Optimal Error Rate Research Articles

Rates in Almost Sure Invariance Principle for Nonuniformly Hyperbolic Maps

We prove the almost sure invariance principle (ASIP) with close to optimal error rates for nonuniformly hyperbolic maps. We do not assume exponential contraction along stable leaves, therefore our result covers in particular slowly mixing invertible dynamical systems as Bunimovich flowers, billiards with flat points as in Chernov and Zhang (Stoch Dyn 5:535–553, 2005a, Nonlinearity 18:1527–1553, 2005b) and Wojtkowski’ (Commun Math Phys 126:507–533, 1990) system of two falling balls.For these examples, the ASIP is a new result, not covered by prior works for various reasons, notably because in absence of exponential contraction along stable leaves, it is challenging to employ the so-called Sinai’s trick (Sinai in Russ Math Surv 27:21–70, 1972; Bowen, Lecture Notes in Math vol. 470 (1975)) of reducing a nonuniformly hyperbolic system to a nonuniformly expanding one. Our strategy follows our previous papers on the ASIP for nonuniformly expanding maps, where we build a semiconjugacy to a specific renewal Markov shift and adapt the argument of Berkes et al. (Ann Probab 42:794–817, 2014). The main difference is that now the Markov shift is two-sided, the observables depend on the full trajectory, both the future and the past.

Efficient Byzantine-robust distributed inference with regularization: A trade-off between compression and adversary

In large-scale distributed learning, the direct application of traditional inference is often not feasible, because it may contain multiple themes, such as communication costs, privacy issues, and Byzantine failures. Nowadays, the internet is vulnerable to attacks, and Byzantine failures frequently occur. For copying with Byzantine failures, the paper develops two Byzantine-robust distributed learning algorithms under a framework of communication-efficient surrogate likelihood. In our algorithms, we adopt the δ-approximate compressors, including sign-based operator and topk sparsification, to improve communication efficiency, and an unsophisticated thresholding of local gradient norms to guard against Byzantine failures. For accelerating convergence and achieving an optimal statistical error rate, error feedback is exploited in the second algorithm. The two algorithms are robust to arbitrary adversaries, although Byzantine workers don't adhere to the mandated compression mechanism. We explicitly establish statistical error rates, which imply that our algorithms don't sacrifice the quality of learning, and attain the order-optimal under some settings. In addition, we provide a trade-off between compression and adversary in the presence of Byzantine worker machines. Extensive numerical experiments validate our theoretical results and demonstrate a good performance of our algorithms.

Exact Policy Recovery in Offline RL with Both Heavy-Tailed Rewards and Data Corruption

We study offline reinforcement learning (RL) with heavy-tailed reward distribution and data corruption: (i) Moving beyond subGaussian reward distribution, we allow the rewards to have infinite variances; (ii) We allow corruptions where an attacker can arbitrarily modify a small fraction of the rewards and transitions in the dataset. We first derive a sufficient optimality condition for generalized Pessimistic Value Iteration (PEVI), which allows various estimators with proper confidence bounds and can be applied to multiple learning settings. In order to handle the data corruption and heavy-tailed reward setting, we prove that the trimmed-mean estimation achieves the minimax optimal error rate for robust mean estimation under heavy-tailed distributions. In the PEVI algorithm, we plug in the trimmed mean estimation and the confidence bound to solve the robust offline RL problem. Standard analysis reveals that data corruption induces a bias term in the suboptimality gap, which gives the false impression that any data corruption prevents optimal policy learning. By using the optimality condition for the generalized PEVI, we show that as long as the bias term is less than the ``action gap'', the policy returned by PEVI achieves the optimal value given sufficient data.

Linear Monte Carlo quadrature with optimal confidence intervals

We study the numerical integration of functions from isotropic Sobolev spaces Wps([0,1]d) using finitely many function evaluations within randomized algorithms, aiming for the smallest possible probabilistic error guarantee ε>0 at confidence level 1−δ∈(0,1). For spaces consisting of continuous functions, non-linear Monte Carlo methods with optimal confidence properties have already been known, in few cases even linear methods that succeed in that respect. In this paper we promote a method called stratified control variates (SCV) and by it show that already linear methods achieve optimal probabilistic error rates in the high smoothness regime without the need to adjust algorithmic parameters to the uncertainty δ. We also analyse a version of SCV in the low smoothness regime where Wps([0,1]d) may contain functions with singularities. Here, we observe a polynomial dependence of the error on δ−1 in contrast to the logarithmic dependence in the high smoothness regime.

