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Biwhitening reveals the rank of a count matrix

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arXiv 2021年

作者： Landa, Boris Zhang, Thomas T.C.K. Kluger, Yuval Program in Applied Mathematics Yale University United States Department of Electrical and Systems Engineering University of Pennsylvania United States Interdepartmental Program in Computational Biology and Bioinformatics Yale University United States Department of Pathology Yale University School of Medicine United States

Estimating the rank of a corrupted data matrix is an important task in data analysis, most notably for choosing the number of components in PCA. Significant progress on this task was achieved using random matrix theory by characterizing the spectral properties of large noise matrices. However, utilizing such tools is not straightforward when the data matrix consists of count random variables, e.g., Poisson, in which case the noise can be heteroskedastic with an unknown variance in each entry. In this work, we consider a Poisson random matrix with independent entries, and propose a simple procedure termed biwhitening for estimating the rank of the underlying signal matrix (i.e., the Poisson parameter matrix) without any prior knowledge. Our approach is based on the key observation that one can scale the rows and columns of the data matrix simultaneously so that the spectrum of the corresponding noise agrees with the standard Marchenko-Pastur (MP) law, justifying the use of the MP upper edge as a threshold for rank selection. Importantly, the required scaling factors can be estimated directly from the observations by solving a matrix scaling problem via the Sinkhorn-Knopp algorithm. Aside from the Poisson, our approach is extended to families of distributions that satisfy a quadratic relation between the mean and the variance, such as the generalized Poisson, binomial, negative binomial, gamma, and many others. This quadratic relation can also account for missing entries in the data. We conduct numerical experiments that corroborate our theoretical findings, and showcase the advantage of our approach for rank estimation in challenging regimes. Furthermore, we demonstrate the favorable performance of our approach on several real datasets of single-cell RNA sequencing (scRNA-seq), High-Throughput Chromosome Conformation Capture (Hi-C), and document topic *** Codes 62H12, 62H25. Copyright © 2021, The Authors. All rights reserved.

关键词： Random variables

DIFFUSION CURVATURE FOR ESTIMATING LOCAL CURVATURE IN HIGH DIMENSIONAL DATA

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arXiv 2022年

作者： Bhaskar, Dhananjay MacDonald, Kincaid Fasina, Oluwadamilola Thomas, Dawson Rieck, Bastian Adelstein, Ian Krishnaswamy, Smita Department of Genetics Yale School of Medicine New HavenCT United States Department of Mathematics Yale University New HavenCT United States Program for Applied Mathematics Yale University New HavenCT United States Department of Physics Yale University New HavenCT United States Institute of AI for Health Helmholtz Pioneer Campus Munich Germany Department of Computer Science Yale University New HavenCT United States Program for Computational Biology and Bioinformatics Yale University New HavenCT United States

We introduce a new intrinsic measure of local curvature on point-cloud data called diffusion curvature. Our measure uses the framework of diffusion maps, including the data diffusion operator, to structure point cloud data and define local curvature based on the laziness of a random walk starting at a point or region of the data. We show that this laziness directly relates to volume comparison results from Riemannian geometry. We then extend this scalar curvature notion to an entire quadratic form using neural network estimations based on the diffusion map of point-cloud data. We show applications of both estimations on toy data, single-cell data and on estimating local Hessian matrices of neural network loss landscapes. © 2022, CC BY.

关键词： Geometry

Doubly-stochastic normalization of the Gaussian kernel is robust to heteroskedastic noise

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arXiv 2020年

作者： Landa, Boris Coifman, Ronald R. Kluger, Yuval Program in Applied Mathematics Yale University Interdepartmental Program in Computational Biology and Bioinformatics Yale University Department of Pathology Yale University School of Medicine

