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A general linear-time inference method for Gaussian processes on one dimension

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The Journal of Machine Learning Research 2021年第1期22卷 10580-10615页

作者： Jackson Loper David Blei John P. Cunningham Liam Paninski Data Science Institute Columbia University New York New York Data Science Institute Departments of Statistics and Computer Science Columbia University New York New York Department of Statistics Mortimer B. Zuckerman Mind Brain Behavior Institute Grossman Center for the Statistics of Mind Columbia University New York New York Departments of Statistics and Neuroscience Mortimer B. Zuckerman Mind Brain Behavior Institute Grossman Center for the Statistics of Mind Columbia University New York New York

Gaussian Processes (GPs) provide powerful probabilistic frameworks for interpolation, forecasting, and smoothing, but have been hampered by computational scaling issues. Here we investigate data sampled on one dimension (e.g., a scalar or vector time series sampled at arbitrarily-spaced intervals), for which state-space models are popular due to their linearly-scaling computational costs. It has long been conjectured that state-space models are general, able to approximate any one-dimensional GP. We provide the first general proof of this conjecture, showing that any stationary GP on one dimension with vector-valued observations governed by a Lebesgue-integrable continuous kernel can be approximated to any desired precision using a specifically-chosen state-space model: the Latent Exponentially Generated (LEG) family. This new family offers several advantages compared to the general state-space model: it is always stable (no unbounded growth), the covariance can be computed in closed form, and its parameter space is unconstrained (allowing straightforward estimation via gradient descent). The theorem's proof also draws connections to Spectral Mixture Kernels, providing insight about this popular family of kernels. We develop parallelized algorithms for performing inference and learning in the LEG model, test the algorithm on real and synthetic data, and demonstrate scaling to datasets with billions of samples.

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Searching for consistent associations with a multi-environment knockoff filter

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arXiv 2021年

作者： Li, Shuangning Sesia, Matteo Romano, Yaniv Candès, Emmanuel Sabatti, Chiara Department of Statistics Stanford University United States Department of Data Sciences and Operations University of Southern California United States Departments of Electrical Engineering and of Computer Science Technion Israel Departments of Statistics and of Mathematics Stanford University United States Departments of Statistics and of Biomedical Data Sciences Stanford University United States

This paper develops a method based on model-X knockoffs to find conditional associations that are consistent across diverse environments, controlling the false discovery rate. The motivation for this problem is that large data sets may contain numerous associations that are statistically significant and yet misleading, as they are induced by confounders or sampling imperfections. However, associations consistently replicated under different conditions may be more interesting. In fact, consistency sometimes provably leads to valid causal inferences even if conditional associations do not. While the proposed method is flexible and can be deployed in a wide range of applications, this paper highlights its relevance to genome-wide association studies, in which consistency across populations with diverse ancestries mitigates confounding due to unmeasured variants. The effectiveness of this approach is demonstrated by simulations and applications to the UK Biobank data. Copyright © 2021, The Authors. All rights reserved.

关键词： Genes

Intermediate layers Matter in momentum contrastive self supervised learning

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arXiv 2021年

作者： Kaku, Aakash Upadhya, Sahana Razavian, Narges Center for Data Science New York University New YorkNY10011 United States Department of Computer Science Courant Institute of Mathematical Sciences New YorkNY10011 United States Departments of Population Health and Radiology NYU Grossman School of Medicine NYU Center for Data Science New YorkNY10016 United States

We show that bringing intermediate layers’ representations of two augmented versions of an image closer together in self supervised learning helps to improve the momentum contrastive (MoCo) method. To this end, in addition to the contrastive loss, we minimize the mean squared error between the intermediate layer representations or make their cross-correlation matrix closer to an identity matrix. Both loss objectives either outperform standard MoCo, or achieve similar performances on three diverse medical imaging datasets: NIH-Chest Xrays, Breast Cancer Histopathology, and Diabetic Retinopathy. The gains of the improved MoCo are especially large in a low-labeled data regime (e.g. 1% labeled data) with an average gain of 5% across three datasets. We analyze the models trained using our novel approach via feature similarity analysis and layer-wise probing. Our analysis reveals that models trained via our approach have higher feature reuse compared to a standard MoCo and learn informative features earlier in the network. Finally, by comparing the output probability distribution of models fine tuned on small versus large labeled data, we conclude that our proposed method of pre-training leads to lower Kolmogorov–Smirnov distance, as compared to a standard MoCo. This provides additional evidence that our proposed method learns more informative features in the pre-training phase which could be leveraged in a low-labeled data regime. © 2021, CC BY-NC-SA.