Analytical Solution of Optimal Symbol Error Rate for Multilevel Pulse-Amplitude-Modulated Signals With One-Bit Quantization

Analytical Solution of Optimal Symbol Error Rate for Multilevel Pulse-Amplitude-Modulated Signals With One-Bit Quantization

Byzantine-Resilient Federated Learning at Edge

Both Byzantine resilience and communication efficiency have attracted tremendous attention recently for their significance in edge federated learning. However, most existing algorithms may fail when dealing with real-world irregular data that behaves in a heavy-tailed manner. To address this issue, we study the stochastic convex and non-convex optimization problem for federated learning at edge and show how to handle heavy-tailed data while retaining the Byzantine resilience, communication efficiency and the optimal statistical error rates simultaneously. Specifically, we first present a Byzantine-resilient distributed gradient descent algorithm that can handle the heavy-tailed data and meanwhile converge under the standard assumptions. To reduce the communication overhead, we further propose another algorithm that incorporates gradient compression techniques to save communication costs during the learning process. Theoretical analysis shows that our algorithms achieve order-optimal statistical error rate in presence of Byzantine devices. Finally, we conduct extensive experiments on both synthetic and real-world datasets to verify the efficacy of our algorithms.

Novel evaluation approach for molecular signature-based deconvolution methods

The tumoral immune microenvironment (TIME) plays a key role in prognosis, therapeutic approach and pathophysiological understanding over oncological processes. Several computational immune cell-type deconvolution methods (DM), supported by diverse molecular signatures (MS), have been developed to uncover such TIME interplay from RNA-seq tumor biopsies. MS-DM pairs were benchmarked against each other by means of different metrics, such as Pearson’s correlation, R2 and RMSE, but these only evaluate the linear association of the estimated proportion related to the expected one, missing the analysis of prediction-dependent bias trends and cell identification accuracy. We present a novel protocol composed of four tests allowing appropriate evaluation of the cell type identification performance and proportion prediction accuracy of molecular signature-deconvolution method pair by means of certainty and confidence cell-type identification scores (F1-score, distance to the optimal point and error rates) as well the Bland-Altman method for error-trend analysis. Our protocol was used to benchmark six state-of-the-art DMs (CIBERSORTx, DCQ, DeconRNASeq, EPIC, MIXTURE and quanTIseq) paired to five murine tissue-specific MSs, revealing a systematic overestimation of the number of different cell types across almost all methods.

Error Vector Magnitude-Based Low Complexity Adaptive Power Allocation in SM-MIMO System

In this article, we propose the error vector magnitude (EVM)-based adaptive power allocation (PA) for spatial modulation (SM) multiple-input-multiple-output (MIMO) system to optimize the minimum squared Euclidean distance and reduce the system complexity. We first investigate the typical Euclidean distance (ED)-based PA (ED-PA) algorithm. Second, an EVM-based ED-PA algorithm is proposed, where a simplified closed-form PA solution for the quadrature amplitude modulation is obtained in the case of two transmit antennas. For more transmit antennas, we further propose a low complexity-PA (LC-PA) algorithm, where all the transmit antennas are grouped with two antennas in each group and the proposed EVM-based ED-PA algorithm is utilized to assign the power within each group. Numerical results reveal that the proposed EVM-based ED-PA and LC-PA algorithms have considerably lower complexity and can achieve the optimal average bit error rate (ABER) and suboptimal ABER performance at low-and-moderate signal-to-noise ratio (SNR) region and high-SNR region, respectively, compared with the typical PA algorithms in SM-MIMO system.

