Sinkhorn-Flow: Predicting Probability Mass Flow in Dynamical Systems Using Optimal Transport

• URL: http://arxiv.org/abs/2303.07675v1
• Date: Tue, 14 Mar 2023 07:25:44 GMT
• Title: Sinkhorn-Flow: Predicting Probability Mass Flow in Dynamical Systems Using Optimal Transport
• Authors: Mukul Bhutani and J. Zico Kolter
• Abstract summary: We propose a new approach to predicting such mass flow over time using optimal transport. We apply our approach to the task of predicting how communities will evolve over time in social network settings.
• Score: 89.61692654941106
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Predicting how distributions over discrete variables vary over time is a common task in time series forecasting. But whereas most approaches focus on merely predicting the distribution at subsequent time steps, a crucial piece of information in many settings is to determine how this probability mass flows between the different elements over time. We propose a new approach to predicting such mass flow over time using optimal transport. Specifically, we propose a generic approach to predicting transport matrices in end-to-end deep learning systems, replacing the standard softmax operation with Sinkhorn iterations. We apply our approach to the task of predicting how communities will evolve over time in social network settings, and show that the approach improves substantially over alternative prediction methods. We specifically highlight results on the task of predicting faction evolution in Ukrainian parliamentary voting.

Related papers

• Evolving Multi-Scale Normalization for Time Series Forecasting under Distribution Shifts [20.02869280775877]
  We propose a novel model-agnostic Evolving Multi-Scale Normalization (EvoMSN) framework to tackle the distribution shift problem. We evaluate the effectiveness of EvoMSN in improving the performance of five mainstream forecasting methods on benchmark datasets.
  arXiv  Detail & Related papers  (2024-09-29T14:26:22Z)
• Time Series Prediction under Distribution Shift using Differentiable Forgetting [0.0]
  We frame time series prediction under distribution shift as a weighted empirical risk minimisation problem. The weighting of previous observations in the empirical risk is determined by a forgetting mechanism. We propose a gradient-based learning method for the parameters of the forgetting mechanism.
  arXiv  Detail & Related papers  (2022-07-23T10:32:37Z)
• Stochastic Trajectory Prediction via Motion Indeterminacy Diffusion [88.45326906116165]
  We present a new framework to formulate the trajectory prediction task as a reverse process of motion indeterminacy diffusion (MID) We encode the history behavior information and the social interactions as a state embedding and devise a Transformer-based diffusion model to capture the temporal dependencies of trajectories. Experiments on the human trajectory prediction benchmarks including the Stanford Drone and ETH/UCY datasets demonstrate the superiority of our method.
  arXiv  Detail & Related papers  (2022-03-25T16:59:08Z)
• Conditional Approximate Normalizing Flows for Joint Multi-Step Probabilistic Electricity Demand Forecasting [32.907448044102864]
  We introduce the conditional approximate normalizing flow (CANF) to make probabilistic multi-step time-series forecasts when correlations are present over long time horizons. Empirical results show that conditional approximate normalizing flows outperform other methods in terms of multi-step forecast accuracy and lead to up to 10x better scheduling decisions.
  arXiv  Detail & Related papers  (2022-01-08T03:42:12Z)
• Quantifying Uncertainty in Deep Spatiotemporal Forecasting [67.77102283276409]
  We describe two types of forecasting problems: regular grid-based and graph-based. We analyze UQ methods from both the Bayesian and the frequentist point view, casting in a unified framework via statistical decision theory. Through extensive experiments on real-world road network traffic, epidemics, and air quality forecasting tasks, we reveal the statistical computational trade-offs for different UQ methods.
  arXiv  Detail & Related papers  (2021-05-25T14:35:46Z)
• Robustness via Cross-Domain Ensembles [0.5801044612920816]
  We present a method for making neural network predictions robust to shifts from the training data distribution. The proposed method is based on making predictions via a diverse set of cues and ensembling them into one strong prediction.
  arXiv  Detail & Related papers  (2021-03-19T17:28:03Z)
• Learning Interpretable Deep State Space Model for Probabilistic Time Series Forecasting [98.57851612518758]
  Probabilistic time series forecasting involves estimating the distribution of future based on its history. We propose a deep state space model for probabilistic time series forecasting whereby the non-linear emission model and transition model are parameterized by networks. We show in experiments that our model produces accurate and sharp probabilistic forecasts.
  arXiv  Detail & Related papers  (2021-01-31T06:49:33Z)
• SMART: Simultaneous Multi-Agent Recurrent Trajectory Prediction [72.37440317774556]
  We propose advances that address two key challenges in future trajectory prediction. multimodality in both training data and predictions and constant time inference regardless of number of agents.
  arXiv  Detail & Related papers  (2020-07-26T08:17:10Z)
• Long-Short Term Spatiotemporal Tensor Prediction for Passenger Flow Profile [15.875569404476495]
  We focus on a tensor-based prediction and propose several practical techniques to improve prediction. For long-term prediction specifically, we propose the "Tensor Decomposition + 2-Dimensional Auto-Regressive Moving Average (2D-ARMA)" model. For short-term prediction, we propose to conduct tensor completion based on tensor clustering to avoid oversimplifying and ensure accuracy.
  arXiv  Detail & Related papers  (2020-04-23T08:30:00Z)
• Ambiguity in Sequential Data: Predicting Uncertain Futures with Recurrent Models [110.82452096672182]
  We propose an extension of the Multiple Hypothesis Prediction (MHP) model to handle ambiguous predictions with sequential data. We also introduce a novel metric for ambiguous problems, which is better suited to account for uncertainties.
  arXiv  Detail & Related papers  (2020-03-10T09:15:42Z)

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.