lahar: extracting events from probabilistic streams

LAHAR: Extracting Events from Probabilistic Streams

Chris Re, Julie Letchner,

Magdalena Balazinska and Dan Suciu

University of Washington

Lahar -- SIGMOD 2008 -- Christopher Re2

What is a Lahar?

This is a Lahar

May 18, 1980 ~ 8:27am … a few minutes later

It’s a massive, fast stream of dirt(y data)

Our system, Lahar, processes queries on massive, dirty streams of data

Event Queries

Lahar -- SIGMOD 2008 -- Christopher Re

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Motivating App: RFID Event queries as Cayuga, Sase and Snoop

Complex sequences using projections, predicates,…

Joe entered office 422 at t=8

Query: “Alert when Joe enters 422”

i.e. Joe outside 422, inside 422


Challenges: Tracking Joe’s Location

6th Floor in CS building

Blue ring is Joe’s Location

Antennas



Challenges: Tracking Joe’s Location

Blue ring is Joe’s Location

Antennas Two Problems:1. Missed Readings2. Granularity Mismatch

Propose: infer location, keep probs & query with Lahar Model Based View [Deshpande et al] of an HMM

Lahar retains probabilities, achieves higher quality (P/R) and is still efficient.


Outline RFID streams to probabilistic streams Lahar queries on probabilistic streams Query algorithms: Regular and Extended Regular Experiments


Tracking Joe’s Location

Blue ring is ground truth

Antennas 6th Floor in CS building


Probabilities via particle filter

Each orange particle is a guess of Joe’s location

Blue ring is ground truth

Antennas

Particles guess many locations per timestep, so data are uncertain



Tag t Loc P

Joe 7 422 0.4

Hall3 0.4

Hall4 0.2

Joe 8 422 0.6

Hall3 0.2

Hall4 0.2

Sue 7 … …

From particles to a probabilistic stream

At(tag,loc)

Query Particle Filter output via At – a model based view


(0.4+0.2) * 0.6 = 0.36

Tag t Loc P

Joe 7 422 0.4

Hall3 0.4

Hall4 0.2

Joe 8 422 0.6

Hall3 0.2

Hall4 0.2

Sue 7 … …

Semantics of the Model

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At(tag,loc)

Tag t Loc

Joe 7 Hall4

Joe 8 422

Sue 7 …

Prob = 0.2 * 0.6 * …

“Joe enters 422” @ t=8A query q returns the probability that q is true at each time t

possible stream (worlds)

Probability outside 422 (in Hall3,Hall4)


(` ',` 4 ') (` ', 4̀ 2 '); 2At Jo At Je H oeall

Lahar Queries by Example

Alert when Joe is in hallway 4 and later in office 422

Inspired by Cayuga [Demers et al 2006, White et al 2007]


Joe in 422

(` ',` 4 ') (` ', 4̀ 2 '); 2At Jo At Je H oeall



Joe in Hall4 Joe in 422



Joe in 422

(` ',` 4 ') (` ', 4̀ 2 '); 2At Jo At Je H oeall





`422' (` ',` 4 ')( ; (` ', ))l At Joe H At Joeall l

Alert when Joe is in hallway 4, and immediately in office 422


Joe in 422

(` ',` 4 ') (` ', 4̀ 2 '); 2At Jo At Je H oeall








Joe

Challenge with probabilities: Naïve approach is exponential; unavoidable (#P)


( (` ',` 4 '); (` ', ))4̀22 '

At Joe Hall At Joe ll

Regular Queries (Efficient, streamable) Alert when Joe enters 422

Extended Regular (Efficient, streamable) Alert when anyone enters 422

A hierarchy of Lahar queries


( (` ',` 4 '); (` ', ))4̀22 '

At Joe Hall At Joe ll

`422' ( ( ,` 4 '); ( , ))l At p Hall At p l

A hierarchy of Lahar queries

Regular Queries (Efficient, streamable) Alert when Joe enters 422

Extended Regular (Efficient, streamable) Alert when anyone enters 422

Safe (Efficient, but not streamable) Unsafe (Inefficient)


