A Posteriori Probability Research Articles

ITS Efficiency Analysis for Multi-Target Tracking in a Clutter Environment

The Integrated Track Splitting (ITS) is a multi-scan algorithm for target tracking in a cluttered environment. The ITS filter models each track as a set of mutually exclusive components, usually in the form of a Gaussian Mixture. The purpose of this research is to determine the limits of the ‘endurance’ of target tracking of the known ITS algorithm by analyzing the impact of target detection probability. The state estimate and the a-posteriori probability of component existence are computed recursively from the target existence probability, which may be used as a track quality measure for false track discrimination (FTD). The target existence probability is also calculated and used for track maintenance and track output. This article investigates the limits of the effectiveness of ITS multi-target tracking using the method of theoretical determination of the dependence of the measurements likelihood ratio on reliable detection and then practical experimental testing. Numerical simulations of the practical application of the proposed model were performed in various probabilities of target detection and dense clutter environments. Additionally, the effectiveness of the proposed algorithm in combination with filters for various types of maneuvers using Interacting Multiple Model ITS (IMMITS) algorithms was comparatively analyzed. The extensive numerical simulation (which assumes both straight and maneuvering targets) has shown which target tracking limits can be performed within different target detection probabilities and clutter densities. The simulations confirmed the derived theoretical limits of the tracking efficiency of the ITS algorithm up to a detection probability of 0.6, and compared to the IMMITS algorithm up to 0.4 in the case of target maneuvers and dense clutter environments.

Bayesian System Identification of a River

Hydrological systems like rivers and lakes are a vital part of any community. Mathematical models of such systems underpin management, decision making and control of rivers. There is always uncertainty associated with the models, and in this paper we consider Bayesian system identification of a river. Bayesian system identification delivers an a-posteriori probability distribution of the unknown parameters. This uncertainty description is useful for solving chance-constrained problems encountered in the control and management of rivers. The Bayesian system identification approach is demonstrated by applying it to the upper part of the Murray River in Australia using real water level and flow measurements. The obtained models show good simulation performance capturing the observed water levels well. Moreover, posterior distributions of the parameters are delivered which are useful for control of rivers.

Semi-Data-Aided Channel Estimation for MIMO Systems via Reinforcement Learning

Data-aided channel estimation is a promising solution to improve channel estimation accuracy by exploiting data symbols as pilot signals for updating an initial channel estimate. In this paper, we propose a semi-data-aided channel estimator for multiple-input multiple-output communication systems. Our strategy is to leverage reinforcement learning (RL) for selecting reliable detected symbols, then update the channel estimate by utilizing only the selected symbols as additional pilot signals. Towards this end, we first define a Markov decision process (MDP) which sequentially decides whether to use each detected symbol as an additional pilot signal. We then develop an RL algorithm to find an effective policy of the MDP based on a Monte Carlo tree search approach. In this algorithm, we exploit the a-posteriori probability for approximating both the optimal future actions and the corresponding state transitions of the MDP and derive a closed-form expression for the optimal policy under the approximations. A key advantage of the proposed channel estimator is that it requires less computational complexity than conventional iterative data-aided channel estimators. Simulation results demonstrate that the proposed channel estimator effectively mitigates both channel estimation error and detection performance loss caused by insufficient pilot signals.

Concatenated Codes for Multiple Reads of a DNA Sequence

Decoding sequences that stem from multiple transmissions of a codeword over an insertion, deletion, and substitution channel is a critical component of efficient deoxyribonucleic acid (DNA) data storage systems. In this paper, we consider a concatenated coding scheme with an outer nonbinary low-density parity-check code or a polar code and either an inner convolutional code or a time-varying block code. We propose two novel decoding algorithms for inference from multiple received sequences, both combining the inner code and channel to a joint hidden Markov model to infer symbolwise a posteriori probabilities (APPs). The first decoder computes the exact APPs by jointly decoding the received sequences, whereas the second decoder approximates the APPs by combining the results of separately decoded received sequences and has a complexity that is linear with the number of sequences. Using the proposed algorithms, we evaluate the performance of decoding multiple received sequences by means of achievable information rates and Monte-Carlo simulations. We show significant performance gains compared to a single received sequence. In addition, we succeed in improving the performance of the aforementioned coding scheme by optimizing both the inner and outer codes.

