In our little universe, since we have the data for everyone hence we have easily created a
rule to predict the next diabetic patient. However, in the real world applications, we do not
store the complete dataset of all the patients, and therefore we can borrow the actual power of
ML to find a viable solution for our problems. ML provides prediction even if our dataset does
not contain all the possible samples. For instance, if in our above example, we delete the last
two records. Now, an ML algorithm would process all the attributes of the incoming record
of a person and try to predict whether or not they can contract diabetes or not. This set of all
predictions is referred to as a model.
ML problems are often categorized under regression and classification.
Regression
Regression is used for predicting “continuous” outcomes. In regression, the answer to a
question is determined from the given values of a model, instead of a finite set of labels. When
you search “regression”, you would find many Statistics-based links. This is because it is one of
the fundamental branches of Statistics used for calculating the relationship between variables.
InML, it helps to calculate predictions for events by determining the relationship of the given
input ( variables) in the dataset. Typically, the regression model adheres to the following model.
Prediction Outcome = Coecient 1 + Coecient 2 * Input.
Logistic Regression
When we use the term “logistic” regression, our focus is on the primary function of the algorithm
known as the logistic function. This function is also referred to as the sigmoid function. It is part
of Statistics which is used to flesh out the characteristics for the growth of population in ecology,
understanding its rise, and height for capacity. The function makes an S-shaped curve; as an
input, it considers real numbers and assigns it a value in the range of 0 and 1.
Logistic regression utilizes an equation for representation. The input values are represented
by x where they make use of coecient values or “weights” for estimation of the outcome. This
output is represented by y. Consider the following equation of logistic regression.
y = e^(b0 + b1*x)/(1 + e^(b0 + b1*x))
Sad
Happy
Logistic regression Model
Input:
X1, X2, X3 II Weights:
θ
1,
θ
2,
θ
3, II Outputs: Happ
y or Sad
θ
1
θ
2
θ
3
X2
X1
X3
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Here y is the prediction result, b0 is the intercept or the bias, and b1 represents x’s (input)
coecient.
This regression applies to the probability of the first class or the default class. For instance,
if we are trying to predict the gender of people through the given data of height values, then we
may have a default class as a male. In such an instance, we can write the probability formally
with the following method where, s = sex, m = male, and h = height.
P(s = m|h)
Observe closely that what we are saying is that the first class y contains our input x.
P(X) = P(Y = 1|X)
It is important to note that while the method of logistic regression is linear, the estimations
are processed with the help of the logistic function. As a result, it diers from linear regression
as input cannot be comprehended with a linear combination.
The estimations for the values of the coecient must be performed via the training data.
For this purpose, the maximum likelihood estimation is used. Predictions are easy with logistic
regression—you just have to put the right value from the data. For instance, suppose we have
a model which is used to predict whether a student is good at study or not. This assessment is
done by going by their marks. Consider in the given data, a student has 40 marks. Provided,
we have the coecient value for b0 = −40 and b1 = 0.4, we can generate an estimation for the
assessment of a student of being deficient in academics, P(bad/marks=40).
y = e^(b0 + b1*X) / (1 + e^(b0 + b1*X))
exp(−18 + 0.4*40) / (1 + EXP(−18 + 0.4*40))
y = 0.1192029220221176
Now, we did get a result, but how will we determine the assessment based on the output, well
for that we must have a benchmark. For instance, going by our benchmark, an intelligent student
has a probability of more than 0.20 and a less intelligent one has a probability of less than 0.20.
Linear Regression
Similar to logistic regression, linear regression also belongs to statistics. In statistics, it is used for
determining the relationship between numerical input and output variables.
Linear regression follows a linear model that is, there is a linear relationship among its
input and output variables. The input is represented by x and the output is represented by y.
To delve further, the value of y is determined by x values with a combination that is linear in
nature.
Whenever the input variable is only a single one, then the method is called simple linear
regression. Otherwise, for multiple values, it is called multiple linear regressions.
The equation of linear regression maps a scale factor for all the input values. This factor is
referred to as a coecient. It is represented by B (Beta). There is one more coecient known as
the bias coecient.
For instance, a regression problem with a single input variable x (simple linear regression),
takes the following equation.
y = B0 + B1*x
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