1. Open universes and nuclear weapons
12/1/2018 3:35:23 PM
Open universes and nuclear weapons
Stuart Russell
Computer Science Division, UC Berkeley

2. Outline Why we need expressive probabilistic languages
12/1/2018 3:35:23 PM
Why we need expressive probabilistic languages
BLOG combines probability and first-order logic
Application to global seismic monitoring for the Comprehensive Nuclear-Test-Ban Treaty (CTBT)

3. The world has things in it!!
12/1/2018 3:35:23 PM
Expressive language => concise models
=> fast learning, sometimes fast reasoning
E.g., rules of chess:
1 page in first-order logic
On(color,piece,x,y,t)
~ pages in propositional logic
WhiteKingOnC4Move12
~ pages as atomic-state model
R.B.KB.RPPP..PPP..N..N…..PP….q.pp..Q..n..n..ppp..pppr.b.kb.r
[Note: chess is a tiny problem compared to the real world]

4. Brief history of expressiveness
12/1/2018 3:35:23 PM
probability
logic
atomic
propositional
first-order/relational

5. Brief history of expressiveness
12/1/2018 3:35:23 PM
probability
5th C B.C.
logic
atomic
propositional
first-order/relational

6. Brief history of expressiveness
12/1/2018 3:35:23 PM
17th C
probability
5th C B.C.
logic
atomic
propositional
first-order/relational

7. Brief history of expressiveness
12/1/2018 3:35:23 PM
17th C
probability
5th C B.C.
19th C
logic
atomic
propositional
first-order/relational

8. Brief history of expressiveness
12/1/2018 3:35:23 PM
17th C
20th C
probability
5th C B.C.
19th C
logic
atomic
propositional
first-order/relational

9. Brief history of expressiveness
12/1/2018 3:35:23 PM
17th C
20th C
21st C
probability
5th C B.C.
19th C
logic
atomic
propositional
first-order/relational

10. Brief history of expressiveness
12/1/2018 3:35:23 PM
17th C
20th C
21st C
probability
(be patient!)
5th C B.C.
19th C
logic
atomic
propositional
first-order/relational

11. First-order probabilistic languages
12/1/2018 3:35:23 PM
Gaifman [1964], Halpern [1990]:
Constraints on distributions over first-order possible worlds
Poole [1993], Sato [1997], Koller and Pfeffer [1998], various others:
KB defines distribution exactly (cf. Bayes nets)
assumes unique names and domain closure
like Prolog, databases (Herbrand semantics)

12. Herbrand vs full first-order
12/1/2018 3:35:23 PM
Given
Father(Bill,William) and Father(Bill,Junior)
How many children does Bill have?

13. Herbrand vs full first-order
12/1/2018 3:35:23 PM
Given
Father(Bill,William) and Father(Bill,Junior)
How many children does Bill have?
Herbrand semantics: 2

14. Herbrand vs full first-order
12/1/2018 3:35:23 PM
Given
Father(Bill,William) and Father(Bill,Junior)
How many children does Bill have?
Herbrand semantics: 2
First-order logical semantics:
Between 1 and ∞

15. 12/1/2018 3:35:23 PM
Possible worlds
Propositional

16. Possible worlds Propositional
12/1/2018 3:35:23 PM
Possible worlds
Propositional
First-order + unique names, domain closure A B C D A B A B A B A B C D C D C D C D

17. Possible worlds Propositional
12/1/2018 3:35:23 PM
Possible worlds
Propositional
First-order + unique names, domain closure
First-order open-universe A B C D A B A B A B A B C D C D C D C D
A B C D
A B C D
A B C D
A B C D
A B C D
A B C D

18. Open-universe models
12/1/2018 3:35:23 PM
Essential for learning about what exists, e.g., vision, NLP, information integration, tracking, life
[Note the GOFAI Gap: logic-based systems going back to Shakey assumed that perceived objects would be named correctly]
Key question: how to define distributions over an infinite, heterogeneous set of worlds?

