Estimating Latent Population Flows from Aggregated Data via Inversing Multi-Marginal Optimal Transport

• URL: http://arxiv.org/abs/2212.14527v1
• Date: Fri, 30 Dec 2022 03:03:23 GMT
• Title: Estimating Latent Population Flows from Aggregated Data via Inversing Multi-Marginal Optimal Transport
• Authors: Sikun Yang, Hongyuan Zha
• Abstract summary: We study the problem of estimating latent population flows from aggregated count data. This problem arises when individual trajectories are not available due to privacy issues or measurement fidelity. We propose to estimate the transition flows from aggregated data by learning the cost functions of the MOT framework.
• Score: 57.16851632525864
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: We study the problem of estimating latent population flows from aggregated count data. This problem arises when individual trajectories are not available due to privacy issues or measurement fidelity. Instead, the aggregated observations are measured over discrete-time points, for estimating the population flows among states. Most related studies tackle the problems by learning the transition parameters of a time-homogeneous Markov process. Nonetheless, most real-world population flows can be influenced by various uncertainties such as traffic jam and weather conditions. Thus, in many cases, a time-homogeneous Markov model is a poor approximation of the much more complex population flows. To circumvent this difficulty, we resort to a multi-marginal optimal transport (MOT) formulation that can naturally represent aggregated observations with constrained marginals, and encode time-dependent transition matrices by the cost functions. In particular, we propose to estimate the transition flows from aggregated data by learning the cost functions of the MOT framework, which enables us to capture time-varying dynamic patterns. The experiments demonstrate the improved accuracy of the proposed algorithms than the related methods in estimating several real-world transition flows.

Related papers

• On the Identification of Temporally Causal Representation with Instantaneous Dependence [50.14432597910128]
  Temporally causal representation learning aims to identify the latent causal process from time series observations. Most methods require the assumption that the latent causal processes do not have instantaneous relations. We propose an textbfIDentification framework for instantanetextbfOus textbfLatent dynamics.
  arXiv  Detail & Related papers  (2024-05-24T08:08:05Z)
• Graph Spatiotemporal Process for Multivariate Time Series Anomaly Detection with Missing Values [67.76168547245237]
  We introduce a novel framework called GST-Pro, which utilizes a graphtemporal process and anomaly scorer to detect anomalies. Our experimental results show that the GST-Pro method can effectively detect anomalies in time series data and outperforms state-of-the-art methods.
  arXiv  Detail & Related papers  (2024-01-11T10:10:16Z)
• Solving multiphysics-based inverse problems with learned surrogates and constraints [1.4747234049753455]
  multimodal time-lapse data is expensive to collect and costly to simulate numerically. We overcome these challenges by combining computationally cheap learned surrogates with learned constraints. We demonstrate the efficacy of the proposed constrained optimization method on two different data modalities.
  arXiv  Detail & Related papers  (2023-07-18T00:55:37Z)
• Probabilistic Learning of Multivariate Time Series with Temporal Irregularity [25.91078012394032]
  temporal irregularities, including nonuniform time intervals and component misalignment. We develop a conditional flow representation to non-parametrically represent the data distribution, which is typically non-Gaussian. The broad applicability and superiority of the proposed solution are confirmed by comparing it with existing approaches through ablation studies and testing on real-world datasets.
  arXiv  Detail & Related papers  (2023-06-15T14:08:48Z)
• Copula-Based Density Estimation Models for Multivariate Zero-Inflated Continuous Data [0.0]
  We propose two copula-based density estimation models that can cope with multivariate correlation among zero-inflated continuous variables. In order to overcome the difficulty in the use of copulas due to the tied-data problem in zero-inflated data, we propose a new type of copula, rectified Gaussian copula.
  arXiv  Detail & Related papers  (2023-04-02T13:43:37Z)
• Training Normalizing Flows from Dependent Data [31.42053454078623]
  We propose a likelihood objective of normalizing flows incorporating dependencies between the data points. We show that respecting dependencies between observations can improve empirical results on both synthetic and real-world data.
  arXiv  Detail & Related papers  (2022-09-29T16:50:34Z)
• Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations [84.42837346400151]
  Estimating counterfactual outcomes over time has the potential to unlock personalized healthcare. Existing causal inference approaches consider regular, discrete-time intervals between observations and treatment decisions. We propose a controllable simulation environment based on a model of tumor growth for a range of scenarios.
  arXiv  Detail & Related papers  (2022-06-16T17:15:15Z)
• Multi-scale Attention Flow for Probabilistic Time Series Forecasting [68.20798558048678]
  We propose a novel non-autoregressive deep learning model, called Multi-scale Attention Normalizing Flow(MANF) Our model avoids the influence of cumulative error and does not increase the time complexity. Our model achieves state-of-the-art performance on many popular multivariate datasets.
  arXiv  Detail & Related papers  (2022-05-16T07:53:42Z)
• Accurate non-stationary short-term traffic flow prediction method [0.0]
  This paper proposes a Long Short-Term Memory (LSTM) based method that can forecast short-term traffic flow precisely. The proposed method performs favorably against other state-of-the-art methods with better performance on extreme outliers, delay effects, and trend-changing responses.
  arXiv  Detail & Related papers  (2022-05-01T17:11:34Z)
• Batch Stationary Distribution Estimation [98.18201132095066]
  We consider the problem of approximating the stationary distribution of an ergodic Markov chain given a set of sampled transitions. We propose a consistent estimator that is based on recovering a correction ratio function over the given data.
  arXiv  Detail & Related papers  (2020-03-02T09:10:01Z)

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.