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Factorization reduces computational complexity, and is therefore an important tool in statistical machine learning of high dimensional systems. Conventional molecular modeling, including molecular dynamics and Monte Carlo simulations of molecular systems, is a large research field based on approximate factorization of molecular interactions. Recently, the local distribution theory was proposed to factorize joint distribution of a given molecular system into trainable local distributions. Belief propagation algorithms are a family of exact factorization algorithms for (junction) trees, and are extended to approximate loopy belief propagation algorithms for graphs with loops. Despite the fact that factorization of probability distribution is the common foundation, computational research in molecular systems and machine learning studies utilizing belief propagation algorithms have been carried out independently with respective track of algorithm development. The connection and differences among these factorization algorithms are briefly presented in this perspective, with the hope to intrigue further development of factorization algorithms for physical modeling of complex molecular systems.

This work presents a data-driven factor graph (FG) model designed to perform anchor-based positioning. The system makes use of the FG to compute the target position, given the distance measurements to the anchor node that know its own position.The aim was to design a hybrid structure (that involves data and modeling approaches) to address positioning models from a Bayesian point of view, customizing them for each technology and scenario. The weighted geometric dilution of precision (WGDOP) metric, which measures the effect on the positioning solution of distance error to the corresponding anchor node and network geometry of the anchor nodes, was taken into account. The presented algorithms were tested with simulated data and also with real-life data collected from IEEE 802.15.4-compliant sensor network nodes with a physical layer based on ultra-wide band (UWB) technology, in scenarios with one target node, three and four anchor nodes, and a time-of-arrival-based range technique. The results showed that the presented algorithm based on the FG technique provided better positioning results than the least squares-based algorithms and even UWB-based commercial systems in various scenarios, with different setups in terms of geometries and propagation conditions.

In this paper, a joint group shuffled scheduling decoding (JGSSD) algorithm for a joint source-channel coding (JSCC) scheme based on double low-density parity-check (D-LDPC) codes is presented. The proposed algorithm considers the D-LDPC coding structure as a whole and applies shuffled scheduling to each group; the grouping relies on the types or the length of the variable nodes (VNs). By comparison, the conventional shuffled scheduling decoding algorithm can be regarded as a special case of this proposed algorithm. A novel joint extrinsic information transfer (JEXIT) algorithm for the D-LDPC codes system with the JGSSD algorithm is proposed, by which the source and channel decoding are calculated with different grouping strategies to analyze the effects of the grouping strategy. Simulation results and comparisons verify the superiority of the JGSSD algorithm, which can adaptively trade off the decoding performance, complexity and latency.

The Belief Propagation (BP) algorithm has the advantages of high-speed decoding and low latency. To improve the block error rate (BLER) performance of the BP-based algorithm, the BP flipping algorithm was proposed. However, the BP flipping algorithm attempts numerous useless flippings for improving the BLER performance. To reduce the number of decoding attempts needed without any loss of BLER performance, in this paper a metric is presented to evaluate the likelihood that the bits would correct the BP flipping decoding. Based on this, a BP-Step-Flipping (BPSF) algorithm is proposed which only traces the unreliable bits in the flip set (FS) to flip and skips over the reliable ones. In addition, a threshold β is applied when the magnitude of the log-likelihood ratio (LLR) is small, and an enhanced BPSF (EBPSF) algorithm is presented to lower the BLER. With the same FS, the proposed algorithm can reduce the average number of iterations efficiently. Numerical results show the average number of iterations for EBPSF-1 decreases by 77.5% when N = 256, compared with the BP bit-flip-1 (BPF-1) algorithm at Eb/N0 = 1.5 dB.

Contact tracing is an essential tool to mitigate the impact of a pandemic, such as the COVID-19 pandemic. In order to achieve efficient and scalable contact tracing in real time, digital devices can play an important role. While a lot of attention has been paid to analyzing the privacy and ethical risks of the associated mobile applications, so far much less research has been devoted to optimizing their performance and assessing their impact on the mitigation of the epidemic. We develop Bayesian inference methods to estimate the risk that an individual is infected. This inference is based on the list of his recent contacts and their own risk levels, as well as personal information such as results of tests or presence of syndromes. We propose to use probabilistic risk estimation to optimize testing and quarantining strategies for the control of an epidemic. Our results show that in some range of epidemic spreading (typically when the manual tracing of all contacts of infected people becomes practically impossible but before the fraction of infected people reaches the scale where a lockdown becomes unavoidable), this inference of individuals at risk could be an efficient way to mitigate the epidemic. Our approaches translate into fully distributed algorithms that only require communication between individuals who have recently been in contact. Such communication may be encrypted and anonymized, and thus, it is compatible with privacy-preserving standards. We conclude that probabilistic risk estimation is capable of enhancing the performance of digital contact tracing and should be considered in the mobile applications., Competing Interests: The authors declare no competing interest., (Copyright © 2021 the Author(s). Published by PNAS.)

