Generalized Log Likelihood Ratio Research Articles

Data-adaptive symmetric CUSUM for sequential change detection

Detecting change points sequentially in a streaming setting, especially when both the mean and the variance of the signal can change, is often a challenging task. A key difficulty in this context often involves setting an appropriate detection threshold, which for many standard change statistics may need to be tuned depending on the prechange and postchange distributions. This presents a challenge in a sequential change detection setting when a signal switches between multiple distributions. Unfortunately, change point detection schemes that use the log-likelihood ratio, such as cumulative sum (CUSUM) and the generalized log-likelihood ratio (GLR), are quick to react to changes but are not symmetric when both the mean and the variance of the signal change. This makes it difficult to set a single threshold to detect multiple change points sequentially in a streaming setting. We propose a modified version of CUSUM that we call data-adaptive symmetric CUSUM (DAS-CUSUM). The DAS-CUSUM procedure is symmetric for changes between distributions, making it suitable to set a single threshold to detect multiple change points sequentially in a streaming setting. We provide results that relate the expected detection delay and average run length for our proposed procedure when both prechange and postchange distributions are normally distributed. Experiments on simulated and real-world data show the utility of DAS-CUSUM.

Anomaly Search Over Discrete Composite Hypotheses in Hierarchical Statistical Models

Detection of anomalies among a large number of processes is a fundamental task that has been studied in multiple research areas, with diverse applications spanning from spectrum access to cyber-security. Anomalous events are characterized by deviations in data distributions, and thus can be inferred from noisy observations based on statistical methods. In some scenarios, one can often obtain noisy observations aggregated from a chosen subset of processes. Such hierarchical search can further minimize the sample complexity while retaining accuracy. An anomaly search strategy should thus be designed based on multiple requirements, such as maximizing the detection accuracy; efficiency, be efficient in terms of sample complexity; and be able to cope with statistical models that are known only up to some missing parameters (i.e., composite hypotheses). In this paper, we consider anomaly detection with observations taken from a chosen subset of processes that conforms to a predetermined tree structure with partially known statistical model. We propose Hierarchical Dynamic Search (HDS), a sequential search strategy that uses two variations of the Generalized Log Likelihood Ratio (GLLR) statistic, and can be used for detection of multiple anomalies. HDS is shown to be order-optimal in terms of the size of the search space, and asymptotically optimal in terms of detection accuracy. An explicit upper bound on the error probability is established for the finite sample regime. In addition to extensive experiments on synthetic datasets, experiments have been conducted on the DARPA intrusion detection dataset, showing that HDS is superior to existing methods.

AN ANALYSIS OF TECHNICAL EFFICIENCY OF STRAWBERRY GROWERS AT KHYBER PAKHTUNKHWA

The mean technical efficiency of strawberry farmers was assessed using a stochastic frontier approach in the districts of Charsadda and Mardan in Khyber Pakhtunkhwa. By using multistage sampling technique, 382 respondent’s data was collected. Cobb Douglass functional form was chosen for stochastic frontier analysis by using a generalized loglikelihood ratio test. Respectively the estimated result indicated that farmers had an average technical efficiency of 81 percent in the research area, with minimum and highest values of 0.42 and 0.98. Showing that by utilizing the available resources efficiently, productivity can be increased

Performance analysis of HFDI computing algorithm in intelligent networks

ABSTRACTCognitive radio (CR) system plays a major role in spectrum sensing. In cognitive radio, the spectrum slot is assigned to user intellectually according to a prescribed algorithm. Different researchers have proposed different spectrum sensing methods to plot the receiver operating characteristics (ROCs), probability of detection (PD), and probability of false alarm (Pfa). Apparently, there is less focus on which samples of Pfa are majorly affected. A method of Hybrid Filter Detection with Inverse covariance matrix (HFDI) is proposed to identify the Pfa affected samples and to minimize the Pfa with maximize of PD. The proposed HFDI method uses generalized log likelihood ratio test (GLRT) to measure the Pfa and PD. The measured Pfa and PD are compared with the NP observer approach, HMF, and Divya Joshi-proposed methods. Additionally, a parameter probability of missed detection (Pmd) is measured between the proposed HFDI and NP observer approach. The proposed HFDI method outperforms Divya Joshi-proposed method by 13% in terms of PD, and the Pfa is also improved by 7.5%. ROC is a parameter used to analyze the performance between PD and Pfa and is compared with the existing compressed sensing method.

Echo Cancellation—The Generalized Likelihood Ratio Test For Double-Talk Versus Channel Change

Echo cancellers (EC) are required in both electrical (impedance mismatch) and acoustic (speaker-microphone coupling) applications. One of the main design problems is the control logic for adaptation. Basically, the algorithm weights should be frozen in the presence of double-talk and adapt quickly in the absence of double-talk. The optimum likelihood ratio test (LRT) for this problem was studied in a recent paper. The LRT requires a priori knowledge of the background noise and double-talk power levels. Instead, this paper derives a generalized log likelihood ratio test (GLRT) that does not require this knowledge. The probability density function of a sufficient statistic under each hypothesis is obtained and the performance of the test is evaluated as a function of the system parameters. The receiver operating characteristics (ROCs) indicate that it is difficult to correctly decide between double-talk and a channel change, based upon a single look. However, detection based on about 200 successive samples yields a detection probability close to unity (0.99) with a small false alarm probability (0.01) for the theoretical GLRT model. Application of a GLRT-based EC to real voice data shows comparable performance to that of the LRT-based EC given in a recent paper.

A Modal Filtering and Statistical Approach for Damage Detection and Diagnosis in Structures using Ambient Vibrations Measurements

The monitoring and diagnosis of structures using output-only ambient vibration tests are becoming increasingly popular nowadays. In this Article a new statistics-based approach is proposed for damage detection and diagnosis (localization and quantification) in structures under their normal working conditions. The proposed approach requires vibration data relative to the current and reference states of the structure as well as a finite element model parameterized using specified damage parameters. Such parameters may include physical and/or geometrical properties of the structure. Modal filtering, combined with an asymptotic local approach, is used to compute an improved residual which turns out to be normally distributed. The mean, covariance and sensitivity of this residual allow the detection of damage based on generalized log-likelihood ratio (GLR) tests. The diagnosis of damage is made possible by applying sensitivity and rejection tests to the residual vector computed directly from the finite element model. Constraints on the damage parameters are also incorporated into these test statistics to ensure that only physically feasible damage is considered. Moreover, in some cases of multiple damage, a branch-and-bound scheme may be necessary to expedite the search for damage. The proposed damage detection and diagnosis algorithm is tested on simulation examples of simple structures.

Soft decision metric generation for QAM with channel estimation error

The channel code bit log likelihood ratio (LLR) for soft decision decoding is derived for quadrature amplitude modulated signals (QAM). The effect of imperfect channel knowledge on soft decision decoding performance is studied. Our results indicate this effect increases with channel estimation error and/or QAM modulation level. A metric based on generalized log likelihood ratio (GLLR) is derived for soft decision channel decoding with imperfect channel knowledge. Numerical results show that the GLLR-based metric outperforms the conventional minimum distance decoding metric that does not take into account channel estimation error.