The work describes an application of a recently developed machine-learning technique called Mondrian predictors to risk assessment of ovarian and breast cancers. The analysis is based on mass spectrometry profiling of human serum samples that were collected in the United Kingdom Collaborative Trial of Ovarian Cancer Screening. The work describes the technique and presents the results of classification (diagnosis) and the corresponding measures of confidence of the diagnostics. The main advantage of this approach is a proven validity of prediction. The work also describes an approach to improve early diagnosis of ovarian and breast cancers since the data in the United Kingdom Collaborative Trial of Ovarian Cancer Screening were collected over a period of 7 years and do allow to make observations of changes in human serum over that period of time. Significance of improvement is confirmed statistically (for up to 11 months for ovarian cancer and 9 months for breast cancer). In addition, the methodology allowed us to pinpoint the same mass spectrometry peaks as previously detected as carrying statistically significant information for discrimination between healthy and diseased patients. The results are discussed.