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Hearing Aid (HA) algorithms need to be tuned ("fitted") to match the impairment of each specific patient. The lack of a fundamental HA fitting theory is a strong contributing factor to an unsatisfying sound experience for about 20% of hearing aid patients. This paper proposes a probabilistic modeling approach to the design of HA algorithms. The proposed method relies on a generative probabilistic model for the hearing loss problem and provides for automated inference of the corresponding (1) signal processing algorithm, (2) the fitting solution as well as a principled (3) performance evaluation metric. All three tasks are realized as message passing algorithms in a factor graph representation of the generative model, which in principle allows for fast implementation on hearing aid or mobile device hardware. The methods are theoretically worked out and simulated with a custom-built factor graph toolbox for a specific hearing loss model.

We introduce Reactive Message Passing (RMP) as a framework for executing schedule-free, robust and scalable message passing-based inference in a factor graph representation of a probabilistic model. RMP is based on the reactive programming style that only describes how nodes in a factor graph react to changes in connected nodes. The absence of a fixed message passing schedule improves robustness, scalability and execution time of the inference procedure. We also present ReactiveMP.jl, which is a Julia package for realizing RMP through minimization of a constrained Bethe free energy. By user-defined specification of local form and factorization constraints on the variational posterior distribution, ReactiveMP.jl executes hybrid message passing algorithms including belief propagation, variational message passing, expectation propagation, and expectation maximisation update rules. Experimental results demonstrate the improved performance of ReactiveMP-based RMP in comparison to other Julia packages for Bayesian inference across a range of probabilistic models. In particular, we show that the RMP framework is able to run Bayesian inference for large-scale probabilistic state space models with hundreds of thousands of random variables on a standard laptop computer., preprint, submitted, 27 pages, 15 figures, 7 tables, 11 listings

Stochastic approximation methods for variational inference have recently gained popularity in the probabilistic programming community since these methods are amenable to automation and allow online, scalable, and universal approximate Bayesian inference. Unfortunately, common Probabilistic Programming Languages (PPLs) with stochastic approximation engines lack the efficiency of message passing-based inference algorithms with deterministic update rules such as Belief Propagation (BP) and Variational Message Passing (VMP). Still, Stochastic Variational Inference (SVI) and Conjugate-Computation Variational Inference (CVI) provide principled methods to integrate fast deterministic inference techniques with broadly applicable stochastic approximate inference. Unfortunately, implementation of SVI and CVI necessitates manually driven variational update rules, which does not yet exist in most PPLs. In this paper, we cast SVI and CVI explicitly in a message passing-based inference context. We provide an implementation for SVI and CVI in ForneyLab, which is an automated message passing-based probabilistic programming package in the open source Julia language. Through a number of experiments, we demonstrate how SVI and CVI extends the automated inference capabilities of message passing-based probabilistic programming.

We present a variational Bayesian identification procedure for polynomial NARMAX models based on message passing on a factor graph. Message passing allows us to obtain full posterior distributions for regression coefficients, precision parameters and noise instances by means of local computations distributed according to the factorization of the dynamic model. The posterior distributions are important to shaping the predictive distribution for outputs, and ultimately lead to superior model performance during 1-step ahead prediction and simulation.

Active inference (ActInf) is an emerging theory that explains perception and action in biological agents in terms of minimizing a free energy bound on Bayesian surprise. Goal-directed behavior is elicited by introducing prior beliefs on the underlying generative model. In contrast to prior beliefs, which constrain all realizations of a random variable, we propose an alternative approach through chance constraints, which allow for a (typically small) probability of constraint violation, and demonstrate how such constraints can be used as intrinsic drivers for goal-directed behavior in ActInf. We illustrate how chance-constrained ActInf weights all imposed (prior) constraints on the generative model, allowing, for example, for a trade-off between robust control and empirical chance constraint violation. Second, we interpret the proposed solution within a message passing framework. Interestingly, the message passing interpretation is not only relevant to the context of ActInf, but also provides a general-purpose approach that can account for chance constraints on graphical models. The chance constraint message updates can then be readily combined with other prederived message update rules without the need for custom derivations. The proposed chance-constrained message passing framework thus accelerates the search for workable models in general and can be used to complement message-passing formulations on generative neural models.

Model evidence is a fundamental performance measure in Bayesian machine learning as it represents how well a model fits an observed data set. Since model evidence is often an intractable quantity, the literature often resorts to computing instead the Bethe Free Energy (BFE), which for cyclefree models is a tractable upper bound on the (negative log-) model evidence. In this paper, we propose a different and faster evidence computation approach by tracking local normalization constants of sum-product messages, termed scale factors. We tabulate scale factor update rules for various elementary factor nodes and by experimental validation we verify the correctness of these update rules for models involving both discrete and continuous variables. We show how tracking scale factors leads to performance improvements compared to the traditional BFE computation approach.