关键词： Computational complexity

Variational and phase response analysis for limit cycles with hard boundaries, with applications to neuromechanical control problems

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arXiv 2022年

作者： Wang, Yangyang Gill, Jeffrey P. Chiel, Hillel J. Thomas, Peter J. Department of Mathematics The University of Iowa Iowa CityIA52242 United States Department of Biology Case Western Reserve University ClevelandOH44106 United States Departments of Biology Neurosciencesand Biomedical Engineering Case Western Reserve University ClevelandOH44106 United States Departments of Mathematics Applied Mathematics and StatisticsBiologyCognitive ScienceData and Computer Scienceand Electrical Control and Systems Engineering Case Western Reserve University ClevelandOH44106 United States

Motor systems show an overall robustness, but because they are highly nonlinear, understanding how they achieve robustness is difficult. In many rhythmic systems, robustness against perturbations involves response of both the shape and the timing of the trajectory. This makes the study of robustness even more challenging. To understand how a motor system produces robust behaviors in a variable environment, we consider a neuromechanical model of motor patterns in the feeding apparatus of the marine mollusk Aplysia californica (Shaw et al., 2015;Lyttle et al., 2017). We established in (Wang et al., 2021) the tools for studying combined shape and timing responses of limit cycle systems under sustained perturbations and here apply them to study robustness of the neuromechanical model against increased mechanical load during swallowing. Interestingly, we discover that nonlinear biomechanical properties confer resilience by immediately increasing resistance to applied loads. In contrast, the effect of changed sensory feedback signal is significantly delayed by the firing rates’ hard boundary properties. Our analysis suggests that sensory feedback contributes to robustness in swallowing primarily by shifting the timing of neural activation involved in the power stroke of the motor cycle (retraction). This effect enables the system to generate stronger retractor muscle forces to compensate for the increased load, and hence achieve strong robustness. The approaches that we are applying to understanding a neuromechanical model in Aplysia, and the results that we have obtained, are likely to provide insights into the function of other motor systems that encounter changing mechanical loads and hard boundaries, both due to mechanical and neuronal firing *** Codes 34C07, 34C15, 58E25, 49J52, 92B20, 93C73 Copyright © 2022, The Authors. All rights reserved.

关键词： Activation analysis

A Refined Deep Learning Architecture for Diabetic Foot Ulcers Detection

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arXiv 2020年

作者： Goyal, Manu Hassanpour, Saeed Department of Biomedical Data Science Dartmouth College HanoverNH United States Departments of Biomedical Data Science Computer Science and Epidemiology Dartmouth College HanoverNH United States

Diabetic Foot Ulcers (DFU) that affect the lower extremities are a major complication of diabetes. Each year, more than 1 million diabetic patients undergo amputation due to failure to recognize DFU and get the proper treatment from clinicians. There is an urgent need to use a CAD system for the detection of DFU. In this paper, we propose using deep learning methods (EfficientDet Architectures) for the detection of DFU in the DFUC2020 challenge dataset, which consists of 4,500 DFU images. We further refined the EfficientDet architecture to avoid false negative and false positive predictions. The code for this method is available at https://***/Manugoyal12345/Yet-Another-EfficientDetPytorch. Copyright © 2020, The Authors. All rights reserved.

关键词： Deep learning

Constructing A Multimodal Biomolecule Embedding Integration Platform to Support Comprehensive Biomedical Knowledge Representation

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Journal of Molecular and Cellular Cardiology Plus

Journal of Molecular and Cellular Cardiology Plus 2025年 12卷

作者： Yu Yan Baradwaj Simha Sankar Yijiao Xiao Alexander R. Pelletier Wei Wang Peipei Ping Departments of Physiology and Medicine @ University of California Los Angeles (UCLA) School of Medicine NHLBI Integrated Cardiovascular Data Science Training Program @ UCLA NIH BRIDGE2AI Center at UCLA & NHLBI Integrated Cardiovascular Data Science Training Program at UCLA Los Angeles USA Department of Computer Science and Scalable Analytics Institute at UCLA School of Engineering Los Angeles USA

Maximum a posteriori inference of random dot product graphs via conic programming

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arXiv 2021年

作者： Wu, David Palmer, David Deford, Daryl Departments of Math and Computer Science Massachusetts Institute of Technology United States Geometric Data Processing Group Massachusetts Institute of Technology United States Department of Mathematics and Statistics Washington State University United States