Joe

Review: A non-probabilistic example

Alert me when Joe enters 422

`422' (` ',` 4 '( ; (` ', )) )l A Att Joe Hal Joe llq

Tag T Loc

Joe 7 Hall 4

Joe 8 422

Tag T Loc

Joe 7 Hall 4

Joe 8 423

Accept at t = 8

{}

{1}

{2}

{}

{1}

{}

Final

Joe in Hall4 Joe in 4221 2

… now with probabilities


Joe Final

Joe in Hall4 Joe in 4221 2

`422' (` ',` 4 '( ; (` ', )) )l A Att Joe Hal Joe llq

Accept t=8 with p = 0.3

Alert me when Joe enters 422

{} 1.0

{} 0.5, {1} 0.5

{} 0.65, {1} 0.05, {2} 0.3

Distribution on States

Tag T Loc P

Joe 7 Hall4 0.5

Joe 8 423 0.3

422 0.6


Lies in the preceding slides… (technical details) Richer predication: “Alert when Joe enters any

office”

Translate query and input into an alphabet

Joe Final


1 2

Key Technical Detail: Alphabet is small in data Streamable

See paper for compilation

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`422' ( ( ,` 4 '); ( , ))lq At p Hall At p l

Extension to Extended regular


“Alert when anyone enters 422”

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`422 '[ ` '] ( (` ',` 4 '); (` ', ))lq p Tom At Tom Hall At Tom l `422 '[ ` '] ( (` ',` 4 '); (` ', ))lq p Joe At Joe Hall At Joe l

`422' ( ( ,` 4 '); ( , ))lq At p Hall At p l

Extension to Extended regular


Algorithm: (Obs1) suggests run automaton for each person (Obs2) suggests multiply to get prob any is true

Space = O(# persons), not # timesteps: can stream

“Alert when anyone enters 422”

(Obs 1) Each query is regular (Obs 2) disjoint sets of eventsHence, probabilistically independent

Summary of Contributions Regular Queries (Efficient, streamable)

Compiled to an automaton,streaming, O(1) space

Extended regular (Efficient, streamable) Streaming with O(m) space, i.e. # of persons.

See paper for Markovian correlations, more sophisticated predication, complete compilation and static analysis algorithms

Safe (Efficient, but not streamable) Unsafe (Inefficient, most #P-hard)


Experimental Setup

Quality: How is P/R affected by keeping probs? 52 objects, 352 locations, 10k sq. ft.

2x30min trace with 10 min break in between Participants marked down true locations


2 1( ), ( ) ( ) 1 2( ( ( , ); ( , ))Person p Coffee l Hallway l At p l At p l

Experimental Setup

Quality: How is P/R affected by keeping probs? 52 objects, 352 locations, 10k sq. ft.

2x30min trace with 10 min break in between Participants marked down true locations “Alert when anyone enters a coffee room”

Baseline: Most Likely Estimate (MLE) Each timestep/Each person: most likely location

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Quality: Realtime – Improve over MLE?


Declare an event “true”, if its Pr > threshold Vary threshold

Precision

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1Recall

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10% improvement in F1


Performance: Is the cost too high?Synthetic Data – Same query


Related Work Event Queries – Deterministic

Cayuga, SASE, SnoopIB

Model-Based Views BBQ, recently, Kanagal et al ICDE 08

Probabilistic Databases Mystiq, Trio, MayBMS, Maryland, Purdue,MCDB

Particle Filters on HMMs Doucet, Godsill


Conclusion Showed Lahar

Processed output of several inference tasks (HMMs) Applies more generally than just RFID

Quality (F1) gains by keeping probability

Performance usable in real-time Lots of concurrent tags No indexing!


Overview of Regular Query Algorithm

1. Compile an event query q1. Automaton (A) over a language L

2. Mapping (M) events to subsets of L

2. Runtime – Input is set of events E1. Map E into subsets of L via M

2. Maintain set of possible states of A

Deterministic Probabilistic

stays same

stays same

distribution

distribution

Size of distribution depends only on the query, q.

