In the One vs Rest method for Multiclass classification, sum of probabilities of all classes(achieved by one model for every class) equals 1.

The statement you provided relates to the One vs Rest (OvR) method in multiclass classification, which is a strategy used in machine learning to handle multiple classes by decomposing the problem into binary classification problems. Let's discuss and analyze this statement further.

Understanding One vs Rest (OvR) Method

1. Definition of One vs Rest: In this approach, for each class in the dataset, a separate binary classifier is trained. This classifier distinguishes between one class and all other classes combined. If there are $n$ classes, $n$ binary classifiers are created.

2. Sum of Probabilities: After training these classifiers, when a new sample is to be classified, each classifier outputs a probability score that indicates the likelihood of the sample belonging to its respective class. The fundamental principle is that these probability scores can be interpreted using a logistic function (or a softmax function).

3. Softmax Function: If softmax is used in the output layer of each binary classifier, the class probabilities for a single sample can be represented as: $P(y_i|x) = \frac{e^{z_i}}{\sum_{j=1}^{n} e^{z_j}}$ where $z_i$ is the score for class $i$, and $j$ indexes all classes.

Conclusion

The sum of these probabilities, as calculated through the softmax function, indeed equals 1: $\sum_{i=1}^{n} P(y_i|x) = 1$

Thus, the provided statement is correct. This property is crucial for ensuring that the probabilities across all classes are valid and can be directly interpreted as a distribution. Each classifier's output is normalized, allowing for an effective decision-making process based on the highest probability.

Final Answer

Yes, in the One vs Rest method for Multiclass classification, the sum of the probabilities of all classes (achieved by one model for every class) equals 1. This ensures that the outputs can be interpreted as a valid probability distribution.