modern machine learning: new challenges and...
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Modern Machine Learning: New Challenges and Connections
Maria-Florina Balcan
Machine Learning is Changing the World
“A breakthrough in machine learning would be worth ten Microsofts” (Bill Gates, Microsoft)
“Machine learning is the hot new thing” (John Hennessy, President, Stanford)
“Web rankings today are mostly a matter of machine learning” (Prabhakar Raghavan, VP Engineering at Google)
The World is Changing Machine Learning
New applications Explosion of data
Modern applications: massive amounts of raw data.
Only a tiny fraction can be annotated by human experts.
Billions of webpages Images Protein sequences
Modern ML: New Learning Approaches
Modern applications: massive amounts of raw data.
Modern ML: New Learning Approaches
Expert
• Semi-supervised Learning, (Inter)active Learning.
Techniques that best utilize data, minimizing need for
expert/human intervention.
Modern applications: massive amounts of data
distributed across multiple locations.
Modern ML: New Learning Approaches
Modern ML: New Learning Approaches
• scientific data
Key new resource communication.
• video data
E.g.,
Modern applications: massive amounts of data
distributed across multiple locations.
The World is Changing Machine Learning
Resource constraints. E.g.,
• Computational efficiency (noise tolerant algos)
• Communication
• Human labeling effort
• Statistical efficiency
• Privacy/Incentives
New approaches. E.g.,
• Semi-supervised learning
• Distributed learning
• Interactive learning
• Multi-task/transfer learning
• Never ending learning
• Community detection
A2 Â
The World is Changing Machine Learning
My research: foundations, robust algorithms.
Applications: vision, comp. biology, social networks.
New approaches. E.g.,
• Semi-supervised learning
• Distributed learning
• Interactive learning
• Never ending learning
• Community detection
• Multi-task/transfer learning
Machine Learning is Changing the World
My research: MLT way to model and tackle challenges other fields. E.g.,
Game Theory Approximation Algorithms
Matroid Theory
Machine Learning Theory
Discrete Optimization
Mechanism Design
Control Theory
• Machine Learning Lenses in Other Areas
Outline of the talk
• Modern Learning Paradigms
• Interactive Learning
• Submodularity, implications to Matroid Theory, Algorithmic Game Theory, Optimization
;
V
• Discussion, Other Exciting Directions
Supervised Learning • E.g., which emails are spam and which are important.
Not spam spam
• E.g., classify objects as chairs vs non chairs.
Not chair chair
Labeled Examples
Learning Algorithm
Expert / Oracle
Data Source
c* : X ! {0,1}
h : X ! {0,1}
(x1,c*(x1)),…, (xm,c*(xm))
• Algo sees (x1,c*(x1)),…, (xm,c*(xm)), xi i.i.d. from D
Distribution D on X
Statistical / PAC learning model
+
+
- - + + - -
-
• Does optimization over S, finds hypothesis h 2 C.
• Goal: h has small error, err(h)=Prx 2 D(h(x) c*(x))
• c* in C, realizable case; else agnostic
14
Two Main Aspects in Classic Machine Learning
Algorithm Design. How to optimize?
Automatically generate rules that do well on observed data.
Generalization Guarantees, Sample Complexity
Confidence for rule effectiveness on future data.
E.g., Boosting, SVM, etc.
O1
ϵVCdim C log
1
ϵ+ log
1
δ
Interactive Machine Learning
• Active Learning
• Learning with more general queries; connections
Active Learning
face
O
O
O
Expert Labeler
raw data
Classifier
not face
Active Learning in Practice
• Text classification: active SVM (Tong & Koller, ICML2000).
• e.g., request label of the example closest to current separator.
• Video Segmentation (Fathi-Balcan-Ren-Regh, BMVC 11).
w
+ -
Exponential improvement.
• Sample with 1/ unlabeled examples; do binary search. -
Active: only O(log 1/) labels.
Passive supervised: (1/) labels to find an -accurate threshold.
