Statistical learning when observations are not iid As far as I am concerned, statistical/machine learning algorithms always suppose that data are independent and identically distributed ($iid$).
My question is: what can we do when this assumption is clearly unsatisfied? For instance, suppose that we have a data set whith repeated measurements on the same observations , so that both the cross-section and the time dimensions are important (what econometricians call a panel data set, or statisticians refer to as longitudinal data, which is distinct from a time series).
An example could be the following. In 2002, we collect the prices (henceforth $Y$) of 1000 houses in New York, together with a set of covariates (henceforth $X$). In 2005, we collect the same variables on the same houses. Similar happens in 2009 and 2012. Say I want to understand the relationship between $X$ and $Y$. Were the data $iid$, I could easily fit a random forest (or any other supervised algorithm, for what matters), thus estimating the conditional expectation of $Y$ given $X$. However, there is clearly some auto-correlation in my data. How can I handle this?

Markov processes are not only very general ways to analyze longitudinal data with statistical models, they also lend themselves to machine learning.  They work because by modeling transition probabilities conditional on previous states the records are conditionally independent and may be treated as coming from different independent subjects.  One can use discrete or continuous time processes, discrete being simpler.  The main work comes from post-estimation processing to convert transition probabilities into unconditional (on previous state) state occupancy probabilities AKA current status probabilities.  See this and other documents in this.