NB: example to follow

For details, see paper


Why are ER queries hard? Regular Queries ~ Regular Expressions

Mapping is non-trivial Inspired by Cayuga [Demers et al. 06]

Queries have #P-combined complexity Encode mDNF as regular expression

Intuition: n-sized automaton leads to Extended regular ~ 1 NFA per/person

k persons implies O(k)-size automaton Exponential cost

time(2 )n

When ER, can avoid blowup


Regular and Extended Regular Query is regular if no variable is shared between

subgoals

Query is extended regular if any variable shared by two subgoals, is shared by all subgoals

p is shared between subgoals

502 ( (' ', '501'); (' ', ))l At Joe At Joe l

502 ( ( , 5̀01 ); ( , ))l At p At p l


Correlations


Sequencing by example Sequencing is parameterized [Cayuga]

502' ( ( , 5̀01'); ( , ))l At p At p l

( ,501)Joe ( ,502)Bob ( ,502)Joe

Time

( ,503)Joe

Semicolon means “the next event among those that match next goal”

Semicolon is not “after”


Compilation by example Each goal “corresponds” to two letters:

move (m) – the query should advance accept (a) – the next subgoal accepts

1 50` 2' ( ( , 5̀01 ); ( , ))lq At Joe At Joe l

1 1 1 2 2{m , , , }L a m a

1a 2a

2{ }m1 1 2( ,501) { , , }Joe m a m

2 2( ,502) { , }Joe m a

Any other maps to empty set0 2( , ) { }Joe l m

Final

Does not contain

Does contain

qM


Subtle example..

What about:

1 50` 2' ( ( , 5̀01 ); ( , ))lq At Joe At Joe l 1 1 1 2 2{m , , , }L a m a

1a 2a

2{ }m

1 1 2( ,501) { , , }Joe m a m

2 2( ,502) { , }Joe m a

Any other maps to empty set0 2( , ) { }Joe l m

Final

Does not contain

Does contain

1M

2 ( , 5̀01 ); ( , 5̀02 ')q At Joe At Joe

0( , )Joe l

2M


CUT II


Motivating Apps RFID apps

Diary and Active Calendar Application. Alert if I go to a database meeting.

Supply chain Alert if Mach 3 razors are being stolen

Many independent HMMs Elder care [Intel/UW]

Alert if elder takes their medicine with water Activity Recognition Financial applications on predictive HMM

Alert if head-and-shoulders market


Compile Select and Filter

Intuition: goal maps to two letters: match (m) : matches filter accept (a) : accepted by select

(` ', 5̀01'); (` ', 5̀02 ')filterq At Joe At Joe

`502' ( (` ', 5̀01 ); (` ', ))select lq At Joe At Joe l

1 1 2 2{m , , , }L a m a

1a 2a

2{ }m Final

Does not contain

Does contain

language and automaton are the same for both queries


Wrinkle in the language:Filter v. Selection

“Alert next time Joe is in 502 after he is in 501”

(` ', 5̀01'); (` ', 5̀02 ')filterq At Joe At Joe

`502' ( (` ', 5̀01 ); (` ', ))select lq At Joe At Joe l

Time

Yes

No

( ,501)Joe ( ,502)Joe( ,503)Joe

“Alert if the next place Joe is in after 501 is 502”

At


Recap of Algorithms Regular Queries

Compiled them to an NFA, then used image Data complexity O(1)

Extended regular Several regulars multiplied together Depends on number of distinct people in the data, not

number of time steps.


Text1 Euclid Eculid Euclid Euclid Euclid Euclid Symbol


(` ',` 4 ') (` ', 4̀ 2 '); 2At Jo At Je H oeall








Joe

Joe in 422

Challenge with probabilities: Naïve approach is exponential; unavoidable (#P)

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Quality: Archived – Improve over Viterbi?


Smoothing v. Viterbi (MAP) Lahar tracks of Markovian Correlations Viterbi leverages correlations for MAP estimate

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1Precision Recall F1

0000000000000000000000000000000000000000000000000000

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Approx ~30% gain in F1

lahar: extracting events from probabilistic streams

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