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Table 1 Comparison of the dynamic modeling approaches for temporal omics data, the detailed methods, mining tasks, and type of problems, examples, and related references

From: Computational dynamic approaches for temporal omics data with applications to systems medicine

General approaches Examples Type of problems, tasks Important features and functions Some Reference
Math based Deterministic, static
Stochastic, dynamic
Differential equations, Fourier transform, topology based matrix factorization
Stochastic differential equations, Gaussian graphical models, Probabilistic Boolean networks
State space model and or hidden Markov model, Markov random fields
Parameter/rate estimations, network inference, prediction, time course (I-III)
Dynamic parameter estimations
transition process
Causal or non-causal temporal relationships
Fixed, stable parameter, structure estimation, time invaried, non-causal
Direct relationship,
Nonlinear or linear.
Probabilistic time varied,
Nonlinear or linear
Direct or indirect relationship time course (I-III)
[23,24,25,26,27,28,29,30] [36,37,38,39,40] [31,32,33,34,35] [41, 42] [43]
Statistical based
Bayesian methods
Regression vector autoregressive (VAR) models, Curve fitting, spline methods, Granger causality
Bayesian models (linear or nonlinear model), growth model
Parameter estimations, predictions, hypothesis testing, biomarker/target identifications
Heterogeneity discovery
Explanatory relationship without prior knowledge, pure data based time course (I-III) or phenotype dependent (IV)
With prior or empirical
Knowledge, probabilistic
[35, 44, 45] [46] [41, 42, 47,48,49,50,51,52,53,54,55,56,57]
Computer sciences based
Machine learning, data mining
discriminative generative
Neural network
Distance or correlation based
Supervised classification with wrapper
Feedback Forward NN, time recurrent NN, convolution NN, Bayesian NN
Subtypes, modular, and heterogeneity discovery, Pattern discovery and identification
Dynamic changes and trajectories
Complex relationship, structure
Time course (I-III) or phenotype dependent (IV)
Without knowing the outcome, classes,
Defined outcomes/classes conditional joint analysis
Time varied or invariaed
Nonlinear or linear
Direct or indirect relationship,
Explanatory or predictive
time course (I-III) or
phenotype dependent (IV)
[26,27,28,29] [58,59,60,61,62,63,64,65,66] [68,69,70,71,72,73,74,75]
Interactions and network, pathway function based Predictions, integrated with public databases phenotype dependent (IV), Graphic based
Causal hypothesis
Direct or indirect relationship,
Nonlinear or linear
integrated with public databases
interactive through manually
or automate
[89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109, 116, 162] [83,84,85] [86] [87]