## 3 Results and Discussions
### Models and Metrics Used
#### 3.2.1 Supervised Learning Algorithms  
Given a set of data points \(\{\text{x}_{1},\ldots,\text{x}_{\text{m}}\}\) associated to a set of outcomes \(\{\text{y}_{1},\ldots,\text{y}_{\text{m}}\}\), the aim of the supervised learning algorithms is to build a classifier that can predict y from x. The supervised learning algorithm prediction can be a regression model producing a continuous output or a classification model predicting a class of the given input values. A broad classification of supervised learning involves two types of mathematical concepts to perform either classification of regression model formulation. Logistic regression, support vector machine, and conditional random fields are popular discriminative models; naive Bayes, Bayesian networks, and hidden Markov models are commonly used generative models. The supervised model is branched up as generative and discriminative models as in Figure 6. The generative model learns the probability distributions of the data and estimates the conditional probability \(P(x|y)\) to then deduce to the posterior \(P(y|x)\), whereas the discriminative model creates a decision boundary to directly estimate \(P(y|x)\).  
In a generative random model, the two models that were used by different authors include naive Bayes and belief networks. Naive Bayes assumes that all features are inde  
Figure 5: (**a**) Taxonomy of the algorithms used. (**b**) Taxonomy of other machine learning models used.  
Figure 6: Supervised learning models.  
pendent, whereas belief networks allows the user to specify which attributes are, in fact, conditionally independent.  
In supervised learning, the hypothesis is noted as \(h_{\theta}\), the model that we choose. For a given input data \(x_{i}\), the model prediction output is \(h_{\theta}(x_{i})\). A loss function is given as \(L\):\((z,y)\in\mathbb{R}\times Y\)\(\longmapsto\)\(L\)(\(z,y)\in\mathbb{R}\) that takes as inputs the predicted value \(z\) corresponding to the real data value \(y\) and outputs how different they are. Some of the loss functions are least squared error, logistic loss, hinge loss, and cross entropy. The loss function then contributes to the calculation of cost function as \(J(\theta)=\sum_{i=1}^{m}L(h_{\theta}(x_{i}),y_{i})\). The update rule for gradient descent is expressed in terms of the cost function calculated, and the learning rate \(\alpha\in\mathbb{R}\) is given as \(\theta\leftarrow\ \theta-\alpha\
abla\ J(\theta)\). With the known parameters \(L(\theta)\), the likelihood and the parameters \(\theta\), the optimal parameters are determined as \(\theta_{optimal}=\text{argmax}(L(\theta))\).  
Some of the linear discriminative models included in the survey articles are linear regression, logistic regression, polynomial regression, ridge regression, and the nonparametric discriminative model, which includes K-nearest neighbor. While discrete discriminative models include support vector machine models, neural networks, and trees in several variants. However, the linear discriminative algorithm works in its own fashion, and the articles taken up for study have included some of the mentionable variations in their work. They include the Widrow-Hoff rule and locally weighted regression parameters in the calculation of optimal parameters. Support vector machines have used the concepts of Lagragian multipliers and Kernel and optimal classifiers in different notations.