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Title: CS194-10 Fall 2011 Introduction to Machine Learning Machine Learning: An Overview


1
CS194-10 Fall 2011Introduction to Machine
LearningMachine Learning An Overview
2
People
Avital Steinitz 2nd year CS PhD student
Stuart Russell 30th-year CS PhD student
Mert Pilanci 2nd year EE PhD student
3
Administrative details
  • Web page
  • Newsgroup

4
Course outline
  • Overview of machine learning (today)
  • Classical supervised learning
  • Linear regression, perceptrons, neural nets,
    SVMs, decision trees, nearest neighbors, and all
    that
  • A little bit of theory, a lot of applications
  • Learning probabilistic models
  • Probabilistic classifiers (logistic regression,
    etc.)
  • Unsupervised learning, density estimation, EM
  • Bayes net learning
  • Time series models
  • Dimensionality reduction
  • Gaussian process models
  • Language models
  • Bandits and other exciting topics

5
Lecture outline
  • Goal Provide a framework for understanding all
    the detailed content to come, and why it matters
  • Learning why and how
  • Supervised learning
  • Classical finding simple, accurate hypotheses
  • Probabilistic finding likely hypotheses
  • Bayesian updating belief in hypotheses
  • Data and applications
  • Expressiveness and cumulative learning
  • CTBT

6
Learning is.
  • a computational process for improving
    performance based on experience

7
Learning Why?
8
Learning Why?
  • The baby, assailed by eyes, ears, nose, skin, and
    entrails at once, feels it all as one great
    blooming, buzzing confusion
  • William James, 1890

9
Learning Why?
  • The baby, assailed by eyes, ears, nose, skin, and
    entrails at once, feels it all as one great
    blooming, buzzing confusion
  • William James, 1890

Learning is essential for unknown environments,
i.e., when the designer lacks omniscience
10
Learning Why?
  • Instead of trying to produce a programme to
    simulate the adult mind, why not rather try to
    produce one which simulates the child's? If this
    were then subjected to an appropriate course of
    education one would obtain the adult brain.
    Presumably the child brain is something like a
    notebook as one buys it from the stationer's.
    Rather little mechanism, and lots of blank
    sheets.
  • Alan Turing, 1950
  • Learning is useful as a system construction
    method, i.e., expose the system to reality rather
    than trying to write it down

11
Learning How?
12
Learning How?
13
Learning How?
14
Learning How?
15
Structure of a learning agent
16
Design of learning element
  • Key questions
  • What is the agent design that will implement the
    desired performance?
  • Improve the performance of what piece of the
    agent system and how is that piece represented?
  • What data are available relevant to that piece?
    (In particular, do we know the right answers?)
  • What knowledge is already available?

17
Examples
Agent design Component Representation Feedback Knowledge
Alpha-beta search Evaluation function Linear polynomial Win/loss Rules of game Coefficient signs
Logical planning agent Transition model (observable envt) Successor-state axioms Action outcomes Available actions Argument types
Utility-based patient monitor Physiology/sensor model Dynamic Bayesian network Observation sequences Gen physiology Sensor design
Satellite image pixel classifier Classifier (policy) Markov random field Partial labels Coastline Continuity scales

Supervised learning correct answers for each
training instance Reinforcement learning reward
sequence, no correct answers Unsupervised
learning just make sense of the data
18
Supervised learning
  • To learn an unknown target function f
  • Input a training set of labeled examples (xj,yj)
    where yj f(xj)
  • E.g., xj is an image, f(xj) is the label
    giraffe
  • E.g., xj is a seismic signal, f(xj) is the label
    explosion
  • Output hypothesis h that is close to f, i.e.,
    predicts well on unseen examples (test set)
  • Many possible hypothesis families for h
  • Linear models, logistic regression, neural
    networks, decision trees, examples
    (nearest-neighbor), grammars, kernelized
    separators, etc etc