Modelling and Simulation of various detection algorithms in uplink Massive MIMO systems: A Comparative Analysis

Signal detection is one of the major issues in uplink massive MIMO (multiple input multiple output) systems due to the deployment of large number of antennas. In this research article, the modelling and comparative investigation of various detection algorithms in massive MIMO systems is done to achieve the optimal error rate performance with low complexity. The simulation-based comparison is conducted between equalization based linear detectors, approximate matrix inversion based linear detectors and non-linear BOX equalization detectors. The error rate performance is evaluated with different MIMO scenarios in terms of different ratio between number of users and base station (BS) antennas (β) and different number of iterations (n). The complexity analysis is also done for all the detectors. Simulation results manifest that the BOX equalization detector ADMIN provides the best performance with the lowest complexity. It is also observed that the approximate matrix inversion based linear detectors and the OCD detector perform better with the increased value of (β).

Mobile jammer enabled secure UAV communication with short packet transmission

This paper studies a mobile jammer enabled secure unmanned aerial vehicle (UAV) communication network in the finite packet length scenario, where the external friendly jammer UAV will transmit jamming signal to deteriorate the quality of eavesdropping channel, and help to improve the secure communication performance of the source UAV. Specifically, an average effective secrecy rate (AESR) maximization problem is formulated by jointly designing the trajectories and transmit power of the source/jammer UAV subject to the UAVs’ mobility constraints and power constraints. It is also verified that there exists a unique optimal packet error rate to maximize the AESR. The formulated problem is mathematically intractable, as it is nonconvex and involves coupled optimization variables. Therefore, we first decompose the trajectories and power optimization problem into four non-convex subproblems, and then transform them into standard convex problems by applying first-order Taylor expansion. Then, an efficient alternating optimization algorithm for AESR problem based on Bisection method and successive convex approximation (SCA) technology is presented by addressing the five subproblems iteratively. Simulation results are provided to verify that our proposed scheme can obtain considerable better AESR gain compared to other four benchmark schemes.

Simulation of Film and Television Transmission Path Based on Ant Colony Optimization Algorithm

Aiming at the stagnation and precocity of the basic ant colony algorithm in solving the film and television transmission path problem, an ant colony optimization algorithm with forgetting factor is proposed. By adding forgetting factor to artificial ants, a new state transition formula is established, and pheromone update strategy is modified. Combined with the optimal error rate of the current solution, the state transition equation is adjusted. Due to the introduction of the forgetting factor, the new formula can be adjusted in time when the original ant colony algorithm calculation falls into the local optimal solution, and the selection and updation of the next node are carried out according to the new state transition scheme. Pheromone, which can be used to reduce the optimal value error, improves the tracking ability of the optimal value, modifies the path evaluation model, and calculates the probability of each path to the current optimal solution. The simulation results of the film transmission path problem (FTPP) example show that the improved algorithm takes less time and the result of path optimization is better.

Component-by-component construction of randomized rank-1 lattice rules achieving almost the optimal randomized error rate

We study a randomized quadrature algorithm to approximate the integral of periodic functions defined over the high-dimensional unit cube. Recent work by Kritzer, Kuo, Nuyens and Ullrich [J. Approx. Theory 240 (2019), pp. 96–113] shows that rank-1 lattice rules with a randomly chosen number of points and good generating vector achieve almost the optimal order of the randomized error in weighted Korobov spaces, and moreover, that the error is bounded independently of the dimension if the weight parameters,γj\gamma _j, satisfy the summability condition∑j=1∞γj1/α>∞\sum _{j=1}^{\infty }\gamma _j^{1/\alpha }>\infty, whereα\alphais a smoothness parameter. The argument is based on the existence result that at least half of the possible generating vectors yield almost the optimal order of the worst-case error in the same function spaces.In this paper we provide a component-by-component construction algorithm of such randomized rank-1 lattice rules, without any need to check whether the constructed generating vectors satisfy a desired worst-case error bound. Similarly to the above-mentioned work, we prove that our algorithm achieves almost the optimal order of the randomized error and that the error bound is independent of the dimension if the same condition∑j=1∞γj1/α>∞\sum _{j=1}^{\infty }\gamma _j^{1/\alpha }>\inftyholds. We also provide analogous results for tent-transformed lattice rules for weighted half-period cosine spaces and for polynomial lattice rules in weighted Walsh spaces, respectively.

