1. Zhu Han University of Houston Thanks for Dr. Nam Nguyen Work
Signal processing and Networking for Big Data Applications Lecture 18: Bayesian Nonparametric learning
Zhu Han
University of Houston
Thanks for Dr. Nam Nguyen Work

2. outline Nonparametric classification techniques Applications
Smart grid
Bio imaging
Security for wireless devices
Location based services

3. Bayesian Nonparametric Classification
Question: How to cluster smart meter big data
For multi-dimension data
Model selection: How many clusters are there?
What’s the hidden process created the observations?
What are the latent parameters of the process?
Classic parametric methods (e.g. K-Means)
Need to estimation the number of clusters
Can have huge performance loss with poor model
Cannot scale well
The questions can be solved by using Nonparametric Bayesian Learning!
Nonparametric: Number of clusters (or classes) can grow as more data are observed and need not to be known as a priori.
Bayesian Inference: Use Bayesian rule to infer about the latent variables.

4. Main Objective Key Idea Posterior Likelihood Prior Bayesian rule
μ contains information such as how many clusters, and which sample belongs to which cluster
μ should be nonparametric and can be any value
Sample the posterior distribution P(μ|Observations), and get values of the parameter μ.
p(μ|Observation)=p(Observation|μ)p(μ)/p(Observation)

5. Examples of Bayesian inference used for parameter update
A Beta distribution is chosen to be prior:
Example: a=2, b=2 (head and tail prob. are equal)
A Binomial distribution is the conjugate likelihood:
One trial (N=1) and the result is one head (m=1)
Lead to the Posterior:
Update of parameters given the observations
The probability of head happening is higher

6. Dirichlet distribution
An extension of the Beta distribution to multiple dimensions.
K: number of clusters
πi: weight with marginal distribution
αi: prior

7. Dirichlet process
A random distribution G on Θ is Dirichlet process distributed with base distribution H and concentration parameter α, written as G ∼ DP(α,H), if for every finite measurable partition A1, . . .,AK of Θ
H(·), the mean of the DP,
α, strength of the prior

8. Bayesian nonparametric update
Have t observation x1,…,xt. Define
The posterior distribution on Θ
The posterior Dirichlet process
Small number of observation t, the prior dominates
When t increases, the prior has less and less impact
 controls the balance between the impact of prior and trials
Can be used to learn and combine any distributions

9. Applications Distribution estimation Primary user spectrum map
Cognitive radio spectrum bidding
Estimate the aggregated effects from all other CR users
Primary user spectrum map
Different CR users see the spectrum differently
How to combine the others’ sensing (as a prior) with own sensing.
Classification
Infinite Gaussian mixture model

10. Bayesian Nonparametric Classification
Generative model vs. Inference algorithm
Generative model
Start with the parameters and end up creating observations
Concept and framework
Inference algorithm
Start with observations and end up inferring about the parameters
Practical applications

11. A Dice with Infinite Number of Faces
Generative model: A general idea
If sample the distribution of each
face, we will obtain the weights, or
the probabilities for each face
(Dirichlet process) 1 2 3 4 5 6 ∞ 7
Question: If we have a dice with infinite number of faces, then how to deal with the situation? π1 π2 π3 π4 π5 π6

12. Model for Infinite Number of Faces
Generative model: Stick breaking process:
Generate an infinite number of faces, and their weights which sum up to 1.
Sample a breaking point:
Calculate the weight: 1
1-π1’
π1’
(1-π2’ )(1-π1’)
π2’ (1-π1’)

13. Infinite Gaussian Mixture Model
Generative model
Stick(α)
Infinite number of faces/classes 1 2 3 4 5 6 ∞ 7 π1 π2 π∞
Indicators are created according to multinomial distribution.
z1, z2 .. = 1
z20, z21 .. = 2
X1:N
The observations follows a distribution such as Gaussian. µ∞ Σ∞ µ1 Σ1 µ2 Σ2

14. Inference Model Obtain label Z from sample X
Finding the posterior of the multivariate distribution P(Z|X)
Given observation X, what are the probability that it belongs to cluster Z
Which cluster a sample belongs to?
Painful due to the integrations needed to carry out.
Finding a univariate distribution is more easily to implement
For new observation, can get marginal distribution of indicator
In other word, find the marginal distribution of Zi given the other indicators.
Gibbs sampling method to sample a value for a variable given all other variables.
The process is repeated and proved to be converged after a few iterations.