19
Supervised learning
  • To learn an unknown target function f
  • Input a training set of labeled examples
    (xj,yj) where yj f(xj)
  • E.g., xj is an image, f(xj) is the label
    giraffe
  • E.g., xj is a seismic signal, f(xj) is the label
    explosion
  • Output hypothesis h that is close to f, i.e.,
    predicts well on unseen examples (test set)
  • Many possible hypothesis families for h
  • Linear models, logistic regression, neural
    networks, decision trees, examples
    (nearest-neighbor), grammars, kernelized
    separators, etc etc

20
Supervised learning
  • To learn an unknown target function f
  • Input a training set of labeled examples
    (xj,yj) where yj f(xj)
  • E.g., xj is an image, f(xj) is the label
    giraffe
  • E.g., xj is a seismic signal, f(xj) is the label
    explosion
  • Output hypothesis h that is close to f, i.e.,
    predicts well on unseen examples (test set)
  • Many possible hypothesis families for h
  • Linear models, logistic regression, neural
    networks, decision trees, examples
    (nearest-neighbor), grammars, kernelized
    separators, etc etc

21
Example object recognition
x
f(x)
giraffe
giraffe
giraffe
llama
llama
llama
22
Example object recognition
x
f(x)
giraffe
giraffe
giraffe
llama
llama
llama
X
f(x)?
23
Example curve fitting
24
Example curve fitting
25
Example curve fitting
26
Example curve fitting
27
Example curve fitting
28
Basic questions
  • Which hypothesis space H to choose?
  • How to measure degree of fit?
  • How to trade off degree of fit vs. complexity?
  • Ockhams razor
  • How do we find a good h?
  • How do we know if a good h will predict well?

29
Philosophy of Science (Physics)
  • Which hypothesis space H to choose?
  • Deterministic hypotheses, usually mathematical
    formulas and/or logical sentences implicit
    relevance determination
  • How to measure degree of fit?
  • Ideally, h will be consistent with data
  • How to trade off degree of fit vs. complexity?
  • Theory must be correct up to experimental error
  • How do we find a good h?
  • Intuition, imagination, inspiration (invent new
    terms!!)
  • How do we know if a good h will predict well?
  • Humes Problem of Induction most philosophers
    give up

30
Kolmogorov complexity (also MDL, MML)
  • Which hypothesis space H to choose?
  • All Turing machines (or programs for a UTM)
  • How to measure degree of fit?
  • Fit is perfect (program has to output data
    exactly)
  • How to trade off degree of fit vs. complexity?
  • Minimize size of program
  • How do we find a good h?
  • Undecidable (unless we bound time complexity of
    h)
  • How do we know if a good h will predict well?
  • (recent theory borrowed from PAC learning)

31
Classical stats/ML Minimize loss function
  • Which hypothesis space H to choose?
  • E.g., linear combinations of features hw(x)
    wTx
  • How to measure degree of fit?
  • Loss function, e.g., squared error Sj (yj wTx)2
  • How to trade off degree of fit vs. complexity?
  • Regularization complexity penalty, e.g., w2
  • How do we find a good h?
  • Optimization (closed-form, numerical) discrete
    search
  • How do we know if a good h will predict well?
  • Try it and see (cross-validation, bootstrap,
    etc.)

32
Probabilistic Max. likelihood, max. a priori
  • Which hypothesis space H to choose?
  • Probability model P(y x,h) , e.g., Y
    N(wTx,s2)
  • How to measure degree of fit?
  • Data likelihood ?j P(yj xj,h)
  • How to trade off degree of fit vs. complexity?
  • Regularization or prior argmaxh P(h) ?j P(yj
    xj,h) (MAP)
  • How do we find a good h?
  • Optimization (closed-form, numerical) discrete
    search
  • How do we know if a good h will predict well?
  • Empirical process theory (generalizes Chebyshev,
    CLT, PAC)
  • Key assumption is (i)id

33
Bayesian Computing posterior over H
  • Which hypothesis space H to choose?
  • All hypotheses with nonzero a priori probability
  • How to measure degree of fit?
  • Data probability, as for MLE/MAP
  • How to trade off degree of fit vs. complexity?
  • Use prior, as for MAP
  • How do we find a good h?
  • Dont! Bayes predictor P(yx,D) Sh P(yx,h)
    P(Dh) P(h)
  • How do we know if a good h will predict well?
  • Silly question! Bayesian prediction is optimal!!

