Predicting Stochastic Demand using a Multi-Task Recurrent Mixture Density Network
Author
Iliev, Ivan
Term
4. Term
Publication year
2020
Abstract
This thesis investigates whether stochastic taxi demand between origin and destination regions can be predicted as probability distributions rather than single values. It proposes a probabilistic, multi-task sequence model that ingests a time series of origin–destination matrices and, using Long Short-Term Memory (LSTM) networks and Mixture Density Networks (MDN), estimates Gaussian Mixture Model (GMM) parameters for each OD pair. The motivation is that historical demands are often multimodal and not well captured by averaging models. The approach ties multiple tasks (one per OD pair) through shared layers to enable joint learning. Training insights include that MDNs are sensitive and benefit from dropout, large batch sizes, and many epochs; moreover, directly connecting an MDN to a ReLU layer led to NaN losses, which were avoided by feeding the MDN directly from the LSTM. The model is applied to a small neighborhood in Manhattan (NYC yellow taxi data, 2018) and evaluated with metrics such as RMSE and MAE. An ablation study finds that the multi-task MDN model underperforms a multi-task single-value prediction model in accuracy, even though both variants achieve similar RMSE and MAE; the reason remains unclear. Overall, the results suggest that probabilistic OD forecasting is feasible and potentially useful for fleet optimization, while further work is needed to close the performance gap to strong point-prediction baselines.
Denne afhandling undersøger, om stochastisk taxiefterspørgsel mellem oprindelses- og destinationsområder kan forudsiges som sandsynlighedsfordelinger frem for enkeltværdier. Der foreslås en probabilistisk, multitask sekvensmodel, der tager en tidsserie af origin–destination-matricer som input og, via Long Short-Term Memory-netværk (LSTM) og Mixture Density Networks (MDN), estimerer parametrene til en Gaussian Mixture Model (GMM) for hver OD-parcelle. Motivationens kerne er, at historiske efterspørgsler ofte er multimodale og derfor ikke fanges godt af gennemsnitsbaserede modeller. Modellen samler flere opgaver (ét per OD-par) gennem fælles lag, så læring deles på tværs af parrene. I arbejdet beskrives træningsmæssige erfaringer: MDN’er er følsomme og drager fordel af dropout, store batch-størrelser og mange epoker; desuden kan MDN-laget give NaN-tab ved direkte forbindelse fra ReLU, hvilket blev undgået ved at forbinde LSTM direkte til MDN. Modellen anvendes på et lille område i Manhattan (NYC yellow taxi-data, 2018) og evalueres blandt andet med RMSE og MAE. En ablationsundersøgelse viser, at den multitask MDN-baserede model præsterer dårligere i nøjagtighed end en multitask enkeltværdimodel, selvom de to varianter opnår lignende RMSE- og MAE-scorer; årsagen hertil er endnu uklar. Resultaterne peger på, at sandsynlighedsbaserede OD-prognoser er gennemførlige og kan være nyttige for flådeoptimering, men at yderligere arbejde er nødvendigt for at lukke præstationsgabet til stærke enkeltværdibaselines.
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