Books
-
Biau, G., Droniou, J. and Herzlich, M. (2010). Mathématiques
et statistique pour les sciences de la nature ---
Modéliser, comprendre et appliquer, EDP Sciences, 531
pages, ISBN 978-2-7598-0481-8.
-
Biau, G. and Devroye, L. (2015).
Lectures on the nearest neighbor method, Springer, Cham,
290 pages, ISBN 978-3-319-25386-2. Errata.
Papers
-
Biau, G. (1999). Estimateurs à noyau
itérés : synthèse bibliographique, Journal
de la Société Française de Statistique, Vol.
1, pp. 41-67.
-
Biau, G., Zorita, E., von Storch, H. and Wackernagel,
H. (1999). Estimation of
precipitation by kriging in the EOF space of the Sea
Level Pressure field, Journal of Climate,
Vol. 12, pp. 1070-1085.
-
Berlinet, A. and Biau, G. (2001). Iterated
Barron density estimators, Comptes Rendus de
l'Académie des Sciences, Vol. 332, pp.
459-464.
-
Berlinet, A. and Biau, G. (2001). Minimax
bounds in nonparametric estimation of
multidimensional deterministic dynamical systems,
Statistical Inference for Stochastic Processes,
Vol. 4, pp. 229-248.
-
Abraham, C., Biau, G. and Cadre, B. (2002). Chaotic properties of mappings on a
probability space, Journal of Mathematical
Analysis and Applications, Vol. 266, pp.
420-431.
-
Beirlant, J., Berlinet, A., Biau, G. and Vajda, I.
(2002). Divergence-type errors of
smooth Barron-type density estimators, TEST,
Vol. 11, pp. 191-217.
-
Biau, G. (2002). Optimal asymptotic
quadratic errors of density estimators on random
fields, Statistics & Probability Letters,
Vol. 60, pp. 297-307.
-
Abraham, C., Biau, G. and Cadre, B. (2003). Simple estimation of the mode of a
multivariate density, The Canadian Journal
of Statistics, Vol. 31, pp. 23-34.
-
Biau, G. and Devroye, L. (2003). On
the risk of estimates for block decreasing densities,
Journal of Multivariate Analysis, Vol. 86,
pp. 143-165.
-
Biau, G. (2003). Spatial kernel
density estimation, Mathematical Methods of
Statistics, Vol. 12, pp. 371-390.
-
Abraham, C., Biau, G. and Cadre, B. (2004). On the asymptotic properties of a
simple estimate of the mode, ESAIM:
Probability and Statistics, Vol. 8, pp.
1-11.
-
Abraham, C., Biau, G. and Cadre, B. (2004). On Lyapunov exponent and sensitivity,
Journal of Mathematical Analysis and Applications,
Vol. 290, pp. 395-404.
-
Biau, G. and Devroye, L. (2004). A
note on density model size testing, IEEE
Transactions on Information Theory, Vol. 50,
pp. 576-581.
-
Biau, G. (2004). Estimation de la
densité et tests par la méthode combinatoire
pénalisée, Journal de la Société Française
de Statistique, Vol. 4, pp. 5-24.
-
Berlinet, A. and Biau, G. (2004). Iterated
modified histograms as dynamical systems, Journal
of Nonparametric Statistics, Vol. 16,
pp. 385-401.
-
Biau, G. and Cadre, B. (2004). Nonparametric
spatial prediction, Statistical Inference
for Stochastic Processes, Vol. 7, pp.
327-349.
-
Biau, G. and Devroye, L. (2005). Density
estimation by the penalized combinatorial method,
Journal of Multivariate Analysis, Vol. 94,
pp. 196-208.
-
Berlinet, A., Biau, G. and Rouvière, L. (2005). Parameter selection in modified
histogram estimates, Statistics, Vol. 39,
pp. 91-105.
-
Biau, G. and Wegkamp, M. (2005). A
note on minimum distance estimation of copula
densities, Statistics
& Probability Letters, Vol. 73, pp.