19. Bayes nets build propositional worlds
Burglary
Earthquake
Alarm

20. Bayes nets build propositional worlds
Burglary
Earthquake
Alarm
Burglary

21. Bayes nets build propositional worlds
Burglary
Earthquake
Alarm
Burglary
not Earthquake

22. Bayes nets build propositional worlds
Burglary
Earthquake
Alarm
Burglary
not Earthquake
Alarm

23. Open-universe models in BLOG
12/1/2018 3:35:23 PM
Open-universe models in BLOG
Construct worlds using two kinds of steps, proceeding in topological order:
Dependency statements: Set the value of a function or relation on a tuple of (quantified) arguments, conditioned on parent values

24. Open-universe models in BLOG
12/1/2018 3:35:23 PM
Open-universe models in BLOG
Construct worlds using two kinds of steps, proceeding in topological order:
Dependency statements: Set the value of a function or relation on a tuple of (quantified) arguments, conditioned on parent values
Number statements: Add some objects to the world, conditioned on what objects and relations exist so far

25. Semantics
12/1/2018 3:35:23 PM
Every well-formed* BLOG model specifies a unique proper probability distribution over open-universe possible worlds; equivalent to an infinite contingent Bayes net
* No infinite receding ancestor chains, no conditioned cycles, all expressions finitely evaluable

26. Example: Citation Matching
12/1/2018 3:35:23 PM
[Lashkari et al 94] Collaborative Interface Agents, Yezdi Lashkari, Max Metral, and Pattie Maes, Proceedings of the Twelfth National Conference on Articial Intelligence, MIT Press, Cambridge, MA, 1994.
Metral M. Lashkari, Y. and P. Maes. Collaborative interface agents. In Conference of the American Association for Artificial Intelligence, Seattle, WA, August 1994.
Are these descriptions of the same object?
Core task in CiteSeer, Google Scholar, over 300 companies in the record linkage industry

27. (Simplified) BLOG model
12/1/2018 3:35:23 PM
#Researcher ~ NumResearchersPrior();
Name(r) ~ NamePrior();
#Paper(FirstAuthor = r) ~
NumPapersPrior(Position(r));
Title(p) ~ TitlePrior();
PubCited(c) ~ Uniform({Paper p});
Text(c) ~ NoisyCitationGrammar (Name(FirstAuthor(PubCited(c))),
Title(PubCited(c)));

28. (Simplified) BLOG model
12/1/2018 3:35:23 PM
#Researcher ~ NumResearchersPrior();
Name(r) ~ NamePrior();
#Paper(FirstAuthor = r) ~
NumPapersPrior(Position(r));
Title(p) ~ TitlePrior();
PubCited(c) ~ Uniform({Paper p});
Text(c) ~ NoisyCitationGrammar (Name(FirstAuthor(PubCited(c))),
Title(PubCited(c)));

29. (Simplified) BLOG model
12/1/2018 3:35:23 PM
#Researcher ~ NumResearchersPrior();
Name(r) ~ NamePrior();
#Paper(FirstAuthor = r) ~
NumPapersPrior(Position(r));
Title(p) ~ TitlePrior();
PubCited(c) ~ Uniform({Paper p});
Text(c) ~ NoisyCitationGrammar (Name(FirstAuthor(PubCited(c))),
Title(PubCited(c)));

30. (Simplified) BLOG model
12/1/2018 3:35:23 PM
#Researcher ~ NumResearchersPrior();
Name(r) ~ NamePrior();
#Paper(FirstAuthor = r) ~
NumPapersPrior(Position(r));
Title(p) ~ TitlePrior();
PubCited(c) ~ Uniform({Paper p});
Text(c) ~ NoisyCitationGrammar (Name(FirstAuthor(PubCited(c))),
Title(PubCited(c)));

31. (Simplified) BLOG model
12/1/2018 3:35:23 PM
#Researcher ~ NumResearchersPrior();
Name(r) ~ NamePrior();
#Paper(FirstAuthor = r) ~
NumPapersPrior(Position(r));
Title(p) ~ TitlePrior();
PubCited(c) ~ Uniform({Paper p});
Text(c) ~ NoisyCitationGrammar (Name(FirstAuthor(PubCited(c))),
Title(PubCited(c)));

32. (Simplified) BLOG model
12/1/2018 3:35:23 PM
#Researcher ~ NumResearchersPrior();
Name(r) ~ NamePrior();
#Paper(FirstAuthor = r) ~
NumPapersPrior(Position(r));
Title(p) ~ TitlePrior();
PubCited(c) ~ Uniform({Paper p});
Text(c) ~ NoisyCitationGrammar (Name(FirstAuthor(PubCited(c))),
Title(PubCited(c)));

33. Citation Matching Results
12/1/2018 3:35:23 PM
Four data sets of ~ citations, referring to ~ papers

34. Example: Sibyl attacks
12/1/2018 3:35:23 PM
Typically between 100 and 10,000 real entities
About 90% are honest, have one identity
Dishonest entities own between 10 and 1000 identities.
Transactions may occur between identities
If two identities are owned by the same entity (sibyls), then a transaction is highly likely;
Otherwise, transaction is less likely (depending on honesty of each identity’s owner).
An identity may recommend another after a transaction:
Sibyls with the same owner usually recommend each other;
Otherwise, probability of recommendation depends on the honesty of the two entities.