+ -
Active Algorithm
• Canonical theoretical example [CAL92, Dasgupta04]
Provable Guarantees, Active Learning
• First noise tolerant algo [Balcan, Beygelzimer, Langford, ICML’06]
[Hanneke07, DasguptaHsuMontleoni’07, Wang’09 , Fridman’09, Koltchinskii10, BHW’08, BeygelzimerHsuLangfordZhang’10, Hsu’10, Minsker’12, Ailon’12, …]
Generic (any class), adversarial label noise.
Substantial follow-up on work.
Lots of exciting activity in recent years.
My work:
Provable Guarantees, Active Learning
• First computationally efficient algos
[Balcan-Long COLT’13] [Awasthi-Balcan-Long STOC’14]
Margin Based Active Learning
• Realizable: exponential improvement in label complex. over passive [only O(d log 1/) labels to find w error ].
[Balcan-Long COLT’13] [Awasthi-Balcan-Long STOC’14]
Learning linear separators, when D logconcave in Rd.
• Agnostic: poly-time AL algo outputs w with err(w) =O(´), ´ =err(best lin. sep).
+
+
- - + + - -
-
• Unexpected Implications for Passive Learning!
• Computational complexity: improves significantly on the best guarantees known for passive [KKMS’05], [KLS’09].
• Sample complexity: resolves open question about ERM.
Margin Based Active-Learning, Realizable Case
Draw m1 unlabeled examples, label them, add them to W(1). iterate k = 2, …, s
• find a hypothesis wk-1 consistent with W(k-1).
• W(k)=W(k-1).
• sample mk unlabeled samples x
satisfying |wk-1T ¢ x| · k-1
• label them and add them to W(k).
w1
1
w2
2
w3
Log-concave distributions: log of density fnc concave.
• wide class: uniform distr. over any convex set, Gaussian, etc.
Theorem If then err(ws)· D log-concave in Rd.
after
Active learning Passive learning
rounds using
label requests label requests
unlabeled examples
labels per round.
Margin Based Active-Learning, Realizable Case
Analysis: Aggressive Localization
Induction: all w consistent with W(k), err(w) · 1/2k
w
w*
Analysis: Aggressive Localization
Induction: all w consistent with W(k), err(w) · 1/2k
wk-1
w
k-1
w*
Suboptimal
wk-1
w
k-1
w*
Analysis: Aggressive Localization
Induction: all w consistent with W(k), err(w) · 1/2k
wk-1
w
k-1
w*
· 1/2k+1
Analysis: Aggressive Localization
Induction: all w consistent with W(k), err(w) · 1/2k
wk-1
w
k-1
w*
· 1/2k+1
Enough to ensure
Need only labels in round k.
Localization in concept space.
Margin Based Active-Learning, Agnostic Case
Draw m1 unlabeled examples, label them, add them to W.
Localization in instance space.
iterate k=2, …, s
• find wk-1 in B(wk-1, rk-1) of small
tk-1 hinge loss wrt W. • Clear working set.
• sample mk unlabeled samples x
satisfying |wk-1 ¢ x| · k-1 ;
• label them and add them to W.
end iterate
• Analysis: exploit localization & variance analysis control the gap between hinge loss and 0/1 loss in each round.
Improves over Passive Learning too!
Passive Learning
Prior Work
Our Work
Malicious
Agnostic
Active Learning [agnostic/malicious]
[KLS’09]
NA
[KLS’09]
err(w) = 𝑂 𝜂 log21
𝜂 err(w) = 𝑂 𝜂1/3 log2/3
𝑑
𝜂
err(w) = 𝑂 𝜂1/3 log1/31
𝜂 err(w) = 𝑂 𝜂 log2
1
𝜂
err(w) = 𝑂 𝜂 log21
𝜂
Improves over Passive Learning too!
Passive Learning
Prior Work
Our Work
Malicious
Agnostic
Active Learning [agnostic/malicious]
Info theoretic optimal
[KKMS’05]
[KLS’09]
[KKMS’05]
NA Info theoretic optimal
Slightly better results for the uniform distribution case.
err(w) = 𝑂(𝜂)
err(w) = 𝑂(𝜂)
err(w) = 𝑂(𝜂)
err(w) = 𝑂(𝜂𝑑1/4)
err(w) = 𝑂 𝜂 log (1/𝜂)
err(w) = 𝑂 𝜂 log (𝑑/𝜂)
Useful for active and passive learning!