In this paper, a QR-decomposition-based scheduled belief propagation (BP) detector with interference cancellation (IC) and candidate constraints is proposed for multiple-input multiple-output (MIMO) systems. Based on a bipartite graph generated from an upper triangular channel matrix following linear transformation using QR decomposition, the proposed detector performs a sequential message updating procedure between bit nodes. During this updating procedure, candidate constraints are imposed to restrict the number of possible candidate vectors for the calculation of observation-to-bit messages. In addition, after obtaining the soft message corresponding to the bit sequence in each transmit symbol, a hard-decision IC operation is performed to reduce the size of the bipartite graph and indirectly update the messages for the remaining symbols. Therefore, the proposed scheme provides a huge complexity reduction compared to conventional BP detectors that perform message updating by using all related messages directly. Simulation results confirm that the proposed detector can achieve suboptimum error performance with significantly improved convergence speed and reduced computational complexity compared to conventional BP detectors in MIMO systems.

Complex network infrastructure systems for power supply, communication, and transportation support our economic and social activities; however, they are extremely vulnerable to frequently increasing large disasters or attacks. Thus, the reconstruction of a damaged network is more advisable than an empirically performed recovery of the original vulnerable one. To reconstruct a sustainable network, we focus on enhancing loops so that they are not trees, which is made possible by node removal. Although this optimization corresponds with an intractable combinatorial problem, we propose self-healing methods based on enhancing loops when applying an approximate calculation inspired by statistical physics. We show that both higher robustness and efficiency are obtained in our proposed methods by saving the resources of links and ports when compared to ones in conventional healing methods. Moreover, the reconstructed network can become more tolerant than the original when some damaged links are reusable or compensated for as an investment of resource. These results present the potential of network reconstruction using self-healing with adaptive capacity in terms of resilience.

To fulfill the increasing demand on low-latency content distribution, this paper considers content distribution using generation-based network coding with the belief propagation decoder. We propose a framework to design generation-based network codes via characterizing them as building an irregular graph, and design the code by evaluating the graph. The and-or tree evaluation technique is extended to analyze the decoding performance. By allowing for non-constant generation sizes, we formulate optimization problems based on the analysis to design degree distributions from which generation sizes are drawn. Extensive simulation results show that the design may achieve both low decoding cost and transmission overhead as compared to existing schemes using constant generation sizes, and satisfactory decoding speed can be achieved. The scheme would be of interest to scenarios where (1) the network topology is not known, dynamically changing, and/or has cycles due to cooperation between end users, and (2) computational/memory costs of nodes are of concern but network transmission rate is spare.

In this work, we propose a natural model for information flow in the brain through a neural message-passing dynamics on a structural network of macroscopic regions, such as the human connectome (HC). In our model, each brain region is assumed to have a binary behavior (active or not), the strengths of interactions among them are encoded in the anatomical connectivity matrix defined by the HC, and the dynamics of the system is defined by the Belief Propagation (BP) algorithm, working near the critical point of the network. We show that in the absence of direct external stimuli the BP algorithm converges to a spatial map of activations that is similar to the Default Mode Network (DMN) of the brain, which has been defined from the analysis of functional MRI data. Moreover, we use Susceptibility Propagation (SP) to compute the matrix of long-range correlations between the different regions and show that the modules defined by a clustering of this matrix resemble several Resting State Networks (RSN) determined experimentally. Both results suggest that the functional DMN and RSNs can be seen as simple consequences of the anatomical structure of the brain and a neural message-passing dynamics between macroscopic regions. With the new model, we explore predictions on how functional maps change when the anatomical brain network suffers structural alterations, like in Alzheimer's disease and in lesions of the Corpus Callosum. The implications and novel interpretations suggested by the model, as well as the role of criticality, are discussed., (Copyright © 2019 Elsevier Ltd. All rights reserved.)

