What will be a suitable model for solving the regression problem? Is there any hybrid algorithm or new model/framework exist to solve this problem in deep learning. How much deep learning is promising for regression tasks.
There are several machine/deep learning options available to solve regression problems. Some basic and easy algorithms to start with are decision trees, support vector regression, lasso regression and aritificial neural networks itself. As deep learning is data driven modelling, so the accuracy of these models will depend upon the quantity and quality of your data. There are some hybrid models based on recurrent neural network and 1D convolutional neural networks are also available for complicated time series problems.
It is very similar to the use of deep learning for the classification problem. Just you use different layers at the end of the network. e.g. in CNN instead of a softmax layer and cross-entropy loss, you can use a regression layer and MSE loss, etc.
It will be as useful as deep classification networks. But it depends on your data and problem. RNNs (especially LSTMs) are useful for time-series and sequential data such as speech, music, and other audio signals, EEG and ECG signals, stock market data, weather forecasting data, etc.
If you are using MATLAB, here are two examples (CNN and LSTM) for the implementation: