---
references:
- id: AbbeelLearning2006
  accessed:
    - year: 2014
      month: 8
      day: 20
  author:
    - family: Abbeel
      given: Pieter
    - family: Koller
      given: Daphne
    - family: Ng
      given: Andrew Y.
  citation-key: AbbeelLearning2006
  container-title: Journal of Machine Learning Research
  ISSN: 1532-4435
  issued:
    - year: 2006
      month: 12
  page: 1743–1788
  title: Learning Factor Graphs in Polynomial Time and Sample Complexity
  type: article-journal
  URL: http://machinelearning.wustl.edu/mlpapers/paper_files/AbbeelKN06.pdf
  volume: '7'

- id: BackursFineGrained2017
  author:
    - family: Backurs
      given: Arturs
    - family: Indyk
      given: Piotr
    - family: Schmidt
      given: Ludwig
  citation-key: BackursFineGrained2017
  container-title: arXiv:1704.02958 [cs, stat]
  issued:
    - year: 2017
      month: 4
      day: 10
  title: >-
    On the Fine-Grained Complexity of Empirical Risk Minimization: Kernel
    Methods and Neural Networks
  type: article-journal
  URL: http://arxiv.org/abs/1704.02958

- id: BanerjeeEstimation2014
  accessed:
    - year: 2016
      month: 7
      day: 11
  author:
    - family: Banerjee
      given: Arindam
    - family: Chen
      given: Sheng
    - family: Fazayeli
      given: Farideh
    - family: Sivakumar
      given: Vidyashankar
  citation-key: BanerjeeEstimation2014
  container-title: Advances in Neural Information Processing Systems 27
  editor:
    - family: Ghahramani
      given: Z.
    - family: Welling
      given: M.
    - family: Cortes
      given: C.
    - family: Lawrence
      given: N. D.
    - family: Weinberger
      given: K. Q.
  issued:
    - year: 2014
  page: 1556–1564
  publisher: Curran Associates, Inc.
  title: Estimation with Norm Regularization
  type: paper-conference
  URL: http://papers.nips.cc/paper/5465-estimation-with-norm-regularization.pdf

- id: BarbierPhase2017
  accessed:
    - year: 2018
      month: 1
      day: 15
  author:
    - family: Barbier
      given: Jean
    - family: Krzakala
      given: Florent
    - family: Macris
      given: Nicolas
    - family: Miolane
      given: Léo
    - family: Zdeborová
      given: Lenka
  citation-key: BarbierPhase2017
  container-title: arXiv:1708.03395 [cond-mat, physics:math-ph]
  issued:
    - year: 2017
      month: 8
      day: 10
  title: >-
    Phase Transitions, Optimal Errors and Optimality of Message-Passing in
    Generalized Linear Models
  type: article-journal
  URL: http://arxiv.org/abs/1708.03395

- id: BarbierStochastic2017
  accessed:
    - year: 2018
      month: 1
      day: 15
  author:
    - family: Barbier
      given: Jean
    - family: Macris
      given: Nicolas
  citation-key: BarbierStochastic2017
  container-title: arXiv:1705.02780 [cond-mat]
  issued:
    - year: 2017
      month: 5
      day: 8
  title: >-
    The stochastic interpolation method: A simple scheme to prove replica
    formulas in Bayesian inference
  type: article-journal
  URL: http://arxiv.org/abs/1705.02780

- id: BarbourIntroduction2005
  call-number: QA273.6 .I58 2005
  citation-key: BarbourIntroduction2005
  collection-number: v. 4
  collection-title: >-
    Lecture notes series / Institute for Mathematical Sciences, National
    University of Singapore
  DOI: 10.1142/5792
  editor:
    - family: Barbour
      given: A. D.
    - family: Chen
      given: Louis H. Y.
  event-place: 'Singapore : Hackensack, N.J'
  ISBN: 978-981-256-280-7 978-981-256-330-9
  issued:
    - year: 2005
  number-of-pages: '225'
  publisher: Singapore University Press ; World Scientific
  publisher-place: 'Singapore : Hackensack, N.J'
  title: An introduction to Stein's method
  type: book
  volume: '4'

- id: BarronMDL2008
  accessed:
    - year: 2016
      month: 5
      day: 4
  author:
    - family: Barron
      given: Andrew R.
    - family: Huang
      given: Cong
    - family: Li
      given: Jonathan Q.
    - family: Luo
      given: Xi
  citation-key: BarronMDL2008
  container-title: Information Theory Workshop, 2008. ITW'08. IEEE
  DOI: 10.1109/ITW.2008.4578660
  issued:
    - year: 2008
  page: 247–257
  publisher: IEEE
  title: MDL, penalized likelihood, and statistical risk
  type: paper-conference
  URL: >-
    http://www.stat.yale.edu/~arb4/publications_files/MDLpenalizedLikelihoodStatisticalRiskITW.pdf

- id: BartlettConvexity2006
  accessed:
    - year: 2016
      month: 10
      day: 11
  author:
    - family: Bartlett
      given: Peter L
    - family: Jordan
      given: Michael I
    - family: McAuliffe
      given: Jon D
  citation-key: BartlettConvexity2006
  container-title: Journal of the American Statistical Association
  DOI: 10.1198/016214505000000907
  ISSN: 0162-1459, 1537-274X
  issue: '473'
  issued:
    - year: 2006
      month: 3
  language: en
  page: 138-156
  title: Convexity, Classification, and Risk Bounds
  type: article-journal
  volume: '101'

