As far as I understand CNN potentially has a future . Regression (dependency control of variables) needs minimizing the "false positive" so that results are not skewed.
Deep learning is a analytical tool for structural decomposition that helps in formulating equation for regression (and observe them at multi-levels)
In general cases, once unsupervised pre-training is performed, one has to attach logistic regression layer to the output of the Net, and then the full system is fine-tuned for the regression-problem using gradient descent (Supervised training).
I consider that advanced regression techniques, like deep neural networks, may be suitable for more complicated regression problems.
Thus, deep learning is good for such problems. In addition, deep learning may give better results (e.g. better coefficient of determination and smaller mean absolute error), than other regression techniques for simpler problems.
The regression problem formulation has to be done based on parameters that change internally (with no external dependency ) . In terms of regression layers that are formed by this internal feedback and you have control over the changes (based on , say likelihood of values) . The depth aspect has to be controlled at the convergence of values based on NN (for entry/excitation and exit/inhibition ) between the layers . so that you do not spiral .
Look at the flip side of using gradient descent !!!
The below paper is a recent example of using Deep Learning for regression problems;
Qureshi, Aqsa Saeed, et al. "Wind power prediction using deep neural network based meta regression and transfer learning." Applied Soft Computing 58 (2017): 742-755.
And Also, this paper uses Deep Learning for regression: " Deep Belief Networks Based Feature Generation and Regression for Predicting Wind Power", 2018, arXiv:1807.11682v1 [cs.LG].
Preprint Deep Belief Networks Based Feature Generation and Regression...