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.

• Fermanian, A., Chang, J., Lyons, T. and Biau, G. (2024). The insertion method to invert the signature of a path, in Festschrift in Honor of Marc Hallin, in press. Codes.

• Stéphanovitch, A., Tanielian, U., Cadre, B., Klutchnikoff, N. and Biau, G. (2024). Optimal 1-Wasserstein distance for WGANs, Bernoulli, in press. Codes.

• Marion, P., Wu, Y.-H., Sander, M.E. and Biau, G. (2024). Implicit regularization of deep residual networks towards neural ODEs, International Conference on Learning Representations, in press.

Preprints

• Marion, P., Fermanian, A., Biau, G. and Vert, J.-P. (2022). Scaling ResNets in the large-depth regime. Codes.

• Doumèche, N., Biau, G. and Boyer, C. (2023). On the convergence of PINNs. Codes.

• Doumèche, N., Bach, F., Biau, G. and Boyer, C. (2024). Physics-informed machine learning as a kernel method.

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.