Alzheimer’s dementia (AD) is a chronic neurodegenerative illness that manifests in a gradual decline of cognitive function. Early identification of AD is essential for managing the ensuing cognitive deficits, which may lead to a better prognostic outcome. Speech data can serve as a window into cognitive functioning and can be used to screen for early signs of AD. This paper describes methods for learning models using speech samples from the DementiaBank database, for identifying which subjects have Alzheimer’s dementia. We consider two machine learning tasks: 1) binary classification to distinguish patients from healthy controls, and 2) regression to estimate each subject’s Mini-Mental State Examination (MMSE) score. To develop models that can use acoustic and/or language features, we explore a variety of dimension reduction techniques, training algorithms, and fusion strategies. Our best performing classification model, using language features with dimension reduction and regularized logistic regression, achieves an accuracy of 85.4% on a held-out test set. On the regression task, a linear regression model trained on a reduced set of language features achieves a root mean square error (RMSE) of 5.62 on the test set. These results demonstrate the promise of using machine learning for detecting cognitive decline from speech in AD patients.