Learning from dependent data ; ISTA Thesis

The most common assumption made in statistical learning theory is the assumption of the independent and identically distributed (i.i.d.) data. While being very convenient mathematically, it is often very clearly violated in practice. This disparity between the machine learning theory and applications underlies a growing demand in the development of algorithms that learn from dependent data and theory that can provide generalization guarantees similar to the independent situations. This thesis is dedicated to two variants of dependencies that can arise in practice. One is a dependence on the level of samples in a single learning task. Another dependency type arises in the multi-task setting when the tasks are dependent on each other even though the data for them can be i.i.d. In both cases we model the data (samples or tasks) as stochastic processes and introduce new algorithms for both settings that take into account and exploit the resulting dependencies. We prove the theoretical guarantees on the performance of the introduced algorithms under different evaluation criteria and, in addition, we compliment the theoretical study by the empirical one, where we evaluate some of the algorithms on two real world datasets to highlight their practical applicability.