A fundamental step in many data-analysis techniques is the construction of an affinity matrix describing similarities between data points. When the data points reside in Euclidean space, a widespread approach is to from an affinity matrix by the Gaussian kernel with pairwise distances, and to follow with a certain normalization (e.g. the row-stochastic normalization or its symmetric variant). We demonstrate that the doubly-stochastic normalization of the Gaussian kernel with zero main diagonal (i.e. no self loops) is robust to heteroskedastic noise. That is, the doubly-stochastic normalization is advantageous in that it automatically accounts for observations with different noise variances. Specifically, we prove that in a suitable high-dimensional setting where heteroskedastic noise does not concentrate too much in any particular direction in space, the resulting (doubly-stochastic) noisy affinity matrix converges to its clean counterpart with rate m−1/2, where m is the ambient dimension. We demonstrate this result numerically, and show that in contrast, the popular row-stochastic and symmetric normalizations behave unfavourably under heteroskedastic noise. Furthermore, we provide a prototypical example of simulated single-cell RNA sequence data with strong intrinsic heteroskedasticity, where the advantage of the doubly-stochastic normalization for exploratory analysis is evident. Copyright © 2020, The Authors. All rights reserved.

关键词： Stochastic systems

Mutually beneficial confluence of structure-based modeling of protein dynamics and machine learning methods

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Current Opinion in Structural Biology 2023年 78卷 102517页

作者： Banerjee, Anupam Saha, Satyaki Tvedt, Nathan C. Yang, Lee-Wei Bahar, Ivet Computational and Systems Biology University of Pittsburgh School of Medicine Pittsburgh 15261 PA United States Computational and Applied Mathematics and Statistics The College of William and Mary Williamsburg 23185 VA United States Institute of Bioinformatics and Structural Biology and PhD Program in Biomedical Artificial Intelligence National Tsing Hua University Hsinchu 300044 Taiwan Physics Division National Center for Theoretical Sciences Taipei 106319 Taiwan

Proteins sample an ensemble of conformers under physiological conditions, having access to a spectrum of modes of motions, also called intrinsic dynamics. These motions ensure the adaptation to various interactions in the cell, and largely assist in, if not determine, viable mechanisms of biological function. In recent years, machine learning frameworks have proven uniquely useful in structural biology, and recent studies further provide evidence to the utility and/or necessity of considering intrinsic dynamics for increasing their predictive ability. Efficient quantification of dynamics-based attributes by recently developed physics-based theories and models such as elastic network models provides a unique opportunity to generate data on dynamics for training ML models towards inferring mechanisms of protein function, assessing pathogenicity, or estimating binding affinities. © 2022 The Authors

关键词：

SCALE RELIANT INFERENCE

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arXiv 2022年

作者： Nixon, Michelle Pistner McGovern, Kyle C. Letourneau, Jeffrey David, Lawrence A. Lazar, Nicole A. Mukherjee, Sayan Silverman, Justin D. College of Information Sciences and Technology The Pennsylvania State University United States Program in Bioinformatics and Genomics The Pennsylvania State University United States Department of Molecular Genetics and Microbiology Duke University United States Department of Statistics The Pennsylvania State University United States Huck Institutes for the Life Sciences The Pennsylvania State University United States Departments of Statistical Science Mathematics Computer Science Biostatistics & Bioinformatics Duke University United States Center for Scalable Data Analytics and Artificial Intelligence University of Leipzig Germany Max Planck Institute for Mathematics in the Natural Sciences Germany Department of Medicine The Pennsylvania State University United States

Many scientific fields, including human gut microbiome science, collect multivariate count data where the sum of the counts is unrelated to the scale of the underlying system being measured (e.g., total microbial load in a subject’s colon). This disconnect complicates downstream analyses such as differential analysis in case-control studies. This article is motivated by a novel study of in vitro human gut microbiome models. Popular tools for analyzing these data led to dramatically elevated rates of both false positives and false negatives. To understand those failures, we provide a formal problem statement that frames these challenges of scale in terms of the classical theory of identifiability. We call this the problem of Scale Reliant Inference (SRI). We use this formulation to prove fundamental limits on SRI in terms of criteria such as consistency and type-I error control. We show that the failures of existing methods stem from a fundamental failure to properly quantify uncertainty in the system scale. We demonstrate that a particular type of Bayesian model called a Bayesian Partially Identified Model (PIMs) can correctly quantify uncertainty in SRI. We introduce Scale Simulation Random Variables (SSRVs) as a flexible and efficient approach to specifying and inferring Bayesian PIMs. In the context of both real and simulated data, we find SSRVs drastically decrease type-I and type-II error rates. © 2022, CC BY.