- id: BartlettRademacher2002
  accessed:
    - year: 2016
      month: 7
      day: 6
  author:
    - family: Bartlett
      given: Peter L.
    - family: Mendelson
      given: Shahar
  citation-key: BartlettRademacher2002
  container-title: Journal of Machine Learning Research
  ISSN: ISSN 1533-7928
  issue: Nov
  issued:
    - year: 2002
  page: 463-482
  title: 'Rademacher and Gaussian Complexities: Risk Bounds and Structural Results'
  type: article-journal
  URL: http://www.jmlr.org/papers/v3/bartlett02a.html
  volume: '3'

- id: BellecBounds2016
  accessed:
    - year: 2016
      month: 9
      day: 28
  author:
    - family: Bellec
      given: Pierre C.
    - family: Tsybakov
      given: Alexandre B.
  citation-key: BellecBounds2016
  container-title: arXiv:1609.06675 [math, stat]
  issued:
    - year: 2016
      month: 9
      day: 21
  title: >-
    Bounds on the prediction error of penalized least squares estimators with
    convex penalty
  type: article-journal
  URL: http://arxiv.org/abs/1609.06675

- id: BertinAdaptive2011
  accessed:
    - year: 2016
      month: 9
      day: 15
  author:
    - family: Bertin
      given: K.
    - family: Pennec
      given: E. Le
    - family: Rivoirard
      given: V.
  citation-key: BertinAdaptive2011
  container-title: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
  container-title-short: Ann. Inst. H. Poincaré Probab. Statist.
  DOI: 10.1214/09-AIHP351
  ISSN: 0246-0203
  issue: '1'
  issued:
    - year: 2011
      month: 2
  language: EN
  page: 43-74
  title: Adaptive Dantzig density estimation
  type: article-journal
  volume: '47'

- id: BirgeModel2008
  accessed:
    - year: 2016
      month: 9
      day: 13
  author:
    - family: Birgé
      given: Lucien
  citation-key: BirgeModel2008
  container-title: arXiv:0808.1416 [math, stat]
  issued:
    - year: 2008
      month: 8
      day: 10
  title: Model selection for density estimation with L2-loss
  type: article-journal
  URL: http://arxiv.org/abs/0808.1416

- id: BlumerLearnability1989
  accessed:
    - year: 2014
      month: 3
      day: 25
  author:
    - family: Blumer
      given: Anselm
    - family: Ehrenfeucht
      given: A.
    - family: Haussler
      given: David
    - family: Warmuth
      given: Manfred K.
  citation-key: BlumerLearnability1989
  container-title: J. ACM
  DOI: 10.1145/76359.76371
  ISSN: 0004-5411
  issue: '4'
  issued:
    - year: 1989
      month: 10
  page: 929–965
  title: Learnability and the Vapnik-Chervonenkis Dimension
  type: article-journal
  URL: http://trhvidsten.com/docs/classics/Blumer-1989.pdf
  volume: '36'

- id: BousquetIntroduction2004
  accessed:
    - year: 2014
      month: 11
      day: 25
  author:
    - family: Bousquet
      given: Olivier
    - family: Boucheron
      given: Stéphane
    - family: Lugosi
      given: Gábor
  citation-key: BousquetIntroduction2004
  collection-number: '3176'
  collection-title: Lecture Notes in Computer Science
  container-title: Advanced Lectures on Machine Learning
  editor:
    - family: Bousquet
      given: Olivier
    - family: Luxburg
      given: Ulrike
      dropping-particle: von
    - family: Rätsch
      given: Gunnar
  ISBN: 978-3-540-23122-6 978-3-540-28650-9
  issued:
    - year: 2004
      month: 1
      day: 1
  language: en
  page: 169-207
  publisher: Springer Berlin Heidelberg
  title: Introduction to Statistical Learning Theory
  type: chapter
  URL: http://www.econ.upf.edu/~lugosi/mlss_slt.pdf

- id: BousquetTheory2020
  author:
    - family: Bousquet
      given: Olivier
    - family: Hanneke
      given: Steve
    - family: Moran
      given: Shay
  citation-key: BousquetTheory2020
  issued:
    - year: 2020
  language: en
  page: '51'
  title: A Theory of Universal Learning
  type: article-journal

- id: BuneaSparse2007
  accessed:
    - year: 2016
      month: 9
      day: 20
  author:
    - family: Bunea
      given: Florentina
    - family: Tsybakov
      given: Alexandre B.
    - family: Wegkamp
      given: Marten H.
  citation-key: BuneaSparse2007
  collection-title: Lecture Notes in Computer Science
  container-title: Learning Theory
  DOI: 10.1007/978-3-540-72927-3_38
  editor:
    - family: Bshouty
      given: Nader H.
    - family: Gentile
      given: Claudio
  ISBN: 978-3-540-72925-9 978-3-540-72927-3
  issued:
    - year: 2007
      month: 6
      day: 13
  language: en
  page: 530-543
  publisher: Springer Berlin Heidelberg
  title: Sparse Density Estimation with ℓ1 Penalties
  type: paper-conference
  URL: http://www.proba.jussieu.fr/pageperso/tsybakov/BTWcolt07.pdf

- id: BuneaSparsity2007
  accessed:
    - year: 2016
      month: 9
      day: 20
  author:
    - family: Bunea
      given: Florentina
    - family: Tsybakov
      given: Alexandre
    - family: Wegkamp
      given: Marten
  citation-key: BuneaSparsity2007
  container-title: Electronic Journal of Statistics
  container-title-short: Electron. J. Statist.
  DOI: 10.1214/07-EJS008
  ISSN: 1935-7524
  issued:
    - year: 2007
  language: EN
  page: 169-194
  title: Sparsity oracle inequalities for the Lasso
  type: article-journal
  volume: '1'