Neural Min-Sum Decoding for Generalized LDPC Codes

In this letter, we investigate the min-sum (MS) and neural MS (NMS) decoding algorithms for generalized low-density parity-check (GLDPC) codes. Although the MS decoder is much simpler than the a posteriori probability (APP) decoder commonly used for GLDPC codes, the MS decoder has not been considered mainly due to its inferior decoding performance. However, we show that the performance can be improved by i) employing the NMS decoding algorithm and ii) optimizing the component parity check matrix (PCM). For the four representative short GLDPC codes in the literature, experimental results show that the NMS decoding performance with the optimized component PCM significantly outperforms the MS decoding performance and even outperforms the APP decoding performance for some cases.

A Study on Performance Evaluation With Neural Network Detector in SMR System

We previously applied a neural network detector (NND) to the low-density parity-check (LDPC) coding and iterative decoding system in a shingled magnetic recording (SMR) system. In this study, we evaluate the performance of iterative decoding using a new NND by computer simulation. The conventional NND gets the log-likelihood ratio (LLR) as the reliability of the sequence recorded from the two-dimensional finite impulse response (TD-FIR) filter output and the sum-product (SP) decoder output, but the new NND finds the LLR by adding the SP decoder input in order to consider the difference between the SP decoder input and the decoding result. Furthermore, we clarify that the new NND brings the almost same effect as the a posteriori probability (APP) decoder in the iterative decoding system.

A Quantum-Inspired Classifier for Early Web Bot Detection

This paper introduces a novel approach, inspired by the principles of Quantum Computing, to address web bot detection in terms of real-time classification of an incoming data stream of HTTP request headers, in order to ensure the shortest decision time with the highest accuracy. The proposed approach exploits the analogy between the intrinsic correlation of two or more particles and the dependence of each HTTP request on the preceding ones. Starting from the a-posteriori probability of each request to belong to a particular class, it is possible to assign a Qubit state representing a combination of the aforementioned probabilities for all available observations of the time series. By leveraging the underlying mathematical details of superposition and entanglement on specific subsequences, it is possible to devise a measure of membership to each class, thus enabling the system to take a reliable decision when a sufficient level of confidence is met or to continue with additional observations. The results reported in this paper objectively show the effectiveness of our quantum-inspired algorithm which outperforms other state-of-the-art approaches, including our own one based on the Sequential Probability Ratio Test.

The a posteriori probability of the number of contributors when conditioned on an assumed contributor

Forensic DNA signal is notoriously challenging to assess, requiring computational tools to support its interpretation. Over-expressions of stutter, allele drop-out, allele drop-in, degradation, differential degradation, and the like, make forensic DNA profiles too complicated to evaluate by manual methods. In response, computational tools that make point estimates on the Number of Contributors (NOC) to a sample have been developed, as have Bayesian methods that evaluate an A Posteriori Probability (APP) distribution on the NOC. In cases where an overly narrow NOC range is assumed, the downstream strength of evidence may be incomplete insofar as the evidence is evaluated with an inadequate set of propositions.In the current paper, we extend previous work on NOCIt, a Bayesian method that determines an APP on the NOC given an electropherogram, by reporting on an implementation where the user can add assumed contributors. NOCIt is a continuous system that incorporates models of peak height (including degradation and differential degradation), forward and reverse stutter, noise, and allelic drop-out, while being cognizant of allele frequencies in a reference population. When conditioned on a known contributor, we found that the mode of the APP distribution can shift to one greater when compared with the circumstance where no known contributor is assumed, and that occurred most often when the assumed contributor was the minor constituent to the mixture.In a development of a result of Slooten and Caliebe (FSI:G, 2018) that, under suitable assumptions, establishes the NOC can be treated as a nuisance variable in the computation of a likelihood ratio between the prosecution and defense hypotheses, we show that this computation must not only use coincident models, but also coincident contextual information. The results reported here, therefore, illustrate the power of modern probabilistic systems to assess full weights-of-evidence, and to provide information on reasonable NOC ranges across multiple contexts.

