Smart Home Technologies Data Mining and Prediction

Smart Home Technologies

Data Mining and Prediction

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

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 ?

Example Patterns Associative pattern

When Bob is in the living room he likes to watch TV and eat popcorn with the light turned off.

ClassificationAction movie fans like to watch Terminator, drink beer, and have pizza.

Sequential patternsAfter 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.

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 modelsIf Bob turns on the TV in the evening then he will 80% of the time go to the kitchen to make popcorn.

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 taskse.g.: prepare coffee in the morning, turn on lights

Eliminate unnecessary steps, improve sequencese.g.: determine if will likely rain based on weather

forecast and external sensors to decide if to water the lawn.

What to Predict Behavior of the Inhabitants

Location Tasks / goals Actions

Behavior of the Environment Device behavior (e.g. heating, AC) Interactions

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

Example: Location PredictionTime Date Day Locationt Locationt+1

6:30 02/25 Monday Bedroom Bathroom

7:00 02/25 Monday Bathroom Kitchen

7:30 02/25 Monday Kitchen Garage

17:30 02/25 Monday Garage Kitchen

18:00 02/25 Monday Kitchen Bedroom

18:10 02/25 Monday Bedroom Living room

22:00 02/25 Monday Living room

Bathroom

22:10 02/25 Monday Bathroom Bedroom

6:30 02/26 Tuesday Bedroom Bathroom

Example: Location Prediction Learned pattern

If Day = Monday…Friday& Time > 0600& Time < 0700& Locationt = Bedroom

Then Locationt+1 = Bathroom

Prediction Techniques Classification-Based Approaches

Nearest Neighbor Neural Networks Bayesian Classifiers Decision Trees

Sequential Behavior Modeling Hidden Markov Models Temporal Belief Networks

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

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)









Bathroom



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

Nearest Neighbor Training instances and similarity metric form

regions where a concept (prediction) applies:

Uncertain information and incorrect training instances lead to incorrect classifications

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:

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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 02/25 Thursday 33 News News

19:00 02/26 Friday 11 News News

12:00 02/27 Saturday 21 Action Terminator I

20:00 02/27 Saturday 8 News News

… … … … … …


13:30 03/20 Sunday 13 Reality Antiques Roadshow

22:00 03/20 Sunday 4 News News

20:00 03/21 Monday 8 News 60 Minutes

22:00 03/22 Tuesday 13 Documentary Nova

… … … … … …

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

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21:00 04/21 Thursday 33 News News

20:00 04/22 Friday 8 News 60 Minutes

… … … … … …

Does he/she like to watch Nova ?

Nearest Neighbor Advantages

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

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 Bathroomelse

Sequence of evaluations are represented as a tree where leaves are labeled with the category

Decision Tree Induction Algorithm (main loop)

1. A = best attribute for next node2. Assign A as attribute for node3. For each value of A, create

descendant node4. Sort training examples to descendants5. If training examples perfectly

classified, then Stop, else iterate over descendants

Decision Tree Induction Best attribute based on

information-theoretic concept of entropy Choose the attribute that reduces the

entropy (~uncertainty) mostA1

Bathroom (25)Kitchen (25)


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Decision Tree Example: Inhabitant Location

Day

Time > 6:00

Locationt

Time < 7:00

Bathroom

M…F

yes

yes

Bedroom …

no

no

SatSun

Locationt

Living Room

Bedroom …









Bathroom



Decision Trees Advantages

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

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

Neural Networks

Computer vs. Human BrainComputer 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

Artificial Neurons Artificial neurons are a much simplified

computational model of neurons Output:

A function is learned by adjusting the weights wj

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Artificial Neuron Activation functions

Perceptrons Perceptrons use a single unit with a

threshold function to distinguish two categories

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).

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Limitation of Perceptrons Learns only linearly-separable

functions

E.g. XOR can not be learned

Feed forward Networks with Sigmoid Units Networks of units with sigmoid

activation functions can learn arbitrary functions

Feed forward Networks with Sigmoid Units General Networks permit arbitrary

state-based categories (predictions) to be learned

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.

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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

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, 447-462.

Neural Networks Advantages

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

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.

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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

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Bayes Classifier Advantages

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

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.

Bayesian Networks Example:Location Prediction All state attributes are represented as

nodes. Nodes can include attributes that are not

observable.

Prediction

RoomGet ready

Time

Day

Gr R

Bedroom

Kitchen

True 0.8 0.1

False 0.2 0.0

P(Bathroom | R, Gr)

Bayesian Networks Advantages

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

Sequential Behavior Prediction Problem

Input: A sequence of states or events States can be represented by their

attributesinhabitant location, device status, etc.

Events can be raw observationsSensor 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.

Sequence Prediction Techniques

String matching algorithms Deterministic best match Probabilistic matching

Markov Models Markov Chains Hidden Markov Models

Dynamic Belief Networks

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 ?

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. 148-154: AAAI Press.

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.

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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*1/5 + 0.1*50/100 = 0.18+0.05 = 0.23

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

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

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.

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

Active LeZi Represent compression phrases as a

parse tree with frequency statistics E.g.: aaababbbbbaabccddcbaaaa

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

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

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10

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Active LeZi Example: Prediction on Simulated MavHome Data

ALZ Performance II - Typical Scenarios with noise

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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

Active LeZi

Advantages 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

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)

Markov Chain Example Example states:

S = {(Room, Time, Day, Previous Room)} Transition probabilities can be calculated

from training data by counting occurrences

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Markov Models

Advantages 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

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

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:

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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

Hidden Markov Model Example Tossing a balanced coin starting with a

biased coin that always starts heads:

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

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]

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 1:6 6 6 6 6 # Output training pattern 1:1.000 # Input training pattern 2:6 6 4 3 4 # Output training pattern 2:0.333 # Input training pattern 3:6 6 6 6 6 # Output training pattern 3:1.000 # Input training pattern 4:6 6 6 6 6 # Output training pattern 4:1.000 # Input training pattern 5:6 6 6 6 6 # Output training pattern 5:1.000

Neural Network Predictor Learning performance depends on:

Network topology Input representation Learning rate

Hidden Markov Model Example Input representation and learned

HMM: Initial and final HMM model

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.

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Smart Home Technologies Data Mining and Prediction

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