- id: CanasLearning2012
  accessed:
    - year: 2018
      month: 11
      day: 23
  author:
    - family: Canas
      given: Guillermo D.
    - family: Rosasco
      given: Lorenzo
  citation-key: CanasLearning2012
  container-title: arXiv:1209.1077 [cs, stat]
  issued:
    - year: 2012
      month: 9
      day: 5
  title: Learning Probability Measures with respect to Optimal Transport Metrics
  type: article-journal
  URL: http://arxiv.org/abs/1209.1077

- id: CarmiCompressive2013
  accessed:
    - year: 2016
      month: 1
      day: 5
  author:
    - family: Carmi
      given: Avishy Y.
  citation-key: CarmiCompressive2013
  container-title: Digital Signal Processing
  container-title-short: Digital Signal Processing
  DOI: 10.1016/j.dsp.2012.12.006
  ISSN: 1051-2004
  issue: '3'
  issued:
    - year: 2013
      month: 5
  page: 751-770
  title: 'Compressive system identification: sequential methods and entropy bounds'
  type: article-journal
  volume: '23'

- id: ChichignoudPractical2014
  author:
    - family: Chichignoud
      given: Michaël
    - family: Lederer
      given: Johannes
    - family: Wainwright
      given: Martin
  citation-key: ChichignoudPractical2014
  container-title: arXiv:1410.0247 [math, stat]
  issued:
    - year: 2014
      month: 10
      day: 1
  title: >-
    A Practical Scheme and Fast Algorithm to Tune the Lasso With Optimality
    Guarantees
  type: article-journal
  URL: http://arxiv.org/abs/1410.0247

- id: DaneshmandEstimating2014
  accessed:
    - year: 2015
      month: 5
      day: 2
  author:
    - family: Daneshmand
      given: Hadi
    - family: Gomez-Rodriguez
      given: Manuel
    - family: Song
      given: Le
    - family: Schölkopf
      given: Bernhard
  citation-key: DaneshmandEstimating2014
  container-title: ICML
  issued:
    - year: 2014
      month: 5
      day: 12
  title: >-
    Estimating Diffusion Network Structures: Recovery Conditions, Sample
    Complexity & Soft-thresholding Algorithm
  type: paper-conference
  URL: http://arxiv.org/abs/1405.2936

- id: DavidStatistical2016
  accessed:
    - year: 2016
      month: 10
      day: 19
  author:
    - family: David
      given: Ofir
    - family: Moran
      given: Shay
    - family: Yehudayoff
      given: Amir
  citation-key: DavidStatistical2016
  container-title: arXiv:1610.03592 [cs, math]
  issued:
    - year: 2016
      month: 10
      day: 11
  title: On statistical learning via the lens of compression
  type: article-journal
  URL: http://arxiv.org/abs/1610.03592

- id: DevroyeProbabilistic1996
  author:
    - family: Devroye
      given: Luc
    - family: Györfi
      given: László
    - family: Lugosi
      given: Gábor
  call-number: Q327 .D5 1996
  citation-key: DevroyeProbabilistic1996
  event-place: New York
  ISBN: 978-0-387-94618-4
  issued:
    - year: 1996
  number-of-pages: '636'
  publisher: Springer
  publisher-place: New York
  title: A probabilistic theory of pattern recognition
  type: book
  URL: http://www.szit.bme.hu/~gyorfi/pbook.pdf

- id: DinhFast2016
  accessed:
    - year: 2016
      month: 10
      day: 5
  author:
    - family: Dinh
      given: Vu
    - family: Ho
      given: Lam Si Tung
    - family: Nguyen
      given: Duy
    - family: Nguyen
      given: Binh T.
  citation-key: DinhFast2016
  container-title: NIPS
  issued:
    - year: 2016
      month: 9
      day: 29
  title: Fast learning rates with heavy-tailed losses
  type: paper-conference
  URL: http://arxiv.org/abs/1609.09481

- id: FlammiaQuantum2012
  accessed:
    - year: 2016
      month: 5
      day: 13
  author:
    - family: Flammia
      given: Steven T.
    - family: Gross
      given: David
    - family: Liu
      given: Yi-Kai
    - family: Eisert
      given: Jens
  citation-key: FlammiaQuantum2012
  container-title: New Journal of Physics
  DOI: 10.1088/1367-2630/14/9/095022
  ISSN: 1367-2630
  issue: '9'
  issued:
    - year: 2012
      month: 9
      day: 27
  page: '095022'
  title: >-
    Quantum Tomography via Compressed Sensing: Error Bounds, Sample Complexity,
    and Efficient Estimators
  type: article-journal
  URL: http://arxiv.org/abs/1205.2300
  volume: '14'

- id: FoygelFastrate2011
  accessed:
    - year: 2016
      month: 7
      day: 27
  author:
    - family: Foygel
      given: Rina
    - family: Srebro
      given: Nathan
  citation-key: FoygelFastrate2011
  container-title: arXiv:1108.0373 [math, stat]
  issued:
    - year: 2011
      month: 8
      day: 1
  title: Fast-rate and optimistic-rate error bounds for L1-regularized regression
  type: article-journal
  URL: http://arxiv.org/abs/1108.0373

- id: GneccoApproximation2008
  accessed:
    - year: 2016
      month: 7
      day: 6
  author:
    - family: Gnecco
      given: Giorgio
    - family: Sanguineti
      given: Marcello
  citation-key: GneccoApproximation2008
  container-title: Applied Mathematical Sciences
  issue: '4'
  issued:
    - year: 2008
  page: 153–176
  title: Approximation Error Bounds via Rademacher’s Complexity
  type: article-journal
  URL: http://users.dibris.unige.it/gnecco/AMS1.pdf
  volume: '2'