34
Bayesian Computing posterior over H
  • Which hypothesis space H to choose?
  • All hypotheses with nonzero a priori probability
  • How to measure degree of fit?
  • Data probability, as for MLE/MAP
  • How to trade off degree of fit vs. complexity?
  • Use prior, as for MAP
  • How do we find a good h?
  • Dont! Bayes predictor P(yx,D) Sh P(yx,h)
    P(Dh) P(h)
  • How do we know if a good h will predict well?
  • Silly question! Bayesian prediction is optimal!!

35
Neon sculpture at Autonomy Corp.
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37
Lots of data
  • Web estimated Google index 45 billion pages
  • Clickstream data 10-100 TB/day
  • Transaction data 5-50 TB/day
  • Satellite image feeds 1TB/day/satellite
  • Sensor networks/arrays
  • CERN Large Hadron Collider 100 petabytes/day
  • Biological data 1-10TB/day/sequencer
  • TV 2TB/day/channel YouTube 4TB/day uploaded
  • Digitized telephony 100 petabytes/day

38
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Real data are messy
40
Arterial blood pressure (high/low/mean) 1s
41
Application satellite image analysis
42
Application Discovering DNA motifs
  • ...TTGGAACAACCATGCACGGTTGATTCGTGCCTGTGACCGCGCGCCTC
    ACACGGAAGACGCAGCCACCGGTTGTGATG
  • TCATAGGGAATTCCCCATGTCGTGAATAATGCCTCGAATGATGAGTAATA
    GTAAAACGCAGGGGAGGTTCTTCAGTAGTA
  • TCAATATGAGACACATACAAACGGGCGTACCTACCGCAGCTCAAAGCTGG
    GTGCATTTTTGCCAAGTGCCTTACTGTTAT
  • CTTAGGACGGAAATCCACTATAAGATTATAGAAAGGAAGGCGGGCCGAGC
    GAATCGATTCAATTAAGTTATGTCACAAGG
  • GTGCTATAGCCTATTCCTAAGATTTGTACGTGCGTATGACTGGAATTAAT
    AACCCCTCCCTGCACTGACCTTGACTGAAT
  • AACTGTGATACGACGCAAACTGAACGCTGCGGGTCCTTTATGACCACGGA
    TCACGACCGCTTAAGACCTGAGTTGGAGTT
  • GATACATCCGGCAGGCAGCCAAATCTTTTGTAGTTGAGACGGATTGCTAA
    GTGTGTTAACTAAGACTGGTATTTCCACTA
  • GGACCACGCTTACATCAGGTCCCAAGTGGACAACGAGTCCGTAGTATTGT
    CCACGAGAGGTCTCCTGATTACATCTTGAA
  • GTTTGCGACGTGTTATGCGGATGAAACAGGCGGTTCTCATACGGTGGGGC
    TGGTAAACGAGTTCCGGTCGCGGAGATAAC
  • TGTTGTGATTGGCACTGAAGTGCGAGGTCTTAAACAGGCCGGGTGTACTA
    ACCCAAAGACCGGCCCAGCGTCAGTGA...

