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Boolean matrix factorization (BMF) has been widely utilized in fields such as recommendation systems, graph learning, text mining, and -omics data analysis. Traditional BMF methods decompose a binary matrix into the Boolean product of two lower-rank Boolean matrices plus homoscedastic random errors. However, real-world binary data typically involves biases arising from heterogeneous row- and column-wise signal distributions. Such biases can lead to suboptimal fitting and unexplainable predictions if not accounted for. In this study, we reconceptualize the binary data generation as the Boolean sum of three components: a binary pattern matrix, a background bias matrix influenced by heterogeneous row or column distributions, and random flipping errors. We introduce a novel Disentangled Representation Learning for Binary matrices (DRLB) method, which employs a dual auto-encoder network to reveal the true patterns. DRLB can be seamlessly integrated with existing BMF techniques to facilitate bias-aware BMF. Our experiments with both synthetic and real-world datasets show that DRLB significantly enhances the precision of traditional BMF methods while offering high scalability. Moreover, the bias matrix detected by DRLB accurately reflects the inherent biases in synthetic data, and the patterns identified in the bias-corrected real-world data exhibit enhanced interpretability. 

Boolean matrix factorization (BMF) has been widely utilized in fields such as recommendation systems, graph learning, text mining, and -omics data analysis. Traditional BMF methods decompose a binary matrix into the Boolean product of two lower-rank Boolean matrices plus homoscedastic random errors. However, real-world binary data typically involves biases arising from heterogeneous row- and column-wise signal distributions. Such biases can lead to suboptimal fitting and unexplainable predictions if not accounted for. In this study, we reconceptualize the binary data generation as the Boolean sum of three components: a binary pattern matrix, a background bias matrix influenced by heterogeneous row or column distributions, and random flipping errors. We introduce a novel Disentangled Representation Learning for Binary matrices (DRLB) method, which employs a dual auto-encoder network to reveal the true patterns. DRLB can be seamlessly integrated with existing BMF techniques to facilitate bias-aware BMF. Our experiments with both synthetic and real-world datasets show that DRLB significantly enhances the precision of traditional BMF methods while offering high scalability. Moreover, the bias matrix detected by DRLB accurately reflects the inherent biases in synthetic data, and the patterns identified in the bias-corrected real-world data exhibit enhanced interpretability. 

Matrix low rank approximation is an effective method to reduce or eliminate the statistical redundancy of its components. Compared with the traditional global low rank methods such as singular value decomposition (SVD), local low rank approximation methods are more advantageous to uncover interpretable data structures when clear duality exists between the rows and columns of the matrix. Local low rank approximation is equivalent to low rank submatrix detection. Unfortunately,existing local low rank approximation methods can detect only submatrices of specific mean structure, which may miss a substantial amount of true and interesting patterns. In this work, we develop a novel matrix computational framework called RPSP (Random Probing based submatrix Propagation) that provides an effective solution for the general matrix local low rank representation problem. RPSP detects local low rank patterns that grow from small submatrices of low rank property, which are determined by a random projection approach. RPSP is supported by theories of random projection. Experiments on synthetic data demonstrate that RPSP outperforms all state-of-the-art methods, with the capacity to robustly and correctly identify the low rank matrices when the pattern has a similar mean as the background, background noise is heteroscedastic and multiple patterns present in the data. On real-world datasets, RPSP also demonstrates its effectiveness in identifying interpretable local low rank matrices. 

Abstract Background There is growing evidence indicating that a number of functional connectivity networks are disrupted at each stage of the full clinical Alzheimer’s disease spectrum. Such differences are also detectable in cognitive normal (CN) carrying mutations of AD risk genes, suggesting a substantial relationship between genetics and AD-altered functional brain networks. However, direct genetic effect on functional connectivity networks has not been measured. Methods Leveraging existing AD functional connectivity studies collected in NeuroSynth, we performed a meta-analysis to identify two sets of brain regions: ones with altered functional connectivity in resting state network and ones without. Then with the brain-wide gene expression data in the Allen Human Brain Atlas, we applied a new biclustering method to identify a set of genes with differential co-expression patterns between these two set of brain regions. Results Differential co-expression analysis using biclustering method led to a subset of 38 genes which showed distinctive co-expression patterns between AD-related and non AD-related brain regions in default mode network. More specifically, we observed 4 sub-clusters with noticeable co-expression difference, where the difference in correlations is above 0.5 on average. Conclusions This work applies a new biclustering method to search for a subset of genes with altered co-expression patterns in AD-related default mode network regions. Compared with traditional differential expression analysis, differential co-expression analysis yielded many more significant hits with extra insights into the wiring mechanism between genes. Particularly, the differential co-expression pattern was observed between two sets of genes, suggesting potential upstream genetic regulators in AD development. 

Abstract Quantitative assessment of single cell fluxome is critical for understanding the metabolic heterogeneity in diseases. Unfortunately, laboratory-based single cell fluxomics is currently impractical, and the current computational tools for flux estimation are not designed for single cell-level prediction. Given the well-established link between transcriptomic and metabolomic profiles, leveraging single cell transcriptomics data to predict single cell fluxome is not only feasible but also an urgent task. In this study, we present FLUXestimator, an online platform for predicting metabolic fluxome and variations using single cell or general transcriptomics data of large sample-size. The FLUXestimator webserver implements a recently developed unsupervised approach called single cell flux estimation analysis (scFEA), which uses a new neural network architecture to estimate reaction rates from transcriptomics data. To the best of our knowledge, FLUXestimator is the first web-based tool dedicated to predicting cell-/sample-wise metabolic flux and metabolite variations using transcriptomics data of human, mouse and 15 other common experimental organisms. The FLUXestimator webserver is available at http://scFLUX.org/, and stand-alone tools for local use are available at https://github.com/changwn/scFEA. Our tool provides a new avenue for studying metabolic heterogeneity in diseases and has the potential to facilitate the development of new therapeutic strategies. 

An immunotherapy trial often uses the phase I/II design to identify the optimal biological dose, which monitors the efficacy and toxicity outcomes simultaneously in a single trial. The progression-free survival rate is often used as the efficacy outcome in phase I/II immunotherapy trials. As a result, patients developing disease progression in phase I/II immunotherapy trials are generally seriously ill and are often treated off the trial for ethical consideration. Consequently, the happening of disease progression will terminate the toxicity event but not vice versa, so the issue of the semi-competing risks arises. Moreover, this issue can become more intractable with the late-onset outcomes, which happens when a relatively long follow-up time is required to ascertain progression-free survival. This paper proposes a novel Bayesian adaptive phase I/II design accounting for semi-competing risks outcomes for immunotherapy trials, referred to as the dose-finding design accounting for semi-competing risks outcomes for immunotherapy trials (SCI) design. To tackle the issue of the semi-competing risks in the presence of late-onset outcomes, we re-construct the likelihood function based on each patient's actual follow-up time and develop a data augmentation method to efficiently draw posterior samples from a series of Beta-binomial distributions. We propose a concise curve-free dose-finding algorithm to adaptively identify the optimal biological dose using accumulated data without making any parametric dose–response assumptions. Numerical studies show that the proposed SCI design yields good operating characteristics in dose selection, patient allocation, and trial duration.