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color: #ff0000;">Regression in AI</span></h1><h3 style="text-align: left;"><span style="font-weight: 400; color: #000000;">What is Regression in AI?</span></h3><p><span style="font-weight: 400;">The mathematical approach to find the relationship between two or more variables is known as </span><b>Regression in AI </b><span style="font-weight: 400;">. Regression is widely used in <a href="https://www.ssla.co.uk/">Machine</a> Learning to predict the behavior of one variable depending upon the value of another variable.</span></p><p><span style="font-weight: 400;">Unlike the classification models, the regression models output numeric values. It also has continuous values for both dependent and independent variables, and for the </span><b>most part,</b><span style="font-weight: 400;"> Regression is classified as </span><b>supervised <a href="https://www.ssla.co.uk/about-us">learning</a></b><span style="font-weight: 400;">.</span></p><h3 style="text-align: left;"><span style="font-weight: 400; color: #000000;">Types of Regression in AI</span></h3><p><span style="font-weight: 400;">Each regression technique has some assumptions that you need to fulfil before using them. Here are a few of the types ranging from famous to less known; each of them has its own pros and cons.</span></p><ul><li style="font-weight: 400;"><span style="font-weight: 400;">Linear Regression: </span><span style="font-weight: 400;">Linear Regression is considered to be the simplest form of Regression. This type of Regression is applicable when the relationship between the dependent and independent variables is </span><b style="font-size: 1rem;">linear in nature</b><span style="font-weight: 400;">. The data is plotted on the graph, and a best-fitted line is calculated using the formula. This line is also known as the line of Regression. The predictions are then made on the basis of this line. </span></li></ul><p><span style="font-weight: 400;"><img data-lazyloaded="1" src="data:image/svg+xml;base64,PHN2ZyB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMjAwMC9zdmciIHdpZHRoPSIzMDAiIGhlaWdodD0iMjI5IiB2aWV3Qm94PSIwIDAgMzAwIDIyOSI+PHJlY3Qgd2lkdGg9IjEwMCUiIGhlaWdodD0iMTAwJSIgc3R5bGU9ImZpbGw6I2NmZDRkYjtmaWxsLW9wYWNpdHk6IDAuMTsiLz48L3N2Zz4=" fetchpriority="high" decoding="async" class="alignnone size-medium wp-image-7521" data-src="https://www.ssla.co.uk/wp-content/uploads/2020/08/regression-in-AI-300x229.png" alt="regression in AI" width="300" height="229" data-srcset="https://www.ssla.co.uk/wp-content/uploads/2020/08/regression-in-AI-300x229.png 300w, https://www.ssla.co.uk/wp-content/uploads/2020/08/regression-in-AI-600x459.png 600w, https://www.ssla.co.uk/wp-content/uploads/2020/08/regression-in-AI.png 688w" data-sizes="(max-width: 300px) 100vw, 300px" /><noscript><img fetchpriority="high" decoding="async" class="alignnone size-medium wp-image-7521" src="https://www.ssla.co.uk/wp-content/uploads/2020/08/regression-in-AI-300x229.png" alt="regression in AI" width="300" height="229" srcset="https://www.ssla.co.uk/wp-content/uploads/2020/08/regression-in-AI-300x229.png 300w, https://www.ssla.co.uk/wp-content/uploads/2020/08/regression-in-AI-600x459.png 600w, https://www.ssla.co.uk/wp-content/uploads/2020/08/regression-in-AI.png 688w" sizes="(max-width: 300px) 100vw, 300px" /></noscript></span></p><p><span style="font-weight: 400;">The graph shows the linear regression model that is fitted on a data set represented by blue dots. For a simple linear regression, the equation is as follows</span></p><p><span style="font-weight: 400;">y=mx+c</span></p><p><span style="font-weight: 400;">Here ‘y’ is the dependent variable, ‘x’ is the independent variable, ‘c’ is the y-intercept of the line of Regression, and ‘m’ is the regression coefficient/slope of the line. If the number of independent co-efficient increases than the formula is as follows</span></p><p><span style="font-weight: 400;">y=</span><span style="font-weight: 400;">m</span><span style="font-weight: 400;">1 </span><span style="font-weight: 400;">x</span><span style="font-weight: 400;">1</span><span style="font-weight: 400;">+</span><span style="font-weight: 400;">m</span><span style="font-weight: 400;">2</span><span style="font-weight: 400;">x</span><span style="font-weight: 400;">2</span><span style="font-weight: 400;">+</span><span style="font-weight: 400;">m</span><span style="font-weight: 400;">3 </span><span style="font-weight: 400;">x</span><span style="font-weight: 400;">3</span><span style="font-weight: 400;">…….