PTML: Perturbation-Theory Machine Learning methods have been developed by Humbert Gonzalez-Diaz et al  to seek models able to predict multiple properties f(si, cj)k of type k of a system (si) at the same time (multi-output and multi-objective) taking into consideration variations (perturbations) in multiple experimental conditions cj = (c0, c1, c2, ..... cn) at the same time with respect to a value of reference or expected. PTML-like models have been applied for different authors to study drugs, proteins, nanoparticles, complex networks, social systems, etc. [1-17]. In the particular case of a PTML linear models we can fit an equation with the general form f(si, cj)new = a0 + a1· f(si, cj)ref + SUM(bk·PTO(cj)k). In this model PTO(cj)k are PT operators measuring the perturbations in the new system si with respect to the system of reference sr with observed or expected property f(si, cj)ref. First, we need to calculate the values of the PTOs in the data pre-processing step. This PTOs allow us to perform an Information Fusion process with variables and conditions from different sources. Moving Averages (MA), Multi-condition MA (MMAs), Double MAs, Co-variance Operators, etc. are some examples of useful PTOs. After that, we can use Multiple Linear Regression (MLR), Linear Discriminant Analysis (LDA), or other linear ML techniques to seek the PTML model. In the non-linear cases, we can fit the PTML models using Artificial Neural Networks (ANN), Support Vector Machines (SVM), Classification Trees, and other ML methods.
General theory for multiple input-output perturbations in complex molecular systems. 1. Linear QSPR electronegativity models in physical, organic, and medicinal chemistry. González-Díaz H, Arrasate S, Gómez-SanJuan A, Sotomayor N, Lete E, Besada-Porto L, Ruso JM. Curr Top Med Chem. 2013;13(14):1713-41.
Simón-Vidal L, García-Calvo O, Oteo U, Arrasate S, Lete E, Sotomayor N, González-Díaz H. Perturbation-Theory and Machine Learning (PTML) Model for High-Throughput Screening of Parham Reactions: Experimental and Theoretical Studies. J Chem Inf Model. 2018 Jul 23;58(7):1384-1396. doi: 10.1021/acs.jcim.8b00286.
Ferreira da Costa J, Silva D, Caamaño O, Brea JM, Loza MI, Munteanu CR, Pazos A, García-Mera X, González-Díaz H. Perturbation Theory/Machine Learning Model of ChEMBL Data for Dopamine Targets: Docking, Synthesis, and Assay of New l-Prolyl-l-leucyl-glycinamide Peptidomimetics. ACS Chem Neurosci. 2018 Jun 25. doi: 10.1021/acschemneuro.8b00083.
Luan F, Kleandrova VV, González-Díaz H, Ruso JM, Melo A, Speck-Planche A, Cordeiro MN. Computer-aided nanotoxicology: assessing cytotoxicity of nanoparticles under diverse experimental conditions by using a novel QSTR-perturbation approach. Nanoscale. 2014 Sep 21;6(18):10623-30. doi: 10.1039/c4nr01285b.
Martínez-Arzate SG, Tenorio-Borroto E, Barbabosa Pliego A, Díaz-Albiter HM, Vázquez-Chagoyán JC, González-Díaz H. PTML Model for Proteome Mining of B-Cell Epitopes and Theoretical-Experimental Study of Bm86 Protein Sequences from Colima, Mexico. J Proteome Res. 2017 Nov 3;16(11):4093-4103. doi: 10.1021/acs.jproteome.7b00477.