arXiv subjects

Benjamin J. Raphael

Publications and source records attributed to Benjamin J. Raphael.

7 recordsLinked to original sources

arXiv2025

Hierarchical Refinement: Optimal Transport to Infinity and Beyond

Optimal transport (OT) has enjoyed great success in machine learning as a principled way to align datasets via a least-cost correspondence, driven in large part by the runtime efficiency of the Sinkhorn algorithm (Cuturi, 2013). However, Sinkhorn has quadratic space and time complexity in the number of points, limiting scalability to larger datasets. Low-rank OT achieves linear complexity, but by definition, cannot compute a one-to-one correspondence between points. When the optimal transport problem is an assignment problem between datasets then an optimal mapping, known as the Monge map, is guaranteed to be a bijection. In this setting, we show that the factors of an optimal low-rank coupling co-cluster each point with its image under the Monge map. We leverage this invariant to derive an algorithm, Hierarchical Refinement (HiRef), that dynamically constructs a multiscale partition of each dataset using low-rank OT subproblems, culminating in the bijective Monge map. Hierarchical Refinement runs in log-linear time and linear space, retaining the advantages of low-rank OT while overcoming its limited resolution. We demonstrate the advantages of Hierarchical Refinement on several datasets, including ones containing over a million points, scaling full-rank OT to problems previously beyond Sinkhorn's reach.

cs.LG↗

arXiv2024

Current and future directions in network biology

Network biology is an interdisciplinary field bridging computational and biological sciences that has proved pivotal in advancing the understanding of cellular functions and diseases across biological systems and scales. Although the field has been around for two decades, it remains nascent. It has witnessed rapid evolution, accompanied by emerging challenges. These challenges stem from various factors, notably the growing complexity and volume of data together with the increased diversity of data types describing different tiers of biological organization. We discuss prevailing research directions in network biology and highlight areas of inference and comparison of biological networks, multimodal data integration and heterogeneous networks, higher-order network analysis, machine learning on networks, and network-based personalized medicine. Following the overview of recent breakthroughs across these five areas, we offer a perspective on the future directions of network biology. Additionally, we offer insights into scientific communities, educational initiatives, and the importance of fostering diversity within the field. This paper establishes a roadmap for an immediate and long-term vision for network biology.

q-bio.MN↗

arXiv2021

Quantifying and Reducing Bias in Maximum Likelihood Estimation of Structured Anomalies

Anomaly estimation, or the problem of finding a subset of a dataset that differs from the rest of the dataset, is a classic problem in machine learning and data mining. In both theoretical work and in applications, the anomaly is assumed to have a specific structure defined by membership in an $\textit{anomaly family}$. For example, in temporal data the anomaly family may be time intervals, while in network data the anomaly family may be connected subgraphs. The most prominent approach for anomaly estimation is to compute the Maximum Likelihood Estimator (MLE) of the anomaly; however, it was recently observed that for normally distributed data, the MLE is a $\textit{biased}$ estimator for some anomaly families. In this work, we demonstrate that in the normal means setting, the bias of the MLE depends on the size of the anomaly family. We prove that if the number of sets in the anomaly family that contain the anomaly is sub-exponential, then the MLE is asymptotically unbiased. We also provide empirical evidence that the converse is true: if the number of such sets is exponential, then the MLE is asymptotically biased. Our analysis unifies a number of earlier results on the bias of the MLE for specific anomaly families. Next, we derive a new anomaly estimator using a mixture model, and we prove that our anomaly estimator is asymptotically unbiased regardless of the size of the anomaly family. We illustrate the advantages of our estimator versus the MLE on disease outbreak and highway traffic data.

cs.LG↗

arXiv2016

A Weighted Exact Test for Mutually Exclusive Mutations in Cancer

The somatic mutations in the pathways that drive cancer development tend to be mutually exclusive across tumors, providing a signal for distinguishing driver mutations from a larger number of random passenger mutations. This mutual exclusivity signal can be confounded by high and highly variable mutation rates across a cohort of samples. Current statistical tests for exclusivity that incorporate both per-gene and per-sample mutational frequencies are computationally expensive and have limited precision. We formulate a weighted exact test for assessing the significance of mutational exclusivity in an arbitrary number of mutational events. Our test conditions on the number of samples with a mutation as well as per-event, per-sample mutation probabilities. We provide a recursive formula to compute $p$-values for the weighted test exactly as well as a highly accurate and efficient saddlepoint approximation of the test. We use our test to approximate a commonly used permutation test for exclusivity that conditions on per-event, per-sample mutation frequencies. However, our test is more efficient and it recovers more significant results than the permutation test. We use our Weighted Exclusivity Test (WExT) software to analyze hundreds of colorectal and endometrial samples from The Cancer Genome Atlas, which are two cancer types that often have extremely high mutation rates. On both cancer types, the weighted test identifies sets of mutually exclusive mutations in cancer genes with fewer false positives than earlier approaches.

