Automatic objective non-invasive detection of pathological voice based on computerized analysis of acoustic signals can play an important role in early diagnosis, progression tracking and even effective treatment of pathological voices. In search towards such a robust voice pathology detection system we investigated 3 distinct classifiers within supervised learning and anomaly detection paradigms. We conducted a set of experiments using a variety of input data such as raw waveforms, spectrograms, mel-frequency cepstral coefficients (MFCC) and conventional acoustic (dysphonic) features (AF). In comparison with previously published works, this article is the first to utilize combination of 4 different databases comprising normophonic and pathological recordings of sustained phonation of the vowel /a/ unrestricted to a subset of vocal pathologies. Furthermore, to our best knowledge, this article is the first to explore gradient boosted trees and deep learning for this application. The following best classification performances measured by F1 score on dedicated test set were achieved: XGBoost (0.733) using AF and MFCC, DenseNet (0.621) using MFCC, and Isolation Forest (0.610) using AF. Even though these results are of exploratory character, conducted experiments do show promising potential of gradient boosting and deep learning methods to robustly detect voice pathologies.