We present an integrated approach for structure and parameter estimation in latent tree graphical models. Our overall approach follows a "divide-and-conquer" strategy that learns models over small groups of variables and iteratively merges onto a global solution. The structure learning involves combinatorial operations such as minimum spanning tree construction and local recursive grouping; the parameter learning is based on the method of moments and on tensor decompositions. Our method is guaranteed to correctly recover the unknown tree structure and the model parameters with low sample complexity for the class of linear multivariate latent tree models which includes discrete and Gaussian distributions, and Gaussian mixtures. Our bulk asynchronous parallel algorithm is implemented in parallel and the parallel computation complexity increases only logarithmically with the number of variables and linearly with dimensionality of each variable.

Adoption of Electronic Health Record (EHR) systems has led to collection of massive healthcare data, which creates oppor- tunities and challenges to study them. Computational phenotyping offers a promising way to convert the sparse and complex data into meaningful concepts that are interpretable to healthcare givers to make use of them. We propose a novel su- pervised nonnegative tensor factorization methodology that derives discriminative and distinct phenotypes. We represented co-occurrence of diagnoses and prescriptions in EHRs as a third-order tensor, and decomposed it using the CP algorithm. We evaluated discriminative power of our models with an Intensive Care Unit database (MIMIC-III) and demonstrated superior performance than state-of-the-art ICU mortality calculators (e.g., APACHE II, SAPS II). Example of the resulted phenotypes are sepsis with acute kidney injury, cardiac surgery, anemia, respiratory failure, heart failure, cardiac arrest, metastatic cancer (requiring ICU), end-stage dementia (requiring ICU and transitioned to comfort-care), intraabdominal conditions, and alcohol abuse/withdrawal.