We address object tracking by radar and the robustness of the current state-of-the-art methods to process outliers. The standard tracking algorithms extract detections from radar image space to use it in the filtering stage. Filtering is performed by a Kalman filter, which assumes Gaussian distributed noise. However, this assumption does not account for large modeling errors and results in poor tracking performance during abrupt motions. We take the Gaussian Sum Filter (single-object variant of the Multi Hypothesis Tracker) as our baseline and propose a modification by modelling process noise with a distribution that has heavier tails than a Gaussian. Variational Bayes provides a fast, computationally cheap inference algorithm. Our simulations show that - in the presence of process outliers - the robust tracker outperforms the Gaussian Sum filter when tracking single objects., Comment: 6 pages, 8 figures. Published as part of the proceedings of the IEEE International Workshop on Signal Processing Systems 2022

Variational Message Passing facilitates automated variational inference in factorized probabilistic models where connected factors are conjugate pairs. Conjugate-computation Variational Inference (CVI) extends the applicability of VMP to models comprising both conjugate and non-conjugate factors. CVI makes use of a gradient that is estimated by Monte Carlo (MC) sampling, which potentially leads to substantial computational load. As a result, for models that feature a large number of non-conjugate pairs, CVI-based inference may not scale well to larger model sizes. In this paper, we propose a Gaussian Process-enhanced CVI approach, called GP-CVI, to amortize the computational costs caused by the MC sampling procedures in CVI. Specifically, we train a Gaussian process regression (GPR) model based on a set of incoming outgoing message pairs that were generated by CVI. In operation, we use the “cheaper” GPR model to produce outgoing messages and resort to the more accurate but expensive CVI message only if the variance of the outgoing message exceeds a threshold. By experimental validation, we show that GP-CVI gradually uses more fast memory-based update rule computations, and less sampling-based update rule computations. As a result, GP-CVI speeds up CVI with a controllable effect on the accuracy of the inference procedure.

Bayesian model reduction provides an efficient approach for comparing the performance of all nested sub-models of a model, without re-evaluating any of these sub-models. Until now, Bayesian model reduction has been applied mainly in the computational neuroscience community. In this paper, we formulate and apply Bayesian model reduction to perform principled pruning of Bayesian neural networks, based on variational free energy minimization. This novel parameter pruning scheme solves the shortcomings of many current state-of-the-art pruning methods that are used by the signal processing community. The proposed approach has a clear stopping criterion and minimizes the same objective that is used during training. Next to these theoretical benefits, our experiments indicate better model performance in comparison to state-of-the-art pruning schemes.

In this paper a modular approach to single-microphone source separation is proposed. A probabilistic model for mixtures of observations is constructed, where the independent underlying source signals are described by non-linear autoregressive models. Source separation in this model is achieved by performing online probabilistic inference through an efficient message passing procedure. For retaining tractability with the non-linear autoregressive models, three different approximation methods are described. A set of experiments shows the effectiveness of the proposed source separation approach. The source separation performance of the different approximation methods is quantified through a set of verification experiments. Our approach is validated in a speech denoising task.

This paper bridges the gap in the literature between neural networks and probabilistic graphical models. Invertible neural networks are incorporated in factor graphs and inference in this model is described by linearization of the network. Consequently, hybrid probabilistic inference in the model is realized through message passing with local constraints on the Bethe free energy. We provide the local Bethe free energy for the invertible neural network node, which allows for evaluation of the performance of the entire probabilistic model. Experimental results show effective hybrid inference in a neural network-based probabilistic model for a binary classification task, paving the way towards a novel class of machine learning models.

The aim of Probabilistic Programming (PP) is to automate inference in probabilistic models. One efficient realization of PP-based inference concerns variational message passing-based (VMP) inference in a factor graph. VMP is efficient but in principle only leads to closed-form update rules in case the model consists of conjugate and/or conditionally conjugate factor pairs. Recently, Extended Variational Message Passing (EVMP) has been proposed to broaden the applicability of VMP by importance sampling-based particle methods for non-linear and non-conjugate factor pairs. EVMP automates the importance sampling procedure by employing forward messages as proposal distributions, which unfortunately may lead to inaccurate estimation results and numerical instabilities in case the forward message is not a good representative of the unknown correct posterior. This paper addresses this issue by integrating an adaptive importance sampling procedure with message passing-based inference. The resulting method is a hyperparameter-free approximate inference engine that combines recent advances in stochastic adaptive importance sampling and optimization methods. We provide an implementation for the proposed method in the Julia package ForneyLab.jl.

