Identifying patients with Mild Cognitive Impairment (MCI) who are likely to convert to dementia has recently attracted increasing attention in Alzheimer's disease (AD) research. An accurate prediction of conversion from MCI to AD can aid clinicians to initiate treatments at early stage and monitor their effectiveness. However, existing prediction systems based on the original biosignatures are not satisfactory. In this paper, we propose to fit the prediction models using pairwise biosignature interactions, thus capturing higher-order relationship among biosignatures. Specifically, we employ hierarchical constraints and sparsity regularization to prune the high-dimensional input features. Based on the significant biosignatures and underlying interactions identified, we build classifiers to predict the conversion probability based on the selected features. We further analyze the underlying interaction effects of different biosignatures based on the so-called stable expectation scores. We have used 293 MCI subjects from Alzheimer's Disease Neuroimaging Initiative (ADNI) database that have MRI measurements at the baseline to evaluate the effectiveness of the proposed method. Our proposed method achieves better classification performance than state-of-the-art methods. Moreover, we discover several significant interactions predictive of MCI-to-AD conversion. These results shed light on improving the prediction performance using interaction features.