1. Smart Home Technologies
Data Mining and Prediction

2. Objectives of Data Mining and Prediction
Large amounts of sensor data have to be “interpreted” to acquire knowledge about tasks that occur in the environment
Patterns in the data can be used to predict future events
Knowledge of tasks facilitates the automation of task components to improve the inhabitants’ experience

3. Data Mining and Prediction
Data Mining attempts to extract patterns from the available data
Associative patterns
What data attributes occur together ?
Classification
What indicates a given category ?
Temporal patterns
What sequences of events occur frequently ?

4. Example Patterns Associative pattern Classification
When Bob is in the living room he likes to watch TV and eat popcorn with the light turned off.
Classification
Action movie fans like to watch Terminator, drink beer, and have pizza.
Sequential patterns
After coming out of the bedroom in the morning, Bob turns off the bedroom lights, then goes to the kitchen where he makes coffee, and then leaves the house.

5. Data Mining and Prediction
Prediction attempts to form patterns that permit it to predict the next event(s) given the available input data.
Deterministic predictions
If Bob leaves the bedroom before 7:00 am on a workday, then he will make coffee in the kitchen.
Probabilistic sequence models
If Bob turns on the TV in the evening then he will 80% of the time go to the kitchen to make popcorn.

6. Objective of Prediction in Intelligent Environments
Anticipate inhabitant actions
Detect unusual occurrences (anomalies)
Predict the right course of actions
Provide information for decision making
Automate repetitive tasks
e.g.: prepare coffee in the morning, turn on lights
Eliminate unnecessary steps, improve sequences
e.g.: determine if will likely rain based on weather forecast and external sensors to decide if to water the lawn.

7. What to Predict Behavior of the Inhabitants
Location
Tasks / goals
Actions
Behavior of the Environment
Device behavior (e.g. heating, AC)
Interactions
Visit course website

8. Example: Location Prediction
Where will Bob go next?
Locationt+1 = f(x)
Input data x:
Locationt, Locationt-1, …
Time, date, day of the week
Sensor data

9. Example: Location Prediction
Time
Date
Day
Locationt
Locationt+1
6:30
02/25
Monday
Bedroom
Bathroom
7:00
Kitchen
7:30
Garage
17:30
18:00
18:10
Living room
22:00
22:10
02/26
Tuesday

10. Example: Location Prediction
Learned pattern
If Day = Monday…Friday
& Time > 0600
& Time < 0700
& Locationt = Bedroom
Then Locationt+1 = Bathroom

11. Prediction Techniques
Classification-Based Approaches
Nearest Neighbor
Neural Networks
Bayesian Classifiers
Decision Trees
Sequential Behavior Modeling
Hidden Markov Models
Temporal Belief Networks

12. Classification-Based Prediction
Problem
Input: State of the environment
Attributes of the current state
inhabitant location, device status, etc.
Attributes of previous states
Output: Concept description
Concept indicates next event
Prediction has to be applicable to future examples

13. Instance-Based Prediction: Nearest Neighbor
Use previous instances as a model for future instances
Prediction for the current instance is chosen as the classification of the most similar previously observed instance.
Instances with correct classifications (predictions) (xi,f(xi)) are stored
Given a new instance xq, the prediction is derived as the one of the most similar instance xk:
f(xq) = f(xk)

14. Example: Location Prediction
Time
Date
Day
Locationt
Locationt+1
6:30
02/25
Monday
Bedroom
Bathroom
7:00
Kitchen
7:30
Garage
17:30
18:00
18:10
Living room
22:00
22:10
02/26
Tuesday

15. Nearest Neighbor Example: Inhabitant Location
Training Instances (with concept):
((Bedroom, 6:30), Bathroom), ((Bathroom, 7:00), Kitchen),
((Kitchen, 7:30), Garage), ((Garage, 17:30), Kitchen), …
Similarity Metric:
d((location1, time1), (location2, time2)) =
1000*(location1  location2) + | time1 – time2 |
Query Instance:
xq = (Bedroom, 6:20)
Nearest Neighbor:
xk = (Bedroom, 6:30) d(xk, xq) = 10
Prediction f(xk):
Bathroom