105-114.
-
Biau, G., Bunea, F. and Wegkamp, M.H. (2005). Functional classification in Hilbert
Spaces, IEEE
Transactions on Information Theory, Vol.
51, pp. 2163-2172.
-
Berlinet, A., Biau, G. and Rouvière, L. (2005). Optimal L1 bandwidth
selection for variable kernel density estimates, Statistics
& Probability Letters, Vol. 74, pp.
116-128.
-
Biau, G. and Györfi, L. (2005). On
the asymptotic properties of a nonparametric L1-test
statistic of homogeneity, IEEE Transactions on
Information Theory, Vol. 51, pp.
3965-3973.
-
Abraham, C., Biau, G. and Cadre, B. (2006). On the kernel rule for function
classification, Annals of the Institute of Statistical
Mathematics, Vol. 58, pp. 619-633.
-
Biau, G. and Bleakley, K. (2006). Statistical
inference on graphs, Statistics & Decisions, Vol.
24, pp. 209-232.
-
Bleakley, K., Giudicelli, V., Wu, Y., Lefranc, M.-P.
and Biau, G. (2006). IMGT
standardization for statistical analyses of T cell
receptor junctions: The TRAV-TRAJ example, In Silico Biology,
Vol. 6, pp. 573-588.
-
Biau, G., Cadre, B. and Pelletier, B. (2007). A graph-based estimator of the number
of clusters, ESAIM: Probability and
Statistics, Vol. 11, pp. 272-280.
-
Bleakley, K., Biau, G. and Vert, J.-P. (2007). Supervised reconstruction of
biological networks with local models, Bioinformatics, Vol.
23, pp. i57-i65.
-
Biau, G., Biau, O. and Rouvière, L. (2007). Nonparametric forecasting of the
manufacturing output growth with firm-level survey
data, Journal of Business
Cycle Measurement and Analysis, Vol. 3,
pp. 317-332.
-
Biau, G., Devroye, L. and Lugosi, G. (2008). On the performance of clustering in
Hilbert spaces, IEEE Transactions on Information Theory,
Vol. 54, pp. 781-790.
-
Beirlant, J., Berlinet, A. and Biau, G. (2008). Higher order estimation at Lebesgue
points, Annals
of the Institute of Statistical Mathematics,
Vol. 60, pp. 651-677.
-
Biau, G., Cadre, B., Devroye, L. and Györfi, L.
(2008). Strongly consistent model
selection for densities, TEST, Vol. 17,
pp. 531-545.
-
Biau, G., Cadre, B. and Pelletier, B. (2008). Exact rates in density support
estimation, Journal
of Multivariate Analysis, Vol. 99,
pp. 2185-2207.
-
Berlinet, A., Biau, G. and Rouvière, L. (2008). Functional supervised classification
with wavelets, Annales de l'ISUP, Vol. 52,
pp. 61-80.
-
Biau, G., Devroye, L. and Lugosi, G. (2008). Consistency of random forests and
other averaging classifiers, Journal of Machine
Learning Research, Vol. 9, pp.
2015-2033.
-
Bleakley, K., Lefranc, M.-P. and Biau, G. (2008). Recovering probabilities for
nucleotide trimming processes for T cell receptor
TRA and TRG V-J junctions analysed with IMGT tools,
BMC Bioinformatics,
Vol. 9, pp. 408-414.
-
Biau, G., Cadre, B., Mason, D.M. and Pelletier, B.
(2009). Asymptotic normality in
density support estimation, Electronic Journal of
Probability, Vol. 14, pp. 2617-2635.
-
Biau, G., Cérou, F. and Guyader, A. (2010). On the rate of convergence of the
bagged nearest neighbor estimate, Journal of Machine
Learning Research, Vol. 11, pp. 687-712.
-
Biau, G., Bleakley, K., Györfi, L. and Ottucsák, G.
(2010). Nonparametric sequential
prediction of time series, Journal of Nonparametric
Statistics, Vol.
22, pp. 297-317.
-
Biau, G., Cadre, B. and Rouvière, L. (2010). Statistical analysis of k-nearest
neighbor collaborative recommendation, The Annals of Statistics,
Vol. 38, pp.
1568-1592.
-
Biau, G., Cérou, F. and Guyader, A. (2010). Rates of convergence of the
functional k-nearest neighbor estimate, IEEE Transactions on
Information Theory, Vol. 56, pp.
2034-2040.
-
Biau, G. and Devroye, L. (2010). On
the layered nearest neighbour estimate, the bagged
nearest neighbour estimate and the random forest
method in regression and classification, Journal of Multivariate
Analysis, Vol.
101, pp. 2499-2518.
-
Biau, G. and Patra, B. (2011). Sequential
quantile prediction of time series, IEEE Transactions on
Information Theory, Vol. 57, pp.
1664-1674.
-
Biau, G., Chazal, F., Cohen-Steiner, D., Devroye, L.
and Rodríguez, C. (2011). A
weighted k-nearest neighbor density estimate for
geometric inference, Electronic Journal of
Statistics, Vol. 5, pp. 204-237.
-
Biau, G. and Fischer, A. (2012). Parameter
selection for principal curves, IEEE Transactions on
Information Theory, Vol. 58, pp.
1924-1939.
-
Biau, G. and Mas, A. (2012). PCA-kernel
estimation, Statistics & Risk Modeling, Vol. 29, pp.
19-46.
-
Biau, G. (2012). Analysis of a
random forests model, Journal of Machine Learning Research,
Vol. 13, pp.
1063-1095. Errata.
-
Biau, G. and Yatracos, Y.G. (2012). On
the shrinkage estimation of variance and Pitman
closeness criterion, Journal de la Société Française de
Statistique, Vol. 153, pp. 5-21.
-
Biau, G., Devroye, L., Dujmović, V. and Krzyżak, A.
(2012). An affine invariant
k-nearest neighbor regression estimate, Journal of Multivariate
Analysis, Vol.
112, pp. 24-34.
-
Alquier, P. and Biau, G. (2013). Sparse
single-index model, Journal of Machine Learning Research,
Vol. 14, pp.
243-280.
-
Biau, G. and Devroye, L. (2013). Cellular
tree classifiers, Electronic Journal of
Statistics, Vol. 7, pp. 1875-1912.
-
Kruppa, J., Liu, Y., Biau, G., Kohler, M., König,
I.R., Malley, J.D. and Ziegler, A. (2014). Probability
estimation with machine learning methods for
dichotomous and multicategory outcome: Theory, Biometrical Journal,
Vol. 56, pp.
534-563.
-
Biau, G., Cérou, F. and Guyader, A. (2015). New insights into Approximate
Bayesian Computation, Annales de l'Institut Henri Poincaré (B)
Probabilités et Statistiques, Vol. 51, pp.
376-403.
-
Biau, G. and Mason, D.M. (2015). High-dimensional
p-norms, in Mathematical
Statistics and Limit Theorems: Festschrift in
Honour
of Paul Deheuvels, ed. Hallin, M.,
Mason, D.M., Pfeifer, D. and Steinebach, J.G., pp.
21-40, Springer, Cham.
-
Scornet, E., Biau, G. and Vert, J.-P. (2015). Consistency of random forests (supplementary material), The Annals of
Statistics, Vol.
43, pp. 1716-1741.
-
Biau, G., Cadre, B. and Paris, Q. (2015). Cox process functional learning,
Statistical
Inference for Stochastic Processes, Vol. 18, pp.
255-277.
-
Biau, G., Fischer, A., Guedj, B. and Malley, J.D.
(2016). COBRA: A combined
regression strategy (supplementary
material), Journal
of Multivariate Analysis, Vol. 146, pp.
18-28. Download COBRA.