We present a convex cone program to infer the latent probability matrix of a random dot product graph (RDPG). The optimization problem maximizes the Bernoulli maximum likelihood function with an added nuclear norm regularization term. The dual problem has a particularly nice form, related to the well-known semidefinite program relaxation of the maxcut problem. Using the primal-dual optimality conditions, we bound the entries and rank of the primal and dual solutions. Furthermore, we bound the optimal objective value and prove asymptotic consistency of the probability estimates of a slightly modified model under mild technical assumptions. Our experiments on synthetic RDPGs not only recover natural clusters, but also reveal the underlying low-dimensional geometry of the original data. We also demonstrate that the method recovers latent structure in the Karate Club Graph and synthetic U.S. Senate vote graphs and is scalable to graphs with up to a few hundred *** Codes 62F15, 90C35, 65F55, 68R10, 15B48 © 2021, CC BY.

关键词： Relaxation processes

Testing for Outliers with Conformal p-values

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arXiv 2021年

作者： Bates, Stephen Candès, Emmanuel Lei, Lihua Romano, Yaniv Sesia, Matteo Departments of Statistics and of EECS UC Berkeley United States Departments of Statistics and of Mathematics Stanford University United States Department of Statistics Stanford University United States Departments of Electrical Engineering and of Computer Science Technion-Israel Institute of Technology Israel Department of Data Sciences and Operations University of Southern California United States

This paper studies the construction of p-values for nonparametric outlier detection, taking a multiple-testing perspective. The goal is to test whether new independent samples belong to the same distribution as a reference data set or are outliers. We propose a solution based on conformal inference, a broadly applicable framework which yields p-values that are marginally valid but mutually dependent for different test points. We prove these p-values are positively dependent and enable exact false discovery rate control, although in a relatively weak marginal sense. We then introduce a new method to compute p-values that are both valid conditionally on the training data and independent of each other for different test points;this paves the way to stronger type-I error guarantees. Our results depart from classical conformal inference as we leverage concentration inequalities rather than combinatorial arguments to establish our finitesample guarantees. Furthermore, our techniques also yield a uniform confidence bound for the false positive rate of any outlier detection algorithm, as a function of the threshold applied to its raw statistics. Finally, the relevance of our results is demonstrated by numerical experiments on real and simulated data. © 2021, CC BY.

关键词： Statistics

GSMorph: Gradient Surgery for cine-MRI Cardiac Deformable Registration

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arXiv 2023年

作者： Dou, Haoran Bi, Ning Han, Luyi Huang, Yuhao Mann, Ritse Yang, Xin Ni, Dong Ravikumar, Nishant Frangi, Alejandro F. Huang, Yunzhi University of Leeds Leeds United Kingdom Department of Radiology and Nuclear Medicine Radboud University Medical Centre Nijmegen Netherlands Department of Radiology Netherlands Cancer Institute Amsterdam Netherlands National-Regional Key Technology Engineering Laboratory for Medical Ultrasound School of Biomedical Engineering Health Science Center Shenzhen University China Lab Shenzhen University China Marshall Laboratory of Biomedical Engineering Shenzhen University China Shenzhen RayShape Medical Technology Co. Ltd China Division of Informatics Imaging and Data Science Schools of Computer Science and Health Sciences University of Manchester Manchester United Kingdom Electrical Engineering and Cardiovascular Sciences Departments KU Leuven Leuven Belgium Alan Turing Institute London United Kingdom Institute for AI in Medicine School of Artificial Intelligence Nanjing University of Information Science and Technology Nanjing China

Deep learning-based deformable registration methods have been widely investigated in diverse medical applications. Learning-based deformable registration relies on weighted objective functions trading off registration accuracy and smoothness of the deformation field. Therefore, they inevitably require tuning the hyperparameter for optimal registration performance. Tuning the hyperparameters is highly computationally expensive and introduces undesired dependencies on domain knowledge. In this study, we construct a registration model based on the gradient surgery mechanism, named GSMorph, to achieve a hyperparameter-free balance on multiple losses. In GSMorph, we reformulate the optimization procedure by projecting the gradient of similarity loss orthogonally to the plane associated with the smoothness constraint, rather than additionally introducing a hyperparameter to balance these two competing terms. Furthermore, our method is model-agnostic and can be merged into any deep registration network without introducing extra parameters or slowing down inference. In this study, We compared our method with state-of-the-art (SOTA) deformable registration approaches over two publicly available cardiac MRI datasets. GSMorph proves superior to five SOTA learning-based registration models and two conventional registration techniques, SyN and Demons, on both registration accuracy and smoothness. © 2023, CC BY.

关键词： Medical applications