CCS355 Neural Network & Deep Learning Unit II Notes with Question bank .pdf
FDSE2015
1. Traffic Speed Data Investigation
with
Hierarchical Modeling
Tomonari MASADA
Nagasaki University
masada@nagasaki-u.ac.jp
2. Real-Time Traffic Speed Data | NYC Open Data
https://data.cityofnewyork.us/Transportation/Real-Time-Traffic-Speed-Data/xsat-x5sa
Traffic speed measurements at 128 streets
(Regrettably, no longer maintained)
3.
4.
5. Problem 1
• Traffic speed data show a clear
periodicity at one day period.
• However, many different traffic speed
distribution patterns can be observed
also within each period.
6. Solution 1 [Masada+ 14]
• We take intuition from topic models
in text mining.
–The data set of each day should be
modeled as a mixture of many
different speed distributions.
7. Latent Dirichlet Allocation (LDA) [Blei+ 03]
• LDA achieves a word token level clustering.
• Not a document level clustering
• Each document is modeled as a mixture of
many different word probability distributions.
topic <-> word probability distribution
document <-> topic probability distribution
9. An important difference
• Words are discrete entities.
– LDA uses multinomial distribution for modeling
per-topic word distribution.
• Speeds (in mph) are continuous entities.
– Our model uses gamma distribution.
13. Problem 2
• Traffic speed data may show a similarity
at the same time point of day.
• Traffic speed data may show a similarity
for the streets whose locations are close
to one another.
14. Solution 2 [Masada+ FDSE15]
• We use metadata in topic models.
–time points
–geographic locations
15. TRINH = TRaffic speed INvestigation
with Hierarchical modeling
• Make topic probabilities dependent on
time points and on locations
– probability that the speed measured by the sensor
s at the time point t is assigned to the topic k
𝜃 𝑑𝑡𝑘 ≡
exp(𝑚 𝑑𝑘 + 𝜆 𝑘𝑠 + 𝜏 𝑘𝑡)
𝑘′ exp(𝑚 𝑑𝑘′ + 𝜆 𝑘′ 𝑠 + 𝜏 𝑘′ 𝑡)
16. Parameters
• 𝑚 𝑑𝑘
– How often the document d provides the topic k
• 𝜆 𝑘𝑠
– How often the sensor s provides the topic k
• 𝜏 𝑘𝑡
– How often the time point t (of day) provides the
topic k
17. Priors for parameters ("hierarchical")
• 𝑚 𝑑𝑘
–K Gaussian priors
• 𝜆 𝑘𝑠
–K Gaussian process priors
• 𝜏 𝑘𝑡
–K Gaussian process priors
19. Inference by MCMC
• Sample from the posterior distribution
–Slice sampling for topic probability
parameters 𝑚 𝑑𝑘, 𝜆 𝑘𝑠, and 𝜏 𝑘𝑡
–Metropolis-Hastings for hyperparameters
23. Comparison experiment
• Log likelihood per measurement
–Larger is better.
• Data
–May 27 ~ June 16, 2013 (three weeks)
• Data files were downloaded every minute.
–20% measurements for testing
26. What we achieved
• We obtained an MCMC for a topic model
whose topic probabilities are defined by
combining multiple factors.
• And the factors are correlated via Gaussian.
– Our model can also be applied to other types of
metadata indicating intrinsic similarity of data.
27. Summary
• We proposed a topic model for traffic data analysis.
• Sensor locations and measurement timestamps
affects topic assignment.
• TRINH achieves better likelihood in earlier iterations.
• However, TRINH gives worse likelihood in later
iterations.
28. Future work
• Control the strength of regularization
– e.g. by weighting the factors.
𝜃 𝑑𝑡𝑘 ≡
exp(𝑚 𝑑𝑘 + 𝜆 𝑘𝑠 + 𝜏 𝑘𝑡)
𝑘′ exp(𝑚 𝑑𝑘′ + 𝜆 𝑘′ 𝑠 + 𝜏 𝑘′ 𝑡)
• Look for other data sets
– Location information should be more relevant.