Background: Mathematical models of biological networks can provide important predictions and insights into complex disease. Constraint-based models of cellular metabolism and probabilistic models of gene regulatory networks are two distinct areas that have progressed rapidly in parallel over the past decade. In principle, gene regulatory networks and metabolic networks underly the same complex phenotypes and diseases. However, systematic integration of these two model systems remains a fundamental challenge., Results: In this work, we address this challenge by fusing probabilistic models of gene regulatory networks into constraint-based models of metabolism. The novel approach utilizes probabilistic reasoning in BN models of regulatory networks serves as the "glue" that enables a natural interface between the two systems. Probabilistic reasoning is used to predict and quantify system-wide effects of perturbation to the regulatory network in the form of constraints for flux variability analysis. In this setting, both regulatory and metabolic networks inherently account for uncertainty. Applications leverage constraint-based metabolic models of brain metabolism and gene regulatory networks parameterized by gene expression data from the hippocampus to investigate the role of the HIF-1 pathway in Alzheimer's disease. Integrated models support HIF-1A as effective target to reduce the effects of hypoxia in Alzheimer's disease. However, HIF-1A activation is far less effective in shifting metabolism when compared to brain metabolism in healthy controls., Conclusions: The direct integration of probabilistic regulatory networks into constraint-based models of metabolism provides novel insights into how perturbations in the regulatory network may influence metabolic states. Predictive modeling of enzymatic activity can be facilitated using probabilistic reasoning, thereby extending the predictive capacity of the network. This framework for model integration is generalizable to other systems.

Compressive sensing originates in the field of signal processing and has recently become a topic of energy-efficient data gathering in wireless sensor networks. In this paper, we propose an energy efficient distributed compressive sensing solution for sensor networks. The proposed solution utilizes sparsity distribution of signals to group sensor nodes into several coalitions and then implements localized compressive sensing inside coalitions. This solution improves data-gathering performance in terms of both data accuracy and energy consumption. The approach curbs both data-transmission costs and number of measurements. Coalition-based data gathering cuts transmission costs, and the number of measurements is reduced by scheduling sensor nodes and adjusting their sampling frequency. Our simulation showed that our approach enhances network performance by minimizing energy cost and improving data accuracy.

Retinal pigment epithelium (RPE) defects are indicated in many blinding diseases, but have been difficult to image. Recently, adaptive optics enhanced indocyanine green (AO-ICG) imaging has enabled direct visualization of the RPE mosaic in the living human eye. However, tracking the RPE across longitudinal images on the time scale of months presents with unique challenges, such as visit-to-visit distortion and changes in image quality. We introduce a coarse-to-fine search strategy that identifies paired patterns and measures their changes. First, longitudinal AO-ICG image displacements are estimated through graph matching of affine invariant maximal stable extremal regions in affine Gaussian scale-space. This initial step provides an automatic means to designate the search ranges for finding corresponding patterns. Next, AO-ICG images are decomposed into superpixels, simplified to a pictorial structure, and then matched across visits using tree-based belief propagation. Results from human subjects in comparison with a validation dataset revealed acceptable accuracy levels for the level of changes that are expected in clinical data. Application of the proposed framework to images from a diseased eye demonstrates the potential clinical utility of this method for longitudinal tracking of the heterogeneous RPE pattern.

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.

Compared to standard frame-based cameras, biologically-inspired event-based sensors capture visual information with low latency and minimal redundancy. These event-based sensors are also far less prone to motion blur than traditional cameras, and still operate effectively in high dynamic range scenes. However, classical framed-based algorithms are not typically suitable for these event-based data and new processing algorithms are required. This paper focuses on the problem of depth estimation from a stereo pair of event-based sensors. A fully event-based stereo depth estimation algorithm which relies on message passing is proposed. The algorithm not only considers the properties of a single event but also uses a Markov Random Field (MRF) to consider the constraints between the nearby events, such as disparity uniqueness and depth continuity. The method is tested on five different scenes and compared to other state-of-art event-based stereo matching methods. The results show that the method detects more stereo matches than other methods, with each match having a higher accuracy. The method can operate in an event-driven manner where depths are reported for individual events as they are received, or the network can be queried at any time to generate a sparse depth frame which represents the current state of the network.

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., Competing Interests: Competing Interests: The authors have declared that no competing interests exist.

A wide class of problems in combinatorics, computer science and physics can be described along the following lines. There are a large number of variables ranging over a finite domain that interact through constraints that each bind a few variables and either encourage or discourage certain value combinations. Examples include the k -SAT problem or the Ising model. Such models naturally induce a Gibbs measure on the set of assignments, which is characterised by its partition function. The present paper deals with the partition function of problems where the interactions between variables and constraints are induced by a sparse random (hyper)graph. According to physics predictions, a generic recipe called the "replica symmetric cavity method" yields the correct value of the partition function if the underlying model enjoys certain properties [Krzkala et al., PNAS (2007) 10318-10323]. Guided by this conjecture, we prove general sufficient conditions for the success of the cavity method. The proofs are based on a "regularity lemma" for probability measures on sets of the form Ωn for a finite Ω and a large n that may be of independent interest. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 694-741, 2016.