We propose a variational Bayesian inference procedure for online nonlinear system identification. For each output observation, a set of parameter posterior distributions is updated, which is then used to form a posterior predictive distribution for future outputs. We focus on the class of polynomial NARMAX models, which we cast into probabilistic form and represent in terms of a Forney-style factor graph. Inference in this graph is efficiently performed by a variational message passing algorithm. We show empirically that our variational Bayesian estimator outperforms an online recursive least-squares estimator, most notably in small sample size settings and low noise regimes, and performs on par with an iterative least-squares estimator trained offline., 6 pages, 4 figures. Accepted to the American Control Conference 2022

Variational Bayesian (VB) inference has become an increasingly popular method for approximating exact Bayesian inference in model-based machine learning. The VB approach provides a way to trade off accuracy versus computational complexity and scales better to large-dimensional inference problems than sampling solutions. The Julia package ReactiveMP.jl implements and automates reactive VB inference by minimization of a constrained Bethe Free Energy functional through message passing on a factor graph representation of a probabilistic model. Moreover, through support for specification of explicit constraints on the Free Energy functional, ReactiveMP.jl allows for comparative analysis of different variational cost function proposals.

The Free Energy Principle (FEP) and its corollary active inference describe a complex theoretical framework with a substantial statistical mechanics foundation that is often expressed in terms of the Fokker-Planck equation. Easy-to-follow examples of this formalism are scarce, leaving a high barrier of entry to the field. In this paper we provide a worked example of an active inference agent as a hierarchical Gaussian generative model. We proceed to write its equations of motion explicitly as a Fokker-Planck equation, providing a clear mapping between theoretical accounts of FEP and practical implementation. Code is available at github.com/biaslab/ai_workshop_2020.

In this paper we present Active Inference-Based Design Agent (AIDA), which is an active inference-based agent that iteratively designs a personalized audio processing algorithm through situated interactions with a human client. The target application of AIDA is to propose on-the-spot the most interesting alternative values for the tuning parameters of a hearing aid (HA) algorithm, whenever a HA client is not satisfied with their HA performance. AIDA interprets searching for the “most interesting alternative” as an issue of optimal (acoustic) context-aware Bayesian trial design. In computational terms, AIDA is realized as an active inference-based agent with an Expected Free Energy criterion for trial design. This type of architecture is inspired by neuro-economic models on efficient (Bayesian) trial design in brains and implies that AIDA comprises generative probabilistic models for acoustic signals and user responses. We propose a novel generative model for acoustic signals as a sum of time-varying auto-regressive filters and a user response model based on a Gaussian Process Classifier. The full AIDA agent has been implemented in a factor graph for the generative model and all tasks (parameter learning, acoustic context classification, trial design, etc.) are realized by variational message passing on the factor graph. All verification and validation experiments and demonstrations are freely accessible at our GitHub repository.

ReactiveMP.jl is a native Julia implementation of reactive message passing-based Bayesian inference in probabilistic graphical models with Factor Graphs. The package does Constrained Bethe Free Energy minimisation and supports both exact and variational Bayesian inference, provides a convenient syntax for model specification and allows for extra factorisation and form constraints specification of the variational family of distributions. In addition, ReactiveMP.jl includes a large range of standard probabilistic models and can easily be extended to custom novel nodes and message update rules. In contrast to non-reactive (imperatively coded) Bayesian inference packages, ReactiveMP.jl scales easily to support inference on a standard laptop for large conjugate models with tens of thousands of variables and millions of nodes.

Large numbers of asynchronies during pressure support ventilation cause discomfort and higher work of breathing in the patient, and are associated with an increased mortality. There is a need for real-time decision support to detect asynchronies and assist the clinician towards lung-protective ventilation. Machine learning techniques have been proposed to detect asynchronies, but they require large datasets with sufficient data diversity, sample size, and quality for training purposes. In this work, we propose a method for generating a large, realistic and labeled, synthetic dataset for training and validating machine learning algorithms to detect a wide variety of asynchrony types. We take a model-based approach in which we adapt a non-linear lung-airway model for use in a diverse patient group and add a first-order ventilator model to generate labeled pressure, flow, and volume waveforms of pressure support ventilation. The model was able to reproduce basic measured lung mechanics parameters. Experienced clinicians were not able to differentiate between the simulated waveforms and clinical data (P = 0.44 by Fisher’s exact test). The detection performance of the machine learning trained on clinical data gave an overall comparable true positive rate on clinical data and on simulated data (an overall true positive rate of 94.3% and positive predictive value of 93.5% on simulated data and a true positive rate of 98% and positive predictive value of 98% on clinical data). Our findings demonstrate that it is possible to generate labeled pressure and flow waveforms with different types of asynchronies.

