Efficient Trajectory Inference in Wasserstein Space Using Consecutive Averaging

• URL: http://arxiv.org/abs/2405.19679v1
• Date: Thu, 30 May 2024 04:19:20 GMT
• Title: Efficient Trajectory Inference in Wasserstein Space Using Consecutive Averaging
• Authors: Amartya Banerjee, Harlin Lee, Nir Sharon, Caroline Moosmüller,
• Abstract summary: Trajectory inference deals with the challenge of reconstructing continuous processes from such observations. We propose methods for B-spline approximation of point clouds through consecutive averaging that is instrinsic to the Wasserstein space. We rigorously evaluate our method by providing convergence guarantees and testing it on simulated cell data.
• Score: 3.8623569699070353
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Capturing data from dynamic processes through cross-sectional measurements is seen in many fields such as computational biology. Trajectory inference deals with the challenge of reconstructing continuous processes from such observations. In this work, we propose methods for B-spline approximation and interpolation of point clouds through consecutive averaging that is instrinsic to the Wasserstein space. Combining subdivision schemes with optimal transport-based geodesic, our methods carry out trajectory inference at a chosen level of precision and smoothness, and can automatically handle scenarios where particles undergo division over time. We rigorously evaluate our method by providing convergence guarantees and testing it on simulated cell data characterized by bifurcations and merges, comparing its performance against state-of-the-art trajectory inference and interpolation methods. The results not only underscore the effectiveness of our method in inferring trajectories, but also highlight the benefit of performing interpolation and approximation that respect the inherent geometric properties of the data.

Related papers

• Beyond Flatland: A Geometric Take on Matching Methods for Treatment Effect Estimation [6.4527669089403155]
  We propose a matching method to estimate treatment effects that takes into account the intrinsic data geometry induced by existing causal mechanisms. We provide theoretical insights and empirical results in synthetic and real-world scenarios, demonstrating that GeoMatching yields more effective treatment effect estimators.
  arXiv  Detail & Related papers  (2024-09-09T09:39:47Z)
• Spatially-Aware Diffusion Models with Cross-Attention for Global Field Reconstruction with Sparse Observations [1.371691382573869]
  We develop and enhance score-based diffusion models in field reconstruction tasks. We introduce a condition encoding approach to construct a tractable mapping mapping between observed and unobserved regions. We demonstrate the ability of the model to capture possible reconstructions and improve the accuracy of fused results.
  arXiv  Detail & Related papers  (2024-08-30T19:46:23Z)
• Dynamical Measure Transport and Neural PDE Solvers for Sampling [77.38204731939273]
  We tackle the task of sampling from a probability density as transporting a tractable density function to the target. We employ physics-informed neural networks (PINNs) to approximate the respective partial differential equations (PDEs) solutions. PINNs allow for simulation- and discretization-free optimization and can be trained very efficiently.
  arXiv  Detail & Related papers  (2024-07-10T17:39:50Z)
• Embedding Trajectory for Out-of-Distribution Detection in Mathematical Reasoning [50.84938730450622]
  We propose a trajectory-based method TV score, which uses trajectory volatility for OOD detection in mathematical reasoning. Our method outperforms all traditional algorithms on GLMs under mathematical reasoning scenarios. Our method can be extended to more applications with high-density features in output spaces, such as multiple-choice questions.
  arXiv  Detail & Related papers  (2024-05-22T22:22:25Z)
• Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers [143.6249073384419]
  In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.
  arXiv  Detail & Related papers  (2024-01-29T02:08:40Z)
• Efficient Large-scale Nonstationary Spatial Covariance Function Estimation Using Convolutional Neural Networks [3.5455896230714194]
  We use ConvNets to derive subregions from the nonstationary data. We employ a selection mechanism to identify subregions that exhibit similar behavior to stationary fields. We assess the performance of the proposed method with synthetic and real datasets at a large scale.
  arXiv  Detail & Related papers  (2023-06-20T12:17:46Z)
• Score-based Data Assimilation [7.215767098253208]
  We introduce score-based data assimilation for trajectory inference. We learn a score-based generative model of state trajectories based on the key insight that the score of an arbitrarily long trajectory can be decomposed into a series of scores over short segments.
  arXiv  Detail & Related papers  (2023-06-18T14:22:03Z)
• A Heat Diffusion Perspective on Geodesic Preserving Dimensionality Reduction [66.21060114843202]
  We propose a more general heat kernel based manifold embedding method that we call heat geodesic embeddings. Results show that our method outperforms existing state of the art in preserving ground truth manifold distances. We also showcase our method on single cell RNA-sequencing datasets with both continuum and cluster structure.
  arXiv  Detail & Related papers  (2023-05-30T13:58:50Z)
• Positive definite nonparametric regression using an evolutionary algorithm with application to covariance function estimation [0.0]
  We propose a novel nonparametric regression framework for estimating covariance functions of stationary processes. Our method can impose positive definiteness, as well as isotropy and monotonicity, on the estimators. Our method provides more reliable estimates for long-range dependence.
  arXiv  Detail & Related papers  (2023-04-25T22:01:14Z)
• Manifold Interpolating Optimal-Transport Flows for Trajectory Inference [64.94020639760026]
  We present a method called Manifold Interpolating Optimal-Transport Flow (MIOFlow) MIOFlow learns, continuous population dynamics from static snapshot samples taken at sporadic timepoints. We evaluate our method on simulated data with bifurcations and merges, as well as scRNA-seq data from embryoid body differentiation, and acute myeloid leukemia treatment.
  arXiv  Detail & Related papers  (2022-06-29T22:19:03Z)
• Scalable Intervention Target Estimation in Linear Models [52.60799340056917]
  Current approaches to causal structure learning either work with known intervention targets or use hypothesis testing to discover the unknown intervention targets. This paper proposes a scalable and efficient algorithm that consistently identifies all intervention targets. The proposed algorithm can be used to also update a given observational Markov equivalence class into the interventional Markov equivalence class.
  arXiv  Detail & Related papers  (2021-11-15T03:16:56Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.