</span><span style="font-weight: 400;">m</span><span style="font-weight: 400;">n </span><span style="font-weight: 400;">x</span><span style="font-weight: 400;">n</span><span style="font-weight: 400;">+c</span></p><p><span style="font-weight: 400;">The slope of the line can be calculated using the simple slope formula</span></p><p><span style="font-weight: 400;">slope= </span><span style="font-weight: 400;">x</span><span style="font-weight: 400;">2</span><span style="font-weight: 400;">–</span><span style="font-weight: 400;">x</span><span style="font-weight: 400;">1</span><span style="font-weight: 400;">y</span><span style="font-weight: 400;">2</span><span style="font-weight: 400;">–</span><span style="font-weight: 400;">y</span><span style="font-weight: 400;">1</span></p><p><span style="font-weight: 400;">After calculating the ‘m’ and ‘c’ for the Regression, we calculate the </span><b>mean square error</b><span style="font-weight: 400;"> (</span><b>MSE</b><span style="font-weight: 400;">) and minimize it using gradient descent. MSE is given by</span></p><p><span style="font-weight: 400;">MSE= </span><span style="font-weight: 400;">1</span><span style="font-weight: 400;">2N</span><span style="font-weight: 400;">i=1</span><span style="font-weight: 400;">n</span><span style="font-weight: 400;">(</span><span style="font-weight: 400;">y</span><span style="font-weight: 400;">i</span><span style="font-weight: 400;"> –</span><span style="font-weight: 400;">(m</span><span style="font-weight: 400;">1 </span><span style="font-weight: 400;">x</span><span style="font-weight: 400;">1</span><span style="font-weight: 400;">+</span><span style="font-weight: 400;">m</span><span style="font-weight: 400;">1 </span><span style="font-weight: 400;">x</span><span style="font-weight: 400;">1</span><span style="font-weight: 400;">+</span><span style="font-weight: 400;">m</span><span style="font-weight: 400;">1 </span><span style="font-weight: 400;">x</span><span style="font-weight: 400;">1</span><span style="font-weight: 400;">) )</span><span style="font-weight: 400;">2</span></p><p><span style="font-weight: 400;">Here ‘N’ is the number of data points, two is multiplied to facilitate when taking derivatives. This MSE is minimized, and the slope is adjusted using </span><b>gradient descent</b><span style="font-weight: 400;">.</span></p><ul><li style="font-weight: 400;"><span style="font-weight: 400;">Logistic Regression: </span><span style="font-size: 1rem;">Logistic Regression is used to predict the probability of a particular variable on the basis of <a href="https://www.ssla.co.uk/referral">independent</a> variables. This regression model is mainly used in classification problems like detecting spams email, diseases, and cancer detection. </span></li></ul><p><span style="font-weight: 400;">Mathematically, this model predicts the probability of an individual variable ‘Y’ on the basis of the independent variable ‘X’. The graphical representation of Logistic Regression is similar to that of a </span><b>sigmoid function</b><span style="font-weight: 400;">. There are generally three types of logistic Regression</span></p><ul><li style="font-weight: 400;"><span style="font-weight: 400;">Binary</span></li><li style="font-weight: 400;"><span style="font-weight: 400;">Multinomial</span></li><li style="font-weight: 400;"><span style="font-weight: 400;">Ordinal</span></li></ul><p><span style="font-weight: 400;">There is a minor difference between all three of these types. In binary logistic regression, there are two possible types of output, i.e., 0 or 1. It is more like a classification model, and 0 or 1 may represent yes/no, success/failure, etc. In multinomial and ordinal logistic Regression, there are three or more possible outcomes. The only difference is that the multinomial has an </span><b>unordered type</b><span style="font-weight: 400;"> and ordinal has </span><b>ordered type</b><span style="font-weight: 400;"> of outcome.