- id: GolowichSizeIndependent2017
  accessed:
    - year: 2018
      month: 1
      day: 26
  author:
    - family: Golowich
      given: Noah
    - family: Rakhlin
      given: Alexander
    - family: Shamir
      given: Ohad
  citation-key: GolowichSizeIndependent2017
  container-title: arXiv:1712.06541 [cs, stat]
  issued:
    - year: 2017
      month: 12
      day: 18
  title: Size-Independent Sample Complexity of Neural Networks
  type: article-journal
  URL: http://arxiv.org/abs/1712.06541

- id: GolubevRisk1990
  accessed:
    - year: 2016
      month: 7
      day: 11
  author:
    - family: Golubev
      given: Grigori K.
    - family: Nussbaum
      given: Michael
  citation-key: GolubevRisk1990
  container-title: The Annals of Statistics
  DOI: 10.1214/aos/1176347624
  ISSN: 0090-5364
  issue: '2'
  issued:
    - year: 1990
      month: 6
  language: en
  page: 758-778
  title: A Risk Bound in Sobolev Class Regression
  type: article-journal
  URL: http://digitalassets.lib.berkeley.edu/sdtr/ucb/text/227.pdf
  volume: '18'

- id: GoodfellowCleverhans2016
  accessed:
    - year: 2016
      month: 10
      day: 6
  author:
    - family: Goodfellow
      given: Ian
    - family: Papernot
      given: Nicolas
    - family: McDaniel
      given: Patrick
  citation-key: GoodfellowCleverhans2016
  container-title: arXiv:1610.00768 [cs, stat]
  issued:
    - year: 2016
      month: 10
      day: 3
  title: 'cleverhans v0.1: an adversarial machine learning library'
  type: article-journal
  URL: http://arxiv.org/abs/1610.00768

- id: GribonvalCompressive2017
  accessed:
    - year: 2017
      month: 7
      day: 23
  author:
    - family: Gribonval
      given: Rémi
    - family: Blanchard
      given: Gilles
    - family: Keriven
      given: Nicolas
    - family: Traonmilin
      given: Yann
  citation-key: GribonvalCompressive2017
  container-title: arXiv:1706.07180 [cs, math, stat]
  issued:
    - year: 2017
      month: 6
      day: 22
  title: Compressive Statistical Learning with Random Feature Moments
  type: article-journal
  URL: http://arxiv.org/abs/1706.07180

- id: HansenLasso2015
  accessed:
    - year: 2016
      month: 6
      day: 7
  author:
    - family: Hansen
      given: Niels Richard
    - family: Reynaud-Bouret
      given: Patricia
    - family: Rivoirard
      given: Vincent
  citation-key: HansenLasso2015
  container-title: Bernoulli
  container-title-short: Bernoulli
  DOI: 10.3150/13-BEJ562
  ISSN: 1350-7265
  issue: '1'
  issued:
    - year: 2015
      month: 2
  language: EN
  page: 83-143
  title: Lasso and probabilistic inequalities for multivariate point processes
  type: article-journal
  URL: http://arxiv.org/abs/1208.0570
  volume: '21'

- id: HasminskiiDensity1990
  accessed:
    - year: 2016
      month: 8
      day: 16
  author:
    - family: Hasminskii
      given: Rafael
    - family: Ibragimov
      given: Ildar
  citation-key: HasminskiiDensity1990
  container-title: The Annals of Statistics
  container-title-short: Ann. Statist.
  DOI: 10.1214/aos/1176347736
  ISSN: 0090-5364, 2168-8966
  issue: '3'
  issued:
    - year: 1990
      month: 9
  language: EN
  page: 999-1010
  title: >-
    On Density Estimation in the View of Kolmogorov's Ideas in Approximation
    Theory
  type: article-journal
  volume: '18'

- id: HastieElements2009
  author:
    - family: Hastie
      given: Trevor
    - family: Tibshirani
      given: Robert
    - family: Friedman
      given: Jerome
  citation-key: HastieElements2009
  ISBN: 0343-6993
  issued:
    - year: 2009
  number-of-pages: '83'
  publisher: Springer
  title: 'The elements of statistical learning: data mining, inference and prediction'
  type: book

- id: HastieStatistical2015
  author:
    - family: Hastie
      given: Trevor J.
    - family: Tibshirani, Rob
      given: ''
    - family: Wainwright
      given: Martin J.
  citation-key: HastieStatistical2015
  event-place: Boca Raton
  ISBN: 978-1-4987-1216-3
  issued:
    - year: 2015
      month: 5
      day: 7
  language: English
  number-of-pages: '367'
  publisher: Chapman and Hall/CRC
  publisher-place: Boca Raton
  title: 'Statistical Learning with Sparsity: The Lasso and Generalizations'
  type: book
  URL: https://web.stanford.edu/~hastie/StatLearnSparsity/index.html

- id: HuangRisk2008
  accessed:
    - year: 2016
      month: 8
      day: 2
  author:
    - family: Huang
      given: Cong
    - family: Cheang
      given: G. L. H.
    - family: Barron
      given: Andrew R.
  citation-key: HuangRisk2008
  issued:
    - year: 2008
  title: >-
    Risk of penalized least squares, greedy selection and l1 penalization for
    flexible function libraries
  type: article-journal
  URL: >-
    http://www.stat.yale.edu/~arb4/publications_files/RiskGreedySelectionAndL1penalization.pdf

