10,370 research outputs found
Quantifying the benefits of vehicle pooling with shareability networks
Taxi services are a vital part of urban transportation, and a considerable
contributor to traffic congestion and air pollution causing substantial adverse
effects on human health. Sharing taxi trips is a possible way of reducing the
negative impact of taxi services on cities, but this comes at the expense of
passenger discomfort quantifiable in terms of a longer travel time. Due to
computational challenges, taxi sharing has traditionally been approached on
small scales, such as within airport perimeters, or with dynamical ad-hoc
heuristics. However, a mathematical framework for the systematic understanding
of the tradeoff between collective benefits of sharing and individual passenger
discomfort is lacking. Here we introduce the notion of shareability network
which allows us to model the collective benefits of sharing as a function of
passenger inconvenience, and to efficiently compute optimal sharing strategies
on massive datasets. We apply this framework to a dataset of millions of taxi
trips taken in New York City, showing that with increasing but still relatively
low passenger discomfort, cumulative trip length can be cut by 40% or more.
This benefit comes with reductions in service cost, emissions, and with split
fares, hinting towards a wide passenger acceptance of such a shared service.
Simulation of a realistic online system demonstrates the feasibility of a
shareable taxi service in New York City. Shareability as a function of trip
density saturates fast, suggesting effectiveness of the taxi sharing system
also in cities with much sparser taxi fleets or when willingness to share is
low.Comment: Main text: 6 pages, 3 figures, SI: 24 page
Stochastic Gradient Hamiltonian Monte Carlo
Hamiltonian Monte Carlo (HMC) sampling methods provide a mechanism for
defining distant proposals with high acceptance probabilities in a
Metropolis-Hastings framework, enabling more efficient exploration of the state
space than standard random-walk proposals. The popularity of such methods has
grown significantly in recent years. However, a limitation of HMC methods is
the required gradient computation for simulation of the Hamiltonian dynamical
system-such computation is infeasible in problems involving a large sample size
or streaming data. Instead, we must rely on a noisy gradient estimate computed
from a subset of the data. In this paper, we explore the properties of such a
stochastic gradient HMC approach. Surprisingly, the natural implementation of
the stochastic approximation can be arbitrarily bad. To address this problem we
introduce a variant that uses second-order Langevin dynamics with a friction
term that counteracts the effects of the noisy gradient, maintaining the
desired target distribution as the invariant distribution. Results on simulated
data validate our theory. We also provide an application of our methods to a
classification task using neural networks and to online Bayesian matrix
factorization.Comment: ICML 2014 versio
Deep Network Flow for Multi-Object Tracking
Data association problems are an important component of many computer vision
applications, with multi-object tracking being one of the most prominent
examples. A typical approach to data association involves finding a graph
matching or network flow that minimizes a sum of pairwise association costs,
which are often either hand-crafted or learned as linear functions of fixed
features. In this work, we demonstrate that it is possible to learn features
for network-flow-based data association via backpropagation, by expressing the
optimum of a smoothed network flow problem as a differentiable function of the
pairwise association costs. We apply this approach to multi-object tracking
with a network flow formulation. Our experiments demonstrate that we are able
to successfully learn all cost functions for the association problem in an
end-to-end fashion, which outperform hand-crafted costs in all settings. The
integration and combination of various sources of inputs becomes easy and the
cost functions can be learned entirely from data, alleviating tedious
hand-designing of costs.Comment: Accepted to CVPR 201
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