Detection of anomalies is a common and important problem, especially when anomalies are rare and labels are difficult to acquire. Here we sequentially detect outliers in the outputs of an unknown function, which have been distorted by noise. We model the sequence of outputs by using Yule-Simon processes and provide an iterative algorithm for learning the function from input and output data using Gaussian processes. We tested our method by using both synthetic and real-world data. The experimental results indicate excellent performance of the proposed method.

The computer-aided interpretation of fetal heart rate (FHR) and uterine contraction (UC) has not been developed well enough for wide use in delivery rooms. The main challenges still lie in the lack of unclear and nonstandard labels for cardiotocography (CTG) recordings, and the timely prediction of fetal state during monitoring. Rather than traditional supervised approaches to FHR classification, this paper demonstrates a way to understand the UC-dependent FHR responses in an unsupervised manner. In this work, we provide a complete method for FHR-UC segment clustering and analysis via the Gaussian process latent variable model, and density-based spatial clustering. We map the UC-dependent FHR segments into a space with a visual dimension and propose a trajectory-based FHR interpretation method. Three metrics of FHR trajectory are defined and an open-access CTG database is used for testing the proposed method.

Regime-switching state-space models (RS-SSMs) are an important class of statistical models that can be used to represent real-world phenomena. Unlike regular state-space models, RS-SSMs allow for dynamic uncertainty in the state transition and observations distributions, making them much more expressive. Unfortunately, there are no existing Bayesian inference techniques for joint estimation of regimes, states, and model parameters in generic RS-SSMs. In this work, we develop a particle Gibbs sampling algorithm for Bayesian learning in RS-SSMs. We demonstrate the proposed inference approach on a synthetic data experiment related to an ecological application, where the goal is in estimating the abundance and demographic rates of penguins in the Antarctic.

Identifying uterine contractions with the aid of machine learning methods is necessary vis-á-vis their use in combination with fetal heart rates and other clinical data for the assessment of a fetus wellbeing. In this paper, we study contraction identification by processing noisy signals due to uterine activities. We propose a complete four-step method where we address the imbalanced classification problem with an ensemble Gaussian process classifier, where the Gaussian process latent variable model is used as a decision-maker. The results of both simulation and real data show promising performance compared to existing methods.

Classification with imbalanced data is a common and challenging problem in many practical machine learning problems. Ensemble learning is a popular solution where the results from multiple base classifiers are synthesized to reduce the effect of a possibly skewed distribution of the training set. In this paper, binary classifiers based on Gaussian processes are chosen as bases for inferring the predictive distributions of test latent variables. We apply a Gaussian process latent variable model where the outputs of the Gaussian processes are used for making the final decision. The tests of the new method in both synthetic and real data sets show improved performance over standard approaches.

Altitude estimation is important for successful control and navigation of unmanned aerial vehicles (UAVs). UAVs do not have indoor access to GPS signals and can only use on-board sensors for reliable estimation of altitude. Unfortunately, most existing navigation schemes are not robust to the presence of abnormal obstructions above and below the UAV. In this work, we propose a novel strategy for tackling the altitude estimation problem that utilizes multiple model adaptive estimation (MMAE), where the candidate models correspond to four scenarios: no obstacles above and below the UAV; obstacles above the UAV; obstacles below the UAV; and obstacles above and below the UAV. The principle of Occam's razor ensures that the model that offers the most parsimonious explanation of the sensor data has the most influence in the MMAE algorithm. We validate the proposed scheme on synthetic and real sensor data.

Identifying the location of a target is a fundamental application in multistatic sonar. Numerous attempts have been made to improve the accuracy, computational efficiency and robustness of target positioning. Previous studies mostly use time delay and angle measurements for localization, or time delays and Doppler shifts if relative motions exist among the transmitters, target and receivers. This paper considers the joint use of time delay, Doppler shift and angle measurements to locate a moving target. We develop an explicit algebraic solution to the problem, and illustrate the benefit of using all three kinds of measurements. The proposed solution is shown by theoretical performance analysis and confirmed by simulations to be able to reach the Cramer-Rao Bound (CRB) accuracy under Gaussian noise, when the noise level is not significant.

A moving target creates the Doppler effect on the transmitted signal, which can be exploited to improve the target localization accuracy in multistatic sonar that normally utilizes differential delay time measurements only. In this letter, we first examine the contribution of Doppler measurements via the Cr$\acute{\text{a}}$mer–Rao lower bound (CRLB) study, and then develop an algebraic closed-form solution for the moving target localization problem. The proposed algorithm is shown in both theory and simulation to be able to reach the CRLB performance under Gaussian noise, when the measurement error is small.