- id: KabanNew2014
  accessed:
    - year: 2015
      month: 6
      day: 27
  author:
    - family: Kabán
      given: Ata
  citation-key: KabanNew2014
  container-title: Journal of Machine Learning Research
  event-title: >-
    Proceedings of the Seventeenth International Conference on Artificial
    Intelligence and Statistics
  issued:
    - year: 2014
  page: 448-456
  title: New Bounds on Compressive Linear Least Squares Regression
  type: paper-conference
  URL: http://jmlr.org/proceedings/papers/v33/kaban14.pdf

- id: KloftUnifying2010
  accessed:
    - year: 2016
      month: 7
      day: 11
  author:
    - family: Kloft
      given: Marius
    - family: Rückert
      given: Ulrich
    - family: Bartlett
      given: Peter L.
  citation-key: KloftUnifying2010
  collection-title: Lecture Notes in Computer Science
  container-title: Machine Learning and Knowledge Discovery in Databases
  DOI: 10.1007/978-3-642-15883-4_5
  editor:
    - family: Balcázar
      given: José Luis
    - family: Bonchi
      given: Francesco
    - family: Gionis
      given: Aristides
    - family: Sebag
      given: Michèle
  event-title: European Conference, ECML PKDD 2010
  ISBN: 978-3-642-15882-7 978-3-642-15883-4
  issued:
    - year: 2010
      month: 9
      day: 20
  language: en
  page: 66-81
  publisher: Springer Berlin Heidelberg
  title: A Unifying View of Multiple Kernel Learning
  type: paper-conference
  URL: http://nma.berkeley.edu/ark:/28722/bk000709632

- id: KoltchinskiiOracle2011
  author:
    - family: Koltchinskii
      given: Prof Vladimir
  citation-key: KoltchinskiiOracle2011
  collection-number: '2033'
  collection-title: Lecture notes in mathematics École d'Été de Probabilités de Saint-Flour
  DOI: 10.1007/978-3-642-22147-7_1
  event-place: Heidelberg
  ISBN: 978-3-642-22146-0 978-3-642-22147-7
  issued:
    - year: 2011
  language: en
  publisher: Springer
  publisher-place: Heidelberg
  title: >-
    Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery
    Problems
  type: book
  URL: http://www.stat.washington.edu/jaw/COURSES/EPWG/PAPERS-11/sflour_book.pdf

- id: KrishnapuramSparse2005
  accessed:
    - year: 2016
      month: 7
      day: 6
  author:
    - family: Krishnapuram
      given: Balaji
    - family: Carin
      given: Lawrence
    - family: Figueiredo
      given: Mario A. T.
    - family: Hartemink
      given: Alexander J.
  citation-key: KrishnapuramSparse2005
  container-title: IEEE Transactions on Pattern Analysis and Machine Intelligence
  DOI: 10.1109/TPAMI.2005.127
  ISSN: 0162-8828
  issue: '6'
  issued:
    - year: 2005
      month: 6
  page: 957–968
  title: >-
    Sparse Multinomial Logistic Regression: Fast Algorithms and Generalization
    Bounds
  type: article-journal
  URL: http://www.lx.it.pt/~mtf/Krishnapuram_Carin_Figueiredo_Hartemink_2005.pdf
  volume: '27'

- id: KuznetsovLearning2015
  accessed:
    - year: 2016
      month: 11
      day: 3
  author:
    - family: Kuznetsov
      given: Vitaly
    - family: Mohri
      given: Mehryar
  citation-key: KuznetsovLearning2015
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2015
  page: 541–549
  publisher: Curran Associates, Inc.
  title: Learning Theory and Algorithms for Forecasting Non-Stationary Time Series
  type: paper-conference
  URL: >-
    http://papers.nips.cc/paper/5836-learning-theory-and-algorithms-for-forecasting-non-stationary-time-series

- id: LedererNew2014
  accessed:
    - year: 2015
      month: 2
      day: 3
  author:
    - family: Lederer
      given: Johannes
    - family: Geer
      given: Sara
      non-dropping-particle: van de
  citation-key: LedererNew2014
  container-title: Bernoulli
  container-title-short: Bernoulli
  DOI: 10.3150/13-BEJ549
  ISSN: 1350-7265
  issue: '4'
  issued:
    - year: 2014
      month: 11
  language: EN
  page: 2020-2038
  title: New concentration inequalities for suprema of empirical processes
  type: article-journal
  volume: '20'

- id: MaclaurinGradientbased2015
  accessed:
    - year: 2022
      month: 4
      day: 23
  author:
    - family: Maclaurin
      given: Dougal
    - family: Duvenaud
      given: David
    - family: Adams
      given: Ryan
  citation-key: MaclaurinGradientbased2015
  container-title: Proceedings of the 32nd International Conference on Machine Learning
  event-title: International Conference on Machine Learning
  ISSN: 1938-7228
  issued:
    - year: 2015
      month: 6
      day: 1
  language: en
  page: 2113-2122
  publisher: PMLR
  title: Gradient-based Hyperparameter Optimization through Reversible Learning
  type: paper-conference
  URL: https://proceedings.mlr.press/v37/maclaurin15.html

- id: MauryaOptimal2018
  author:
    - family: Maurya
      given: Abhinav
  citation-key: MauryaOptimal2018
  issued:
    - year: 2018
  title: >-
    Optimal Transport in Statistical Machine Learning : Selected Review and Some
    Open Questions
  type: paper-conference

- id: McDonaldEstimated2011
  author:
    - family: McDonald
      given: Daniel J
    - family: Shalizi
      given: Cosma Rohilla
    - family: Schervish
      given: Mark
  citation-key: McDonaldEstimated2011
  container-title: eprint arXiv:1111.3404
  issued:
    - year: 2011
  title: Estimated VC dimension for risk bounds
  type: article-journal
  URL: http://arxiv.org/abs/1111.3404

