Mean-field theory of Boltzmann machine learning

Tanaka, Toshiyuki

doi:10.1103/physreve.58.2302

Cited by 157 publications

(208 citation statements)

References 13 publications

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“…4 provides another way to score ligands. However, the classification accuracy does not significantly improve if the energy is estimated using the leading-order mean-field approximation (37). Although interpreting our algorithm in terms of a binding energy function requires experimental verification through binding energy measurements, we note that this interpretation offers several conceptual insights.…”

Section: Physical Modelmentioning

confidence: 86%

Predicting protein–ligand affinity with a random matrix framework

Lee

Brenner

Colwell

2016

Proc. Natl. Acad. Sci. U.S.A.

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Rapid determination of whether a candidate compound will bind to a particular target receptor remains a stumbling block in drug discovery. We use an approach inspired by random matrix theory to decompose the known ligand set of a target in terms of orthogonal "signals" of salient chemical features, and distinguish these from the much larger set of ligand chemical features that are not relevant for binding to that particular target receptor. After removing the noise caused by finite sampling, we show that the similarity of an unknown ligand to the remaining, cleaned chemical features is a robust predictor of ligand-target affinity, performing as well or better than any algorithm in the published literature. We interpret our algorithm as deriving a model for the binding energy between a target receptor and the set of known ligands, where the underlying binding energy model is related to the classic Ising model in statistical physics.drug discovery | random matrix theory | protein-ligand affinity | computational pharmacology | statistical physics F inding new ligands that bind to a given target is both a crucial step and a major stumbling block in modern drug discovery. Numerous attempts have been made to develop computational algorithms to predict the binding affinity of a ligand to a given receptor, which would allow potential compounds to be screened in silico, reducing costs and saving time. In particular, in response to the wealth of experimental data that exists both within pharmaceutical companies, and also in freely accessible online databases such as ChEMBL (1), approaches that attempt to "learn" from these data are increasingly gaining attention (2).An intuitive data-driven approach builds on the hypothesis that chemical commonalities among the known ligand set reveal salient features of the binding site. A corollary is that ligands with similar chemical functionality are expected to share similar binding affinity toward a particular receptor (3,4). This suggests that the known ligand set of a given target can be used to learn criteria that predict whether a novel ligand will bind to the target. This ligand-based approach is a powerful paradigm that does not require structural information about the receptor, which is potentially arduous to obtain, unlike other more atomistic methods such as docking or molecular dynamics.Any ligand-based method requires a way to quantify the chemical functionalities of a ligand, and various chemical descriptors have been proposed. Examples include a vector of measured or predicted physical properties (5-8), a vector enumerating the presence or absence of known functional groups on the ligand (9, 10), a vectorial representation of connectivities in the molecular graph (11, 12) (known also as molecular fingerprints), and simply the 3D shape of the ligand (13-16). Existing approaches then take the descriptor associated with each ligand and compare ligands with each other, for example through the Tanimoto coefficient (17, 18).Nonetheless, regardless of how ligand chemical func...

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Section: Physical Modelmentioning

confidence: 86%

Predicting protein–ligand affinity with a random matrix framework

Lee

Brenner

Colwell

2016

Proc. Natl. Acad. Sci. U.S.A.

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“…As a general remark, note that the parameter estimation involves two kinds of approximations: one in the inverse problem formulas (5) and (6), that require m and χ, i.e.…”

Section: Inverse Problem For the Curie-weiss Modelmentioning

confidence: 99%

“…This amounts to study how to infer the parameters of a model starting from the observation of real data. In particular, the application of the inverse Ising model, although known for a long time as Boltzmann machine learning [5,6], has aroused interest in recent years in many different fields (physics [1,2], neuroscience [7,8], biology [9,10], social and health sciences [11][12][13][14]), especially since the advent of the big-data age. In these applications, stemming from the assumption that the real world system of interest is described by an Ising model with hamiltonian H, the inverse problem amounts to fit H to the system, i.e.…”

Section: Introductionmentioning

confidence: 99%

Inverse problem for multispecies ferromagneticlike mean-field models in phase space with many states

Fedele

Vernia

2017

Phys. Rev. E

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In this paper we solve the inverse problem for a class of mean field models (CurieWeiss model and its multi-species version) when multiple thermodynamic states are present, as in the low temperature phase where the phase space is clustered. The inverse problem consists in reconstructing the model parameters starting from configuration data generated according to the distribution of the model. We show that the application of the inversion procedure without taking into account the presence of many states produces very poor inference results. This problem is overcomed using the clustering algorithm. When the system has two symmetric states of positive and negative magnetization, the parameter reconstruction can be also obtained with smaller computational effort simply by flipping the sign of the magnetizations from positive to negative (or viceversa). The parameter reconstruction fails when the system is critical: in this case we give the correct inversion formulas for the Curie-Weiss model and we show that they can be used to measuring how much the system is close to criticality.

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“…Statistical physicists have contributed significantly to building approximate learning methods for the equilibrium Ising model. Among them the most studied are Naïve Mean Field [6,7], Thouless-Anderson-Palmer approximation (TAP, i.e., first and second order Plefka expansion) [8] and a message passing algorithm called Belief Propagation [9,10,11]. Nevertheless the assumption of symmetric connectivity in biological networks is not realistic, and making it can lead to incorrect identification of interactions.…”

Section: Introductionmentioning

confidence: 99%

Belief propagation and replicas for inference and learning in a kinetic Ising model with hidden spins

Battistin¹,

Hertz²,

Tyrcha³

et al. 2015

J. Stat. Mech.

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Abstract. We propose a new algorithm for inferring the state of hidden spins and reconstructing the connections in a synchronous kinetic Ising model, given the observed history. Focusing on the case in which the hidden spins are conditionally independent of each other given the state of observable spins, we show that calculating the likelihood of the data can be simplified by introducing a set of replicated auxiliary spins. Belief Propagation (BP) and Susceptibility Propagation (SusP) can then be used to infer the states of hidden variables and learn the couplings. We study the convergence and performance of this algorithm for networks with both Gaussian-distributed and binary bonds. We also study how the algorithm behaves as the fraction of hidden nodes and the amount of data are changed, showing that it outperforms the TAP equations for reconstructing the connections.

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Mean-field theory of Boltzmann machine learning

Cited by 157 publications

References 13 publications

Predicting protein–ligand affinity with a random matrix framework

Predicting protein–ligand affinity with a random matrix framework

Inverse problem for multispecies ferromagneticlike mean-field models in phase space with many states

Belief propagation and replicas for inference and learning in a kinetic Ising model with hidden spins

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