I am familiar with the definition of conditional independence, however I am not sure if practically and especially in the case of features independent from class label I understand the concept correctly. So, conditional independence of features given class means that given I know the class label, knowledge about one feature does not provide me with any further knowledge about other features.

I am explaining it to myself with an example like this: Given I have two classes of people - say diabetic and healthy - and two features - say the level of blood sugar and weight. Now we would know that people with diabetes have on average a higher level of both features than healthy subjects. But if we assume independence for the features given class, that would mean that if I know the blood sugar level, this gives me no information on weight (any information about in which range the weight is more likely to be is given by the class information, so class information in some way already restricts the domain of values, but information on blood sugar does not add anything to this information). Is my understanding correct?

Thank you


Your understanding is correct. What conditional independence implies is that the joint distribution of the features is dependent on the class (as you've pointed out). But, more importantly, the conditional joint distribution of the features factors into a product of their individual marginal distributions.

So, to use your example, lets say that $D$ represents the class of diabetics, $W$ is the weight, and $G$ is blood glucose. Then:


Which is just another way to say that they are independent given the class.


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