35. 12/1/2018 3:35:23 PM
#Entity ~ LogNormal[6.9, 2.3]();
Honest(x) ~ Boolean[0.9]();
#Identity(Owner = x) ~
if Honest(x) then 1 else LogNormal[4.6,2.3]();
Transaction(x,y) ~
if Owner(x) = Owner(y) then SibylPrior()
else TransactionPrior(Honest(Owner(x)),
Honest(Owner(y)));
Recommends(x,y) ~
if Transaction(x,y) then
if Owner(x) = Owner(y) then Boolean[0.99]()
else RecPrior(Honest(Owner(x)),
Evidence: lots of transactions and recommendations, maybe some Honest(.) assertions
Query: Honest(x)

36. 12/1/2018 3:35:23 PM
#Entity ~ LogNormal[6.9, 2.3]();
Honest(x) ~ Boolean[0.9]();
#Identity(Owner = x) ~
if Honest(x) then 1 else LogNormal[4.6,2.3]();
Transaction(x,y) ~
if Owner(x) = Owner(y) then SibylPrior()
else TransactionPrior(Honest(Owner(x)),
Honest(Owner(y)));
Recommends(x,y) ~
if Transaction(x,y) then
if Owner(x) = Owner(y) then Boolean[0.99]()
else RecPrior(Honest(Owner(x)),
Evidence: lots of transactions and recommendations, maybe some Honest(.) assertions
Query: Honest(x)

37. 12/1/2018 3:35:23 PM
#Entity ~ LogNormal[6.9, 2.3]();
Honest(x) ~ Boolean[0.9]();
#Identity(Owner = x) ~
if Honest(x) then 1 else LogNormal[4.6,2.3]();
Transaction(x,y) ~
if Owner(x) = Owner(y) then SibylPrior()
else TransactionPrior(Honest(Owner(x)),
Honest(Owner(y)));
Recommends(x,y) ~
if Transaction(x,y) then
if Owner(x) = Owner(y) then Boolean[0.99]()
else RecPrior(Honest(Owner(x)),
Evidence: lots of transactions and recommendations, maybe some Honest(.) assertions
Query: Honest(x)

38. 12/1/2018 3:35:23 PM
#Entity ~ LogNormal[6.9, 2.3]();
Honest(x) ~ Boolean[0.9]();
#Identity(Owner = x) ~
if Honest(x) then 1 else LogNormal[4.6,2.3]();
Transaction(x,y) ~
if Owner(x) = Owner(y) then SibylPrior()
else TransactionPrior(Honest(Owner(x)),
Honest(Owner(y)));
Recommends(x,y) ~
if Transaction(x,y) then
if Owner(x) = Owner(y) then Boolean[0.99]()
else RecPrior(Honest(Owner(x)),
Evidence: lots of transactions and recommendations, maybe some Honest(.) assertions
Query: Honest(x)

39. 12/1/2018 3:35:23 PM
#Entity ~ LogNormal[6.9, 2.3]();
Honest(x) ~ Boolean[0.9]();
#Identity(Owner = x) ~
if Honest(x) then 1 else LogNormal[4.6,2.3]();
Transaction(x,y) ~
if Owner(x) = Owner(y) then SibylPrior()
else TransactionPrior(Honest(Owner(x)),
Honest(Owner(y)));
Recommends(x,y) ~
if Transaction(x,y) then
if Owner(x) = Owner(y) then Boolean[0.99]()
else RecPrior(Honest(Owner(x)),
Evidence: lots of transactions and recommendations, maybe some Honest(.) assertions
Query: Honest(x)

40. Example: classical data association
12/1/2018 3:35:23 PM

41. Example: classical data association
12/1/2018 3:35:23 PM

42. Example: classical data association
12/1/2018 3:35:23 PM

43. Example: classical data association
12/1/2018 3:35:23 PM

44. Example: classical data association
12/1/2018 3:35:23 PM

45. Example: classical data association
12/1/2018 3:35:23 PM

46. #Aircraft(EntryTime = t) ~ NumAircraftPrior();
12/1/2018 3:35:23 PM
#Aircraft(EntryTime = t) ~ NumAircraftPrior();
Exits(a, t) if InFlight(a, t) then ~ Bernoulli(0.1);
InFlight(a, t) if t < EntryTime(a) then = false elseif t = EntryTime(a) then = true else = (InFlight(a, t-1) & !Exits(a, t-1));
State(a, t) if t = EntryTime(a) then ~ InitState() elseif InFlight(a, t) then ~ StateTransition(State(a, t-1));
#Blip(Source = a, Time = t) if InFlight(a, t) then ~ NumDetectionsCPD(State(a, t));
#Blip(Time = t) ~ NumFalseAlarmsPrior();
ApparentPos(r) if (Source(r) = null) then ~ FalseAlarmDistrib() else ~ ObsCPD(State(Source(r), Time(r)));