Active Inference (AIF) is a framework that can be used both to describe information processing in naturally intelligent systems, such as the human brain, and to design synthetic intelligent systems (agents). In this paper we show that Expected Free Energy (EFE) minimisation, a core feature of the framework, does not lead to purposeful explorative behaviour in linear Gaussian dynamical systems. We provide a simple proof that, due to the specific construction used for the EFE, the terms responsible for the exploratory (epistemic) drive become constant in the case of linear Gaussian systems. This renders AIF equivalent to KL control. From a theoretical point of view this is an interesting result since it is generally assumed that EFE minimisation will always introduce an exploratory drive in AIF agents. While the full EFE objective does not lead to exploration in linear Gaussian dynamical systems, the principles of its construction can still be used to design objectives that include an epistemic drive. We provide an in-depth analysis of the mechanics behind the epistemic drive of AIF agents and show how to design objectives for linear Gaussian dynamical systems that do include an epistemic drive. Concretely, we show that focusing solely on epistemics and dispensing with goal-directed terms leads to a form of maximum entropy exploration that is heavily dependent on the type of control signals driving the system. Additive controls do not permit such exploration. From a practical point of view this is an important result since linear Gaussian dynamical systems with additive controls are an extensively used model class, encompassing for instance Linear Quadratic Gaussian controllers. On the other hand, linear Gaussian dynamical systems driven by multiplicative controls such as switching transition matrices do permit an exploratory drive.

The Gamma mixture model is a flexible probability distribution for representing beliefs about scale variables such as precisions. Inference in the Gamma mixture model for all latent variables is non-trivial as it leads to intractable equations. This paper presents two variants of variational message passing-based inference in a Gamma mixture model. We use moment matching and alternatively expectation-maximization to approximate the posterior distributions. The proposed method supports automated inference in factor graphs for large probabilistic models that contain multiple Gamma mixture models as plug-in factors. The Gamma mixture model has been implemented in a factor graph package and we present experimental results for both synthetic and real-world data sets.

Effective noise reduction and speech enhancement algorithms have great potential to enhance lives of hearing aid users by restoring speech intelligibility. An open problem in today’s commercial hearing aids is how to take into account users’ preferences, indicating which acoustic sources should be suppressed or enhanced, since they are not only user-specific but also depend on many situational factors. In this paper, we develop a fully probabilistic approach to “situated soundscaping”, which aims at enabling users to make on-the-spot (“situated”) decisions about the enhancement or suppression of individual acoustic sources. The approach rests on a compact generative probabilistic model for acoustic signals. In this framework, all signal processing tasks (source modeling, source separation and soundscaping) are framed as automatable probabilistic inference tasks. These tasks can be efficiently executed using message passing-based inference on factor graphs. Since all signal processing tasks are automatable, the approach supports fast future model design cycles in an effort to reach commercializable performance levels. The presented results show promising performance in terms of SNR, PESQ and STOI improvements in a situated setting.

Pure-tone audiometry—the process of estimating a person's hearing threshold from “audible” and “inaudible” responses to tones of varying frequency and intensity—is the basis for diagnosing and quantifying hearing loss. By taking a probabilistic modeling approach, both optimal tone selection (in terms of expected information gain) and hearing threshold estimation can be derived through Bayesian inference methods. The performance of probabilistic model-based audiometry methods is directly linked to the quality of the underlying model. In recent years, Gaussian process (GP) models have been shown to provide good results in this context. We present methods to improve the efficiency of GP-based audiometry procedures by improving the underlying model. Instead of a single GP, we propose to use a GP mixture model that can be conditioned on side-information about the subject. The underlying idea is that one can typically distinguish between different types of hearing thresholds, enabling a mixture model to better capture the statistical properties of hearing thresholds among a population. Instead of modeling all hearing thresholds by a single GP, a mixture model allows specific types of hearing thresholds to be modeled by independent GP models. Moreover, the mixing coefficients can be conditioned on side-information such as age and gender, capturing the correlations between age, gender, and hearing threshold. We show how a GP mixture model can be optimized for a specific target population by learning the parameters from a data set containing annotated audiograms. We also derive an optimal tone selection method based on greedy information gain maximization, as well as hearing threshold estimation through Bayesian inference. The proposed models are fitted to a data set containing roughly 176 thousand annotated audiograms collected in the Nordic countries. We compare the predictive accuracies of optimized mixture models of varying sizes with that of an optimized single-GP model. The usefulness of the optimized models is tested in audiometry simulations. Simulation results indicate that an optimized GP mixture model can significantly outperform an optimized single-GP model in terms of predictive accuracy, and leads to significant increases the efficiency of the resulting Bayesian audiometry procedure.