A series of developmental validation tests for Number of Contributors platforms: Exemplars using NOCIt and a neural network

Complex DNA mixtures are challenging to interpret and require computational tools that aid in that interpretation. Recently, several computational methods that estimate the number of contributors (NOC) to a sample have been developed. Unlike analogous tools that interpret profiles and report LRs, NOC tools vary widely in their operational principle where some are Bayesian and others are machine learning tools. Conjunctionally, NOC tools may return a single n estimate, or a distribution on n. This vast array of constructs, coupled with a gap in standardized methods by which to validate NOC systems, warrants an exploration into the measures by which differing NOC systems might be tested for operations. In the current paper, we use two exemplar NOC systems: a probabilistic system named NOCIt, which renders an a posteriori probability (APP) distribution on the number of contributors given an electropherogram and an artificial neural network (ANN). NOCIt is a continuous Bayesian inference system incorporating models of peak height, degradation, differential degradation, forward and reverse stutter, noise and allelic drop-out while considering allele frequencies in a reference population. The ANN is also a continuous method, taking all the same features (barring degradation) into account. Unlike its Bayesian counterpart, it demands substantively more data to parameterize, requiring synthetic data. We explore each system’s performance by conducting tests on 214 PROVEDIt mixtures where the limit of detection was 1-copy of DNA. We found that after a lengthy training period of approximately 24 h, the ANN’s evaluation process was very fast and perfectly repeatable. In contrast, NOCIt only took a few minutes to train but took tens of minutes to complete each sample and was less repeatable. In addition, it rendered a probability distribution that was more sensitive and specific, affording a reasonable method by which to report all reasonable n that explain the evidence for a given sample. Whatever the method, by acknowledging the inherent differences between NOC systems, we demonstrate that validation constructs will necessarily be guided by the needs of the forensic domain and be dependent upon whether the laboratory seeks to assign a single n or range of n.

Reliable control based on dual control for ARMAX system with abrupt faults

This paper studies the reliable control problem for abrupt faults of autoregressive moving average with exogenous input (ARMAX) system. A set of models are used to cover the potential dynamics of the system and for each model minimum variance control (MVC) is designed. By taking the a-posteriori probabilities of models as weight coefficients, a multi-model reliable control (MMRC) is proposed. If the system is normal, MMRC is MVC. When faults occur, the controller can quickly learn the true model of system and degenerate into the corresponding MVC by adjusting weight coefficients, which ensures the acceptable performance of the system. The effectiveness of MMRC is verified by a numerical simulation. In addition, since MMRC is a fusion of control law of each model, it indicates that soft switching is implemented and the jitter to system due to hard switching can be avoided.

Optimal Detection of Multiple Symbol-Slotted Random Access-Based Packet Transmissions

Random access (RA) protocols are suitable for the support of massive connectivity especially in machine-type communications, such as the Internet of Things (IoT). In this context, ALOHA protocols (both slotted and unslotted) have been re-introduced as promising enablers due to a potentially high throughput when enhanced via successive interference cancellation (SIC). Meanwhile, SIC has become the most popular solution for RA detection problems. In this letter, we first point out the weaknesses of SIC and then propose a novel method based on joint detection of all randomly scheduled data packets. The proposed method is based on the joint computation of a-posteriori probabilities for all data symbols and packet localizations, such that optimal detection for RA is obtained.

Evolutionary Programming: A Population-Based Optimization Algorithm for Coded Multiuser Systems

We consider iterative channel detection and estimation for coded multiuser systems. The conventional A Posteriori Probability (APP) channel detector has a computational complexity growing exponentially with the number of users. In this paper, we study the channel detection problem from a combinatorial optimization viewpoint and derive a low-complexity soft-output channel detector based on the Evolutionary Programming (EP) optimization algorithm. An iterative channel estimator based on tentative soft estimates fed back from channel decoders is used to provide refined channel parameters to the channel detector. It is shown that the proposed iterative receiver can significantly reduce the computational complexity with slight performance degradation compared to the conventional receiver based on APP detection.

A combined geostatistical approach of data fusion and stochastic simulation for probabilistic assessment of shallow water table depth risk

In general, water table depth risks are estimated from monitoring networks that mostly provide scarce and irregular data. When jointly analysed, environmental, agricultural and geotechnical variables, treated as stochastic spatial variables, can better describe and interpret the states of a certain system subject to estimation uncertainty. Risk assessment consists essentially in calculating the frequency (probability) with which specified criteria are exceeded or fail to be met by creating multiple stochastic realizations. The aim of this paper is to propose a novel geostatistical methodology, based on the integration into one approach of multi-source data fusion and stochastic simulation, to estimate the risk of extreme (shallow) water table depth, and illustrate a demonstrative example of application of the approach to a case study in a Cerrado conservation area in Brazil. The risk of shallow water table depth was determined by using critical thresholds for water table level and a binary transformation into an indicator variable depending on whether the conditions expressed by the threshold values are met or not. Firstly, auxiliary variables were jointly, analysed to provide a delineation of the study area into homogeneous zones. Secondly, sequential indicator simulation provided a-posteriori probabilities taking into account spatial proximity. The final maps show the most probable risk category for the whole area and spatial entropy as a measure of local uncertainty. Areas nearby watershed divisors and in the north part of the region have a high risk of shallow groundwater. Informed decision-making supported by probabilistic maps and uncertainty evaluation is essential for the success of the projects of Cerrado restoration.

