Inverse statistical problems: from the inverse Ising problem to data science. Nguyen, H. C., Zecchina, R., & Berg, J. Advances in Physics, 0(0):1--65, June, 2017.
Inverse statistical problems: from the inverse Ising problem to data science [link]Paper  doi  abstract   bibtex   
Inverse problems in statistical physics are motivated by the challenges of ‘big data’ in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be reversed: Instead of calculating observables on the basis of model parameters, we seek to infer parameters of a model based on observations. In this review, we focus on the inverse Ising problem and closely related problems, namely how to infer the coupling strengths between spins given observed spin correlations, magnetizations, or other data. We review applications of the inverse Ising problem, including the reconstruction of neural connections, protein structure determination, and the inference of gene regulatory networks. For the inverse Ising problem in equilibrium, a number of controlled and uncontrolled approximate solutions have been developed in the statistical mechanics community. A particularly strong method, pseudolikelihood, stems from statistics. We also review the inverse Ising problem in the non-equilibrium case, where the model parameters must be reconstructed based on non-equilibrium statistics.
@article{nguyen_inverse_2017,
	title = {Inverse statistical problems: from the inverse {Ising} problem to data science},
	volume = {0},
	issn = {0001-8732},
	shorttitle = {Inverse statistical problems},
	url = {http://dx.doi.org/10.1080/00018732.2017.1341604},
	doi = {10.1080/00018732.2017.1341604},
	abstract = {Inverse problems in statistical physics are motivated by the challenges of ‘big data’ in different fields, in particular high-throughput experiments in biology. In inverse problems, the usual procedure of statistical physics needs to be reversed: Instead of calculating observables on the basis of model parameters, we seek to infer parameters of a model based on observations. In this review, we focus on the inverse Ising problem and closely related problems, namely how to infer the coupling strengths between spins given observed spin correlations, magnetizations, or other data. We review applications of the inverse Ising problem, including the reconstruction of neural connections, protein structure determination, and the inference of gene regulatory networks. For the inverse Ising problem in equilibrium, a number of controlled and uncontrolled approximate solutions have been developed in the statistical mechanics community. A particularly strong method, pseudolikelihood, stems from statistics. We also review the inverse Ising problem in the non-equilibrium case, where the model parameters must be reconstructed based on non-equilibrium statistics.},
	number = {0},
	journal = {Advances in Physics},
	author = {Nguyen, H. Chau and Zecchina, Riccardo and Berg, Johannes},
	month = jun,
	year = {2017},
	keywords = {02.30.Zz inverse problems, 02.50.Tt inference methods, 89.75.-k complex systems, Data analysis, inference methods, inverse problems, network reconstruction, statistical physics of complex systems},
	pages = {1--65}
}
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