15. Chinese Restaurant Process
Nonparametric Bayesian Classification inference
Goal:
is the set of all other labels except the current one, ith
Prior
(Chinese Restaurant Process)
Likelihood
(e.g. given as Gaussian)
Posterior
Probability assigned to a represented class
Probability assigned to an unrepresented class
is the number of observations in the same class, k, excluding the current one, ith ? ?

16. Student t Distribution
Inference model: Posterior distributions
Given the prior and the likelihood, we come up with the posterior:
Probability of assigning to a unrepresented cluster:
Probability of assigning to a represented cluster:
(1)
t is the student-t distribution
(2)
Intuitive:
Provide a stochastic
gradient!

17. Gibbs Sampler Inference model: Gibbs sampler STOP
Start with random indicator for each observation.
Remove the current ith observation from its cluster
Update the indicator zi according to (1) and (2) given all the other indicators No
Converge?
Yes
STOP

18. Amazing Clustering Results
Two Gaussian distributed clusters with KL divergence (KLD) 4.5
Intuition why it works so well
Not the boundary or threshold. But clustering so that each cluster looks more like the distribution (Gaussian).
No prior information on probabilities

19. Indian Buffet Process (IBP)
Chinese restaurant problem: one point only belongs to one cluster
Indian buffet process: Multiple assignment clustering, in which, one observation can be caused by multiple hidden sources:
Binary matrix rep. of IBP:

20. Nonparametric classification: Mean shift
Density estimation:
The gradient of the density:
Move toward the densest region of the observations, i.e., the region with 0 gradient.

21. outline Nonparametric classification techniques Applications
Smart grid
Bio imaging
Security for wireless devices
Location based services

22. Smart Pricing for Maximizing Profit
The profit = sum of utility bill – cost to buy power
Different shape of loads cost different
Incentive using pricing to change the loads
The cost reduction is greater than loss of bills

23. Load Profiling
From smart meter data, try to tell users’ usage behaviors
CEO, 1%, UH Computer Science people
Worker, middle class, myself
Homeless, slave, Ph.D. students

24. Load Profiling Results
Utility company wants to know benchmark distributions
Nonparametric: do not know how many benchmarks
Bayesian: posterior distribution might be time varying
Scale: Daily, weekday, weekend, monthly, yearly.

25. outline Nonparametric classification techniques Applications
Smart grid
Bio imaging
Security for wireless devices
Location based services

26. Image processing pipeline
A maximum-intensity projection of a small region from the 3-D image montage;
Middle 2-D optical slice from the 3-D microglial soma segmentation results (in orange);
3-D volume rendering of automated microglia reconstruction results (in white) overlaid on the Iba-1 channel (green), and the soma segmentations in orange.
Illustrating the L-measure feature computation at multiple levels of granularity, at the compartment, segment, branch and cell levels.

27. Image processing pipeline
(E) Heatmap summary display of the combined L- measure feature table for the datasets in Figs. 1(a) and 1(c), with each row corresponding to a cell and each column corresponding to an L-measure feature.

28. Comparison of IGMM with other Techniques

29. Comparisons of the correlation matrices

30. outline Nonparametric classification techniques Applications
Smart grid
Bio imaging
Security for wireless devices
Location based services

31. Introduction: Security
Security Enhancement for Wireless Network
Sybil attack
Use device dependent radio-metrics as fingerprints.
Contributions:
Unique and hard-to-spoof device fingerprint
An unsupervised and passive attack detection method.
Upper bound and lower bound of classification performance.
Masquerade attack

32. Wireless device security
00-B0-D0-86-BB-F7
Device2
00-0C-F AD
Device3
Masquerade attack
Device1
00-B0-D0-86-BB-F7
00-0C-F AD
Device2
00-A0-C9-14-C8-29
Sybil attack
Mechanism:
If the number of devices can be found, compare that number to the number of associated devices to detect an attack.
Based on the label of the observations generated from the devices to mark the malicious nodes.

33. Security – Features selection
The Carrier Frequency Difference (CFD)
Defined as the difference between the carrier frequency of the ideal signal and that of the transmitted signal.
Depends on the oscillator within each device.
The Phase Shift Difference (PSD)
Using QPSK modulation technique.
Transmitter amplifiers for I-phase and Q-phase might be different. Consequently, the degree shift can have some variances.

