Joint estimation of posterior probability and propensity score function for positive and unlabelled data

Positive and unlabelled learning is an important problem which arises naturally in many applications. The significant limitation of almost all existing methods lies in assuming that the propensity score function is constant (SCAR assumption), which is unrealistic in many practical situations. Avoiding this assumption, we consider parametric approach to the problem of joint estimation of posterior probability and propensity score functions. We show that under mild assumptions when both functions have the same parametric form (e.g. logistic with different parameters) the corresponding parameters are identifiable. Motivated by this, we propose two approaches to their estimation: joint maximum likelihood method and the second approach based on alternating maximization of two Fisher consistent expressions. Our experimental results show that the proposed methods are comparable or better than the existing methods based on Expectation-Maximisation scheme.Comment:

Joint feature selection and classification for positive unlabelled multi-label data using weighted penalized empirical risk minimization

We consider the positive-unlabelled multi-label scenario in which multiple target variables are not observed directly. Instead, we observe surrogate variables indicating whether or not the target variables are labelled. The presence of a label means that the corresponding variable is positive. The absence of the label means that the variable can be either positive or negative. We analyze embedded feature selection methods based on two weighted penalized empirical risk minimization frameworks. In the first approach, we introduce weights of observations. The idea is to assign larger weights to observations for which there is a consistency between the values of the true target variable and the corresponding surrogate variable. In the second approach, we consider a weighted empirical risk function which corresponds to the risk function for the true unobserved target variables. The weights in both the methods depend on the unknown propensity score functions, whose estimation is a challenging problem. We propose to use very simple bounds for the propensity score, which leads to relatively simple forms of weights. In the experiments we analyze the predictive power of the methods considered for different labelling schemes

Predicting Physical Appearance from DNA Data—Towards Genomic Solutions

The idea of forensic DNA intelligence is to extract from genomic data any information that can help guide the investigation. The clues to the externally visible phenotype are of particular practical importance. The high heritability of the physical phenotype suggests that genetic data can be easily predicted, but this has only become possible with less polygenic traits. The forensic community has developed DNA-based predictive tools by employing a limited number of the most important markers analysed with targeted massive parallel sequencing. The complexity of the genetics of many other appearance phenotypes requires big data coupled with sophisticated machine learning methods to develop accurate genomic predictors. A significant challenge in developing universal genomic predictive methods will be the collection of sufficiently large data sets. These should be created using whole-genome sequencing technology to enable the identification of rare DNA variants implicated in phenotype determination. It is worth noting that the correctness of the forensic sketch generated from the DNA data depends on the inclusion of an age factor. This, however, can be predicted by analysing epigenetic data. An important limitation preventing whole-genome approaches from being commonly used in forensics is the slow progress in the development and implementation of high-throughput, low DNA input sequencing technologies. The example of palaeoanthropology suggests that such methods may possibly be developed in forensics