How to model a binary classification problem in a evolving environment Suppose you have a problem with two classes YES or NO. While the YES class is fixed, in the sense that the observations do not evolve, the observations of class NO may evolve during time and may change to the class YES. I would like to predict the probability of a given observation change to YES.

What kind of ML models could be used here? Could Bayesian Networks be a solution?

I would also like to observe what changed in the variables (or which variables were most important) that turned a NO into a YES.

Thank you
If you are trying to predict something that looks like probabilities, but don't actually need a "real" probability (for instance, if you aim at ranking observations to find those who are the most likely to switch to no), you could probably use logistic regression over the dataset. This would require the model to be refitted every once in a while.

If you are looking for actual probability, it has to be a probability to switch from NO to YES over a period of time. In that case, you are falling into time series analysis. This is a more complicated problem.

My intuition would be to consider the state change as a physical random phenomenon, such as a radioactive decay, where the probability of having decayed over a $\Delta t$ time period is $e^{-\lambda \Delta t}$. Based on cases who have switched in the past, you could build a rgression model to predict a $\lambda$ value for each observation. Of course you can use other decay functions than the exponential (find the best one through the validation step). This will eventually allow predicting a switch probability over any given time period.