Construction-Free Median Quasi-Monte Carlo Rules for Function Spaces with Unspecified Smoothness and General Weights

We study quasi-Monte Carlo (QMC) integration of smooth functions defined over the multi-dimensional unit cube. Inspired by a recent work of Pan and Owen, we study a new construction-free median QMC rule which can exploit the smoothness and the weights of function spaces adaptively. For weighted Korobov spaces, we draw a sample of $r$ independent generating vectors of rank-1 lattice rules, compute the integral estimate for each, and approximate the true integral by the median of these $r$ estimates. For weighted Sobolev spaces, we use the same approach but with the rank-1 lattice rules replaced by high-order polynomial lattice rules. A major advantage over the existing approaches is that we do not need to construct good generating vectors by a computer search algorithm, while our median QMC rule achieves almost the optimal worst-case error rate for the respective function space with any smoothness and weights, with a probability that converges to 1 exponentially fast as $r$ increases. Numerical experiments illustrate and support our theoretical findings.

Novel approach to classify skin malignancy through deep convolutional neural network and image preprocessing approaches

Melanoma is a malignant skin disease that kills roughly one million people per year, as per WHO records. The proposed work's major goal is to create and develop an enhanced deep neural network model that can evaluate, recognize, and predict cutaneous skin disease in its early stages with more accuracy, lowering the chance of death. The dataset, which was gathered from dermatologists and the public domain, contains roughly 3606 images of various types of skin lesions; some of the images were distorted. Gaussian and bilateral filters were used to decrease the noise in the images. After cleaning the data, the proposed six Convolutional layered Deep-CNN networks deployed to identify and predict skin cancer. The proposed CNN network was able to recognize skin diseases such Malignant Melanoma, Squamous cellcarcinoma, and Basal cellcarcinoma with an optimal error rate and good accuracy of 98.07 percent.

Clustering high-dimensional data via feature selection.

High-dimensional clustering analysis is a challenging problem in statistics and machine learning, with broad applications such as the analysis of microarray data and RNA-seq data. In this paper, we propose a new clustering procedure called spectral clustering with feature selection (SC-FS), where we first obtain an initial estimate of labels via spectral clustering, then select a small fraction of features with the largest R-squared with these labels, that is, the proportion of variation explained by group labels, and conduct clustering again using selected features. Under mild conditions, we prove that the proposed method identifies all informative features with high probability and achieves the minimax optimal clustering error rate for the sparse Gaussian mixture model. Applications of SC-FS to four real-world datasets demonstrate its usefulness in clustering high-dimensionaldata.

Comparing Machine Learning Algorithms for Improving the Maintenance of LTE Networks Based on Alarms Analysis

Mobile network operators are facing many challenges to satisfy their subscribers in terms of quality of service and quality of experience provided. To achieve this goal, technological progress and scientific advances offer good opportunities for efficiency in the management of faults occurring in a mobile network. Machine learning techniques allow systems to learn from past experiences and can predict, solutions to be applied to correct the root cause of a failure. This paper evaluates machine learning techniques and identifies the decision tree as a learning model that provides the most optimal error rate in predicting outages that may occur in a mobile network. Three machine learning techniques are presented in this study and compared with regard to accuracy. This study demonstrates that the appropriate machine learning technique improves the accuracy of the model. By using the decision tree as a machine learning model, it was possible to predict solutions to network failures, with an error rate less than 2%. In addition, the use of Machine Learning makes it possible to eliminate steps in the network failure processing chain; resulting in reduced service disruption time and improved the network availability which is a key network performance index.

An Intelligent Task Scheduling Mechanism for Autonomous Vehicles via Deep Learning

