Machine learning algorithms rely heavily on the representation of the data they are presented with. In particular, text documents (and often images) are traditionally expressed as bag-of-words feature vectors (e.g. as tf-idf). Recently Glorot et al. showed that stacked denoising autoencoders (SDA), a deep learning algorithm, can learn representations that are far superior over variants of bag-of-words. Unfortunately, training SDAs often requires a prohibitive amount of computation time and is non-trivial for non-experts.In this work, we show that with a few modifications of the SDA model, we can relax the optimization over the hidden weights into convex optimization problems with closed form solutions. Further, we show that the expected value of the hidden weights after infinitely many training iterations can also be computed in closed form. The resulting transformation (which we call marginalized-SDA) can be computed in no more than 20 lines of straight-forward Matlab code and requires no prior expertise in machine learning. The representations learned with mSDA behave similar to those obtained with SDA, but the training time is reduced by several orders of magnitudes. For example, mSDA matches the world-record on the Amazon transfer learning benchmark, however the training time shrinks from several days to a few minutes.