1000 pieces of fruit. The fruit being a Banana, Orange or some Other fruit and imagine we know 3 features of each fruit, whether it’s long or not, sweet or not and yellow or not, as displayed in the table below:

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

A piece of an unknown fruit with these features are provided: Long, Sweet and Yellow.

Calculate probability of each of these 3 classes based on Naive Bayes Classification algorithm and report the class.

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 calculate the class probabilities and classify using Naive Bayes classifier for NLP?

Wed, 26 Jun 2019 19:43:41 +0000

We want to use Naive Bayes for tagging documents. It is a classification task that we want to assign a class (tag) to each string. We currently have two tags: Sport and Not Sport

Which tag does the sentence A very close game belong to? Using Naive Bayes classifier, calculate the class probability for Sport and Not sport for this sentence based on the dataset and decide about the tag.

Text	Tag
“A great game”	Sports
“The election was over”	Not sports
“Very clean match”	Sports
“A clean but forgettable game”	Sports
“It was a close election”	Not sports

How to calculate convolutions on a CONV layer for a Convolutional Neural Network?

Wed, 26 Jun 2019 08:54:12 +0000

Assume we have a $5\times5$ px RGB image with 3 channels respectively for R, G, and B. If

R
2	0	0	0	0
1	2	0	0	1
2	0	1	0	2
1	2	1	0	1
0	1	0	2	0

G
0	2	1	2	2
1	1	1	0	0
0	0	2	2	0
2	0	0	2	0
0	2	1	1	1

B
0	1	0	0	1
1	1	2	0	1
1	0	2	0	2
1	0	1	1	0
1	2	1	1	2

We have one $3\times3$ px kernel (filter) with 3 channels as follows:

Filter - R
0	0	1
1	0	1
1	0	0

Filter - G
0	0	-1
1	0	0
1	-1	0

Filter - B
1	0	1
0	1	-1
1	-1	0

a) If Stride = 2, and Zero-padding = 1, and Bias = 1, what will be the result of convolution?

b) What is the result after applying a ReLU layer ($max(z,0)$)on the result with the same size of the reuslt in part a?

c) Calculate the output by applying max-pooling layer with the size of $2\times2$ on the output of part b, and Stride = 1. (hint: max-pooling layer here and usually do not include any zero-paddings)

d) What is the result after applying flatten on the output of part c and creating a vector?

e) Assume the vector you created contains m elements. Consider it as the input vector for a Softmax Regression classifier (without any hidden layers and biases and it is fully connected). Assume there are 2 classes of 0 and 1. For all the weights from each element in the feature vector, the optimized weights are 1 for odd elements and 2 for even elements. For example, if the feature vector is [10,11,12,13,14], all the weights from 10 are 1 (because 10 is element 1 and 1 is odd), all the weights from 11 are 2, all the weights from 12 are 1, all the weights from 13 are 2 and all the weights from 14 are 1 and so on. Draw the Softmax Regression network and calculate the class should be 0 or 1?

Hint:
Softmax Regression: $p_{i}=\frac{e^{z_{i}}}{\sum_{i=1}^{c} e^{z_{i}}}$
Where $p_{i}$ is the probability of class $i$ anc $c$ is the number of classes.

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 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?

What is the difference between a batch and an epoch in a Neural Network?

Tue, 30 Oct 2018 14:45:56 +0000

Both of the batch size and number of epochs are integer values and seem to do the same thing in Stochastic gradient descent. What are these two hyper-parameters of this learning algorithm?