Inverse statistical problems: from the inverse Ising problem to data science
By H. C. Nguyen, Riccardo Zecchina, Johannes Berg. 2017
299 citations recorded by the source corpus.
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.
Subfields: Computational Mathematics, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/fde0b586e3bc9e5139a14493044bce9ff61706d4
How researchers see this paper
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In Mathematical Physics
In Statistics and Probability
- Kyle Cranmer
- I. Cirac
- Leslie Vogt-Maranto
- Laurent Daudet
- Naftali Tishby
- Lenka Zdeborov'a
- Maria Schuld
- Giuseppe Carleo
Citations in the corpus
- A high-bias, low-variance introduction to Machine Learning for physicists (2018, unknown): “Therefore, we largely ignore the incredibly rich physics-based literature on fitting Ising-like MaxEnt models (see the recent reviews (Baldassi et al., 2018; Nguyen et al., 2017) and references therein).”
- Machine learning and the physical sciences (2019, methodology): “Indeed the Boltzmann machine is often called the inverse Ising model in the physics literature and used extensively a range of area, for a recent review on the physics of Boltzmann machines see (Nguyen et al., 2017).”