At the end of 2019, the World Health Organization (WHO) referred that the Public Health Commission of Hubei Province, China, reported cases of severe and unknown pneumonia. A new coronavirus, SARS-CoV-2, was identified as responsible for the lung infection, called COVID-19 (COronaVIrus Disease 2019). Although the definitive COVID-19 diagnosis is made through specific molecular tests, an early diagnosis by imaging became crucial to contain the spread, morbidity and mortality of the pandemic. In such context, chest X-ray radiography, as an element that assists the diagnosis allowing also the follow-up of the disease, plays a very important role since it is the most easily available and least expensive alternative. This work focuses on applying different linear type instance-level Multiple Instance Learning techniques to discriminate between COVID-19 and common viral pneumonia chest X-ray images, which is a difficult task due to the strong similarity characterizing the two classes. A relevant advantage of such approaches is that they are also suitable in terms of interpretability, as they easily allow clinicians to identify abnormal subregions in a positive radiographic image. Numerical experiments have been performed on a set of 200 images, obtaining the following results: accuracy = 95%, sensitivity = 99.29%, specificity = 91.24% and MCC = 0.9. The used algorithms appear promising in practical applications, taking into account their high speed and considering that no particular pre-processing techniques have been employed.