34. Security – Features selection
Autocorrelation
BPSK Spectral coherence
Spectral coherence
Cycle frequency
Frequency
The Second- Order Cyclostationary Feature (SOCF)
The Received Signal Amplitude

35. Security – Inference Algorithm
Collect data
Unsupervised clustering method
Two clusters with the same MAC addresses?
Two MAC address with the same cluster?
Masquerade attack.
Sybil attack.
Determine the number of attackers
Update the “black” list with the Mac address
Yes No

36. Masquerade and Sybil attack detection: Preliminary USRP2 experiment
We collected the fingerprints from some WiFi devices by the USRP2 and tried the algorithm, below is the result:

37. Applications: Prime User emulation (PEU) attack detection
In Cognitive radio, a malicious node can pretend to be a Primary User (PU) to keep the network resources (bandwidth) for his own use.
How to detect that? We use the same approach, collect device dependent fingerprints and classify the fingerprints.
We limit our study to OFDM system using QPSK modulation technique.

38. PUE attack detection
DECLOAK algorithm
ROC curve

39. outline Nonparametric classification techniques Applications
Smart grid
Bio imaging
Security for wireless devices
Location based services

40. Introduction: Location Based Service (LBS)

41. Introduction: LBS Major tasks to enable LBS: Localize.
Estimate dwelling time.
Prediction: Where to go next?

42. LBS – Problem statements
What’s given:
Mobile devices are in indoor environments.
WiFi scans.
Goals:
Identifying revisited location.
Automatically profiling new location.
Unsupervised approach. No labeling required.
Online sampling to reduce the complexity.
Predicting the next possible locations.

43. LBS – Current indoor localization solutions
Ngram:
Based on the order of the APs.
Need at least 400 samples per each location to achieve a good result  not energy efficient.
SensLoc:
Solely based on APs names  not fine grained.
Continuously scans for WiFi signals  not energy efficient.

44. LBS – Indoor place identification (LOIRE)
LOIRE is different from the previous approaches the following aspects:
Unsupervised and nonparametric approach.
Energy efficiency (requires only 50 samples/place).
A framework to handle missing data.
An online batch sampling approach.
A quickest way to stop the algorithm.

45. LBS – Missing data
Use WiFi scans as signature to identify a revisited place and to detect a new place.
Problems:
Variable length observations
1 room Or
2 rooms?
Missing

46. LBS: IGMM The number of rooms is not given:
How to identify revisited room?
How to detect a new room?
Batch sampling, how to utilize?
WiFi scans from 4 rooms share the same list of Aps.

47. LBS: Online sampling Assume there are K stored places.
Place identification purpose:
Find a label, zi, for a new observed WiFi scan, Xi, in the set of 1:K.
Detect a new place:
Find the label, zi, for a new observed WiFi scan, Xi to see if zi = K+1 (a new place).
A stochastic way to detect a new place, not a threshold based approach.

48. LBS – Experimental results.
Dataset:
4 weeks long
5 phones

49. LBS – Future location prediction
Once the locations can be determined, we can build algorithm to predict the next visiting location.
Propose two models to predict
Based on Markov model: A Dynamic Hidden Markov Model.
Based on Deep Learning.

50. LBS – Future location prediction 1
Proposed Dynamic hidden Markov model (DHMM)
Hidden States/locations: propose to use NBC to determine the states.
Dimensions of the observations : GPS coordinates, time and RSS from either WiFi signal or cell tower signal.
Dynamic Hidden Markov Model: Every time the user comes to a new place, the model automatically updates itself with the new state. S1 S2 S3 SK
Rss1
Rss2
Rss3
RssK

51. LBS – Future location prediction 1
Proposed algorithm
N data points-Training data
Gibb Sampler
Determine the number of states and the current state.
Observe more data
MDP
Optimal scheduling result
DHMM:
Calculate the transition matrix
Calculate the distributions of signal strengths in each state
Schedule tolerant data package:
Each data package has a deadline to be sent.
When to sent?
Wait until the signal strength profile is at its best to send.
How to predict the future signal strength?
Predict the next locations of the users, estimate the signal strength at the locations.
Use Markov Decision Process (MDP) to calculate the expected reward.

52. LBS – Future location prediction 1
Simulation results
Two states
Same room

53. LBS – Future location prediction 1
Cost saving
Naïve: Send immediately
Proposed
Approach
UPDATE

54. LBS – Future location prediction 2
Based on Deep Learning
Purpose: Find the typical moving patterns (E1, E2), based on that, identify users and predict the future locations.
User identification: E2 E1
Location prediction:

55. LBS – Future location prediction 2
Bottom up:
Initiate random weights.
Learn the activation energy of the first hidden layer.
Treat the first hidden layer as the observation layer for the second layer. Repeat the process for all layers.
Top down:
Regenerate the observations based on the parameters and optimize the weights according to equation (1).
Repeat the above two steps until converge.

56. LBS – Future location prediction 2
Experiment results
Deep
learning:
PCA:

57. Thanks