The Fisher–Rao loss for learning under label noise

Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, New York (2006)

Goodfellow, I., Bengio, Y., Courville, A.: Deep Learning. MIT Press, Cambridge (2016)

Calin, O.: Deep Learning Architectures: A Mathematical Approach. Springer, Cham (2020)

Kline, D.M., Berardi, V.L.: Revisiting squared-error and cross-entropy functions for training neural network classifiers. Neural Comp. Appl. 14(4), 310–318 (2005)

Golik, P., Doetsch, P., Ney, H.: Cross-entropy vs. squared error training: a theoretical and experimental comparison. In: Proc. Interspeech, pp. 1756–1760 (2013)

Janocha, K., Czarnecki, W.M.: On loss functions for deep neural networks in classification. In: Schedae Informaticae, vol. 25 (2017)

Demirkaya, A., Chen, J., Oymak, S.: Exploring the role of loss functions in multiclass classification. In: Proc. 54th Annu. Conf. Inf. Sci. Syst. (CISS), pp. 1–5 (2020)

Hui, L., Belkin, M.: Evaluation of neural architectures trained with square loss vs cross-entropy in classification tasks. In: Proc. 9th Int. Conf. Learn. Representations (ICLR) (2021)

Singh, A., Príncipe, J.C.: A loss function for classification based on a robust similarity metric. In: Proc. Int. Joint Conf. Neural Netw. (IJCNN), pp. 1–6 (2010)

Frogner, C., Zhang, C., Mobahi, H., Araya-Polo, M., Poggio T.: Learning with a Wasserstein loss. In: Proc. 29th Conf. Neural Inf. Process. Syst. (NIPS), pp. 2053–2061 (2015)

Hou, L., Yu, C.-P., Samaras, D.: Squared earth movers distance loss for training deep neural networks on ordered-classes. In: Proc. 31st Conf. Neural Inf. Process. Syst. (NIPS) (2017)

Clough, J., Byrne, N., Oksuz, I., Zimmer, V.A., Schnabel, J.A., King, A.: A topological loss function for deep-learning based image segmentation using persistent homology. IEEE Trans. Pattern Anal. Mach. Intell. (2020) (early access)

Frenay, B., Verleysen, M.: Classification in the presence of label noise: a survey. IEEE Trans. Neural Netw. Learn. Syst. 25(5), 845–869 (2014)

Sastry, P.S., Manwani, N.: Robust learning of classifiers in the presence of label noise. In: Pal, A., Pal, S.K. (eds.) Pattern Recognition and Big Data. World Scientific, New Jersey (2016)

Ghosh, A., Manwani, N., Sastry, P.: Making risk minimization tolerant to label noise. Neurocomputing 160, 93–107 (2015)

Ghosh, A., Kumar, H., Sastry, P.S.: Robust loss functions under label noise for deep neural networks. In: Proc. 31st AAAI Conf. Artif. Intell., pp. 1919–1925 (2017)

Kumar, H., Sastry, P.S.: Robust loss functions for learning multi-class classifiers. In: Proc. IEEE Int. Conf. Syst. Man Cybern. (SMC), pp. 687–692 (2018)

Zhang, Z., Sabuncu, M.: Generalized cross entropy loss for training deep neural networks with noisy labels. In: Proc. 32nd Conf. Neural Inf. Process. Syst. (NeurIPS) (2018)

Amari, S.: Natural gradient works efficiently in learning. Neural Comput. 10(2), 251–276 (1998)

Amari, S., Nagaoka, H.: Methods of Information Geometry. American Mathematical Society, Providence (2000)

Ay, N., Jost, J., Lê, H.V., Schwachhöfer, L.: Information geometry and sufficient statistics. Probab. Theory Relat. Fields 162(1), 327–364 (2015)

Gattone, S.A., De Sanctis, A., Russo, T., Pulcini, D.: A shape distance based on the Fisher–Rao metric and its application for shapes clustering. Phys. A Stat. Mech. Appl. 487, 93–102 (2017)

Taylor, S.: Clustering financial return distributions using the Fisher information metric. Entropy 21(2) (2019)

Pinele, J., Strapasson, J.E., Costa, S.I.R.: The Fisher–Rao distance between multivariate normal distributions: special cases, bounds and applications. Entropy 22(4) (2020)

Picot, M., Messina, F., Boudiaf, M., Labeau, F., Ayed, I.B., Piantanida, P.: Adversarial robustness via Fisher–Rao regularization. IEEE Trans. Pattern Anal. Mach. Intell. (2022) (early access)

Gomes, E.D.C., Alberge, F., Duhamel, P., Piantanida, P.: Igeood: an information geometry approach to out-of-distribution detection. In: Proc. Int. Conf. Learn. Representations (ICLR) (2022)

Arvanitidis, G., González-Duque, M., Pouplin, A., Kalatzis, D., Hauberg, S.: Pulling back information geometry. In: Proc. 25th Int. Conf. Artif. Intell. Stat. (AISTATS), pp. 4872–4894 (2022)

Atkinson, C., Mitchell, A.F.S.: Rao’s distance measure. Sankhyā Indian J. Stat. Ser. A (1961–2002), 43(3), 345–365 (1981)

Calin, O., Udrişte, C.: Geometric Modeling in Probability and Statistics. Springer, Cham (2014)

Costa, S.I.R., Santos, S.A., Strapasson, J.E.: Fisher information distance: a geometrical reading. Discrete Appl. Math. 197, 59–69 (2015)

Kass, R.E., Vos, P.W.: Geometrical Foundations of Asymptotic Inference. Wiley, New York (1997)

Tsybakov, A.B.: Introduction to Nonparametric Estimation. Springer, New York (2009)

Tsallis, C.: What are the numbers that experiments provide? Quim. Nova 17, 468–471 (1994)

Manwani, N., Sastry, P.S.: Noise tolerance under risk minimization. IEEE Trans. Cybern. 43(3), 1146–1151 (2013)

Pedregosa, F., et al.: Scikit-learn: machine learning in Python. J. Mach. Learn. Res. 12, 2825–2830 (2011)

LeCun, Y., Cortes, C., Burges, C.J.C.: The MNIST database of handwritten digits. http://yann.lecun.com/exdb/mnist/

Nix, D., Weigend, A.: Estimating the mean and variance of the target probability distribution. In: Proc. IEEE Int. Conf. Neural Netw. (ICNN), vol. 1, pp. 55–60 (1994)