16. Nearest Neighbor
Training instances and similarity metric form regions where a concept (prediction) applies:
Uncertain information and incorrect training instances lead to incorrect classifications

17. k-Nearest Neighbor
Instead of using the most similar instance, use the average of the k most similar instances
Given query xq, estimate concept (prediction) using majority of k nearest neighbors
Or, estimate concept by establishing the concept with the highest sum of inverse distances:

18. k-Nearest Neighbor Example
TV viewing preferences
Distance Function?
What are the important attributes ?
How can they be compared ?
Time
Date
Day
Channel
Genre
Title
19:30
02/25
Thursday 27
Reality
Cops
21:00 33
News
19:00
02/26
Friday 11
12:00
02/27
Saturday 21
Action
Terminator I
20:00 8 …
Time
Date
Day
Channel
Genre
Title
13:30
03/20
Sunday 13
Reality
Antiques Roadshow
22:00 4
News
20:00
03/21
Monday 8
60 Minutes
03/22
Tuesday
Documentary
Nova …

19. k-Nearest Neighbor Example
Distance function example:
Most important matching attribute: Show name
Second most important attribute: Time
Third most important attribute: Genre
Fourth most important attribute: Channel
Time
Date
Day
Channel
Genre
Title
16:30
04/20
Wednesday 13
Documentary
WW II Planes
21:00
04/21
Thursday 33
News
20:00
04/22
Friday 8
60 Minutes …
Does he/she like to watch Nova ?

20. Nearest Neighbor Advantages Problems
Fast training (just store instances)
Complex target functions
No loss of information
Problems
Slow at query time (have to evaluate all instances)
Sensitive to correct choice of similarity metric
Easily fooled by irrelevant attributes

21. Decision Trees
Use training instances to build a sequence of evaluations that permits to determine the correct category (prediction)
If Bob is in the Bedroom then
if the time is between 6:00 and 7:00 then
Bob will go to the Bathroom
else
Sequence of evaluations are represented as a tree where leaves are labeled with the category

22. Decision Tree Induction
Algorithm (main loop)
A = best attribute for next node
Assign A as attribute for node
For each value of A, create descendant node
Sort training examples to descendants
If training examples perfectly classified, then Stop, else iterate over descendants

23. Decision Tree Induction
Best attribute based on information-theoretic concept of entropy
Choose the attribute that reduces the entropy (~uncertainty) most A1 A2 v1 v2 v1 v2 ? ? B K
Bathroom (25)
Kitchen (25)
Bathroom (25)
Kitchen (25)
Bathroom (50)
Kitchen (0)
Bathroom (0)
Kitchen (50)

24. Decision Tree Example: Inhabitant Location
Day
Sun
M…F
Sat
Time > 6:00
yes no
Time < 7:00
yes no
Locationt
Locationt
Bedroom …
Bedroom …
Bathroom
Living Room

25. Example: Location Prediction
Time
Date
Day
Locationt
Locationt+1
6:30
02/25
Monday
Bedroom
Bathroom
7:00
Kitchen
7:30
Garage
17:30
18:00
18:10
Living room
22:00
22:10
02/26
Tuesday

26. Decision Trees Advantages Problems Understandable rules
Fast learning and prediction
Lower memory requirements
Problems
Replication problem (each category requires multiple branches)
Limited rule representation (attributes are assumed to be locally independent)
Numeric attributes can lead to large branching factors

27. Artificial Neural Networks
Use a numeric function to calculate the correct category. The function is learned from the repeated presentation of the set of training instances where each attribute value is translated into a number.
Neural networks are motivated by the functioning of neurons in the brain.
Functions are computed in a distributed fashion by a large number of simple computational units

28. Neural Networks

29. Computer vs. Human Brain
Computational units
1 CPU, 108 gates
1011 neurons
Storage units
1010 bits RAM,
1012 bits disk
1011 neurons,
1014 synapses
Cycle time
10-9 sec
10-3 sec
Bandwidth
109 bits/sec
1014 bits/sec
Neuron updates / sec
106
1014

30. Artificial Neurons
Artificial neurons are a much simplified computational model of neurons
Output:
A function is learned by adjusting the weights wj

31. Artificial Neuron
Activation functions

32. Perceptrons
Perceptrons use a single unit with a threshold function to distinguish two categories

33. Perceptron Learning
Weights are updated based on the treaining instances (x(i), f(x(i))) presented.
Adjusts the weights in order to move the output closer to the desired target concept.
Learning rate  determines how fast to adjust the weights (too slow will require many training steps, too fast will prevent learning).

