Amit Kumar Tyagi - Data Science and Data Analytics

Sumika Chauhan, Manmohan Singh, and Ashwani Kumar Aggarwal

In the previous few decades, all companies have produced data in large amounts from different sources. It can be from business applications of their own, social media or other web outlets, from smartphones, and client computing devices or from the Internet of Things sensors and software. This knowledge is highly useful for companies that have resources in place to build on it. The overall toolbox for these methods is called data analytics.

Data analytics is used to represent those methods that provide an essential arrangement of the data. It can be classified into four categories, including descriptive, predictive, diagnostic, and prescriptive data analytics. Out of these methods, predictive analytics is the most dynamic approach for data analytics that involves an advanced statistical approach, Artificial Intelligencebased algorithms. Predictive analytics (PA) is the member of advanced analytics that is broadly utilized in the prediction of uncertain future events. A variety of data analysis, statistical modeling, and theoretical approaches are used to bring management, information technology, and business process forecasting together to forecast these predictive events. To define threats and possibilities in the future, the trends contained in historical and transactional data may be used. PA models may track relationships with a complex set of conditions to distribute a score or weighting among several variables to determine risk.

Predictive analytics helps companies to anticipate, construct, and focus on the evidence and not on a hunch or expectations, forecasting findings and actions. The value chain of predictive analytics is seen in .

Figure 1.1 Predictive analytics value chain.

Artificial Intelligence (AI) invokes the simulation of computers based on human intelligence that is designed to think and imitate their behavior like humans. The word can also be extended to any system that shows features similar to a human mind, such as understanding and diagnostic. AI has an outstanding feature that is its capability to rationalize and perform decisions that have the greatest chance of fulfilling a specific target [].

The principle idea behind AI is that it is vital to interpret human intelligence in a manner that a machine can effectively imitate and perform functioning from the easiest to those that are much more complex. The purpose of AI involves comprehension, logic, and interpretation. AI is based on the scenic concept that originally burst, followed later by Machine Learning (ML), and eventually, Deep Learning (DL) that continues to accelerate developments of AI to another level.

From it is observed that there are three concentric circles, DL is a subspace of ML, which is also a subspace of AI.

Figure 1.2 Distinction between AI, machine learning, and deep learning.

ML is based on the AI that equips systems with the learning ability and upgrades from experience without being programmed directly. It can be categorized in supervised learning, unsupervised learning, and reinforcement.

Supervised learning is the assignment for ML to learn an operation that outlines a vector input to an output vector, based on the I/O relationship. Classification is the method of foreseeing the class or labels of given datasets. Classification forecast methodology is the duty of estimating mapping operation from input variables to distinct output variables. Basically, the methods for supervised learning are classified into two categories: regression and classification.

Regression is the most powerful statistical method in data analytics that pursues to describe the power and aspects of the relationship between one dependent variable to a series of other independent variables. Various types of regression are available in the literature []. A few of them are discussed as follows.

It attempts to relate the two features by fitting a linear relation with corresponding estimated regression parameters. One variable is taken as an explanatory vector, and the second one is considered as a vulnerable vector. The linear regression is used in cost prediction and estimation of some data analysis in the data analytics. Let us consider a sample of N objects with m variables, which can be represented as Nm matrix X and the predicted output is a vector YT=(y1,y2,,ym). For a particular individual i, let Xi=xi1,xi2,,xim, which indicates the covariate vector. The output is a continuous variable denoted by Yi. Mathematically linear regression is given as

yi=0+j=1mxijjy (1.1)

The 0 indicates the intercept and is also called the bias in machine learning, and T=(1,2,,m) is the coefficient vector. The values of all input variates should be numeric for the feasible computation of the covariate values. The equation can be rewritten as

Y=XT (1.2)

Parameter estimation is considered as minimization of loss function over a dataset in the supervised learning. The least-squares approach is the commonly used technique for an appropriate regression line. In this method, the calculation of the best-fitting line is accomplished using observed data to minimize the sum of the square of the vertical deviations from each data point. The cost function is defined in terms of residual sum of squares, which is computed using Euclidean distance between the measured and projected outputs, Y. This can be written mathematically as

RSS=i=1NyixiT2 (1.3)

RSS represent the quadratic operation of the parameters; thus, the minimum value of it is always present. The solution is easily obtained in matrix representation, written as

RSS=yXTyX (1.4)

The minimization of the above-mentioned equation can be obtained by setting the first derivative of RSS equal to zero. Differentiating w.r.t. , the obtained normal equation is given as

XTyX=0 (1.5)

If XTX is non-singular, then a unique solution is obtained by

=XTX1XTy (1.6)

and obtained value, which is fitted at the ith input xi, is yi=yxi=xiT. At an arbitrary input x0, the prediction is yx0=x0T.

Logistic regression searches for the relationship between an unambiguous dependent variable and a number of autonomous (explainable) variables. It is a binary classification technique. The dependent variables have only two values, such as 0 or 1, or these variables are the binary type. The probabilitys log-odds and feature share a linear relation. For a convinced particle Xi=xi1,xi2,,xim, the predicted output yi can be labeled as either 0 or 1. The equation of the logistic regression is given as

logPryi=1|XiPryi=0|Xi=k=0mxikk=Xi (1.7)

The value of xi0 is 1 and represents the intercept. As we know that in the case of two-class classification Pryi=1|Xi+Pryi=0|Xi=1; thus, from equation (1.7) we have

Pryi=1|Xi=expXi1+expXi (1.8)

The parameter estimation is accomplished by maximizing the cost function in the logistic regression models. The joint conditional probability for all N points in training data is

Pr(y=y1|X1)Pr(y=y2|X2).....Pr(y=yN|XN)=i=1NPr(y=yi|Xi) (1.9)

where yi;i=1,2,,N is the predicted labels in the training set. The log-likelihood for N observations is

()=i=1Nlog[(Pr(y=yi)|Xi)] (1.10)

where the logit transformation of conditional probability for an individual Xi is

log[(Pr(y=yi)|Xi)]={Xilog[1+exp(Xi)]:yi=1log[1+exp(Xi)]:yi=0 (1.11)