-
Biau, G. and Scornet, E. (2016). A random forest guided tour
(with comments and a rejoinder
by the authors),
TEST, Vol.
25, pp. 197-227.
-
Biau, G., Bleakley, K. and Mason, D.M. (2016). Long signal change-point detection,
Electronic Journal of
Statistics, Vol. 10, pp. 2097-2123.
-
Biau, G., Bleakley, K. and Cadre, B. (2016). The statistical performance of
collaborative inference, Journal of Machine
Learning Research, Vol. 17(62), pp. 1-29.
-
Biau, G. and Zenine, R. (2018). Online
asynchronous distributed regression, Annales de l'ISUP,
Vol. 62, pp.
29-58. Download
Dolphin.
-
Biau, G., Cadre, B. and Rouvière, L. (2019). Accelerated gradient boosting, Machine Learning,
Vol. 108, pp.
971-992. Download AGB.
-
Biau, G., Scornet, E. and Welbl, J. (2019). Neural random forests, Sankhyā A, Vol. 81, pp.
347-386.
-
Biau, G., Cadre, B., Sangnier, M. and Tanielian, U.
(2020). Some theoretical
properties of GANs, The Annals of Statistics, Vol. 48, pp.
1539-1566.
-
Bénard, C., Biau, G., Da Veiga, S. and Scornet, E.
(2021). SIRUS: Stable and
Interpretable RUle Set for classification, Electronic Journal of
Statistics, Vol. 15, pp. 427-505. Download SIRUS.
-
Tanielian, U., Sangnier, M. and Biau, G. (2021). Approximating Lipschitz continuous
functions with GroupSort neural networks, in Proceedings of The 24th
International Conference on Artificial
Intelligence and Statistics, ed.
Banerjee, A. and Fukumizu, K., Proceedings of Machine
Learning Research, Vol. 130, pp. 442-450,
PMLR. Codes.
-
Bénard, C., Biau, G., Da Veiga, S. and Scornet, E.
(2021). Interpretable random
forests via rule extraction, in Proceedings of The 24th
International Conference on Artificial
Intelligence and Statistics, ed.
Banerjee, A. and Fukumizu, K., Proceedings of Machine
Learning Research, Vol. 130, pp. 937-945,
PMLR. Download SIRUS.
-
Du, Q., Biau, G., Petit, F. and Porcher, R. (2021). Wasserstein random forests and
applications in heterogeneous treatment effects,
in Proceedings of The 24th
International Conference on Artificial
Intelligence and Statistics, ed.
Banerjee, A. and Fukumizu, K., Proceedings of Machine
Learning Research, Vol. 130, pp. 1729-1737,
PMLR.
-
Biau, G., Sangnier, M. and Tanielian, U. (2021). Some theoretical insights into
Wasserstein GANs, Journal of Machine Learning Research,
Vol. 22(119),
pp. 1-45. Codes.
-
Biau, G. and Cadre, B. (2021). Optimization
by gradient boosting (supplementary
material), in
Advances in Contemporary Statistics and
Econometrics: Festschrift in Honor of Christine
Thomas-Agnan, ed. Daouia, A. and Ruiz-Gazen,
A., pp. 23-44, Springer, Cham.
-
Fermanian, A., Marion, P., Vert, J.-P. and Biau, G.
(2021). Framing RNN as a kernel
method: A neural ODE approach, in Advances in Neural
Information Processing Systems, ed.
Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S.
and Wortman Vaughan, J., Vol. 34, pp.
3121-3134, Curran Associates, Inc. Codes.
-
Bénard, C., Biau, G., Da Veiga, S. and Scornet, E.
(2022). SHAFF: Fast and
consistent SHApley eFfect estimates via random
Forests, in Proceedings of The 25th
International Conference on Artificial
Intelligence and Statistics, ed.
Camps-Valls, G., Ruiz, F.J.R. and Valera, I.,
Proceedings of Machine Learning Research, Vol. 151,
pp. 5563-5582, PMLR. Download SHAFF.