34. Limitation of Perceptrons
Learns only linearly-separable functions
E.g. XOR can not be learned

35. Feed forward Networks with Sigmoid Units
Networks of units with sigmoid activation functions can learn arbitrary functions

36. Feed forward Networks with Sigmoid Units
General Networks permit arbitrary state-based categories (predictions) to be learned

37. Learning in Multi-Layer Networks: Error Back-Propagation
As in Perceptrons, differences between the output of the network and the target concept are propagated back to the input weights.
Output errors for hidden units are computed based on the propagated errors for the inputs of the output units.
Weight updates correspond to gradient descent on the output error function in weight space.

38. Neural Network Examples
Prediction
Predict steering commands in cars
Modeling of device behavior
Face and object recognition
Pose estimation
Decision and Control
Heating and AC control
Light control
Automated vehicles

39. Neural Network Example: Prediction of Lighting
University of Colorado Adaptive Home [DLRM94]
Neural network learns to predict the light level after a set of lights are changed
Input:
The current light device levels (7 inputs)
The current light sensor levels (4 inputs)
The new light device levels (7 inputs)
Output:
The new light sensor levels (4 outputs)
[DLRM94] Dodier, R. H., Lukianow, D., Ries, J., & Mozer, M. C. (1994).
A comparison of neural net and conventional techniques for lighting control. Applied Mathematics and Computer Science, 4,

40. Neural Networks Advantages Problems
General purpose learner (can learn arbitrary categories)
Fast prediction
Problems
All inputs have to be translated into numeric inputs
Slow training
Learning might result in a local optimum

41. Bayes Classifier
Use Bayesian probabilities to determine the most likely next event for the given instance given all the training data.
Conditional probabilities are determined from the training data.

42. Naive Bayes Classifier
Bayes classifier required estimating P(x|f) for all x and f by counting occurrences in the training data.
Generally too complex for large systems
Naive Bayes classifier assumes that attributes are statistically independent

43. Bayes Classifier Advantages Problems
Yields optimal prediction (given the assumptions)
Can handle discrete or numeric attribute values
Naive Bayes classifier easy to compute
Problems
Optimal Bayes classifier computationally intractable
Naive Bayes assumption usually violated

44. Bayesian Networks
Bayesian networks explicitly represent the dependence and independence of various attributes.
Attributes are modeled as nodes in a network and links represent conditional probabilities.
Network forms a causal model of the attributes
Prediction can be included as an additional node.
Probabilities in Bayesian networks can be calculated efficiently using analytical or statistical inference techniques.

45. Bayesian Networks Example: Location Prediction
All state attributes are represented as nodes.
Nodes can include attributes that are not observable.
Prediction
Room
Get ready
Time
Day
P(Bathroom | R, Gr)
Gr R
Bedroom
Kitchen
True
0.8
0.1
False
0.2
0.0

46. Bayesian Networks Advantages Problems Efficient inference mechanism
Readable structure
For many problems relatively easy to design by hand
Mechanisms for learning network structure exist
Problems
Building network automatically is complex
Does not handle sequence information

47. Sequential Behavior Prediction
Problem
Input: A sequence of states or events
States can be represented by their attributes
inhabitant location, device status, etc.
Events can be raw observations
Sensor readings, inhabitant input, etc.
Output: Predicted next event
Model of behavior has to be built based on past instances and be usable for future predictions.

48. Sequence Prediction Techniques
String matching algorithms
Deterministic best match
Probabilistic matching
Markov Models
Markov Chains
Hidden Markov Models
Dynamic Belief Networks

49. String-Based Prediction
Use the string of previous events or states to find a part that matches the current history.
Prediction is either the event that followed the best (longest) matching string or the most likely event to follow strings partially matching the history.
Issues:
How to determine quality of match ?
How can such a predictor be represented efficiently if the previous event string is long ?

