Section: New Results

Stochastic algorithms with descent guarantees for ICA

Independent component analysis (ICA) is a widespread data exploration technique, where observed signals are modeled as linear mixtures of independent components. From a machine learning point of view, it amounts to a matrix factorization problem with a statistical independence criterion. Infomax is one of the most used ICA algorithms. It is based on a loss function which is a non-convex log-likelihood. We develop a new majorization-minimization framework adapted to this loss function. We derive an online algorithm for the streaming setting, and an incremental algorithm for the finite sum setting, with the following benefits. First, unlike most algorithms found in the literature, the proposed methods do not rely on any critical hyper-parameter like a step size, nor do they require a line-search technique. Second, the algorithm for the finite sum setting, although stochas-tic, guarantees a decrease of the loss function at each iteration. Experiments demonstrate progress on the state-of-the-art for large scale datasets, without the necessity for any manual parameter tuning.

Figure 8. Online algorithms applied on a 32 GB real dataset with p = 100 and n = $4\times {10}^7$ . Time is in logarithmic scale. Values of the loss on left out data greater than its initial value are truncated.

More information can be found in [39].