A concave pairwise fusion approach to subgroup analysis

An important step in developing individualized treatment strategies is to correctly identify subgroups of a heterogeneous population, so that specific treatment can be given to each subgroup. In this paper, we consider the situation with samples drawn from a population consisting of subgroups with different means, along with certain covariates. We propose a penalized approach for subgroup analysis based on a regression model, in which heterogeneity is driven by unobserved latent factors and thus can be represented by using subject-specific intercepts. We apply concave penalty functions to pairwise differences of the intercepts. This procedure automatically divides the observations into subgroups. We develop an alternating direction method of multipliers algorithm with concave penalties to implement the proposed approach and demonstrate its convergence. We also establish the theoretical properties of our proposed estimator and determine the order requirement of the minimal difference of signals between groups in order to recover them. These results provide a sound basis for making statistical inference in subgroup analysis. Our proposed method is further illustrated by simulation studies and analysis of the Cleveland heart disease dataset

Unsupervised Neural Machine Translation with SMT as Posterior Regularization

Without real bilingual corpus available, unsupervised Neural Machine Translation (NMT) typically requires pseudo parallel data generated with the back-translation method for the model training. However, due to weak supervision, the pseudo data inevitably contain noises and errors that will be accumulated and reinforced in the subsequent training process, leading to bad translation performance. To address this issue, we introduce phrase based Statistic Machine Translation (SMT) models which are robust to noisy data, as posterior regularizations to guide the training of unsupervised NMT models in the iterative back-translation process. Our method starts from SMT models built with pre-trained language models and word-level translation tables inferred from cross-lingual embeddings. Then SMT and NMT models are optimized jointly and boost each other incrementally in a unified EM framework. In this way, (1) the negative effect caused by errors in the iterative back-translation process can be alleviated timely by SMT filtering noises from its phrase tables; meanwhile, (2) NMT can compensate for the deficiency of fluency inherent in SMT. Experiments conducted on en-fr and en-de translation tasks show that our method outperforms the strong baseline and achieves new state-of-the-art unsupervised machine translation performance.Comment: To be presented at AAAI 2019; 9 pages, 4 figure

Detecting latent communities in network formation models

This paper proposes a logistic undirected network formation model which allows for assortative matching on observed individual characteristics and the presence of edge-wise fixed effects. We model the coefficients of observed characteristics to have a latent community structure and the edge-wise fixed effects to be of low rank. We propose a multi-step estimation procedure involving nuclear norm regularization, sample splitting, iterative logistic regression and spectral clustering to detect the latent communities. We show that the latent communities can be exactly recovered when the expected degree of the network is of order log n or higher, where n is the number of nodes in the network. The finite sample performance of the new estimation and inference methods is illustrated through both simulated and real datasets.Comment: 63 page