Design of Optimal Non-Uniform Quantizer in Imperfect Noisy Reporting Channels for Collaborative Spectrum Sensing

We design an optimal non-uniform quantizer for collaborative spectrum sensing (CSS) in cognitive radio networks (CRNs). We assume non-ideal reporting channels are and consist of additive white Gaussian noise (AWGN). To design the optimum quantization at the transmitter, we minimize the mean square error (MMSE) at the receiver. The local data at each secondary user (SU) is quantized and transmitted via an AWGN reporting channel. Then, quantized symbols are received and decoded at the fusion center (FC) by a maximum a-posteriori probability (MAP) rule and, the final collaborative decision is made. By this method, a prediction is done for representation points of the quantizer and moreover, quantization and reporting channel noises are minimized, simultaneously. In addition, by taking into account the reporting channel noise in quantizer design, detection performance will be adaptive to change of signal to noise ratio (SNR) in the reporting channel. The simulation results demonstrate the superiority of the proposed quantizer compared to different quantizers in practical noisy reporting channels.

Improvement of Iterative Decoding With LLR Modulator by Neural Network Using Magnetic Transition Information in SMR System

We have previously focused on a log-likelihood ratio (LLR) computed as the decoding reliability by a posteriori probability (APP) decoder on the low-density parity-check (LDPC) coding and iterative decoding system for the shingled magnetic recording (SMR). Then, we clarified that the LLR modulator applying a neural network realizes an effective iterative decoding. In this article, we propose a new neural network LLR modulator considering magnetic transition information obtained from LLRs to reduce the influence of intersymbol interferences (ISIs).

Deep Neural Network a Posteriori Probability Detector for Two-Dimensional Magnetic Recording

In two-dimensional magnetic recording (TDMR) channels, intersymbol interference (within and between tracks) and pattern-dependent media noise are impediments to reaching higher areal density. We propose a novel deep neural network (DNN)-based a posteriori probability (APP) detection system with parallel multi-track detection for TDMR channels. The proposed DNN-based APP detector replaces the trellis-based Bahl–Cocke–Jelinek–Raviv (BCJR) or Viterbi algorithm and pattern-dependent noise prediction (PDNP) in a typical TDMR scenario, in which it directly outputs log-likelihood ratios of the coded bits and iteratively exchanges them with a subsequent channel decoder to minimize bit error rate (BER). We investigate three DNN architectures—fully connected DNN, convolutional neural network (CNN), and long short-term memory (LSTM) network. The DNN’s complexity is limited by employing linear partial response (PR) equalizer pre-processing. The best performing DNN architecture, CNN, is selected for iterative decoding with a channel decoder. Simulation results on a grain-flipping-probability (GFP) media model show that all three DNN architectures yield significant BER reductions over a recently proposed 2D-PDNP system and a previously proposed local area influence probabilistic (LAIP)-BCJR system. On a GFP model with 18 nm track pitch and 11.4 Teragrains/in2, the CNN detection system achieves an information areal density of 3.08 Terabits/in2, i.e., a 21.72% density gain over a standard BCJR-based 1D-PDNP; the CNN-based system also has $3\times $ the throughput of 1D-PDNP, yet requires only 1/10th the computer run time.

A large-scale validation of NOCIt’s a posteriori probability of the number of contributors and its integration into forensic interpretation pipelines