</span></p><p><span style="font-weight: 400;">The mathematical formula for a simple binary logistic regression is given by </span></p><p><span style="font-weight: 400;">g</span><span style="font-weight: 400;">z</span><span style="font-weight: 400;">= </span><span style="font-weight: 400;">1</span><span style="font-weight: 400;">1+</span><span style="font-weight: 400;">e</span><span style="font-weight: 400;">-z</span></p><p><span style="font-weight: 400;">Here ‘z’ is the hypothesis, which is assumed to be </span></p><p><span style="font-weight: 400;">z=W*X+B</span></p><p><span style="font-weight: 400;">The cost function of this Regression is given as follows</span></p><p><span style="font-weight: 400;">cost</span><span style="font-weight: 400;">g</span><span style="font-weight: 400;">z</span><span style="font-weight: 400;">,y(actual)</span><span style="font-weight: 400;">= </span><span style="font-weight: 400;">{</span><span style="font-weight: 400;">–</span><span style="font-weight: 400;">log</span> <span style="font-weight: 400;">g</span><span style="font-weight: 400;">z</span><span style="font-weight: 400;"> if y=1</span><span style="font-weight: 400;"> </span><span style="font-weight: 400;">–</span><span style="font-weight: 400;">log</span> <span style="font-weight: 400;">1-g</span><span style="font-weight: 400;">z</span><span style="font-weight: 400;"> if y=0</span><span style="font-weight: 400;"> </span></p><ul><li style="font-weight: 400;"><span style="font-weight: 400;">Ridge Regression: </span><span style="font-weight: 400;">It is the type of Regression in which we add a </span><b style="font-size: 1rem;">plenty term</b><span style="font-weight: 400;"> equal to the summation of the square of the regression coefficients. This term is added to the cost function, and it helps us </span><b style="font-size: 1rem;">reduce</b><span style="font-weight: 400;"> the </span><b style="font-size: 1rem;">complexity</b><span style="font-weight: 400;"> of the model and also </span><b style="font-size: 1rem;">prevents</b><span style="font-weight: 400;"> the </span><b style="font-size: 1rem;">overfitting</b><span style="font-weight: 400;"> problem, which occurs due to simple Regression. Overfitting occurs when the model performs well for the training data, but the results on testing data are not satisfactory. </span></li></ul><p><span style="font-weight: 400;">Mathematically the cost function is expressed as </span></p><p><span style="font-weight: 400;">i=1</span><span style="font-weight: 400;">M</span><span style="font-weight: 400;">y</span><span style="font-weight: 400;">i</span><span style="font-weight: 400;">–</span><span style="font-weight: 400;">y</span><span style="font-weight: 400;">i</span><span style="font-weight: 400;">2</span><span style="font-weight: 400;">=</span><span style="font-weight: 400;">i=1</span><span style="font-weight: 400;">M</span><span style="font-weight: 400;">y</span><span style="font-weight: 400;">i</span><span style="font-weight: 400;">–</span><span style="font-weight: 400;">j=0</span><span style="font-weight: 400;">p</span><span style="font-weight: 400;">w</span><span style="font-weight: 400;">i</span><span style="font-weight: 400;">–</span><span style="font-weight: 400;">x</span><span style="font-weight: 400;">ij</span><span style="font-weight: 400;">2</span><span style="font-weight: 400;">+</span><span style="font-weight: 400;">j=0</span><span style="font-weight: 400;">p</span><span style="font-weight: 400;">w</span><span style="font-weight: 400;">j</span><span style="font-weight: 400;">2</span></p><p><span style="font-weight: 400;">Here λ acts as the regularization parameter, which is always a positive number. It must be noted that there is no plenty applied to the intercept term. Only the summation of the square of the regression coefficient is affected by it. </span></p><p><span style="font-weight: 400;">Choosing the value for the regularization parameter (λ) is also very important. If we decide λ=0, then the plenty term will get excluded, and if the value of λ is kept high, then it will result in under-fitting. To find the optimal value, we plot the parameter against the different values of λ and select the minimum value for which the parameter is stable. </span></p><ul><li style="font-weight: 400;"><span style="font-weight: 400;">Support Vector Regression: </span><span style="font-weight: 400;">When a support vector <a href="https://www.ssla.co.uk/buy">machine</a> is used