- id: McDonaldGeneralization2011
  accessed:
    - year: 2015
      month: 12
      day: 13
  author:
    - family: McDonald
      given: Daniel J.
    - family: Shalizi
      given: Cosma Rohilla
    - family: Schervish
      given: Mark
  citation-key: McDonaldGeneralization2011
  container-title: arXiv:1103.0942 [cs, stat]
  issued:
    - year: 2011
      month: 3
      day: 4
  title: Generalization error bounds for stationary autoregressive models
  type: article-journal
  URL: http://arxiv.org/abs/1103.0942

- id: McDonaldRisk2011
  accessed:
    - year: 2016
      month: 10
      day: 31
  author:
    - family: McDonald
      given: Daniel J.
    - family: Shalizi
      given: Cosma Rohilla
    - family: Schervish
      given: Mark
  citation-key: McDonaldRisk2011
  container-title: arXiv:1106.0730 [cs, stat]
  issued:
    - year: 2011
      month: 6
      day: 3
  title: Risk bounds for time series without strong mixing
  type: article-journal
  URL: http://arxiv.org/abs/1106.0730

- id: MeiLandscape2016
  accessed:
    - year: 2016
      month: 7
      day: 26
  author:
    - family: Mei
      given: Song
    - family: Bai
      given: Yu
    - family: Montanari
      given: Andrea
  citation-key: MeiLandscape2016
  container-title: arXiv:1607.06534 [stat]
  issued:
    - year: 2016
      month: 7
      day: 21
  title: The Landscape of Empirical Risk for Non-convex Losses
  type: article-journal
  URL: http://arxiv.org/abs/1607.06534

- id: MengGeneralization2016
  accessed:
    - year: 2016
      month: 9
      day: 28
  author:
    - family: Meng
      given: Qi
    - family: Wang
      given: Yue
    - family: Chen
      given: Wei
    - family: Wang
      given: Taifeng
    - family: Ma
      given: Zhi-Ming
    - family: Liu
      given: Tie-Yan
  citation-key: MengGeneralization2016
  container-title: arXiv:1609.08397 [stat]
  issued:
    - year: 2016
      month: 9
      day: 27
  page: 441–474
  title: Generalization Error Bounds for Optimization Algorithms via Stability
  type: paper-conference
  URL: http://arxiv.org/abs/1609.08397
  volume: '10'

- id: NatarajanLearning1989
  accessed:
    - year: 2016
      month: 7
      day: 6
  author:
    - family: Natarajan
      given: B. K.
  citation-key: NatarajanLearning1989
  container-title: Machine Learning
  container-title-short: Mach Learn
  DOI: 10.1007/BF00114804
  ISSN: 0885-6125, 1573-0565
  issue: '1'
  issued:
    - year: 1989
  language: en
  page: 67-97
  title: On learning sets and functions
  type: article-journal
  volume: '4'

- id: OnetoModel2018
  accessed:
    - year: 2020
      month: 9
      day: 15
  author:
    - family: Oneto
      given: Luca
  citation-key: OnetoModel2018
  container-title: WIREs Data Mining and Knowledge Discovery
  DOI: 10.1002/widm.1252
  ISSN: 1942-4795
  issue: '4'
  issued:
    - year: 2018
  language: en
  page: e1252
  title: Model selection and error estimation without the agonizing pain
  type: article-journal
  volume: '8'

- id: PascanuDifficulty2013
  author:
    - family: Pascanu
      given: Razvan
    - family: Mikolov
      given: Tomas
    - family: Bengio
      given: Yoshua
  citation-key: PascanuDifficulty2013
  container-title: arXiv:1211.5063 [cs]
  event-title: Proceedings of The 30th International Conference on Machine Learning
  issued:
    - year: 2013
  page: 1310-1318
  title: On the difficulty of training Recurrent Neural Networks
  type: paper-conference
  URL: http://arxiv.org/abs/1211.5063

- id: ReidInformation2011
  accessed:
    - year: 2016
      month: 7
      day: 22
  author:
    - family: Reid
      given: Mark D.
    - family: Williamson
      given: Robert C.
  citation-key: ReidInformation2011
  container-title: Journal of Machine Learning Research
  ISSN: ISSN 1533-7928
  issue: Mar
  issued:
    - year: 2011
  page: 731-817
  title: Information, Divergence and Risk for Binary Experiments
  type: article-journal
  URL: http://www.jmlr.org/papers/v12/reid11a.html
  volume: '12'

- id: ReinertStein2000
  accessed:
    - year: 2016
      month: 10
      day: 18
  author:
    - family: Reinert
      given: Gesine
  citation-key: ReinertStein2000
  container-title: Complex Stochastic Systems
  event-place: Boca Raton
  ISBN: 978-1-4200-3598-8
  issued:
    - year: 2000
  page: 235–275
  publisher: Chapman & Hall/CRC
  publisher-place: Boca Raton
  title: Stein's Method for Epidemic Processes
  type: chapter
  URL: http://www.stats.ox.ac.uk/~reinert/papers/episemrevnew.pdf

- id: Reynaud-BouretAdaptive2003
  accessed:
    - year: 2016
      month: 8
      day: 22
  author:
    - family: Reynaud-Bouret
      given: Patricia
  citation-key: Reynaud-BouretAdaptive2003
  container-title: Probability Theory and Related Fields
  container-title-short: Probab. Theory Relat. Fields
  DOI: 10.1007/s00440-003-0259-1
  ISSN: 0178-8051, 1432-2064
  issue: '1'
  issued:
    - year: 2003
      month: 5
  language: en
  title: >-
    Adaptive estimation of the intensity of inhomogeneous Poisson processes via
    concentration inequalities
  type: article-journal
  URL: http://math1.unice.fr/~reynaudb/ptrf.pdf
  volume: '126'

