**Factor analysis for INteraction (FIN)**

This article is motivated by the problem of inference on interactions among chemical exposures impacting human health outcomes. Chemicals often co-occur in the environment or in synthetic mixtures and as a result exposure levels can be highly correlated. We propose a latent factor joint model, which includes shared factors in both the predictor and response components while assuming conditional independence. By including a quadratic regression in the latent variables in the response component, we induce flexible dimension reduction in characterizing main effects and interactions. We propose a Bayesian approach to inference under this Factor analysis for INteractions (FIN) framework. Through appropriate modifications of the factor modeling structure, FIN can accommodate higher order interactions and multivariate outcomes. We provide theory on posterior consistency and the impact of misspecifying the number of factors. We evaluate the performance using a simulation study and data from the National Health and Nutrition Examination Survey (NHANES). Code is available on GitHub. … **Plackett-Luce Model**

Plackett-Luce model is based on the concept of permutation probability. This model has been extended from Bradley Terry model, where the permutation between two objects for pairwise comparison are applied. Plackett-luce model extends the Bradley Terry in comparing multiple objects at a time by permutation probability of a list of objects to be ranked. The key idea is that for the best ranked list of objects, the permutation probability is maximum, decreases with worse ranked list and is minimum at the worst ranked list of objects. … **Value of Unlabeled Data**

We quantify the separation between the numbers of labeled examples required to learn in two settings: Settings with and without the knowledge of the distribution of the unlabeled data. More specifically, we prove a separation by $\Theta(\log n)$ multiplicative factor for the class of projections over the Boolean hypercube of dimension $n$. We prove that there is no separation for the class of all functions on domain of any size. Learning with the knowledge of the distribution (a.k.a. fixed-distribution learning) can be viewed as an idealized scenario of semi-supervised learning where the number of unlabeled data points is so great that the unlabeled distribution is known exactly. For this reason, we call the separation the value of unlabeled data. … **Adversarial Clustering**

Nowadays more and more data are gathered for detecting and preventing cyber attacks. In cyber security applications, data analytics techniques have to deal with active adversaries that try to deceive the data analytics models and avoid being detected. The existence of such adversarial behavior motivates the development of robust and resilient adversarial learning techniques for various tasks. Most of the previous work focused on adversarial classification techniques, which assumed the existence of a reasonably large amount of carefully labeled data instances. However, in practice, labeling the data instances often requires costly and time-consuming human expertise and becomes a significant bottleneck. Meanwhile, a large number of unlabeled instances can also be used to understand the adversaries’ behavior. To address the above mentioned challenges, in this paper, we develop a novel grid based adversarial clustering algorithm. Our adversarial clustering algorithm is able to identify the core normal regions, and to draw defensive walls around the centers of the normal objects utilizing game theoretic ideas. Our algorithm also identifies sub-clusters of attack objects, the overlapping areas within clusters, and outliers which may be potential anomalies. …

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