Reliability-Informed Beat Tracking of Musical Signals

Abstract—A new probabilistic framework for beat tracking of musical audio is presented. The method estimates the time between consecutive beat events and exploits both beat and non-beat information by explicitly modeling non-beat states. In addition to the beat times, a measure of the expected accuracy of the estimated beats is provided. The quality of the observations used for beat tracking is measured and the reliability of the beats is automatically calculated. A k-nearest neighbor regression algorithm is proposed to predict the accuracy of the beat estimates. The performance of the beat tracking system is statistically evaluated using a database of 222 musical signals of various genres. We show that modeling non-beat states leads to a significant increase in performance. In addition, a large experiment where the parameters of the model are automatically learned has been completed. Results show that simple approximations for the parameters of the model can be used. Furthermore, the performance of the system is compared with existing algorithms. Finally, a new perspective for beat tracking evaluation is presented. We show how reliability information can be successfully used to increase the mean performance of the proposed algorithm and discuss how far automatic beat tracking is from human tapping. Index Terms—Beat-tracking, beat quality, beat-tracking reliability, k-nearest neighbor (k-NN) regression, music signal processing. I

Reliable Linear, Sesquilinear and Bijective Operations On Integer Data Streams Via Numerical Entanglement

A new technique is proposed for fault-tolerant linear, sesquilinear and bijective (LSB) operations on $M$ integer data streams ($M\geq3$), such as: scaling, additions/subtractions, inner or outer vector products, permutations and convolutions. In the proposed method, the $M$ input integer data streams are linearly superimposed to form $M$ numerically-entangled integer data streams that are stored in-place of the original inputs. A series of LSB operations can then be performed directly using these entangled data streams. The results are extracted from the $M$ entangled output streams by additions and arithmetic shifts. Any soft errors affecting any single disentangled output stream are guaranteed to be detectable via a specific post-computation reliability check. In addition, when utilizing a separate processor core for each of the $M$ streams, the proposed approach can recover all outputs after any single fail-stop failure. Importantly, unlike algorithm-based fault tolerance (ABFT) methods, the number of operations required for the entanglement, extraction and validation of the results is linearly related to the number of the inputs and does not depend on the complexity of the performed LSB operations. We have validated our proposal in an Intel processor (Haswell architecture with AVX2 support) via fast Fourier transforms, circular convolutions, and matrix multiplication operations. Our analysis and experiments reveal that the proposed approach incurs between $0.03\%$ to $7\%$ reduction in processing throughput for a wide variety of LSB operations. This overhead is 5 to 1000 times smaller than that of the equivalent ABFT method that uses a checksum stream. Thus, our proposal can be used in fault-generating processor hardware or safety-critical applications, where high reliability is required without the cost of ABFT or modular redundancy.Comment: to appear in IEEE Trans. on Signal Processing, 201

MDN-VO: Estimating Visual Odometry with Confidence

Visual Odometry (VO) is used in many applications including robotics and autonomous systems. However, traditional approaches based on feature matching are computationally expensive and do not directly address failure cases, instead relying on heuristic methods to detect failure. In this work, we propose a deep learning-based VO model to efficiently estimate 6-DoF poses, as well as a confidence model for these estimates. We utilise a CNN - RNN hybrid model to learn feature representations from image sequences. We then employ a Mixture Density Network (MDN) which estimates camera motion as a mixture of Gaussians, based on the extracted spatio-temporal representations. Our model uses pose labels as a source of supervision, but derives uncertainties in an unsupervised manner. We evaluate the proposed model on the KITTI and nuScenes datasets and report extensive quantitative and qualitative results to analyse the performance of both pose and uncertainty estimation. Our experiments show that the proposed model exceeds state-of-the-art performance in addition to detecting failure cases using the predicted pose uncertainty

Spike Clustering and Neuron Tracking over Successive Time Windows

This paper introduces a new methodology for tracking signals from individual neurons over time in multiunit extracellular recordings. The core of our strategy relies upon an extension of a traditional mixture model approach, with parameter optimization via expectation-maximimization (EM), to incorporate clustering results from the preceding time period in a Bayesian manner. EM initialization is also achieved by utilizing these prior clustering results. After clustering, we match the current and prior clusters to track persisting neurons. Applications of this spike sorting method to recordings from macaque parietal cortex show that it provides significantly more consistent clustering and tracking results

Mixture Representations of Reliability in Coherent Systems and Preservation Results under Double Monitoring

The mixture representations of the reliability functions of the residual life and inactivity time of a coherent system with n independent and identically distributed components are obtained, given that before time t1(t1 ≥ 0), exactly r(r \u3c n) components have failed and at time t2(t2 ≥ t1), the system is either still working or has failed. Based on the stochastically ordered coefficient vectors between systems, some preservation results of the residual life and the inactivity time of the system are obtained. The results in this paper extend previous results in the literature and are useful for comparing similar systems that have different structure functions