50. Example System: IPAM [DH98]
Predict UNIX commands issued by a user
Calculate p(xt,xt-1) based on frequency
Update current p(Predicted, xt-1) by 
Update current p(Observed, xt-1) by 1- 
Weight more recent events more heavily
Data
77 users, 2-6 months, >168,000 commands
Accuracy less than 40% for one guess, but better than Naïve Bayes Classifier
[DH98] B. D. Davison and H. Hirsh. Probabilistic Online Action Prediction. Intelligent Environments: Papers from the AAAI 1998 Spring Symposium, Technical Report SS-98-02, pp : AAAI Press.

51. Example System: ONISI [GP00]
Look for historical state/action sequences that match immediate history and determine the quality of the predictions from these sequences
In state s at time t, compute lt(s,a)
Average length of the k longest sequences ending in a
In state s, compute f(s,a)
Frequency of action a executed from state s
Rank predictions using
[GP00] Peter Gorniak and David Poole, Predicting Future User Actions by Observing Unmodified Applications, Seventeenth National Conference on Artificial Intelligence (AAAI-2000), August 2000.

52. Onisi Example [GP00]
k=3, for action a3 there are only two matches of length 1 and 2, so lt(s3,a3) = (0+1+2)/3 = 1
If =0.9, the sum of averaged lengths for all actions is 5, a3 has occurred 50 times in s3, and s3 is visited 100 times, then Rt(s3,a3) = 0.9*1/ *50/100 = = 0.23

53. Example Sequence Predictors
Advantages
Permits predictions based on sequence of events
Simple learning mechanism
Problems
Relatively ad hoc weighting of sequence matches
Limited prediction capabilities
Large overhead for long past state/action sequences

54. Markov Chain Prediction
Use the string of previous events or states to create a model of the event generating process.
Models are probabilistic and can be constructed from the observed behavior of the system
Prediction is the most event that is most likely to be generated by the model.
Issues:
What form should the model take ?
String-based models
State-based models

55. Example System: Active LeZi [GC03]
Assumptions:
Event sequences are fairly repeatable
Generated by deterministic source
Construct model as parse tree of possible event sequences
Nodes are events with associated frequencies
Model constructed using LZ78 text compression algorithm
[DH98] K. Gopalratnam and D. J. Cook, Active LeZi: An Incremental Parsing Algorithm for Device Usage Prediction in the Smart Home, In Proceedings of the Florida Artificial Intelligence Research Symposium, 2003.

56. Text Compression: LZ78 Parses string x1 , x2 , …. xi into c(i)
substrings w1 , w2 , …. wc(i) that form the set of phrases used for compression
Each prefix of a phrase wj is also a phrase wi in the set used for compression
Example:
input aaababbbbbaabccddcbaaaa
yields phrases a,aa,b,ab,bb,bba,abc,c,d,dc,ba,aaa

57. Active LeZi
Represent compression phrases as a parse tree with frequency statistics
E.g.: aaababbbbbaabccddcbaaaa

58. Prediction in Active LeZi
Calculate the probability for each possible event
To calculate the probability, transitions across phrase boundaries have to be considered
Slide window across the input sequence
Length k equal to longest phrase seen so far
Gather statistics on all possible contexts
Order k-1 Markov model
Output event with greatest probability across all contexts as prediction

59. Example: Probability of a
Order 2
2/5 times that aa appears
Order 1
5/10 times that a appears
Order 0
10/23 total symbols
Blended probability is
Probability of escaping to lower order = frequency of null endings

60. Active LeZi Example: Prediction on Simulated MavHome Data
Data simulates a single inhabitant interacting with the devices in the home
Repetitive behavior patterns are embedded in the data (e.g. morning routine )
Time is ignored in the prediction
Only device interactions are recorded

61. Active LeZi Advantages Problems
Permits predictions based on sequence of events
Does not require the construction of states
Permits probabilistic predictions
Problems
Tree can become very large (long prediction times)
Nonoptimal predictions if the tree is not sufficiently deep