Consider a domain-adaptive supervised learning setting, where a classifier learns from labeled data in a source domain and unlabeled data in a target domain to predict the corresponding target labels. If the classifier’s assumption on the relationship between domains (e.g. covariate shift, common subspace, etc.) is valid, then it will usually outperform a non-adaptive source classifier. If its assumption is invalid, it can perform substantially worse. Validating assumptions on domain relationships is not possible without target labels. We argue that, in order to make domain-adaptive classifiers more practical, it is necessary to focus on robustness; robust in the sense that an adaptive classifier will still perform at least as well as a non-adaptive classifier without having to rely on the validity of strong assumptions. With this objective in mind, we derive a conservative parameter estimation technique, which is transductive in the sense of Vapnik and Chervonenkis, and show for discriminant analysis that the new estimator is guaranteed to achieve a lower risk on the given target samples compared to the source classifier. Experiments on problems with geographical sampling bias indicate that our parameter estimator performs well.

In this paper we discuss variational message passing-based (VMP) inference in a switching Hierarchical Gaussian Filter (HGF). An HGF is a flexible hierarchical state space model that supports closed-form VMP-based approximate inference for tracking of both states and slowly time-varying parameters. Since natural signals often submit to regime-switching dynamics, there is a need for low-complexity closed-form inference in switching state space models. Here we extend the HGF model with parameter switching mechanics and derive closed-form VMP update rules for plug-in applications in factor graph-based models. These VMP rules support both tracking of latent variables and variational free energy as a model performance measure. We show that the switching HGF performs better than a non-switching HGF on modelling of a stock market data set.

This paper proposes a generative hierarchical probabilistic model for acoustic signals where both the frequency decomposition and log-power spectrum appear as latent variables. In order to facilitate efficient inference, we represent the model in a factor graph that includes a probabilistic Fourier transform and a Gaussian scale model as modules. We derive novel ways of performing variational message passing-based inference in the Gaussian scale model. As a result, in this model a probabilistic representation of the log-power spectrum of an acoustic signal can be effectively inferred online. The proposed model may find applications as a front end wherever probabilistic log-power spectral features of a signal are needed. We validate the model and message passing-based inference methods by tracking the log-power spectrum of a speech signal.

An array with MEMS microphones can distinguish individual noise sources in an environment through spatial filtering. Its effectiveness depends on the variations in microphone sensitivity and phase. Quantification of these variations is valuable, because it enables assessment and optimization of array performance. This is particularly important if the measurements are to be used for enforcement of noise regulations.Nominal microphone sensitivity and phase are manufacturer-specified, but the distribution (histogram) around these values is not. Hence, this work demonstrates a free-field comparison method for measuring these variations in a batch of arrays. We also provide the histograms at 1 kHz for a sample population of 8384 Knowles SPH0641LM4H-1 MEMS microphones (131 arrays of 64 microphones). The histograms follow t-distributions, resulting in 95% confidence intervals of ±0.39dB for sensitivity and ±0.82◦ for phase. Finally, we illustrate that delay-and-sum beamforming with these microphones results in a Gumbel-distributed gain with −0.13/+0.10dB 95% confidence interval.

Time-varying autoregressive (TVAR) models are widely used for modeling of non-stationary signals. Unfortunately, online joint adaptation of both states and parameters in these models remains a challenge. In this paper, we represent the TVAR model by a factor graph and solve the inference problem by automated message passing-based inference for states and parameters. We derive structured variational update rules for a composite “AR node” with probabilistic observations that can be used as a plug-in module in hierarchical models, for example, to model the time-varying behavior of the hyper-parameters of a time-varying AR model. Our method includes tracking of variational free energy (FE) as a Bayesian measure of TVAR model performance. The proposed methods are verified on a synthetic data set and validated on real-world data from temperature modeling and speech enhancement tasks.

In this work, we study the problem of user preference learning on the example of parameter setting for a hearing aid (HA). We propose to use an agent that interacts with a HA user, in order to collect the most informative data, and learns user preferences for HA parameter settings, based on these data. We model the HA system as two interacting sub-systems, one representing a user with his/her preferences and another one representing an agent. In this system, the user responses to HA settings, proposed by the agent. In our user model, the responses are driven by a parametric user preference function. The agent comprises the sequential mechanisms for user model inference and HA parameter proposal generation. To infer the user model (preference function), Bayesian approximate inference is used in the agent. Here we propose the normalized weighted Kullback-Leibler (KL) divergence between true and agent-assigned predictive user response distributions as a metric to assess the quality of learned preferences. Moreover, our agent strategy for generating HA parameter proposals is to generate HA settings, responses to which help resolving uncertainty associated with prediction of the user responses the most. The resulting data, consequently, allows for efficient user model learning. The normalized weighted KL-divergence plays an important role here as well, since it characterizes the informativeness of the data to be used for probing the user. The efficiency of our approach is validated by numerical simulations.