43
Application Discovering DNA motifs
  • ...TTGGAACAACCATGCACGGTTGATTCGTGCCTGTGACCGCGCGCCTC
    ACACGGAAGACGCAGCCACCGGTTGTGATG
  • TCATAGGGAATTCCCCATGTCGTGAATAATGCCTCGAATGATGAGTAATA
    GTAAAACGCAGGGGAGGTTCTTCAGTAGTA
  • TCAATATGAGACACATACAAACGGGCGTACCTACCGCAGCTCAAAGCTGG
    GTGCATTTTTGCCAAGTGCCTTACTGTTAT
  • CTTAGGACGGAAATCCACTATAAGATTATAGAAAGGAAGGCGGGCCGAGC
    GAATCGATTCAATTAAGTTATGTCACAAGG
  • GTGCTATAGCCTATTCCTAAGATTTGTACGTGCGTATGACTGGAATTAAT
    AACCCCTCCCTGCACTGACCTTGACTGAAT
  • AACTGTGATACGACGCAAACTGAACGCTGCGGGTCCTTTATGACCACGGA
    TCACGACCGCTTAAGACCTGAGTTGGAGTT
  • GATACATCCGGCAGGCAGCCAAATCTTTTGTAGTTGAGACGGATTGCTAA
    GTGTGTTAACTAAGACTGGTATTTCCACTA
  • GGACCACGCTTACATCAGGTCCCAAGTGGACAACGAGTCCGTAGTATTGT
    CCACGAGAGGTCTCCTGATTACATCTTGAA
  • GTTTGCGACGTGTTATGCGGATGAAACAGGCGGTTCTCATACGGTGGGGC
    TGGTAAACGAGTTCCGGTCGCGGAGATAAC
  • TGTTGTGATTGGCACTGAAGTGCGAGGTCTTAAACAGGCCGGGTGTACTA
    ACCCAAAGACCGGCCCAGCGTCAGTGA...

44
Application User website behavior from
clickstream data (from P. Smyth, UCI)
128.195.36.195, -, 3/22/00, 103511, W3SVC,
SRVR1, 128.200.39.181, 781, 363, 875, 200, 0,
GET, /top.html, -, 128.195.36.195, -, 3/22/00,
103516, W3SVC, SRVR1, 128.200.39.181, 5288,
524, 414, 200, 0, POST, /spt/main.html, -,
128.195.36.195, -, 3/22/00, 103517, W3SVC,
SRVR1, 128.200.39.181, 30, 280, 111, 404, 3, GET,
/spt/images/bk1.jpg, -, 128.195.36.101, -,
3/22/00, 161850, W3SVC, SRVR1, 128.200.39.181,
60, 425, 72, 304, 0, GET, /top.html, -,
128.195.36.101, -, 3/22/00, 161858, W3SVC,
SRVR1, 128.200.39.181, 8322, 527, 414, 200, 0,
POST, /spt/main.html, -, 128.195.36.101, -,
3/22/00, 161859, W3SVC, SRVR1, 128.200.39.181,
0, 280, 111, 404, 3, GET, /spt/images/bk1.jpg, -,
128.200.39.17, -, 3/22/00, 205437, W3SVC,
SRVR1, 128.200.39.181, 140, 199, 875, 200, 0,
GET, /top.html, -, 128.200.39.17, -, 3/22/00,
205455, W3SVC, SRVR1, 128.200.39.181, 17766,
365, 414, 200, 0, POST, /spt/main.html, -,
128.200.39.17, -, 3/22/00, 205455, W3SVC,
SRVR1, 128.200.39.181, 0, 258, 111, 404, 3, GET,
/spt/images/bk1.jpg, -, 128.200.39.17, -,
3/22/00, 205507, W3SVC, SRVR1, 128.200.39.181,
0, 258, 111, 404, 3, GET, /spt/images/bk1.jpg, -,
128.200.39.17, -, 3/22/00, 205536, W3SVC,
SRVR1, 128.200.39.181, 1061, 382, 414, 200, 0,
POST, /spt/main.html, -, 128.200.39.17, -,
3/22/00, 205536, W3SVC, SRVR1, 128.200.39.181,
0, 258, 111, 404, 3, GET, /spt/images/bk1.jpg, -,
128.200.39.17, -, 3/22/00, 205539, W3SVC,
SRVR1, 128.200.39.181, 0, 258, 111, 404, 3, GET,
/spt/images/bk1.jpg, -, 128.200.39.17, -,
3/22/00, 205603, W3SVC, SRVR1, 128.200.39.181,
1081, 382, 414, 200, 0, POST, /spt/main.html, -,
128.200.39.17, -, 3/22/00, 205604, W3SVC,
SRVR1, 128.200.39.181, 0, 258, 111, 404, 3, GET,
/spt/images/bk1.jpg, -, 128.200.39.17, -,
3/22/00, 205633, W3SVC, SRVR1, 128.200.39.181,
0, 262, 72, 304, 0, GET, /top.html, -,
128.200.39.17, -, 3/22/00, 205652, W3SVC,
SRVR1, 128.200.39.181, 19598, 382, 414, 200, 0,
POST, /spt/main.html, -,
3
3
3
3
1
3
1
1
1
3
3
3
2
2
3
2
User 1
1
1
1
3
3
3
User 2
User 3
7
7
7
7
7
7
7
7
1
1
1
1
1
1
5
1
5
1
1
1
5
1
User 4
5
1
1
5
User 5


