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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.

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.

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.

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.

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.

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.

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.

Based on a generative model (GM) and beliefs over hidden states, the free energy principle (FEP) enables an agent to sense and act by minimizing a free energy bound on Bayesian surprise, i.e., the negative logarithm of the marginal likelihood. Inclusion of desired states in the form of prior beliefs in the GM leads to active inference (ActInf). In this work, we aim to reveal connections between ActInf and stochastic optimal control. We reveal that, in contrast to standard cost and constraint-based solutions, ActInf gives rise to a minimization problem that includes both an information-theoretic surprise term and a model-predictive control cost term. We further show under which conditions both methodologies yield the same solution for estimation and control. For a case with linear Gaussian dynamics and a quadratic cost, we illustrate the performance of ActInf under varying system parameters and compare to classical solutions for estimation and control.

Factor graphs provide a convenient framework for automatically generating (approximate) Bayesian inference algorithms based on message passing. Examples include the sum-product algorithm (belief propagation), expectation maximization (EM), expectation propagation (EP) and variational message passing (VMP). While these message passing algorithms can be generated automatically, they depend on a library of precomputed message update rules. As a result, the applicability of the factor graph approach depends on the availability of such rules for all involved nodes. This paper describes the probit factor node for linking continuous and binary random variables in a factor graph. We derive (approximate) sum-product message update rules for this node through constrained moment matching, which leads to a robust version of the EP algorithm in which all messages are guaranteed to be proper. This enables automatic Bayesian inference in probabilistic models that involve both continuous and discrete latent variables, without the need for model-specific derivations. The usefulness of the node as a factor graph building block is demonstrated by applying it to perform Bayesian inference in a linear classification model with corrupted class labels.

In order to personalize the behavior of hearing aid devices in different acoustic environments, we need to develop personalized acoustic scene classifiers. Since we cannot afford to burden an individual hearing aid user with the task to collect a large acoustic database, we aim instead to train a scene classifier on just one (or maximally a few) in-situ recorded acoustic waveform of a few seconds duration per scene. In this paper we develop such a”one-shot” personalized scene classifier, based on a Hidden Semi-Markov model. The presented classifier consistently outperforms a more classical Dynamic-Time-Warping-Nearest-Neighbor classifier, and correctly classifies acoustic scenes about twice as well as a (random) chance classifier after training on just one recording of 10 seconds duration per scene.

State-space modeling of non-stationary natural signals is a notoriously difficult task. As a result of context switches, the memory depth of the model should ideally be adapted online. Stabilized linear forgetting (SLF) has been proposed as an elegant method for state-space tracking in context-switching environments. In practice, SLF leads to state and parameter estimation tasks for which no analytical solutions exist. In the literature, a few approximate solutions have been derived, making use of specific model simplifications. This paper proposes an alternative approach, in which SLF is described as an inference task on a generative probabilistic model. SLF is then executed by a variational message passing algorithm on a factor graph representation of the generative model. This approach enjoys a number of advantages relative to previous work. First, variational message passing (VMP) is an automatable procedure that adapts appropriately under changing model assumptions. This eases the search process for the best model. Secondly, VMP easily extends to estimate model parameters. Thirdly, the modular make-up of the factor graph framework allows SLF to be used as a click-on feature in a large variety of complex models. The functionality of the proposed method is verified by simulating an SLF state-space model in a context-switching data environment.

Active inference is a corollary of the Free Energy Principle that prescribes how self-organizing biological agents interact with their environment. The study of active inference processes relies on the definition of a generative probabilistic model and a description of how a free energy functional is minimized by neuronal message passing under that model. This paper presents a tutorial introduction to specifying active inference processes by Forney-style factor graphs (FFG). The FFG framework provides both an insightful representation of the probabilistic model and a biologically plausible inference scheme that, in principle, can be automatically executed in a computer simulation. As an illustrative example, we present an FFG for a deep temporal active inference process. The graph clearly shows how policy selection by expected free energy minimization results from free energy minimization per se, in an appropriate generative policy model.

Nowadays, despite the use of efficient LED lighting, lighting consumes a considerable amount of energy. To reduce the energy consumption, many office lighting systems are equipped with occupancy sensors. Since these sensors have a limited reliability in detecting presence, usually very conservative strategies are used such as keeping the lights on for fifteen minutes after the last detected presence. In this paper, we propose a novel lighting control strategy for an office that considers the sensor output as a noisy observation of the real occupancy status. Simulation results show that compared with conventional "on/off" strategy, it saves more energy.

We describe a computationally efficient method to produce a specific Bayesian mixture of all the models in a finite set of feature-based models that assign a probability to the observed data set. Special attention is given to the bound on the regret of using the mixture instead of the best model in the set. It is proven theoretically and verified through synthetic data that this bound is relatively tight. Comparing the workload of the proposed method with the direct implementation of the Bayesian mixture shows an almost exponential improvement of computing time.

In this paper, we propose an intelligent lighting system that is able to learn the most preferred light level of a user by iteratively interacting with the user. In each iteration, the system offers the user a certain amount of light and the user gives his feedback to the system. When the user is satisfied, implicit feedback is given by not intervening the system. Otherwise explicit feedback such as "too bright" or "too dark" will be given. Each user feedback is modeled as a probabilistic event, which means that it is possible that sometimes the user will give different feedback for the same light level. To avoid disturbing the user to much, we propose a learning algorithm which learns the most preferred light level of the user with only a few explicit interventions.

Being an established marker for cancer growth, neovascularization is probed by several approaches with the aim of cancer imaging. Recently, analysis of the dispersion kinetics of ultrasound contrast agents (UCAs) has been proposed as a promising approach for localizing neovascularization in prostate cancer. Determined by multipath trajectories through the microvasculature, dispersion enables characterization of the microvascular architecture and, therefore, localization of cancer neovascularization. Analysis of the spatiotemporal similarity among indicator dilution curves (IDCs) measured at each pixel by dynamic contrast-enhanced ultrasound imaging has been proposed to assess the local dispersion kinetics of UCAs. Only linear similarity measures, such as temporal correlation or spectral coherence, have been used up until now. Here we investigate the use of nonlinear similarity measures by estimation of the statistical dependency between IDCs. In particular, dispersion maps are generated by estimation of the mutual information between IDCs. The method is tested for prostate cancer localization and the results compared with the histology results in 15 patients referred for radical prostatectomy because of biopsy-proven prostate cancer. With sensitivity and specificity equal to 84% and 85%, respectively, and receiver operating characteristic curve area equal to 0.92, our results outperformed those obtained by any other parameter, motivating further validation with a larger dataset and with other types of cancer.