Missing modalities are common in real-world healthcare datasets. They make supervised learning challenging as traditional algorithms cannot be applied directly. Although widely used in practice, imputing missing modalities before supervised learning relies on complex and computationally costly strategies, which can introduce bias in the data and impact subsequent prediction models. Therefore, their use can be risky in certain sensitive applications such as healthcare. To palliate these limitations, this thesis studies the usage of imputation-free techniques and proposes a novel algorithm, MMARE, which consists of an end-to-end imputation-free strategy designed for supervised learning with missing modalities that can handle inputs of varying dimensions.