Major depressive disorder, referred to as depression, is a leading cause of disability, absence from work, and premature death. Automatic assessment of depression from speech is a critical step towards improving diagnosis and treatment of depression. Previous works on depression assessment from speech considered various acoustic features extracted from speech to estimate depression severity. But performance of these approaches is not at clinical standards, and thus requires further improvement. In this work, we examine two novel approaches for improving depression severity estimation from short audio recordings of speech. Specifically, in audio recordings of a narrative by individuals diagnosed with major depressive disorder, we analyze spectral-based and excitation source-based features extracted from speech, and significance of sentiment and emotion classification in estimation of depression severity. Initial results indicate synchrony between depression scores and the sentiment and emotion labels. We propose the use of sentiment and emotion based embeddings obtained using machine learning techniques in estimation of depression severity. We also propose use of multi-task training to better estimate depression severity. We show that the proposed approaches provide additive improvements in the estimation of depression severity.