In a complex system, perturbations propagate by following paths on the network of interactions among the system's units. In contrast to what happens with the spreading of epidemics, observations of general perturbations are often very sparse in time (there is a single observation of the perturbed system) and in "space" (only a few perturbed and unperturbed units are observed). A major challenge in many areas, from biology to the social sciences, is to infer the propagation paths from observations of the effects of perturbation under these sparsity conditions. We address this problem and show that it is possible to go beyond the usual approach of using the shortest paths connecting the known perturbed nodes. Specifically, we show that a simple and general probabilistic model, which we solved using belief propagation, provides fast and accurate estimates of the probabilities of nodes being perturbed.

The advance in human genome sequencing technology has significantly reduced the cost of data generation and overwhelms the computing capability of sequence analysis. Efficiency, efficacy, and scalability remain challenging in sequence alignment, which is an important and foundational operation for genome data analysis. In this paper, we propose a two-stage approach to tackle this problem. In the preprocessing step, we match blocks of reference and target sequences based on the similarities between their empirical transition probability distributions using belief propagation. We then conduct a refined match using our recently published sparse-coding belief propagation (SCoBeP) technique. Our experimental results demonstrated robustness in nucleotide sequence alignment, and our results are competitive to those of the SOAP aligner and the BWA algorithm. Moreover, compared to SCoBeP alignment, the proposed technique can handle sequences of much longer lengths.

Renal lesions are important extracolonic findings on computed tomographic colonography (CTC). They are difficult to detect on non-contrast CTC images due to low image contrast with surrounding objects. In this paper, we developed a novel computer-aided diagnosis system to detect a subset of renal lesions, exophytic lesions, by (1) exploiting efficient belief propagation to segment kidneys, (2) establishing an intrinsic manifold diffusion on kidney surface, (3) searching for potential lesion-caused protrusions with local maximum diffusion response, and (4) exploring novel shape descriptors, including multi-scale diffusion response, with machine learning to classify exophytic renal lesions. Experimental results on the validation dataset with 167 patients revealed that manifold diffusion significantly outperformed conventional shape features (p<1e-3) and resulted in 95% sensitivity with 15 false positives per patient for detecting exophytic renal lesions. Fivefold cross-validation also demonstrated that our method could stably detect exophytic renal lesions. These encouraging results demonstrated that manifold diffusion is a key means to enable accurate computer-aided diagnosis of renal lesions., (Published by Elsevier B.V.)

Labeling of cerebral vasculature is important for characterization of anatomical variation, quantification of brain morphology with respect to specific vessels, and inter-subject comparisons of vessel properties and abnormalities. We propose an automated method to label the anterior portion of cerebral arteries using a statistical inference method on the Bayesian network representation of the vessel tree. Our approach combines the likelihoods obtained from a random forest classifier trained using vessel centerline features with a belief propagation method integrating the connection probabilities of the cerebral artery network. We evaluate our method on 30 subjects using a leave-one-out validation, and show that it achieves an average correct vessel labeling rate of over 92%.

A new global stereo matching method is presented that focuses on the handling of disparity, discontinuity and occlusion. The Bayesian approach is utilized for dense stereo matching problem formulated as a maximum a posteriori Markov Random Field (MAP-MRF) problem. In order to improve stereo matching performance, edges are incorporated into the Bayesian model as a soft constraint. Accelerated belief propagation is applied to obtain the maximum a posteriori estimates in the Markov random field. The proposed algorithm is evaluated using the Middlebury stereo benchmark. Our experimental results comparing with some state-of-the-art stereo matching methods demonstrate that the proposed method provides superior disparity maps with a subpixel precision.

Distributed video coding (DVC) is rapidly increasing in popularity by the way of shifting the complexity from encoder to decoder, whereas no compression performance degrades, at least in theory. In contrast with conventional video codecs, the inter-frame correlation in DVC is explored at decoder based on the received syndromes of Wyner-Ziv (WZ) frame and side information (SI) frame generated from other frames available only at decoder. However, the ultimate decoding performances of DVC are based on the assumption that the perfect knowledge of correlation statistic between WZ and SI frames should be available at decoder. Therefore, the ability of obtaining a good statistical correlation estimate is becoming increasingly important in practical DVC implementations. Generally, the existing correlation estimation methods in DVC can be classified into two main types: pre-estimation where estimation starts before decoding and on-the-fly (OTF) estimation where estimation can be refined iteratively during decoding. As potential changes between frames might be unpredictable or dynamical, OTF estimation methods usually outperforms pre-estimation techniques with the cost of increased decoding complexity (e.g., sampling methods). In this paper, we propose a low complexity adaptive DVC scheme using expectation propagation (EP), where correlation estimation is performed OTF as it is carried out jointly with decoding of the factor graph-based DVC code. Among different approximate inference methods, EP generally offers better tradeoff between accuracy and complexity. Experimental results show that our proposed scheme outperforms the benchmark state-of-the-art DISCOVER codec and other cases without correlation tracking, and achieves comparable decoding performance but with significantly low complexity comparing with sampling method.