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Noise is a basic ingredient in data, since observed data are always contaminated by unwanted deviations, i.e., noise, which, in the case of overdetermined systems (with more data than model parameters), cause the corresponding linear system of equations to have an imperfect solution. In addition, in the case of highly underdetermined parameterization, noise can be absorbed by the model, generating spurious solutions. This is a very undesirable situation that might lead to incorrect conclusions. We presented mathematical formalism based on the inverse problem theory combined with artificial intelligence methodologies to perform an enhanced sampling of noisy biomedical data to improve the finding of meaningful solutions. Random sampling methods fail for high-dimensional biomedical problems. Sampling methods such as smart model parameterizations, forward surrogates, and parallel computing are better suited for such problems. We applied these methods to several important biomedical problems, such as phenotype prediction and a problem related to predicting the effects of protein mutations, i.e., if a given single residue mutation is neutral or deleterious, causing a disease. We also applied these methods to de novo drug discovery and drug repositioning (repurposing) through the enhanced exploration of huge chemical space. The purpose of these novel methods that address the problem of noise and uncertainty in biomedical data is to find new therapeutic solutions, perform drug repurposing, and accelerate and optimize drug discovery, thus reestablishing homeostasis. Finding the right target, the right compound, and the right patient are the three bottlenecks to running successful clinical trials from the correct analysis of preclinical models. Artificial intelligence can provide a solution to these problems, considering that the character of the data restricts the quality of the prediction, as in any modeling procedure in data analysis. The use of simple and plain methodologies is crucial to tackling these important and challenging problems, particularly drug repositioning/repurposing in rare diseases.

We present the analysis of the defective genetic pathways of the Late-Onset Alzheimer's Disease (LOAD) compared to the Mild Cognitive Impairment (MCI) and Healthy Controls (HC) using different sampling methodologies. These algorithms sample the uncertainty space that is intrinsic to any kind of highly underdetermined phenotype prediction problem, by looking for the minimum-scale signatures (header genes) corresponding to different random holdouts. The biological pathways can be identified performing posterior analysis of these signatures established via cross-validation holdouts and plugging the set of most frequently sampled genes into different ontological platforms. That way, the effect of helper genes, whose presence might be due to the high degree of under determinacy of these experiments and data noise, is reduced. Our results suggest that common pathways for Alzheimer's disease and MCI are mainly related to viral mRNA translation, influenza viral RNA transcription and replication, gene expression, mitochondrial translation, and metabolism, with these results being highly consistent regardless of the comparative methods. The cross-validated predictive accuracies achieved for the LOAD and MCI discriminations were 84% and 81.5%, respectively. The difference between LOAD and MCI could not be clearly established (74% accuracy). The most discriminatory genes of the LOAD-MCI discrimination are associated with proteasome mediated degradation and G-protein signaling. Based on these findings we have also performed drug repositioning using Dr. Insight package, proposing the following different typologies of drugs: isoquinoline alkaloids, antitumor antibiotics, phosphoinositide 3-kinase PI3K, autophagy inhibitors, antagonists of the muscarinic acetylcholine receptor and histone deacetylase inhibitors. We believe that the potential clinical relevance of these findings should be further investigated and confirmed with other independent studies., Competing Interests: The authors declare no conflict of interest.