Rui Kuang

E. Kulman, R. Kuang, Q. Morris

Phylogenies depicting the evolutionary history of genetically heterogeneous subpopulations of cells from the same cancer, i.e., cancer phylogenies, offer valuable insights about cancer development and guide treatment strategies. Many methods exist that reconstruct cancer phylogenies using point mutations detected with bulk DNA sequencing. However, these methods become inaccurate when reconstructing phylogenies with more than 30 mutations, or, in some cases, fail to recover a phylogeny altogether. Here, we introduce Orchard, a cancer phylogeny reconstruction algorithm that is fast and accurate using up to 1000 mutations. Orchard samples without replacement from a factorized approximation of the posterior distribution over phylogenies, a novel result derived in this paper. Each factor in this approximate posterior corresponds to a conditional distribution for adding a new mutation to a partially built phylogeny. Orchard optimizes each factor sequentially, generating a sequence of incrementally larger phylogenies that ultimately culminate in a complete tree containing all mutations. Our evaluations demonstrate that Orchard outperforms state-of-the-art cancer phylogeny reconstruction methods in reconstructing more plausible phylogenies across 90 simulated cancers and 14 B-progenitor acute lymphoblastic leukemias (B-ALLs). Remarkably, Orchard accurately reconstructs cancer phylogenies using up to 1,000 mutations. Additionally, we demonstrate that the large and accurate phylogenies reconstructed by Orchard are useful for identifying patterns of somatic mutations and genetic variations among distinct cancer cell subpopulations.

Zhuliu Li, Raphael Petegrosso, Shaden Smith et al.

Multi-relational learning on knowledge graphs infers high-order relations among the entities across the graphs. This learning task can be solved by label propagation on the tensor product of the knowledge graphs to learn the high-order relations as a tensor. In this paper, we generalize a widely used label propagation model to the normalized tensor product graph, and propose an optimization formulation and a scalable Low-rank Tensor-based Label Propagation algorithm (LowrankTLP) to infer multi-relations for two learning tasks, hyperlink prediction and multiple graph alignment. The optimization formulation minimizes the upper bound of the noisy tensor estimation error for multiple graph alignment, by learning with a subset of the eigen-pairs in the spectrum of the normalized tensor product graph. We also provide a data-dependent transductive Rademacher bound for binary hyperlink prediction. We accelerate LowrankTLP with parallel tensor computation which enables label propagation on a tensor product of 100 graphs each of size 1000 in less than half hour in the simulation. LowrankTLP was also applied to predicting the author-paper-venue hyperlinks in publication records, alignment of segmented regions across up to 26 CT-scan images and alignment of protein-protein interaction networks across multiple species. The experiments demonstrate that LowrankTLP indeed well approximates the original label propagation with better scalability and accuracy.

Raphael Petegrosso, Wei Zhang, Zhuliu Li et al.

The success of semi-supervised learning crucially relies on the scalability to a huge amount of unlabelled data that are needed to capture the underlying manifold structure for better classification. Since computing the pairwise similarity between the training data is prohibitively expensive in most kinds of input data, currently, there is no general ready-to-use semi-supervised learning method/tool available for learning with tens of millions or more data points. In this paper, we adopted the idea of two low-rank label propagation algorithms, GLNP (Global Linear Neighborhood Propagation) and Kernel Nyström Approximation, and implemented the parallelized version of the two algorithms accelerated with Nesterov's accelerated projected gradient descent for Big-data Label Propagation (BigLP). The parallel algorithms are tested on five real datasets ranging from 7000 to 10,000,000 in size and a simulation dataset of 100,000,000 samples. In the experiments, the implementation can scale up to datasets with 100,000,000 samples and hundreds of features and the algorithms also significantly improved the prediction accuracy when only a very small percentage of the data is labeled. The results demonstrate that the BigLP implementation is highly scalable to big data and effective in utilizing the unlabeled data for semi-supervised learning.