In Multinomial method for Multi class classification, sum of probabilities of every classes equals 1.

Yes, in the multinomial method for multi-class classification, the sum of the probabilities of all classes indeed equals 1. This property is crucial for valid probability distributions.

Explanation

1. Multinomial Distribution: In a multinomial classification problem, you have multiple classes (let's say $C_1, C_2, \ldots, C_k$). The multinomial distribution describes the probabilities of each class when an observation is classified into one of these classes.

2. Probability Representation: Let $P(C_i)$ represent the probability of class $C_i$. The probabilities are typically calculated using a softmax function in many models like logistic regression, neural networks, etc.

   $P(C_i) = \frac{e^{z_i}}{\sum_{j=1}^{k} e^{z_j}}$

   where $z_i$ is the raw output (logits) of the model for class $C_i$, and the denominator sums over all classes.

3. Sum of Probabilities: The requirement that the sum equals 1 can be mathematically expressed as:

   $\sum_{i=1}^{k} P(C_i) = 1$

   This characteristic is integral to classification tasks, ensuring that the model's predictions are consistent with probability theory.

In summary, the multinomial classification ensures that all class probabilities are non-negative and sum to one, which aligns with the fundamental properties of probability distributions.