47. Inference
12/1/2018 3:35:23 PM
BLOG inference algorithms (rejection sampling, importance sampling, MCMC) converge to correct posteriors for any well-formed model, for any first-order query
Current generic MCMC engine is quite slow
Applying compiler technology
Developing user-friendly methods for specifying piecemeal MCMC proposals

48. CTBT Bans testing of nuclear weapons on earth
12/1/2018 3:35:23 PM
Bans testing of nuclear weapons on earth
Allows for outside inspection of 1000km2
182/195 states have signed
153/195 have ratified
Need 9 more ratifications including US, China
US Senate refused to ratify in 1998
“too hard to monitor”

49. 2053 nuclear explosions
12/1/2018 3:35:23 PM

50. 12/1/2018 3:35:23 PM

51. 254 monitoring stations
12/1/2018 3:35:23 PM

52. 12/1/2018 3:35:23 PM

53. Vertically Integrated Seismic Analysis
12/1/2018 3:35:23 PM
The problem is hard:
~10000 “detections” per day, 90% false
CTBT system (SEL3) finds 69% of significant events plus about twice as many spurious (nonexistent) events
16 human analysts find more events, correct existing ones, throw out spurious events, generate LEB (“ground truth”)
Unreliable below magnitude 4 (1kT)
Solve it by global probabilistic inference
NET-VISA finds around 88% of significant events

54. 12/1/2018 3:35:23 PM

55. 12/1/2018 3:35:23 PM

56. 12/1/2018 3:35:23 PM

57. 12/1/2018 3:35:23 PM

58. 12/1/2018 3:35:23 PM

59. 12/1/2018 3:35:23 PM

60. 12/1/2018 3:35:23 PM

61. 12/1/2018 3:35:23 PM

62. 12/1/2018 3:35:23 PM

63. 12/1/2018 3:35:23 PM

64. Generative model for IDC arrival data
12/1/2018 3:35:23 PM
Events occur in time and space with magnitude
Natural spatial distribution a mixture of Fisher-Binghams
Man-made spatial distribution uniform
Time distribution Poisson with given spatial intensity
Magnitude distribution Gutenberg-Richter (exponential)
Aftershock distribution (not yet implemented)
Travel time according to IASPEI91 model plus Laplacian error distribution for each of 14 phases
Detection depends on magnitude, distance, station*
Detected azimuth, slowness plus Laplacian error
False detections with station-dependent distribution

65. # SeismicEvents ~ Poisson[TIME_DURATION*EVENT_RATE];
12/1/2018 3:35:23 PM
# SeismicEvents ~ Poisson[TIME_DURATION*EVENT_RATE];
IsEarthQuake(e) ~ Bernoulli(.999);
EventLocation(e) ~ If IsEarthQuake(e) then EarthQuakeDistribution()
Else UniformEarthDistribution();
Magnitude(e) ~ Exponential(log(10)) + MIN_MAG;
Distance(e,s) = GeographicalDistance(EventLocation(e), SiteLocation(s));
IsDetected(e,p,s) ~ Logistic[SITE_COEFFS(s,p)](Magnitude(e), Distance(e,s);
#Arrivals(site = s) ~ Poisson[TIME_DURATION*FALSE_RATE(s)];
#Arrivals(event=e, site) = If IsDetected(e,s) then 1 else 0;
Time(a) ~ If (event(a) = null) then Uniform(0,TIME_DURATION)
else IASPEI(EventLocation(event(a)),SiteLocation(site(a)),Phase(a)) + TimeRes(a);
TimeRes(a) ~ Laplace(TIMLOC(site(a)), TIMSCALE(site(a)));
Azimuth(a) ~ If (event(a) = null) then Uniform(0, 360)
else GeoAzimuth(EventLocation(event(a)),SiteLocation(site(a)) + AzRes(a);
AzRes(a) ~ Laplace(0, AZSCALE(site(a)));
Slow(a) ~ If (event(a) = null) then Uniform(0,20)
else IASPEI-SLOW(EventLocation(event(a)),SiteLocation(site(a)) + SlowRes(site(a));

66. Forward model structure
12/1/2018 3:35:23 PM
Seismic event
Seismic event
Propagation
Propagation
Detected at
Station 1?
Detected at
Station 2?
Station 1
noise
Station 2
noise
Station 1
picks
Station 2
picks

