# A Bayesian Modeling Approach to Situated Design of Personalized Soundscaping Algorithms
###### Abstract
On the other hand, the probabilistic generative acoustic modeling approach supports computationally cheap and automatable parameter and state estimation [25], in particular when variational Bayesian inference techniques are employed [26; 27]. Therefore, we see the probabilistic modeling approach to be better suited for situated hearing aid algorithm design. The approach that we envision differs markedly from a conventional algorithm design cycle. For instance, in the hearing aid industry, engineering teams develop noise reduction algorithms in an offline fashion. Their companies push commercial algorithm updates about once a year when new versions are developed. In contrast, our proposed framework supports end users to create personalized noise reduction algorithms in an online fashion under situated conditions, thus providing them with more control over their desired acoustic environment (\"soundscaping\"). The main idea of our approach is as follows. To design a noise reduction algorithm in-the-field with users rather than engineers, we need an automated design loop. In order to create an automated design loop, we propose a fully probabilistic framework where all design tasks can be formulated as (automatable) probabilistic inference tasks on a generative model for mixtures of acoustic signals. Concretely, we first specify a generative probabilistic model for observed acoustic signals by decomposing the observed signal into its constituent acoustic sources and by modeling these as dynamic latent variable models [28; 29]. Each constituent signal will be modeled and these models will be combined to create a model for the observed mixture. Next, all signal processing tasks (source modeling, source separation and soundscaping) are expressed as automatable inference tasks on the generative model. In order to provide relevant data for algorithm design, users can record short fragments of their acoustic environment under situated conditions. After the fragment has been recorded the proposed framework will automatically train the corresponding signal models to help separate these sources in the observed mixture. The estimated source signals in the generative model are then individually amplified (or suppressed) according to the user preferences and subsequently added back together,resulting in a \"re-weighted\" mixture signal. Technically, this idea is based on the method of informed source separation [6], using on-the-spot trained probabilistic signal models. The rest of this paper is organized as follows. In Section 2 we present our methodology. Specifically, in Section 2.1 we propose a modular generative probabilistic modeling framework for situated design of soundscaping algorithms. We specify two distinct probabilistic models for mixtures of acoustic signals in Section 2.2, which we will use to demonstrate our framework. In the proposed design framework, all computational tasks (source modeling, source separation and soundscaping) are framed as probabilistic inference tasks that can be automatically executed through message passing-based inference in a factor graph representation of the underlying model. In Section 2.3, we review factor graphs and automated inference by message passing in these graphs. We perform experiments using these message passing methods to demonstrate our framework and discuss performance results in Section 3. Finally, Section 4 provides a discussion on the presented framework. In terms of theoretical contributions, in Section 2.2.1 we generalize the model used in the Algonquin algorithm [9], which models the non-linear interaction of two signal in the log-power spectrum as a factor graph node for multiple inputs and unknown noise precision; and we derive variational message passing update rules for this node in Section 2.3.5. Furthermore, we provide an intuitive explanation for the derived messages. Additionally, in Section 2.2.2 we introduce an alternative source mixing model based on Gaussian scale models [30] for acoustic signals, represented by their pseudo log-power spectrum.