How hummingbirds hum is not fully understood, but its biophysical origin is encoded in the acoustic nearfield. Hence, we studied six freely hovering Anna’s hummingbirds, performing acoustic nearfield holography using a 2176 microphone array in vivo, while also directly measuring the 3D aerodynamic forces using a new aerodynamic force platform. We corroborate the acoustic measurements by developing an idealized acoustic model that integrates the aerodynamic forces with wing kinematics, which shows how the timbre of the hummingbird’s hum arises from the oscillating lift and drag forces on each wing. Comparing birds and insects, we find that the characteristic humming timbre and radiated power of their flapping wings originates from the higher harmonics in the aerodynamic forces that support their bodyweight. Our model analysis across insects and birds shows that allometric deviation makes larger birds quieter and elongated flies louder, while also clarifying complex bioacoustic behavior.

Although mechanical ventilation is a lifesaving intervention in the ICU, it has harmful side-effects, such as barotrauma and volutrauma. These harms can occur due to asynchronies. Asynchronies are defined as a mismatch between the ventilator timing and patient respiratory effort. Automatic detection of these asynchronies, and subsequent feedback, would improve lung ventilation and reduce the probability of lung damage. Neural networks to detect asynchronies provide a promising new approach but require large annotated data sets, which are difficult to obtain and require complex monitoring of inspiratory effort. In this work, we propose a model-based approach to generate a synthetic data set for machine learning and educational use by extending an existing lung model with a first-order ventilator model. The physiological nature of the derived lung model allows adaptation to various disease archetypes, resulting in a diverse data set. We generated a synthetic data set using 9 different patient archetypes, which are derived from measurements in the literature. The model and synthetic data quality have been verified by comparison with clinical data, review by a clinical expert, and an artificial intelligence model that was trained on experimental data. The evaluation showed it was possible to generate patient-ventilator waveforms including asynchronies that have the most important features of experimental patient-ventilator waveforms.

We address the problem of online state and parameter estimation in the Hierarchical Gaussian Filter (HGF), which is a multi-layer dynamic model with non-conjugate couplings between upper-layer hidden states and parameters of a lower layer. These non-conjugacies necessitate the approximation of marginalization and expectation integrals, while the online inference constraint renders batch learning and Monte Carlo sampling unsuitable. Here we formulate the problem as a message passing task on a factor graph and propose an online variational message passing-based state and parameter tracking algorithm, which uses Gaussian quadrature to deal with non-conjugacies. We present improved message update rules for all non-conjugate couplings, thus allowing a plug-in inference method for alternative models with equivalent non-conjugate layer couplings. The method is validated on a recorded time series of Bitcoin prices.

Fetal electrocardiography is a valuable alternative to standard fetal monitoring. Suppression of the maternal electrocardiogram (ECG) in the abdominal measurements, results in fetal ECG signals, from which the fetal heart rate (HR) can be determined. This HR detection typically requires fetal R-peak detection, which is challenging, especially during low signal-to-noise ratio periods, caused for example by uterine activity. In this paper, we propose the combination of a convolutional neural network and a long short-term memory network that directly predicts the fetal HR from multichannel fetal ECG. The network is trained on a dataset, recorded during labor, while the performance of the method is evaluated both on a test dataset and on set-A of the 2013 Physionet /Computing in Cardiology Challenge. The algorithm achieved a positive percent agreement of 92.1% and 98.1% for the two datasets respectively, outperforming a top-performing state-of-the-art signal processing algorithm.

Hierarchical autoregressive (AR) models can describe many complex physical processes. Unfortunately, online adaptation in these models under non-stationary conditions remains a challenge. In this paper, we track states and parameters in a hierarchical AR filter by means of variational message passing (VMP) in a factor graph. We derive VMP update rules for an "AR node" that can be re-used at various hierarchical levels and supports automated message passing-based inference for states and parameters. The proposed method is experimentally validated for a 2-level hierarchical AR model.

Development of hearing aid (HA) signal processing algorithms entails an iterative process between two design steps, namely algorithm development and the embedded implementation. Algorithm designers favor high-level programming languages for several reasons including higher productivity, code readability and, perhaps most importantly, availability of state-of-the-art signal processing frameworks that open new research directions. Embedded software, on the other hand, is preferably implemented using a low-level programming language to allow finer control of the hardware, an essential trait in real-time processing applications. In this paper we present a technique that allows deploying DSP algorithms written in Julia, a modern high-level programming language, on a real-time HA processing platform known as openMHA. We demonstrate this technique by using a model-based Bayesian inference framework to perform real-time audio processing.

