Sparse model selection in the highly under-sampled regime
This addresses the challenge of model selection in data-scarce scenarios for fields like finance and neuroscience, though it is incremental as it builds on existing graphical model methods.
The authors tackled the problem of recovering sparse graphical model structures with very few samples by proposing a fast, non-optimization-based method using closed-form formulas. Numerical results showed it is comparable to best existing algorithms for sparse topologies and more accurate with hidden variables, as demonstrated on US stock market and neural data.
We propose a method for recovering the structure of a sparse undirected graphical model when very few samples are available. The method decides about the presence or absence of bonds between pairs of variable by considering one pair at a time and using a closed form formula, analytically derived by calculating the posterior probability for every possible model explaining a two body system using Jeffreys prior. The approach does not rely on the optimisation of any cost functions and consequently is much faster than existing algorithms. Despite this time and computational advantage, numerical results show that for several sparse topologies the algorithm is comparable to the best existing algorithms, and is more accurate in the presence of hidden variables. We apply this approach to the analysis of US stock market data and to neural data, in order to show its efficiency in recovering robust statistical dependencies in real data with non stationary correlations in time and space.