Régression vers la moyenne | EPFL Graph Search

En statistique, la régression vers la moyenne décrit le phénomène suivant : si une variable est extrême à sa première mesure, elle va généralement se rapprocher de la moyenne à sa seconde mesure. Si elle est extrême à sa seconde mesure elle va tendre à être proche de la moyenne à sa première mesure. Afin d'éviter des inférences erronées, la régression vers la moyenne doit être considérée à la base de la conception des expériences scientifiques et prise en compte lors de l'interprétation des données. Exemple On soumet une classe à un test de 100 questions auxquelles il n'y a que deux réponses possibles (vrai ou faux). Si on suppose que les élèves répondent tous purement au hasard, alors le score d'un étudiant est une réalisation d'un ensemble de variables aléatoires indépendantes et identiquement distribuées, dont l'espérance mathématique est de 50. Parmi les étudiants, certains auront un score très supérieur à 50 et d'autres un score très inférieur, par le seul effet du h

Multivariate time series forecasting for freeway networks

Semin Kwak

This dissertation introduces traffic forecasting methods for different network configurations and data availability.Chapter 2 focuses on single freeway cases.Although its topology is simple, the non-linearity of traffic features makes this prediction still a challenging task.We propose the dynamic linear model (DLM) to approximate the non-linear traffic features. Unlike a static linear regression model, the DLM assumes that its parameters change over time.We design the DLM with time-dependent model parameters to describe the spatiotemporal characteristics of time-series traffic data. Based on our DLM and its model parameters analytically trained using historical data, we suggest the optimal linear predictor in the minimum mean square error (MMSE) sense.We compare our prediction accuracy by estimating expected travel time based on the traffic prediction for freeways in California (I210-E and I5-S) under highly congested traffic conditions with other baselines. We show significant improvements in accuracy, especially for short-term prediction.Chapter 3 aims to generalize the DLM to extensive freeway networks with more complex topologies.Most resources would be consumed to estimate unnecessary spatiotemporal correlations if the DLM was directly used for a large-scale network.Defining features on graphs relaxes such issues by cutting unnecessary connections in advance based on predefined topology information.Exploiting the graph signal processing, we represent traffic dynamics over freeway networks using multiple graph heat diffusion kernels and integrate the kernels into DLM with Bayes' rule. We optimize the model parameters using Bayesian inference to minimize the prediction errors.The proposed model demonstrates prediction accuracy comparable to state-of-the-art deep neural networks with lower computational effort. It notably achieves excellent performance for long-term prediction through the inheritance of periodicity modeling in DLM.Chapter 4 proposes a deep neural network model to predict traffic features on large-scale freeway networks.These days, deep learning methods have heavily tackled traffic forecasting problems of freeway networks because they are outstanding at learning highly complex correlations between variables both in time and space, which the linear models might be limited to.Adopting a graph convolutional network (GCN) becomes a standard to extract spatial correlations; therefore, most works have achieved great prediction accuracy by implanting it into their architecture.However, the conventional GCN has the drawback that receptive field size should be small, i.e., barely refers to traffic features of remote sensors, resulting in inaccurate long-term prediction.We suggest a forecasting model called two-level resolution deep neural network (TwoResNet) that overcomes the limitation.It consists of two resolution blocks:The low-resolution block predicts traffic on a macroscopic scale, such as regional traffic changes.On the other hand, the high-resolution block predicts traffic on a microscopic scale by using GCN to extract spatial correlations, referring to the regional changes produced by the low-resolution block.This process allows the GCN to refer to the traffic features from remote sensors.As a result, TwoResNet achieves competitive prediction accuracy compared to state-of-the-art methods, especially showing excellent performance for long-term predictions.

EPFL2022

Multivariate time series forecasting for freeway networks

Semin Kwak

EPFL2022