62. Markov Chain Models
Markov chain models represent the event generating process probabilistically.
Markov models can be described by a tuple <S, T> representing states and transition probabilities.
Markov assumption: The current state contains all information about the past that is necessary to predict the probability of the next state.
P(xt+1|xt, xt-1, …, x0) = P(xt+1 | xt)
Transitions correspond to events that occurred in the environment (inhabitant actions, etc)
Prediction of next state (and event)

63. Markov Chain Example Example states:
S = {(Room, Time, Day, Previous Room)}
Transition probabilities can be calculated from training data by counting occurrences x1 x4 x6 x2 x5 x3

64. Markov Models Advantages Problems Permits probabilistic predictions
Transition probabilities are easy to learn
Representation is easy to interpret
Problems
State space has to have Markov property
State space selection is not automatic
States might have to include previous information
State attributes might not be observable

65. Partially Observable MMs
Partially Observable Markov Models extend Markov models by permitting states to be only partially observable.
Systems can be represented by a tuple <S, T, O, V> where <S, T> is a Markov model and O, V are mapping observations about the state to probabilities of a given state
O = {oi} is the set of observations
V: V(x, o) = P(o | x)
To determine a prediction the probability of being in any given state is computed

66. Partially Observable MMs
Prediction is the most likely next state given the information about the current state (i.e. the current belief state):
Belief state B is a probability distribution over the state space:
B = ((x1, P(x1)), …, (xn, P(xn))
Prediction of the next state:

67. Hidden Markov Models
Hidden Markov Models (HMM) provide mechanisms to learn the Markov Model <S, T> underlying a POMM from the sequence of observations.
Baum-Welch algorithm learns transition and observation probabilities as well as the state space (only the number of states has to be given)
Model learned is the one that is most likely to explain the observed training sequences

68. Hidden Markov Model Example
Tossing a balanced coin starting with a biased coin that always starts heads:

69. Partially Observable MMs
Advantages
Permits optimal predictions
HMM provide algorithms to learn the model
In HMM, Markovian state space description has not to be known
Problems
State space can be enormous
Learning of HMM is generally very complex
Computation of belief state is computationally expensive

70. Example Location Prediction Task
Environment and observations:
[0, 1, 0, 2, 4, 5, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 4, 5, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]
[0, 1, 0, 2, 4, 5, 4, 6, 4, 3, 4, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 4, 5, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 3, 4, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2]
[0, 1, 0, 2, 4, 5, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 3, 4, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
[0, 1, 0, 2, 0, 2, 0, 2, 4, 5, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 3, 4, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 4, 5, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6]
[0, 1, 0, 2, 0, 2, 4, 5, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 3, 4, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6]
[4, 3, 4, 2, 0, 1, 0, 0, 0, 1, 2, 4, 5, 4, 6, 6, 4, 3, 4, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 4, 5, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 4, 3, 4, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 4, 5, 4, 6, 6]

71. Neural Network Predictor
Example network and training data
Data has to be divided into training instances
Inputs represent current and 4 past locations
# Input training pattern 1:
# Output training pattern 1:
1.000
# Input training pattern 2:
# Output training pattern 2:
0.333
# Input training pattern 3:
# Output training pattern 3:
# Input training pattern 4:
# Output training pattern 4:
# Input training pattern 5:
# Output training pattern 5:

72. Neural Network Predictor
Learning performance depends on:
Network topology
Input representation
Learning rate

73. Hidden Markov Model Example
Input representation and learned HMM:
Initial and final HMM model

74. Dynamic Bayesian Networks
Dynamic Bayesian Networks use a Bayesian network to represent the belief state.
State is constructed from a set of attributes (nodes)
Transitions over time are modeled as links between a model at time t and a model at time t+1
Get ready
Time
Day
Room
Time t
Time t+1

75. Dynamic Bayesian Networks
Advantages
Handles partial observability
More compact model
Belief state is inherent in the network
Simple prediction of next belief state
Problems
State attributes have to be predetermined
Learning of probabilities is very complex

76. Conclusions Prediction is important in intelligent environments
Captures repetitive patterns (activities)
Helps automating activities (But: only tells what will happen next; not what the system should do next)
Different prediction algorithms have different strength and weaknesses:
Select a prediction approach that is suitable for the particular problem.
There is no “best” prediction approach
Optimal prediction is a very hard problem and is not yet solved.