Alzheimer's disease (AD) is the most common form of dementia, while mild cognitive impairment (MCI) causes a slight but measurable decline in cognitive abilities. A person with MCI has an increased risk of developing AD or another dementia. Thus, it is of medical interest to develop predictive tools to assess this risk. A growing awareness exists that pro-oxidative state and neuro-inflammation are both involved in AD. However, the extent of this relationship is still a matter of debate. Due to the expected non-linear correlations between oxidative and inflammatory markers, traditional statistics is unsuitable to dissect their relationship with the disease. Artificial neural networks (ANNs) are computational models inspired by central nervous system networks, capable of machine learning and pattern recognition. The aim of this work was to disclose the relationship between immunological and oxidative stress markers in AD and MCI by the application of ANNs. Through a machine learning approach, we were able to construct an algorithm to classify MCI and AD with high accuracy. Such an instrument, requiring a small amount of immunological and oxidative-stress parameters, would be useful in the clinical practice. Moreover, applying an innovative non-linear mathematical technique, a global immune deficit was shown to be associated with cognitive impairment. Surprisingly, both adaptive and innate immunity were peripherally defective in AD and MCI patients. From this study, new pathogenetic aspects of these diseases could emerge.