关键词： Bayesian networks

ReLSO: A Transformer-based Model for Latent Space Optimization and Generation of Proteins

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arXiv 2022年

作者： Castro, Egbert Godavarthi, Abhinav Rubinfien, Julian Givechian, Kevin Bhaskar, Dhananjay Krishnaswamy, Smita Computational Biology and Bioinformatics Program Yale University New HavenCT06511 United States Department of Applied Mathematics Yale University New HavenCT06511 United States Department of Genetics Yale University New HavenCT06511 United States Department of Computer Science Yale University New HavenCT06511 United States

The development of powerful natural language models have increased the ability to learn meaningful representations of protein sequences. In addition, advances in high-throughput mutagenesis, directed evolution, and next-generation sequencing have allowed for the accumulation of large amounts of labeled fitness data. Leveraging these two trends, we introduce Regularized Latent Space Optimization (ReLSO), a deep transformer-based autoencoder which features a highly structured latent space that is trained to jointly generate sequences as well as predict fitness. Through regularized prediction heads, ReLSO introduces a powerful protein sequence encoder and novel approach for efficient fitness landscape traversal. Using ReLSO, we explicitly model the sequence-function landscape of large labeled datasets and generate new molecules by optimizing within the latent space using gradient-based methods. We evaluate this approach on several publicly-available protein datasets, including variant sets of anti-ranibizumab and GFP. We observe a greater sequence optimization efficiency (increase in fitness per optimization step) by ReLSO compared to other approaches, where ReLSO more robustly generates high-fitness sequences. Furthermore, the attention-based relationships learned by the jointly-trained ReLSO models provides a potential avenue towards sequence-level fitness attribution information. © 2022, CC BY-NC-ND.

关键词： Proteins

How Retroactivity Affects the Behavior of Incoherent Feed-Forward Loops

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arXiv 2020年

作者： Wang, Junmin Belta, Calin Isaacson, Samuel A. Bioinformatics Graduate Program Boston University BostonMA United States Department of Mathematics and Statistics Boston University BostonMA United States

An incoherent feed-forward loop (IFFL) is a network motif known for its ability to accelerate responses and generate pulses. Though functions of IFFLs are well studied, most previous computational analysis of IFFLs used ordinary differential equation (ODE) models where retroactivity, the effect downstream binding sites exert on the dynamics of an upstream transcription factor (TF), was not considered. It remains an open question to understand the behavior of IFFLs in contexts with high levels of retroactivity, e.g., in cells transformed/transfected with high-copy plasmids, or in eukaryotic cells where a TF binds to numerous high-affinity binding sites in addition to one or more functional target sites. Here we study the behavior of IFFLs by simulating and comparing ODE models with different levels of retroactivity. We find that increasing retroactivity in an IFFL can increase, decrease, or keep the network’s response time and pulse amplitude constant. This suggests that increasing retroactivity, traditionally considered as an impediment to designing robust synthetic systems, could be exploited to improve the performance of IFFLs. We compare the behaviors of IFFLs to negative autoregulatory loops, another sign-sensitive response-accelerating network motif, and find that increasing retroactivity in a negative autoregulated circuit can only slow the response. The inability of a negative autoregulatory loop to flexibly handle retroactivity may have contributed to its lower abundance in eukaryotic relative to bacterial regulatory networks, a sharp contrast to the significant abundance of IFFLs in both cell types. Copyright © 2020, The Authors. All rights reserved.