- id: Reynaud-BouretAdaptive2010
  accessed:
    - year: 2014
      month: 12
      day: 8
  author:
    - family: Reynaud-Bouret
      given: Patricia
    - family: Schbath
      given: Sophie
  citation-key: Reynaud-BouretAdaptive2010
  container-title: The Annals of Statistics
  container-title-short: Ann. Statist.
  DOI: 10.1214/10-AOS806
  ISSN: 0090-5364, 2168-8966
  issue: '5'
  issued:
    - year: 2010
      month: 10
  language: EN
  page: 2781-2822
  title: Adaptive estimation for Hawkes processes; application to genome analysis
  type: article-journal
  volume: '38'

- id: ScholkopfLearning2002
  author:
    - family: Schölkopf
      given: Bernhard
    - family: Smola
      given: Alexander J.
  citation-key: ScholkopfLearning2002
  ISBN: 978-0-262-19475-4
  issued:
    - year: 2002
      month: 1
  language: en
  number-of-pages: '658'
  publisher: MIT Press
  title: >-
    Learning with Kernels: Support Vector Machines, Regularization,
    Optimization, and Beyond
  type: book

- id: ScholkopfShort2003
  accessed:
    - year: 2016
      month: 4
      day: 13
  author:
    - family: Schölkopf
      given: Bernhard
    - family: Smola
      given: Alexander J.
  citation-key: ScholkopfShort2003
  collection-number: '2600'
  collection-title: Lecture Notes in Computer Science
  container-title: Advanced Lectures on Machine Learning
  DOI: 10.1007/3-540-36434-X_2
  editor:
    - family: Mendelson
      given: Shahar
    - family: Smola
      given: Alexander J.
  ISBN: 978-3-540-00529-2 978-3-540-36434-4
  issued:
    - year: 2003
  language: en
  page: 41-64
  publisher: Springer Berlin Heidelberg
  title: A Short Introduction to Learning with Kernels
  type: chapter
  URL: http://alex.smola.org/papers/2003/SchSmo03c.pdf

- id: SemenovaStudy2021
  accessed:
    - year: 2021
      month: 7
      day: 5
  author:
    - family: Semenova
      given: Lesia
    - family: Rudin
      given: Cynthia
    - family: Parr
      given: Ronald
  citation-key: SemenovaStudy2021
  container-title: arXiv:1908.01755 [cs, stat]
  issued:
    - year: 2021
      month: 4
      day: 9
  language: en
  title: >-
    A study in Rashomon curves and volumes: A new perspective on generalization
    and model simplicity in machine learning
  type: article-journal
  URL: http://arxiv.org/abs/1908.01755

- id: SimsekliHausdorff2020
  accessed:
    - year: 2020
      month: 6
      day: 19
  author:
    - family: Şimşekli
      given: Umut
    - family: Sener
      given: Ozan
    - family: Deligiannidis
      given: George
    - family: Erdogdu
      given: Murat A.
  citation-key: SimsekliHausdorff2020
  container-title: CoRR
  issued:
    - year: 2020
  title: >-
    Hausdorff Dimension, Stochastic Differential Equations, and Generalization
    in Neural Networks
  type: article-journal
  URL: http://arxiv.org/abs/2006.09313
  volume: abs/2006.09313

- id: SinghMinimax2018
  accessed:
    - year: 2018
      month: 11
      day: 23
  author:
    - family: Singh
      given: Shashank
    - family: Póczos
      given: Barnabás
  citation-key: SinghMinimax2018
  container-title: arXiv:1802.08855 [cs, math, stat]
  issued:
    - year: 2018
      month: 2
      day: 24
  title: Minimax Distribution Estimation in Wasserstein Distance
  type: article-journal
  URL: http://arxiv.org/abs/1802.08855

- id: TroppIntroduction2015
  accessed:
    - year: 2015
      month: 1
      day: 20
  author:
    - family: Tropp
      given: Joel A.
  citation-key: TroppIntroduction2015
  issued:
    - year: 2015
      month: 1
      day: 7
  title: An Introduction to Matrix Concentration Inequalities
  type: book
  URL: http://arxiv.org/abs/1501.01571

- id: TulabandhulaGeneralization2014
  accessed:
    - year: 2016
      month: 7
      day: 11
  author:
    - family: Tulabandhula
      given: Theja
    - family: Rudin
      given: Cynthia
  citation-key: TulabandhulaGeneralization2014
  container-title: arXiv preprint arXiv:1405.7764
  issued:
    - year: 2014
  title: >-
    Generalization bounds for learning with linear, polygonal, quadratic and
    conic side knowledge
  type: article-journal
  URL: http://arxiv.org/abs/1405.7764

- id: VainsencherSample2011
  accessed:
    - year: 2016
      month: 7
      day: 18
  author:
    - family: Vainsencher
      given: Daniel
    - family: Mannor
      given: Shie
    - family: Bruckstein
      given: Alfred M.
  citation-key: VainsencherSample2011
  container-title: Journal of Machine Learning Research
  ISSN: ISSN 1533-7928
  issue: Nov
  issued:
    - year: 2011
  page: 3259-3281
  title: The Sample Complexity of Dictionary Learning
  type: article-journal
  URL: http://www.jmlr.org/papers/v12/vainsencher11a.html
  volume: '12'