-
Marion, P., Wu, Y.-H., Sander, M.E. and Biau, G.
(2024). Implicit regularization of
deep residual networks towards neural ODEs, in The Twelfth
International Conference on Learning
Representations. Codes.
-
Doumèche, N., Bach, F., Biau, G. and Boyer, C.
(2024). Physics-informed machine
learning as a kernel method, in Proceedings of Thirty
Seventh Conference on Learning Theory,
ed. Agrawal, S. and Roth, A., Proceedings of Machine
Learning Research, Vol. 247, pp. 1399-1450,
PMLR. Codes.
-
Stéphanovitch, A., Tanielian, U., Cadre, B.,
Klutchnikoff, N. and Biau, G. (2024). Optimal 1-Wasserstein distance for
WGANs (supplementary
material), Bernoulli,
Vol. 30, pp.
2955-2978. Codes.
-
Fermanian, A., Chang, J., Lyons, T. and Biau, G.
(2024). The insertion method to
invert the signature of a path, in Recent Advances in
Econometrics and Statistics: Festschrift in Honour
of Marc Hallin, ed. Barigozzi, M.,
Hörmann, S. and Paindaveine, D., pp. 575-595,
Springer, Cham. Codes.
-
Doumèche, N., Biau, G. and Boyer, C. (2025). On the convergence of PINNs (supplementary material), Bernoulli, in
press. Codes.
Preprints
-
Marion, P., Fermanian, A., Biau, G. and Vert, J.-P.
(2022). Scaling ResNets in the
large-depth regime. Codes.
-
Doumèche, N., Bach, F., Biau, G. and Boyer, C.
(2024). Physics-informed kernel
learning. Codes.
-
Marion, P., Berthier, R., Biau, G. and Boyer, C.
(2024). Attention layers provably
solve single-location regression. Codes.
Book chapters, conference proceedings and technical
reports
-
Biau, G. (1999). Downscaling of
precipitation combining kriging and Empirical
Orthogonal Function analysis, in GeoENV II --
Geostatistics for Environmental Applications,
ed. Gómez-Hernàndez, J., Soares, A. and Froidevaux,
R., pp. 151-162, Kluwer, Dordrecht.
-
Berlinet, A. and Biau, G. (1999). A
chaotic non-uniform random variate generator, University Montpellier
II, Technical Report 99-06.
-
Berlinet, A. and Biau, G. (2002). Estimation
de densité et prise de décision, in Décision et
Reconnaissance de Formes en Signal, ed.
Lengellé, R., pp. 141-179, Hermès, Paris.
-
Biau, G. and Györfi, L. (2006). On
a L1-test statistic of homogeneity, Proceedings of the BMS
Conference BeNeLuxFra2005, Bulletin of the Belgian
Mathematical Society Simon Stevin, Vol.
13, pp. 877-881.
-
Biau, G. and Devroye, L. (2014). Cellular
tree classifiers, in Algorithmic Learning Theory: Proceedings of
the 25th International Conference, ALT 2014,
ed. Auer, P., Clark, A., Zeugmann, T. and Zilles, S.,
Lecture Notes in Computer Science, Vol. 8776,
pp. 8-17, Springer, Cham.
-
Biau, G. and Levrard, C. (2016). Comments
on: Probability
enhanced effective dimension reduction for
classifying sparse functional data by Yao,
F., Wu, Y. and Zou, J., TEST, Vol. 25, pp. 41-43.
-
Biau, G. and Massart, P. (2017). Science des données
: naissance ou renaissance ?, in Les Big Data à
Découvert, ed. Bouzeghoub, M. et
Mosseri, R., pp. 134-135, CNRS Editions, Paris.
-
Biau, G. and Fermanian, A. (2020). Learning with signatures, in Functional and
High-Dimensional Statistics and Related Fields,
ed. Aneiros, G., Horová, I., Hušková, M. and Vieu, P.,
pp. 19-26, Springer, Cham.
|