Forensic DNA signal is notoriously challenging to interpret and requires the implementation of computational tools that support its interpretation. While data from high-copy, low-contributor samples result in electropherogram signal that is readily interpreted by probabilistic methods, electropherogram signal from forensic stains is often garnered from low-copy, high-contributor-number samples and is frequently obfuscated by allele sharing, allele drop-out, stutter and noise. Since forensic DNA profiles are too complicated to quantitatively assess by manual methods, continuous, probabilistic frameworks that draw inferences on the Number of Contributors (NOC) and compute the Likelihood Ratio (LR) given the prosecution’s and defense’s hypotheses have been developed.In the current paper, we validate a new version of the NOCIt inference platform that determines an A Posteriori Probability (APP) distribution of the number of contributors given an electropherogram. NOCIt is a continuous inference system that incorporates models of peak height (including degradation and differential degradation), forward and reverse stutter, noise and allelic drop-out while taking into account allele frequencies in a reference population. We established the algorithm’s performance by conducting tests on samples that were representative of types often encountered in practice. In total, we tested NOCIt’s performance on 815 degraded, UV-damaged, inhibited, differentially degraded, or uncompromised DNA mixture samples containing up to 5 contributors. We found that the model makes accurate, repeatable and reliable inferences about the NOCs and significantly outperformed methods that rely on signal filtering.By leveraging recent theoretical results of Slooten and Caliebe (FSI:G, 2018) that, under suitable assumptions, establish the NOC can be treated as a nuisance variable, we demonstrated that when NOCIt’s APP is used in conjunction with a downstream likelihood ratio (LR) inference system that employs the same probabilistic model, a full evaluation across multiple contributor numbers is rendered. This work, therefore, illustrates the power of modern probabilistic systems to report holistic and interpretable weights-of-evidence to the trier-of-fact without assigning a specified number of contributors or filtering signal.

A comparison of four vowel overlap measures

Multiple measures of vowel overlap have been proposed that use F1, F2, and duration to calculate the degree of overlap between vowel categories. The present study assesses four of these measures: the spectral overlap assessment metric [SOAM; Wassink (2006). J. Acoust. Soc. Am. 119(4), 2334-2350], the a posteriori probability (APP)-based metric [Morrison (2008). J. Acoust. Soc. Am. 123(1), 37-40], the vowel overlap analysis with convex hulls method [VOACH; Haynes and Taylor, (2014). J. Acoust. Soc. Am. 136(2), 883-891], and the Pillai score as first used for vowel overlap by Hay, Warren, and Drager [(2006). J. Phonetics 34(4), 458-484]. Summaries of the measures are presented, and theoretical critiques of them are performed, concluding that the APP-based metric and Pillai score are theoretically preferable to SOAM and VOACH. The measures are empirically assessed using accuracy and precision criteria with Monte Carlo simulations. The Pillai score demonstrates the best overall performance in these tests. The potential applications of vowel overlap measures to research scenarios are discussed, including comparisons of vowel productions between different social groups, as well as acoustic investigations into vowel formant trajectories.

Iterative Decision Feedback Equalization Using Online Prediction

In this article, a new category of soft-input soft-output (SISO) minimum-mean square error (MMSE) finite-impulse response (FIR) decision feedback equalizers (DFEs) with iteration-wise static filters (i.e. iteration variant) is investigated. It has been recently shown that SISO MMSE DFE with dynamic filters (i.e. time-varying) reaches very attractive operating points for high-data rate applications, when compared to alternative turbo-equalizers of the same category, thanks to sequential estimation of data symbols [1]. However the dependence of filters on the feedback incurs high amount of latency and computational costs, hence SISO MMSE DFEs with static filters provide an attractive alternative for computational complexity-performance trade-off. However, the latter category of receivers faces a fundamental design issue on the estimation of the decision feedback reliability for filter computation. To address this issue, a novel approach to decision feedback reliability estimation through online prediction is proposed and applied for SISO FIR DFE with either a posteriori probability (APP) or expectation propagation (EP) based soft feedback. This novel method for filter computation is shown to improve detection performance compared to previously known alternative methods, and finite-length and asymptotic analysis show that DFE with static filters still remains well-suited for high-spectral efficiency applications.

A Study on Iterative Decoding With LLR Modulator by Neural Network Using Adjacent Track Information in SMR System

Our previous work focused on a log-likelihood ratio (LLR) computed as the decoding reliability by a posteriori probability (APP) decoder in a two-dimensional magnetic recording (TDMR) system using shingled magnetic recording (SMR). In this article, we propose a neural network LLR modulator to reduce the influence of pattern dependent medium noise and to perform efficiently iterative decoding using a low-density parity-check (LDPC) code. In this study, we clarify that the performance improvement of iterative decoding can be obtained by considering LLRs of the adjacent track bits affecting the decoding bit as the input of the neural network. Furthermore, we clarify that the application of a hybrid genetic algorithm (HGA) selects LLRs by using the adjacent track LLRs affecting the decoding bit and realizes more effective iterative decoding.