- id: vandeGeerHighdimensional2008
  accessed:
    - year: 2016
      month: 9
      day: 16
  author:
    - family: Geer
      given: Sara A.
      non-dropping-particle: van de
  citation-key: vandeGeerHighdimensional2008
  container-title: The Annals of Statistics
  container-title-short: Ann. Statist.
  DOI: 10.1214/009053607000000929
  ISSN: 0090-5364, 2168-8966
  issue: '2'
  issued:
    - year: 2008
      month: 4
  language: EN
  page: 614-645
  title: High-dimensional generalized linear models and the lasso
  type: article-journal
  volume: '36'

- id: vandeGeerHoeffdoing2002
  author:
    - family: Geer
      given: Sara
      non-dropping-particle: van de
  citation-key: vandeGeerHoeffdoing2002
  container-title: Empirical Process Techniques for Dependent Data
  issued:
    - year: 2002
  publisher: Birkhhäuser
  title: On Hoeffdoing's inequality for dependent random variables
  type: chapter

- id: vandeGeerWorst2014
  accessed:
    - year: 2015
      month: 10
      day: 8
  author:
    - family: Geer
      given: Sara
      non-dropping-particle: van de
  citation-key: vandeGeerWorst2014
  container-title: arXiv:1403.7023 [math, stat]
  event-title: >-
    Third Edition of the International Workshop on Functional and Operatorial
    Statistics
  issued:
    - year: 2014
      month: 3
      day: 27
  title: Worst possible sub-directions in high-dimensional models
  type: paper-conference
  URL: http://arxiv.org/abs/1403.7023
  volume: '131'

- id: VapnikMeasuring1994
  accessed:
    - year: 2016
      month: 7
      day: 6
  author:
    - family: Vapnik
      given: Vladimir
    - family: Levin
      given: Esther
    - family: Cun
      given: Yann Le
  citation-key: VapnikMeasuring1994
  container-title: Neural Computation
  container-title-short: Neural Computation
  DOI: 10.1162/neco.1994.6.5.851
  ISSN: 0899-7667
  issue: '5'
  issued:
    - year: 1994
      month: 9
      day: 1
  page: 851-876
  title: Measuring the VC-Dimension of a Learning Machine
  type: article-journal
  URL: >-
    https://pdfs.semanticscholar.org/9fab/fe40ce7ad0b1241fa049648478acc590ed76.pdf
  volume: '6'

- id: VapnikNature2010
  author:
    - family: Vapnik
      given: Vladimir
  citation-key: VapnikNature2010
  edition: Softcover reprint of hardcover 2nd ed. 2000
  ISBN: 1-4419-3160-0
  issued:
    - year: 2010
      month: 12
      day: 1
  number-of-pages: '334'
  publisher: Springer
  title: The Nature of Statistical Learning Theory
  type: book

- id: VapnikUniform1971
  accessed:
    - year: 2015
      month: 4
      day: 2
  author:
    - family: Vapnik
      given: V.
    - family: Chervonenkis
      given: A.
  citation-key: VapnikUniform1971
  container-title: Theory of Probability & Its Applications
  container-title-short: Theory Probab. Appl.
  DOI: 10.1137/1116025
  ISSN: 0040-585X
  issue: '2'
  issued:
    - year: 1971
      month: 1
      day: 1
  page: 264-280
  title: >-
    On the Uniform Convergence of Relative Frequencies of Events to Their
    Probabilities
  type: article-journal
  URL: https://courses.engr.illinois.edu/ece544na/fa2014/vapnik71.pdf
  volume: '16'

- id: vonLuxburgStatistical2008
  accessed:
    - year: 2015
      month: 5
      day: 2
  author:
    - family: Luxburg
      given: Ulrike
      non-dropping-particle: von
    - family: Schölkopf
      given: Bernhard
  citation-key: vonLuxburgStatistical2008
  container-title: arXiv:0810.4752 [math, stat]
  issued:
    - year: 2008
      month: 10
      day: 27
  title: 'Statistical Learning Theory: Models, Concepts, and Results'
  type: article-journal
  URL: http://arxiv.org/abs/0810.4752

- id: WuLearning2008
  accessed:
    - year: 2016
      month: 7
      day: 24
  author:
    - family: Wu
      given: Qiang
    - family: Zhou
      given: Ding-Xuan
  citation-key: WuLearning2008
  container-title: Computers & Mathematics with Applications
  container-title-short: Computers & Mathematics with Applications
  DOI: 10.1016/j.camwa.2008.09.014
  ISSN: 0898-1221
  issue: '11'
  issued:
    - year: 2008
      month: 12
  page: 2896-2907
  title: Learning with sample dependent hypothesis spaces
  type: article-journal
  volume: '56'

- id: XuInformationtheoretic2017
  accessed:
    - year: 2017
      month: 11
      day: 9
  author:
    - family: Xu
      given: Aolin
    - family: Raginsky
      given: Maxim
  citation-key: XuInformationtheoretic2017
  container-title: Advances In Neural Information Processing Systems
  issued:
    - year: 2017
      month: 5
      day: 22
  publisher: Curran Associates, Inc.
  title: >-
    Information-theoretic analysis of generalization capability of learning
    algorithms
  type: paper-conference
  URL: http://arxiv.org/abs/1705.07809

- id: ZhangUnderstanding2017
  author:
    - family: Zhang
      given: Chiyuan
    - family: Bengio
      given: Samy
    - family: Hardt
      given: Moritz
    - family: Recht
      given: Benjamin
    - family: Vinyals
      given: Oriol
  citation-key: ZhangUnderstanding2017
  container-title: Proceedings of ICLR
  event-title: ICLR
  issued:
    - year: 2017
  title: Understanding deep learning requires rethinking generalization
  type: paper-conference
  URL: http://arxiv.org/abs/1611.03530
...