Localization both algorithmic and analysis tool!
Important direction: richer interactions with the expert.
Expert
Fewer queries
Natural interaction
Better Accuracy
raw data
Expert Labeler
Classifier
New Types of Interaction
Class Conditional Query
Mistake Query raw data
Expert Labeler
) Classifier
dog cat penguin
wolf
Class Conditional & Mistake Queries
• Used in practice, e.g. Faces in IPhoto.
• Lack of theoretical understanding.
• Realizable (Folklore): much fewer queries than label requests.
[Balcan-Hanneke COLT’12]
Tight bounds on the number of CCQs to learn in the presence of noise (agnostic and bounded noise)
Our Work
Important direction: richer interactions with the expert.
Expert
Fewer queries
Natural interaction
Better Accuracy
3.5
2.4
9.1
Interaction for Faster Algorithms
E.g., clustering protein sequences by function
Expert an expensive computer program.
Voevodski-Balcan-Roglin-Teng-Xia, [UAI 10, SIMBAD 11, JMLR’12]
• Strong guarantees under natural stability condition:
produce accurate clusterings with only k one-vs-all queries.
• BLAST to computes similarity to all other objects in
dataset (one-vs-all queries).
• Better accuracy than state of the art techniques using limited info on standard datasets (pFam and SCOP datasets).
Voevodski-Balcan-Roglin-Teng-Xia [UAI 10, SIMBAD 11, JMLR’12]
Better accuracy than state of the art techniques using limited info on standard datasets (pFam and SCOP datasets).
Interaction for Faster Algorithms
Interactive Learning
• First noise tolerant poly time, label efficient algos for high dim. cases. [BL’13] [ABL’14]
• Learning with more general queries.
• Active & Differentially Private [Balcan-Feldman, NIPS’13]
[BH’12]
• Communication complexity, distributed learning.
Cool Implications:
• Sample & computational complexity of passive learning
[Balcan-Blum-Fine-Mansour, COLT’12] Runner UP Best Paper
Summary:
Related Work:
Learning Theory Lenses on Submodularity
Submodular functions • Discrete fns that model laws of diminishing returns.
• Optimization, operations research
• Algorithmic Game Theory
• Machine Learning
[Lehman-Lehman-Nisan’01], ….
[Bilmes’03] [Guestrin-Krause’07], …
• Social Networks [Kleinberg-Kempe-Tardos’03]
[Balcan&Harvey, STOC 2011 & Necktar Track, ECML-PKDD 2012]
Novel structural results
New Lenses on Submodularity
Learning Submodular Functions
Alg. Game Theory Economics
Matroid Theory
Discrete Optimization
Applications: Economics, Social Networks, …
Submodular functions
x S T
x
+
+
Large improvement
Small improvement
For T µ S, xS, f(T [ {x}) – f(T) ¸ f(S [ {x}) – f(S)
• V={1,2, …, n}; set-function f : 2V ! R submodular if
E.g.,
+
Submodular functions
• Concave Functions Let h : R ! R be concave. For each S µ V, let f(S) = h(|S|)
• Vector Spaces Let V={v1,,vn}, each v
i 2 Rn.
For each S µ V, let f(S) = rank(V[S])
More examples:
• Coverage Fns Let A1,,An be sets. For each S µ V, let f(S) = | 𝐴𝑗𝑗∈𝑆 |
Learning submodular functions
• Influence Function in Social Networks • V = set of nodes.
• f(S) = expected influence when S is the
originating set of nodes in the difusion.
• Valuation Functions in Economics • V = all the items you sell.
• f(S) = valuation on set of items S.
PMAC model for learning real valued functions
Distribution D on 2[n]
Labeled Examples
Learning Algorithm
Expert / Oracle
Data Source
Alg.outputs f : 2[n] R+ g :2[n] R+
(S1,f(S1)),…, (Sm,f(Sm))
• Algo sees (S1,f(S1)),…, (Sm,f(Sm)), Si i.i.d. from D, produces g.