Probabilistic programming provides a structured approach to signal processing algorithm design. The design task is formulated as a generative model, and the algorithm is derived through automatic inference. Efficient inference is a major challenge; e.g., the Shafer-Shenoy algorithm (SS) performs badly on models with large treewidth, which arise from various real-world problems. We focus on reducing the size of discrete models with large treewidth by storing intermediate factors in compressed form, thereby decoupling the variables through conditioning on introduced weights. This work proposes pruning of these weights using Kullback-Leibler divergence. We adapt a strategy from the Gaussian mixture reduction literature, leading to Kullback-Leibler Tensor Belief Propagation (KL-TBP), in which we use agglomerative hierarchical clustering to subsequently merge pairs of weights. Experiments using benchmark problems show KL-TBP consistently achieves lower approximation error than existing methods with competitive runtime.

Active Inference is an emerging framework for designing intelligent agents. In an Active Inference setting, any task is formulated as a variational free energy minimisation problem on a generative probabilistic model. Goal-directed behaviour relies on a clear specification of desired future observations. Learning desired observations would open up the Active Inference approach to problems where these are difficult to specify a priori. This paper introduces the BAyesian Target Modelling for Active iNference (BATMAN) approach, which augments an Active Inference agent with an additional, separate model that learns desired future observations from a separate data source. The main contribution of this paper is the design of a coupled generative model structure that facilitates learning desired future observations for Active Inference agents and supports integration of Active Inference and classical methods in a joint framework. We provide proof-of-concept validation for BATMAN through simulations.

The benefits of automating design cycles for Bayesian inference-based algorithms are becoming increasingly recognized by the machine learning community. As a result, interest in probabilistic programming frameworks has much increased over the past few years. This paper explores a specific probabilistic programming paradigm, namely message passing in Forney-style factor graphs (FFGs), in the context of automated design of efficient Bayesian signal processing algorithms. To this end, we developed "ForneyLab" (https://github.com/biaslab/ForneyLab.jl) as a Julia toolbox for message passing-based inference in FFGs. We show by example how ForneyLab enables automatic derivation of Bayesian signal processing algorithms, including algorithms for parameter estimation and model comparison. Crucially, due to the modular makeup of the FFG framework, both the model specification and inference methods are readily extensible in ForneyLab. In order to test this framework, we compared variational message passing as implemented by ForneyLab with automatic differentiation variational inference (ADVI) and Monte Carlo methods as implemented by state-of-the-art tools "Edward" and "Stan". In terms of performance, extensibility and stability issues, ForneyLab appears to enjoy an edge relative to its competitors for automated inference in state-space models., Accepted for publication in the International Journal of Approximate Reasoning

Feature selection and inference through modeling are combined into one method based on a network that can be used to point out irrelevant, redundant and dependent features in the data. It is shown that this network method is efficient in terms of reducing the number of calculations for estimating the probabilities under different model assumptions by breaking the data into fractions. We prove that the probability estimations within the network method lead to the detection of non-informative features with probability one if the data is sufficiently large. The proposed method’s accuracy in detecting complex relations between features, selecting informative features and classifying data-sets with different dimensions is assessed through experiments using both synthetic and real data. The results from the network method compare favorably with those from the well-known and powerful feature selection algorithms. It is further shown that the network method can handle complex relations between the features that are intractable for other algorithms.

This paper considers functional integration in the brain from a computational perspective. We ask what sort of neuronal message passing is mandated by active inference—and what implications this has for context-sensitive connectivity at microscopic and macroscopic levels. In particular, we formulate neuronal processing as belief propagation under deep generative models. Crucially, these models can entertain both discrete and continuous states, leading to distinct schemes for belief updating that play out on the same (neuronal) architecture. Technically, we use Forney (normal) factor graphs to elucidate the requisite message passing in terms of its form and scheduling. To accommodate mixed generative models (of discrete and continuous states), one also has to consider link nodes or factors that enable discrete and continuous representations to talk to each other. When mapping the implicit computational architecture onto neuronal connectivity, several interesting features emerge. For example, Bayesian model averaging and comparison, which link discrete and continuous states, may be implemented in thalamocortical loops. These and other considerations speak to a computational connectome that is inherently state dependent and self-organizing in ways that yield to a principled (variational) account. We conclude with simulations of reading that illustrate the implicit neuronal message passing, with a special focus on how discrete (semantic) representations inform, and are informed by, continuous (visual) sampling of the sensorium. Author Summary This paper considers functional integration in the brain from a computational perspective. We ask what sort of neuronal message passing is mandated by active inference—and what implications this has for context-sensitive connectivity at microscopic and macroscopic levels. In particular, we formulate neuronal processing as belief propagation under deep generative models that can entertain both discrete and continuous states. This leads to distinct schemes for belief updating that play out on the same (neuronal) architecture. Technically, we use Forney (normal) factor graphs to characterize the requisite message passing, and link this formal characterization to canonical microcircuits and extrinsic connectivity in the brain.