in the regression model, it becomes support vector regression (SVR). These types of regression models help us to define a </span><b style="font-size: 1rem;">boundary</b><span style="font-weight: 400;"> for an acceptable amount of </span><b style="font-size: 1rem;">error</b><span style="font-weight: 400;"> and find a </span><b style="font-size: 1rem;">hyperplane</b><span style="font-weight: 400;"> to fit the data. The SVR </span><b style="font-size: 1rem;">minimizes the coefficient</b><span style="font-weight: 400;"> rather than minimizing the </span><b style="font-size: 1rem;">squared error</b><span style="font-weight: 400;"> as done in other regression models. </span></li></ul><p><span style="font-weight: 400;">The cost function to minimize is </span></p><p><span style="font-weight: 400;">min(</span><span style="font-weight: 400;">1</span><span style="font-weight: 400;">2</span><span style="font-weight: 400;">|w|</span><span style="font-weight: 400;">2</span><span style="font-weight: 400;">)</span></p><p><span style="font-weight: 400;">Constraints are as follows</span></p><p><span style="font-weight: 400;">y</span><span style="font-weight: 400;">i</span><span style="font-weight: 400;">–</span><span style="font-weight: 400;">w</span><span style="font-weight: 400;">i</span><span style="font-weight: 400;">x</span><span style="font-weight: 400;">i</span><span style="font-weight: 400;">≤e</span></p><p><span style="font-weight: 400;">We can also add a </span><b>slack variable</b><span style="font-weight: 400;"> to the cost function in order to obtain better results.</span></p><ul><li style="font-weight: 400;"><span style="font-weight: 400;">Decision Tree Regression: </span><span style="font-weight: 400;">The decision tree regression works on the principle of </span><b style="font-size: 1rem;">standard deviation</b><span style="font-weight: 400;">. In order to understand the standard deviation, we need to understand the variance. Variance is defined as the average of the squared distance of each value from the Mean value.</span></li></ul><p><span style="font-weight: 400;">By taking the square root of the variance the deviation can be calculated . In decision tree regression, the main aim is to reduce the standard deviation by segmenting the data into independent variables. </span></p><h3 style="text-align: left;"><span style="font-weight: 400; color: #000000;">How to choose the best model?</span></h3><p><span style="font-weight: 400;">There are many other models of Regression in AI other than the described above. But in order to choose the best one, we need to consider the following points</span></p><ul><li style="font-weight: 400;"><span style="font-weight: 400;">If the dependent variable is continuous and the resulting model has collinearity, then you should go for the ridge, lasso, or elastic net Regression. The final model can be selected on the basis of r-square error or RMSE. </span></li><li style="font-weight: 400;"><span style="font-weight: 400;">Support vector regression is the best choice when dealing with <a href="https://en.wikipedia.org/wiki/Artificial_intelligence">non-linear</a> models</span></li><li style="font-weight: 400;"><span style="font-weight: 400;">The cross-validation method is handy to eliminate the overfitting issue. Ridge and lasso models can also be used to reduce the overfitting problem</span></li><li style="font-weight: 400;"><span style="font-weight: 400;">For count data, it is a better choice to use negative binomial Regression</span></li><li style="font-weight: 400;"><span style="font-weight: 400;">Compare linear regression models for the same dataset</span></li><li style="font-weight: 400;"><span style="font-weight: 400;">Find a model with a more adjusted R2 value </span></li><li style="font-weight: 400;"><span style="font-weight: 400;">Errors of the model should be within a small bandwidth</span></li></ul></div></div><div class="vc_btn3-container red-button vc_btn3-inline" ><a class="vc_general vc_btn3 vc_btn3-size-md vc_btn3-shape-rounded vc_btn3-style-modern vc_btn3-color-danger" href="https://www.ssla.co.uk/contact/" title="">Contact Us</a></div></div></div></div></div></div><div class="container"><div class="vc_row vc_row-fluid boxed"><div class="wpb_column vc_column_container 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