Probably Mostly Approximately Correct
• With probability ¸ 1-± we have PrS[g(S) · f(S)· ® g(S)]¸ 1-²
Learning submodular functions [BH’11]
No algo can PMAC learn the class of submodular fns with approx. factor õ(n1/3).
Theorem: (General lower bound)
Corollary: Matroid rank fns do not have a concise, approximate representation.
Surprising answer to open question in Economics of
Theorem: (General upper bound) Poly time alg. for PMAC-learning (w.r.t. an arbitrary
distribution) with an approx. factor ®=O(n1/2).
• Even if value queries allowed; even for rank fns of matroids.
Noam Nisan Paul Milgrom
A General Lower Bound
Construct a hard family of matroid rank functions.
A1 A2 AL A3
X
X X
Low=log2n
High=n1/3
X
… … …. ….
L=nlog log n
No algo can PMAC learn the class of non-neg., monotone, submodular fns with an approx. factor õ(n1/3).
Theorem
Vast generalization of partition matroids.
Exploit Additional Properties
• E.g., product distribution
• BH’11, Lipschitz submodular
• FV’13 general submodular
• Learning valuation fns from AGT and Economics.
• Learning influence function in social networks.
Learning Valuation Functions Target dependent learnability for classes from Algorithmic Game Theory and Economics
Additive µ OXS µ GS µ Submodular µ XOS µ Subadditive
XOR
OR
({1}, $2) ({2}, $5)
Romania Switzerland OR
({2}, $6) ({1}, $10) ({3}, $5)
[Balcan-Constantin-Iwata-Wang, COLT 2012]
Theorem: (Poly number of XOR trees) O(n²) approximation in time O(n1/²).
Learning the Influence Function Influence function in social networks: coverage function.
[Du, Liang, Balcan, Song 2014]
• Maximum likelihood approach; promising performance
• Memetracker Dataset, blog data cascades : “apple and jobs”, “tsunami earthquake”, “william kate marriage”
[Balcan&Harvey, STOC 2011 & Necktar Track, ECML-PKDD 2012]
Novel structural results
New Lenses on Submodularity
Learning Submodular Functions
Algo Game Theory Economics
Matroid Theory
Discrete Optimization
Follow-up work: Algo Game Theory, Machine Learning, Discrete Optimization, Privacy.
Discussion. Other Exciting Directions
• Foundations for Modern ML and Applications
Themes of My Research
Game Theory Approx. Algorithms
Matroid Theory
Machine Learning Theory
Discrete Optimization
Mechanism Design
Control Theory
• Learning Lens on Other Fields, Connections
Foundations for Modern Paradigms
Resource constraints. E.g.,
• Computational efficiency (noise tolerant algos)
• Communication
• Human labeling effort
• Statistical efficiency
• Privacy/Incentives
New approaches. E.g.,
• Semi-supervised learning
• Distributed learning
• Interactive learning
• Never ending learning
• Community detection
• Multi-task/transfer learning
Analysis Beyond the Worst Case
• Identify ways to capture structure of real world instances, analysis beyond the worst case.
• E.g., circumvent NP-hardness barriers for objective based clustering (e.g., k-means, k-median)
• Perturbation resilience: small changes
to input distances shouldn’t move
optimal solution by much.
• Approximation stability: near-optimal
solutions shouldn’t look too different from
optimal solution.
0.7
[BBG’09] [BB’09] [BRT’10] [BL’12]
Analysis Beyond the Worst Case
• Understand characteristics of practical tasks that makes them easier to learn.
• Develop learning tools that take advantage of such characteristics.
Major Direction:
• Identify ways to capture structure of real world instances, analysis beyond the worst case.
Understanding & Influencing Multi-agent Systems
What do we expect to happen?
More realistic: view agents as adapting, learning entities.
Major Question: Can we “guide” or “nudge” dynamics to high-quality states quickly [using minimal intervention]?
Traditional: analyze equilibria (static concept)
• Foundations for Modern ML and Applications
Themes of My Research
Game Theory Approx. Algorithms
Matroid Theory
Machine Learning Theory
Discrete Optimization
Mechanism Design
Control Theory
• Learning Lens on Other Fields, Connections