45
Application social network analysis
HP Labs email data 500 users, 20k
connections evolving over time
46
Application spam filtering
  • 200 billion spam messages sent per day
  • Asymmetric cost of false positive/false negative
  • Weak label discarded without reading
  • Strong label (this is spam) hard to come by
  • Standard iid assumption violated spammers alter
    spam generators to evade or subvert spam filters
    (adversarial learning task)

47
Learning
Learning
knowledge
data
48
Learning
prior knowledge
Learning
knowledge
data
49
Learning
prior knowledge
Learning
knowledge
data
50
Learning
prior knowledge
Learning
knowledge
data
Crucial open problem weak intermediate forms of
knowledge that support future generalizations
51
Example
52
Example
53
Example
54
Example arriving at Sao Paulo, Brazil
Bem-vindo!
55
Example arriving at Sao Paulo, Brazil
Bem-vindo!
56
Example arriving at Sao Paulo, Brazil
Bem-vindo!
Bem-vindo!
57
Example arriving at Sao Paulo, Brazil
Bem-vindo!
Bem-vindo!
58
Weak prior knowledge
  • In this case, people in a given country (and
    city) tend to speak the same language
  • Where did this knowledge come from?

59
Weak prior knowledge
  • In this case, people in a given country (and
    city) tend to speak the same language
  • Where did this knowledge come from?
  • Experience with other countries
  • Common sense i.e., knowledge of how societies
    and languages work

60
Weak prior knowledge
  • In this case, people in a given country (and
    city) tend to speak the same language
  • Where did this knowledge come from?
  • Experience with other countries
  • Common sense i.e., knowledge of how societies
    and languages work
  • And where did that knowledge come from?

61
Knowledge? What is knowledge? All I know is
samples!! V. Vapnik
  • All knowledge derives, directly or indirectly,
    from experience of individuals
  • Knowledge serves as a directly applicable
    shorthand for all that experience better than
    requiring constant review of the entire
    sensory/evolutionary history of the human race

62
Expressiveness
63
The world has things in it!!
  • Expressive language gt concise models
  • gt fast learning, sometimes fast reasoning
  • E.g., rules of chess
  • 1 page in first-order logic
  • On(color,piece,x,y,t)
  • 100000 pages in propositional logic
  • WhiteKingOnC4Move12
  • 100000000000000000000000000000000000000 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

64
Brief history of expressiveness
probability
logic
atomic
propositional
first-order/relational
65
Brief history of expressiveness
probability
5th C B.C.
logic
atomic
propositional
first-order/relational
66
Brief history of expressiveness
17th C
probability
5th C B.C.
logic
atomic
propositional
first-order/relational
67
Brief history of expressiveness
17th C
probability
5th C B.C.
19th C
logic
atomic
propositional
first-order/relational
68
Brief history of expressiveness
17th C
20th C
probability
5th C B.C.
19th C
logic
atomic
propositional
first-order/relational
69
Brief history of expressiveness
17th C
20th C
21st C
probability
5th C B.C.
19th C
logic
atomic
propositional
first-order/relational
70
Brief history of expressiveness
Bernoulli Categorical Uni. Gaussian (H)MMs
Bayes nets MRFs Multi. Gaussians DBNs Kalman
filters
RPMs BLOG MLNs (DBLOG)
probability
First-order logic Database systems Programs First-
order STRIPS Temporal logic
OBDDs, k-CNF Decision trees Perceptrons Propositio
nal STRIPS Register circuits
Finite automata
logic
atomic
propositional
first-order/relational
71
CTBT Comprehensive Nuclear-Test-Ban Treaty
  • 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