With the rapid development of the Internet of Things (IoT) and artificial intelligence, autonomous vehicles have received much attention in recent years. Safe driving is one of the essential concerns of self-driving cars. The main problem in providing better safe driving requires an efficient inference system for real-time task management and autonomous control. Due to limited battery life and computing power, reducing execution time and resource consumption can be a daunting process. This paper addressed these challenges and developed an intelligent task management system for IoT-based autonomous vehicles. For each task processing, a supervised resource predictor is invoked for optimal hardware cluster selection. Tasks are executed based on the earliest hyper period first (EHF) scheduler to achieve optimal task error rate and schedule length performance. The single-layer feedforward neural network (SLFN) and lightweight learning approaches are designed to distribute each task to the appropriate processor based on their emergency and CPU utilization. We developed this intelligent task management module in python and experimentally tested it on multicore SoCs (Odroid Xu4 and NVIDIA Jetson embedded platforms). Connected Autonomous Vehicles (CAV) and Internet of Medical Things (IoMT) benchmarks are used for training and testing purposes. The proposed modules are validated by observing the task miss rate, resource utilization, and energy consumption metrics compared with state-of-art heuristics. SLFN-EHF task scheduler achieved better results in an average of 98% accuracy, and in an average of 20–27% reduced in execution time and 32–45% in task miss rate metric than conventional methods.

Additive functional regression in reproducing kernel Hilbert spaces under smoothness condition

Additive functional model is one popular semiparametric approach for regression with a functional predictor. Optimal prediction error rate has been demonstrated in the framework of reproducing kernel Hilbert spaces (RKHS), which only depends on the property of the RKHS but not on the smoothness of the function. We extend this previous theoretical result by establishing faster convergence rates under stronger conditions which is reduced to existing results when the stronger condition is removed. In particular, our result shows that with a smoother function the convergence rate of the estimator is faster.

Adversarial Hypothesis Testing and a Quantum Stein’s Lemma for Restricted Measurements

Recall the classical hypothesis testing setting with two sets of probability distributions P and Q. One receives either n i.i.d. samples from a distribution p E P or from a distribution q E Q and wants to decide from which set the points were sampled. It is known that the optimal exponential rate at which errors decrease can be achieved by a simple maximum-likelihood ratio test which does not depend on p or q, but only on the sets P and Q. We consider an adaptive generalization of this model where the choice of p E P and q E Q can change in each sample in some way that depends arbitrarily on the previous samples. In other words, in the kth round, an adversary, having observed all the previous samples in rounds 1, . . . , k - 1, chooses pk E P and qk E Q, with the goal of confusing the hypothesis test. We prove that even in this case, the optimal exponential error rate can be achieved by a simple maximum-likelihood test that depends only on P and Q. We then show that the adversarial model has applications in hypothesis testing for quantum states using restricted measurements. For example, it can be used to study the problem of distinguishing entangled states from the set of all separable states using only measurements that can be implemented with local operations and classical communication (LOCC). The basic idea is that in our setup, the deleterious effects of entanglement can be simulated by an adaptive classical adversary. We prove a quantum Stein's Lemma in this setting: In many circumstances, the optimal hypothesis testing rate is equal to an appropriate notion of quantum relative entropy between two states. In particular, our arguments yield an alternate proof of Li and Winter's recent strengthening of strong subadditivity for von Neumann entropy.

Real-Time Software-Reconfigurable Hybrid In-House Access With OFDM-NOMA

In this paper, a real-time software-reconfigurable orthogonal frequency division multiplexing based non-orthogonal multiple access (OFDM-NOMA) scheme with dynamic power allocation is proposed and experimentally demonstrated for hybrid in-house access over single-mode fiber (SMF) and visible light communication (VLC). Such hybrid access can provide both wired and wireless transmission, which can accommodate the increasingly heterogeneous in-home network and realize seamless coverage. The fiber link is used to provide high-speed and stable transmission for a wired user whilst the VLC link can support flexible and secured wireless access. With the help of power-domain multiplexing based NOMA, the power ratio between both the fiber user and the VLC user can be adjusted in a software-reconfigurable manner, which can satisfy various user demands and also ensure user fairness. Experimental results validate that an aggregate data rate of 1.84 Gbit/s can be achieved in a 1-GSa/s hybrid access system. In addition, it is demonstrated that the power ratio between the fiber user and the VLC user can be adjusted in real-time, facilitating the optimal overall system bit error rate (BER) performance and hence the balanced user fairness. The proposed real-time software-reconfigurable dynamic power allocation scheme for OFDM-NOMA is a promising scheme for the future heterogeneous in-house network, as it allows the flexible power allocation according to users’ demands and enables better user fairness.