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algorithm

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[CS] Fundamental concepts of Computer Science 1. What is Computer Science? Computer Science is the study of problems, problem-solving, and the solutions that come out of the problem-solving process. Given a problem, a computer scientist's goal is to develop an algorithm. However, we must be careful to include the fact that some problems may not have solutions. So we can say that computer science is the study of problems that are and that ar..
[Theorem] Neural Network 1. What is Neural Network Polynomial terms in linear regression and logistic regression, we have heavy features to set hypothesis. For example, if we have \(50 \times 50\) pixel images, then total pixels becomes 2500. So total features of logistic regression becomes \(n = 2500 + \alpha\) (very big, when applying polynomial term). If we have too many features, we can have overfitting problem and ..
[Theorem] Regularization 1. Regularization of Logistic Regression Because we don't know how many theta can affect overfitting, we make all theta become small. $$ \left(J(\theta )=\frac{1}{2m}\sum _{i=1}^m(h_{\theta }(x^{(i)})-y^{(i)})^2+\lambda \sum _{j=1}^m\theta _j^2)\right) $$ \(\lambda\) is called the regularization parameter which controls a trade off between two different goals. The first goal is that we would lik..
[Theorem] Logistic Regression 1. What is Classification Problem? Usually classification have two discrete output zero and one which first one is 'negative output', the other is a 'positive output'. For example, in classification for spam mail, zero means mail is not spam mail, one means mail is spam mail. $$ y \in 0, 1 $$ Multivariate classification have multiple discrete output. $$ y \in 0, 1, 2, ... $$ 2. Logistic Regressi..
[Theorem] Multivariate Linear Regression 1. Multivariate Hypothesis feet(x1) number of rooms(x2) Built Age(x3) Price of House 1412 5 30 3520 1530 3 45 2420 642 2 56 1238 \(x^{i}_{j}\) : value of feature j in ith training example \(x^i\) : the input features of the ith training example \(m\) : the number of training examples \(n\) : the number of features if \(x_{2}^{2}\), it means 45, if \(x_2\), it means [30, 45, 56] 3 dimensional vec..
[Theorem] Linear Regression 1. What is Hypothesis function? In Supervised Learning, we use 'Regression Algorithm' when we meet problem such as predicting continuous output. Using knowing data x, y in linear regression, we can predict \(y(n)\) when we have \(x(n)\) and function of \((x, y)\). Below is the function of \((x, y)\) when we have one variable. $$ H_{\theta}(x)=Y=\theta _0 + \theta _1 X $$ \(m\) : number of record..