72
2053 nuclear explosions
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254 monitoring stations
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The problem
  • Given waveform traces from all seismic stations,
    figure out what events occurred when and where
  • Traces at each sensor station may be preprocessed
    to form detections (90 are not real)
  • ARID ORID STA PH BEL DELTA
    SEAZ ESAZ TIME TDEF AZRES
    ADEF SLORES SDEF WGT VMODEL
    LDDATE
  • 49392708 5295499 WRA P -1.0 23.673881 342.00274
    163.08123 0.19513991 d -1.2503497 d 0.24876981
    d -999.0 0.61806399 IASP 2009-04-02 125427
  • 49595064 5295499 FITZ P -1.0 20.835616
    4.3960142 184.18581 1.2515257 d 2.7290018 d
    5.4541182 n -999.0 0.46613527 IASP 2009-04-02
    125427
  • 49674189 5295499 MKAR P -1.0 58.574266 124.26633
    325.35514 -0.053738765 d -4.6295428 d 1.5126035
    d -999.0 0.76750542 IASP 2009-04-02 125427
  • 49674227 5295499 ASAR P -1.0 27.114852 345.18433
    166.42383 -0.71255454 d -6.4901126 d 0.95510033
    d -999.0 0.66453657 IASP 2009-04-02 125427

77
What do we know?
  • Events happen randomly each has a time,
    location, depth, magnitude seismicity varies
    with location
  • Seismic waves of many kinds (phases) travel
    through the Earth
  • Travel time and attenuation depend on phase and
    source/destination
  • Arriving waves may or may not be detected,
    depending on sensor and local noise environment
  • Local noise may also produce false detections

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  • SeismicEvents PoissonTIME_DURATIONEVENT_RATE
  • IsEarthQuake(e) Bernoulli(.999)
  • EventLocation(e) If IsEarthQuake(e) then
    EarthQuakeDistribution()
  • Else UniformEarthDistrib
    ution()
  • Magnitude(e) Exponential(log(10)) MIN_MAG
  • Distance(e,s) GeographicalDistance(EventLocation
    (e), SiteLocation(s))
  • IsDetected(e,p,s) LogisticSITE_COEFFS(s,p)(Mag
    nitude(e), Distance(e,s)
  • Arrivals(site s) PoissonTIME_DURATIONFALSE_
    RATE(s)
  • Arrivals(evente, 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)),SiteLoca
    tion(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)),SiteLocat
    ion(site(a)) SlowRes(site(a))

89
Learning with prior knowledge
  • Instead of learning a mapping from detection
    histories to event bulletins, learn local pieces
    of an overall structured model
  • Event location prior (A6)
  • Predictive travel time model (A1)
  • Phase type classifier (A2)

90
Event location prior (A6)
91
Travel time prediction (A1)
  • How long does it take for a seismic signal to get
    from A to B? This is the travel time T(A,B)
  • If we know this accurately, and we know the
    arrival times t1, t2, t3, at several stations
    B1, B2, B3, , we can find an accurate estimate
    of the location A and time t for the event, such
    that
  • T(A,Bi) ti t for all i

92
Earth 101
93
Seismic phases (wave types/paths)
  • Seismic energy is emitted in different types of
    waves there are also qualitatively distinct
    paths (e.g., direct vs reflected from surface vs.
    refracted through core). P and S are the direct
    waves P is faster

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IASP 91 reference velocity model
  • Spherically symmetric, Vphase(depth) from this,
    obtain Tpredicted(A,B).

96
IASP91 inaccuracy is too big!
  • Earth is inhomogeneous variations in crust
    thickness and rock properties (fast and slow)

97
Travel time residuals (Tactual Tpredicted)
  • Residual surface (wrt a particular station) is
    locally smooth estimate by local regression
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