q-bio.QM↗

arXiv2016

Multi-State Perfect Phylogeny Mixture Deconvolution and Applications to Cancer Sequencing

The reconstruction of phylogenetic trees from mixed populations has become important in the study of cancer evolution, as sequencing is often performed on bulk tumor tissue containing mixed populations of cells. Recent work has shown how to reconstruct a perfect phylogeny tree from samples that contain mixtures of two-state characters, where each character/locus is either mutated or not. However, most cancers contain more complex mutations, such as copy-number aberrations, that exhibit more than two states. We formulate the Multi-State Perfect Phylogeny Mixture Deconvolution Problem of reconstructing a multi-state perfect phylogeny tree given mixtures of the leaves of the tree. We characterize the solutions of this problem as a restricted class of spanning trees in a graph constructed from the input data, and prove that the problem is NP-complete. We derive an algorithm to enumerate such trees in the important special case of cladisitic characters, where the ordering of the states of each character is given. We apply our algorithm to simulated data and to two cancer datasets. On simulated data, we find that for a small number of samples, the Multi-State Perfect Phylogeny Mixture Deconvolution Problem often has many solutions, but that this ambiguity declines quickly as the number of samples increases. On real data, we recover copy-neutral loss of heterozygosity, single-copy amplification and single-copy deletion events, as well as their interactions with single-nucleotide variants.

cs.DS↗

arXiv2015

CoMEt: A Statistical Approach to Identify Combinations of Mutually Exclusive Alterations in Cancer

Cancer is a heterogeneous disease with different combinations of genetic and epigenetic alterations driving the development of cancer in different individuals. While these alterations are believed to converge on genes in key cellular signaling and regulatory pathways, our knowledge of these pathways remains incomplete, making it difficult to identify driver alterations by their recurrence across genes or known pathways. We introduce Combinations of Mutually Exclusive Alterations (CoMEt), an algorithm to identify combinations of alterations de novo, without any prior biological knowledge (e.g. pathways or protein interactions). CoMEt searches for combinations of mutations that exhibit mutual exclusivity, a pattern expected for mutations in pathways. CoMEt has several important feature that distinguish it from existing approaches to analyze mutual exclusivity among alterations. These include: an exact statistical test for mutual exclusivity that is more sensitive in detecting combinations containing rare alterations; simultaneous identification of collections of one or more combinations of mutually exclusive alterations; simultaneous analysis of subtype-specific mutations; and summarization over an ensemble of collections of mutually exclusive alterations. These features enable CoMEt to robustly identify alterations affecting multiple pathways, or hallmarks of cancer. We show that CoMEt outperforms existing approaches on simulated and real data. Application of CoMEt to hundreds of samples from four different cancer types from TCGA reveals multiple mutually exclusive sets within each cancer type. Many of these overlap known pathways, but others reveal novel putative cancer genes. *Equal contribution.

q-bio.QM↗

arXiv2013

Accurate Computation of Survival Statistics in Genome-wide Studies

A key challenge in genomics is to identify genetic variants that distinguish patients with different survival time following diagnosis or treatment. While the log-rank test is widely used for this purpose, nearly all implementations of the log-rank test rely on an asymptotic approximation that is not appropriate in many genomics applications. This is because: the two populations determined by a genetic variant may have very different sizes; and the evaluation of many possible variants demands highly accurate computation of very small p-values. We demonstrate this problem for cancer genomics data where the standard log-rank test leads to many false positive associations between somatic mutations and survival time. We develop and analyze a novel algorithm, Exact Log-rank Test (ExaLT), that accurately computes the p-value of the log-rank statistic under an exact distribution that is appropriate for any size populations. We demonstrate the advantages of ExaLT on data from published cancer genomics studies, finding significant differences from the reported p-values. We analyze somatic mutations in six cancer types from The Cancer Genome Atlas (TCGA), finding mutations with known association to survival as well as several novel associations. In contrast, standard implementations of the log-rank test report dozens-hundreds of likely false positive associations as more significant than these known associations.

q-bio.QM↗