67. Forward model structure
12/1/2018 3:35:23 PM
Seismic event
Seismic event
Type
Time
Location
Depth
Magnitude
Phase
Propagation
Propagation
Detected at
Station 1?
Detected at
Station 2?
Station 1
noise
Station 2
noise
Station 1
picks
Station 2
picks

68. Forward model structure
12/1/2018 3:35:23 PM
Seismic event
Seismic event
Propagation
Propagation
Detected at
Station 1?
Travel time
Amplitude decay
Detected at
Station 2?
Station 1
noise
Station 2
noise
Station 1
picks
Station 2
picks

69. Forward model structure
12/1/2018 3:35:23 PM
Seismic event
Seismic event
Propagation
Propagation
Detected at
Station 1?
Detected at
Station 2?
Arrival time*
Amplitude*
Azimuth*
Slowness*
Phase*
Station 1
noise
Station 2
noise
Station 1
picks
Station 2
picks

70. Forward model structure
12/1/2018 3:35:23 PM
Seismic event
Seismic event
Propagation
Propagation
Detected at
Station 1?
Detected at
Station 2?
Station 1
noise
Station 2
noise
Station 1
picks
Station 2
picks

71. 12/1/2018 3:35:23 PM

72. 12/1/2018 3:35:23 PM

73. Forward model structure
12/1/2018 3:35:23 PM
Seismic event
Seismic event
Propagation
Propagation
Detected at
Station 1?
Detected at
Station 2?
Station 1
noise
Station 2
noise
Station 1
picks
Station 2
picks

74. Travel-time residual (station 6)
12/1/2018 3:35:23 PM

75. Forward model structure
12/1/2018 3:35:23 PM
Seismic event
Seismic event
Propagation
Propagation
Detected at
Station 1?
Detected at
Station 2?
Station 1
noise
Station 2
noise
Station 1
picks
Station 2
picks

76. Detection probability as a function of distance (station 6, mb 3.5)
12/1/2018 3:35:23 PM
Detection probability as a function of distance (station 6, mb 3.5)
S phase
P phase

77. Forward model structure
12/1/2018 3:35:23 PM
Seismic event
Seismic event
Propagation
Propagation
Detected at
Station 1?
Detected at
Station 2?
Station 1
noise
Station 2
noise
Station 1
picks
Station 2
picks

78. Overall Pick Error
12/1/2018 3:35:23 PM

79. Overall Azimuth Error
12/1/2018 3:35:23 PM

80. Phase confusion matrix
12/1/2018 3:35:23 PM

81. Fraction of LEB events missed
12/1/2018 3:35:23 PM

82. Fraction of LEB events missed
12/1/2018 3:35:23 PM

83. Event distribution: LEB vs SEL3
12/1/2018 3:35:23 PM
Event distribution: LEB vs SEL3

84. Event distribution: LEB vs NET-VISA
12/1/2018 3:35:23 PM

85. Why does NET-VISA work?
12/1/2018 3:35:23 PM
Multiple empirically calibrated seismological models
Improving model structure and quality improves the results
Sound Bayesian combination of evidence
Measured arrival times, phase labels, azimuths, etc., NOT taken literally
Absence of detections provides negative evidence
More detections per event than SEL3 or LEB

86. Example of using extra detections
12/1/2018 3:35:23 PM

87. NEIC event (3.0) missed by LEB
12/1/2018 3:35:23 PM
>python debug.py 15 visa 254 -w 4 -r .1 87

88. NEIC event (3.7) missed by LEB
12/1/2018 3:35:23 PM
python debug.py 15 visa w 4 -r .1 88

89. NEIC event (2.6) missed by LEB
12/1/2018 3:35:23 PM
python debug.py 15 visa w 4 -r .1 89

90. Why does NET-VISA not work (perfectly)?
12/1/2018 3:35:23 PM
Needs hydroacoustic for mid-ocean events
Weaknesses in model:
Travel time residuals for all phases along a single path are assumed to be uncorrelated
Each phase arrival is assumed to generate at most one detection; in fact, multiple detections occur
Arrival detectors use high SNR thresholds, look only at local signal to make hard decisions

91. Detection-based and signal-based monitoring
12/1/2018 3:35:23 PM
events
SEL NET-VISA SIG-VISA
detections
waveform signals

92. Summary Expressive probability models are very useful
12/1/2018 3:35:23 PM
Expressive probability models are very useful
BLOG provides a generative language for defining first-order, open-universe models
Inference via MCMC over possible worlds
Other methods welcome!
CTBT application is typical of multi-sensor monitoring applications that need vertical integration and involve data association
Scaling up inference is the next step