stochprofML: stochastic profiling using maximum likelihood estimation in R

Background Tissues are often heterogeneous in their single-cell molecular expression, and this can govern the regulation of cell fate. For the understanding of development and disease, it is important to quantify heterogeneity in a given tissue. Results We present the R package stochprofML which uses the maximum likelihood principle to parameterize heterogeneity from the cumulative expression of small random pools of cells. We evaluate the algorithm’s performance in simulation studies and present further application opportunities. Conclusion Stochastic profiling outweighs the necessary demixing of mixed samples with a saving in experimental cost and effort and less measurement error. It offers possibilities for parameterizing heterogeneity, estimating underlying pool compositions and detecting differences between cell populations between samples.

Classification from positive and unlabeled data based on likelihood invariance for measurement

We propose novel approaches for classification from positive and unlabeled data (PUC) based on maximum likelihood principle. These are particularly suited to measurement tasks in which the class prior of the target object in each measurement is unknown and significantly different from the class prior used for training, while the likelihood function representing the observation process is invariant over the training and measurement stages. Our PUCs effectively work without estimating the class priors of the unlabeled objects. First, we present a PUC approach called Naive Likelihood PUC (NL-PUC) using the maximum likelihood principle in a nontrivial but rather straightforward manner. The extended version called Enhanced Likelihood PUC (EL-PUC) employs an algorithm iteratively improving the likelihood estimation of the positive class. This is advantageous when the availability of the labeled positive data is limited. These characteristics are demonstrated both theoretically and experimentally. Moreover, the practicality of our PUCs is demonstrated in a real application to single molecule measurement.

Maximum Likelihood-Based Measurement Noise Covariance Estimation Using Sequential Quadratic Programming for Cubature Kalman Filter Applied in INS/BDS Integration

With the completion of the Beidou-3 system (BDS) in China, INS/BDS integration will become a promising navigation and positioning strategy. However, due to the nonlinear propagation characteristic of INS error and inevitable involvement of inaccurate measurement noise statistics, it is difficult to achieve the optimal solution through the INS/BDS integration. This paper proposes a method of cubature Kalman filter (CKF) with the measurement noise covariance estimation by using the maximum likelihood principle to solve the abovementioned problem. It establishes an estimation model for measurement noise covariance according to the maximum likelihood principle, and then, its estimation is calculated by utilizing the sequential quadratic programming. The estimated measurement noise covariance will be fed back to the procedure of CKF to improve its adaptability. Simulation and comparison analysis verify that the proposed method can accurately estimate measurement noise covariance to effectively restrain its influence on navigation solution, leading to improved navigation performance for the INS/BDS integration.

Probabilistic regression and Bayes nets

This chapter revises regression with the inclusion of uncertainty in the data in probabilistic models. It shows how modern probabilistic machine learning can be formulated. First, a simple stochastic generalization of the linear regression example is offered to introduce the formalism. This leads to the important maximum likelihood principle on which learning will be based. This concept is then generalized to non-linear problems in higher dimensions and the chapter relates this to Bayes nets. The chapter ends with a discussion about how such a probabilistic approach is related to deep learning.

Spoofing Detection and Mitigation in a Multi-correlator GPS Receiver Based on the Maximum Likelihood Principle

As a structural interference, spoofing is difficult to detect by the target receiver while the advent of a repeater makes the implementation of spoofing much easier. Most existing anti-spoofing methods are merely capable of detecting the spoofing, i.e., they cannot effectively remove counterfeit signals. Therefore, based on the similarities between multipath and spoofing, the feasibility of applying multipath mitigation methods to anti-spoofing is first analyzed in this paper. We then propose a novel algorithm based on maximum likelihood (ML) estimation to resolve this problem. The tracking channels with multi-correlators are constructed and a set of corresponding steps of detecting and removing the counterfeit signals is designed to ensure that the receiver locks the authentic signals in the presence of spoofing. Finally, the spoofing is successfully executed with a software receiver and the saved intermediate frequency (IF) signals, on this basis, the effectiveness of the proposed algorithm is verified by experiments.