Predicting the Future Behavior of a Time-Varying Probability Distribution
This work addresses the challenge of adapting machine learning models to changing data distributions, which is crucial for applications like domain adaptation, though it appears incremental by combining existing techniques.
The paper tackles the problem of predicting the future state of a time-varying probability distribution, proposing a method that uses kernel embeddings and vector-valued regression, and demonstrates its effectiveness through experiments on synthetic and real data, including an application in domain adaptation for classifiers.
We study the problem of predicting the future, though only in the probabilistic sense of estimating a future state of a time-varying probability distribution. This is not only an interesting academic problem, but solving this extrapolation problem also has many practical application, e.g. for training classifiers that have to operate under time-varying conditions. Our main contribution is a method for predicting the next step of the time-varying distribution from a given sequence of sample sets from earlier time steps. For this we rely on two recent machine learning techniques: embedding probability distributions into a reproducing kernel Hilbert space, and learning operators by vector-valued regression. We illustrate the working principles and the practical usefulness of our method by experiments on synthetic and real data. We also highlight an exemplary application: training a classifier in a domain adaptation setting without having access to examples from the test time distribution at training time.