In this paper we propose an algorithm for finding inspiratory holds in bedside waveforms using a probabilistic modeling approach. Inspiratory holds contain useful information about the properties of the patient. Finding inspiratory holds in bedside waveforms is a problem the author ran into when working on research with flow and pressure measurements from mechanical ventilators. In this paper, we propose a simple solution for detecting the inspiratory holds.

Language evolves over time in many ways relevant to natural language processing tasks. For example, recent occurrences of tokens 'BERT' and 'ELMO' in publications refer to neural network architectures rather than persons. This type of temporal signal is typically overlooked, but is important if one aims to deploy a machine learning model over an extended period of time. In particular, language evolution causes data drift between time-steps in sequential decision-making tasks. Examples of such tasks include prediction of paper acceptance for yearly conferences (regular intervals) or author stance prediction for rumours on Twitter (irregular intervals). Inspired by successes in computer vision, we tackle data drift by sequentially aligning learned representations. We evaluate on three challenging tasks varying in terms of time-scales, linguistic units, and domains. These tasks show our method outperforming several strong baselines, including using all available data. We argue that, due to its low computational expense, sequential alignment is a practical solution to dealing with language evolution., AAAI 2020

In this paper we consider efficient message passing based inference in a factor graph representation of a probabilistic model. Current message passing methods, such as belief propagation, variational message passing or expectation propagation, rely on analytically pre-computed message update rules. In practical models, it is often not feasible to analytically derive all update rules for all factors in the graph and as a result, efficient message passing-based inference cannot proceed. In related research on (non-message passing-based) inference, a “reparameterization trick” has lead to a considerable extension of the class of models for which automated inference is possible. In this paper, we introduce Reparameterization Gradient Message Passing (RGMP), which is a new message passing method based on the reparameterization gradient. In most models, the large majority of messages can be analytically derived and we resort to RGMP only when necessary. We will argue that this kind of hybrid message passing leads naturally to low-variance gradients.

Towards automated personalization of wearable devices

Acoustic smart sensor networks can provide valuable actionable intelligence to authorities for managing safety in the urban environment. A spatial filter (beamformer) for localization and separation of acoustic sources is a key component of such a network. However, classical methods such as delay-and-sum beamforming fail, because sources are located at varying distances from the sensor array. This causes a regularization problem where either far-away sources are wrongly attenuated, or noise is wrongly amplified.We solve this by considering source strength and location as random variables. The posterior distributions are approximated using Gibbs sampling. Each marginal is computed by combining importance sampling and inverse transform sampling using Chebyshev polynomial approximation. This leads to an iterative algorithm with similarities to deconvolution beamforming.Our method is robust against deviations in manifold model, can deal with sources at different distances and power levels, and does not require an a priori known number of sources.

The free energy principle (FEP) offers a variational calculus-based description for how biological agents persevere through interactions with their environment. Active inference (AI) is a corollary of the FEP, which states that biological agents act to fulfill prior beliefs about preferred future observations (target priors). Purposeful behavior then results from variational free energy minimization with respect to a generative model of the environment with included target priors. However, manual derivations for free energy minimizing algorithms on custom dynamic models can become tedious and error-prone. While probabilistic programming (PP) techniques enable automatic derivation of inference algorithms on free-form models, full automation of AI requires specialized tools for inference on dynamic models, together with the description of an experimental protocol that governs the interaction between the agent and its simulated environment. The contributions of the present paper are two-fold. Firstly, we illustrate how AI can be automated with the use of ForneyLab, a recent PP toolbox that specializes in variational inference on flexibly definable dynamic models. More specifically, we describe AI agents in a dynamic environment as probabilistic state space models (SSM) and perform inference for perception and control in these agents by message passing on a factor graph representation of the SSM. Secondly, we propose a formal experimental protocol for simulated AI. We exemplify how this protocol leads to goal-directed behavior for flexibly definable AI agents in two classical RL examples, namely the Bayesian thermostat and the mountain car parking problems.

Accurate evaluation of Bayesian model evidence for a given data set is a fundamental problem in model development. Since evidence evaluations are usually intractable, in practice variational free energy (VFE) minimization provides an attractive alternative, as the VFE is an upper bound on negative model log-evidence (NLE). In order to improve tractability of the VFE, it is common to manipulate the constraints in the search space for the posterior distribution of the latent variables. Unfortunately, constraint manipulation may also lead to a less accurate estimate of the NLE. Thus, constraint manipulation implies an engineering trade-off between tractability and accuracy of model evidence estimation. In this paper, we develop a unifying account of constraint manipulation for variational inference in models that can be represented by a (Forney-style) factor graph, for which we identify the Bethe Free Energy as an approximation to the VFE. We derive well-known message passing algorithms from first principles, as the result of minimizing the constrained Bethe Free Energy (BFE). The proposed method supports evaluation of the BFE in factor graphs for model scoring and development of new message passing-based inference algorithms that potentially improve evidence estimation accuracy.