3.3 Statistical Estimation in Machine Learning

-

3.3 Statistical Estimation in Machine Learning

  • Statistical estimation is a method used in machine learning to estimate unknown values or parameters from sample data.
  • In simple terms: We use sample data to estimate information about the whole dataset (population).
  • Instead of checking all data, we take a small sample and estimate the result.
  • In machine learning, statistical estimation helps models learn patterns, estimate probabilities, and make predictions from training data.
  • Examples include estimating average marks, probability of spam emails, and relationships between variables.

Example: Suppose a college has 1000 students.

Instead of asking all students their average marks, we select 100 students and estimate the average.

The calculated value is called an estimate.


Example – Average Marks

Suppose we collect marks of 5 students:


We estimate the average marks using the mean formula.


Where:

  • x̄ (x bar) = estimated mean or average

  • Σx = sum of all values

  • n = number of observations

Calculation:

Mean = (60 + 70 + 80 + 75 + 65) / 5
Mean = 70

So we estimate that the average marks ≈ 70.

A machine learning model uses similar estimates to understand data patterns.


Machine learning models learn by estimating parameters from data.

Examples:

  • Estimating average height of people

  • Estimating probability of spam emails

  • Estimating relationship between study hours and marks

Without estimation, the model cannot learn from data.


Types of Statistical Estimation

1. Point Estimation

        Point estimation gives one single value as the estimate.

Example:

                    Average marks = 70

                    The value 70 is the point estimate.


2. Interval Estimation

            Interval estimation gives a range of values where the true value is likely to lie.

Example:

                Average marks may lie between:    68 to 72

                This range is called a confidence interval.


Example – Probability Estimation

Suppose in 100 emails:

  • 30 are spam

  • 70 are not spam

The estimated probability of spam is:

P(Spam)=30/100=0.30

So the machine learning model estimates that 30% of emails are spam.


Statistical estimation is used in many machine learning algorithms such as:

  • Linear Regression

  • Naive Bayes

  • Logistic Regression

  • Gaussian Models

  • Bayesian Models

These algorithms estimate parameters like mean, variance, and probability from data.


















































Popular posts from this blog

operators in c programming

-
Image
v Operators: - An operator is a symbol that tells or intimates to the compiler to perform specific calculations or manipulations on one or more operands. Operators are essential for performing computations and making decisions in programs.   a + b is an operation a & b are operands + is an operator   Based on number of operands involved: 1.      Unary operators: - unary operators can be applied on only one operator. Example: -   ++ , -- , - (unary minus) , sizeof , ~ (compliment) , ! (not).   2.      Binary operators: - binary operators can be applied on two operands. Example: -   + , -,   * , / , etc.   3.    Ternary operators: - Ternary operator can be applied on three operands. Example: -   ?: (ternary conditional operator).   C supports several operators, can be classified into following...
Read more

2.4 Arrays in c programming

-
Image
  Arrays: - An array is a collection of elements of the same data type stored in contiguous memory locations. It is a derived data type and a homogenous data structure. It is a variable which can store multiple values of the same type under a single variable name, making it easier to manage and manipulate related data. The size of an array is fixed. To access the elements of an array, we use indexes or subscripts accordingly. array index or subscript is used to identify array elements address. Array index or subscript starts with 0 to n-1.   Declaration of an array: - The declaration of an array means telling the compiler to create an array variable and reserving memory for a fixed number of elements of the same data type. Initialization of an array: - Initializing an array means assigning initial values to its elements. Types of arrays: - Arrays are classified based on the number of dimensions they have:             ...
Read more

Variables in c

-
Image
  Variables: - A variable is a data name or an identifier which stores a value that can be changed during the program execution.  Every variable might belong to any of the data types, like int, float, char, etc.  The name of a variable can be composed of letters, digits, and the underscore character. It must begin with either a letter or an underscore.  Variables are case-sensitive because uppercase and lowercase letters are distinct. C programming language also allows defining various other types of variables, like numeric array, character array, pointer, Structure, Union, Enumeration and etc.               Example: - sum, height, _value Declaring a variable in C: - Variable declaration means telling the compiler about the name and type of a variable before using it in the program. Variable declaration is the process of reserving a memory location and defining the type of data that will be stored in that locatio...
Read more