Bayesian linear regression for user-adaptive hearing aids

Modern digital hearing aids are devices with a Digital Signal Processor (DSP) which allows implementation of advanced signal processing algorithms. These algorithms have a lot of parameters which should to be set to values that ideally match the preferences and the behavior of the user. The optimization procedure is a very complex task. As a result many parameters of a hearing aid algorithm are fixed by the manufacturer at a best guess value. A few of the user parameters are personalized by the hearing aid dispenser based on the nature of the hearing loss. Not every individual user preference can be put into the hearing aid: some particularities of the user may be hard to represent into the algorithm, the typical acoustic environments or user preference patterns may be changing. We would like to personalize the hearing aid to the preferences of the user during usage. An adaptive model introduced in [Ypma et al., 2006] is used to learn the preferred parameters from the control operations of the user. In this report we have evaluated several methods for finding optimal linear models that can control the user preferred parameters in the adaptive hearing aid when the user preferences change. The underlying model that controls the adaptive hearing aid is based on the assumption that user preferred steering signal is linearly dependent on acoustic environmental features. Under this assumption the project focused on analysis of a few properties of a multiple linear regression problem. This properties were irrelevancy, redundancy, computational efficiency, probabilistic embedding and adaptivity. These analysis leads to a deeper study for one specific algorithm, named Variational Bayesian Least Square (VBLS). One of the advantages of VBLS in comparison to other methods discussed in this report is its numerical robustness. This is due to the fact that VBLS requires no matrix inversions and has linear computational complexity in the number of dimensions d which results in an algorithm which scales easily to high dimensional data sets. The performance of VBLS was tested with experiments on artificial regression data and real data. From our artificial regression data experiments, we concluded that VBLS does well at feature selection under the condition that a minimum number of samples is available for training. Data sets with large sample sizes and dimensions takes longer training time because of required computations increases. Therefore VBLS is a useful method for doing accurate regression and feature selection when we use it off-line. One further advantage of the VBLS method over the other analyzed methods is that one can compute a predictive distribution using the inferred parameter posteriors, allowing for a prediction with confidence levels. We can also extend VBLS algorithm into a sequential algorithm. The VBLS method presented in this report is a suitable method that can handle with irrelevancy, redundancy, computational efficiency, probabilistic embedding and therefore it is widely applicable over a certain range of data sets in off-line usage. The required large training times for high dimensional data sets provides that the VBLS method is not efficient for on-line (adaptive) usage. For that reason a further research is necessary to the VBLS method in order to improve it on computational efficiency for sequential (on-line) usage.