关键词： Transcription

Enhancing healthcare AI stability with edge computing and machine learning for extubation prediction

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Scientific Reports 2025年第1期15卷 1-11页

作者： Huang, Kuo-Yang Hsu, Ying-Lin Chung, Che-Liang Chen, Huang-Chi Horng, Ming-Hwarng Lin, Ching-Hsiung Liu, Ching-Sen Xu, Jia-Lang Division of Chest Medicine Department of Internal Medicine Changhua Christian Hospital Changhua Taiwan Institute of Genomics and Bioinformatics National Chung Hsing University Taichung Taiwan Ph.D. Program in Medical Biotechnology National Chung Hsing University Taichung Taiwan Institute of Statistics National Chung Hsing University Taichung Taiwan Division of Chest Medicine Department of Internal Medicine Yuanlin Christian Hospital Changhua Taiwan Department of Applied Mathematics National Chung Hsing University Taichung Taiwan Department of Computer Science and Information Engineering Chaoyang University of Technology Taichung Taiwan

The advancement of the Internet of Medical Things (IoMT) has revolutionized data acquisition and processing in critical care settings. Given the pivotal role of ventilators, accurately predicting extubation outcomes is essential to optimize patient care. This study presents an edge computing-based framework that incorporates machine learning algorithms to predict ventilator extubation success using real-time data collected directly from ventilators. The system was deployed on edge devices to enable on-site inference with minimal latency. Among the evaluated models, Random Forest and XGBoost, the latter demonstrated superior predictive performance under both holdout and tenfold cross-validation schemes. Notably, the edge-based architecture reduced server data transmissions by 83.33%, while improving system stability, resilience, and sustainability. This paper details the model evaluation and demonstrates the feasibility and efficiency of edge intelligence in ventilator weaning decision support. © The Author(s) 2025.

关键词： Clinical decision support system Edge-computing Extubation Internet of medical things Machine learning

Improved LSTM hyperparameters alongside sentiment walk-forward validation for time series prediction

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Journal of Open Innovation: Technology, Market, and Complexity 2025年第1期11卷

作者： Wahyuddin, Eko Putra Caraka, Rezzy Eko Kurniawan, Robert Caesarendra, Wahyu Gio, Prana Ugiana Pardamean, Bens Department of Statistical Computing Politeknik Statistika STIS Jakarta 13330 Indonesia Statistics Indonesia (BPS) Jl. Dr Sutomo 6-8 Jakarta Indonesia School of Economics and Business Telkom University Bandung 40257 Indonesia Research Center for Data and Information Sciences Research Organization for Electronics and Informatics National Research and Innovation Agency (BRIN) Bandung 40135 Indonesia Faculty of Integrated Technologies Universiti Brunei Darussalam Gadong BE1410 Brunei Darussalam Department of Mathematics Universitas Sumatera Utara Medan 20155 Indonesia Bioinformatics and Data Science Research Centre Bina Nusantara University DKI Jakarta 11480 Indonesia Computer Science Department BINUS Graduate Program Master of Computer Science Program Bina Nusantara University DKI Jakarta 11480 Indonesia

This study aims to address the common issue of biased estimation errors in time series modeling by analyzing the error in locating ideal hyperparameters and defining appropriate validation methods. Specifically, it focuses on predicting the stock price of Bank Rakyat Indonesia using a combination of historical stock prices, technical indicators, exchange rates, and news sentiment data, while determining the optimal variables for deep learning models. Employing a deep learning-based Long-Short Term Memory (LSTM) model, the study optimizes hyperparameters alongside walk-forward validation for time series prediction. It explores different combinations of variables and adapts the sliding window approach to the context of the data. The results highlight the importance of optimizing hyperparameters and utilizing walk-forward validation for accurate time series prediction. The model incorporating historical stock prices and sentiment scores outperforms others, achieving an RMSE of 96.61 and MAE of 86.97. Incorporating sentiment scores reduces RMSE by 39.55 % compared to models using only historical stock prices, while adding technical indicators does not yield improvement. This study contributes to the field by addressing the issue of biased estimation errors in time series modeling, offering insights into the optimization of hyperparameters and validation methods for accurate predictions. It also underscores the significance of incorporating sentiment analysis alongside historical stock prices for improved forecasting accuracy. © 2024 The Authors

关键词： LSTM Sentiment analysis Stock price prediction Time series modeling Validation methods