Fetching the paper…
Reading the bibliography…
Divergences, also known as contrast functions, are distance-like quantities defined on manifolds of non-negative or probability measures.
In: Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Volume 1: Contributions to the Theory of Statistics. The Regents of the University of California (1961)
Rényi, A.: On measures of entropy and information · 1961
Earlier work this paper cites.
Tech. Rep. METR 82–7, University of Tokyo (1982)
Nagaoka, H., Amari, S.i.: Differential geometry of smooth families of probability distributions · 1982
Earlier work this paper cites.
The Annals of Statistics 11
Eguchi, S.: Second order efficiency of minimum contrast estimators in a curved exponential family · 1983
Earlier work this paper cites.
Monatshefte für Mathematik 109
Dillen, F., Nomizu, K., Vranken, L.: Conjugate connections and radon’s theorem in affine differential geometry · 1990
Earlier work this paper cites.
Mathematische Zeitschrift 203
Kurose, T.: Dual connections and affine geometry · 1990
Earlier work this paper cites.
Communications on Pure and Applied Mathematics 44
Brenier, Y.: Polar factorization and monotone rearrangement of vector-valued functions · 1991
Earlier work this paper cites.
Hiroshima Mathematical Journal 22
Eguchi, S., et al.: Geometry of minimum contrast · 1992
Earlier work this paper cites.
Tohoku Mathematical Journal, Second Series 46
Kurose, T.: On the divergences of 1-conformally flat statistical manifolds · 1994
Earlier work this paper cites.
SIAM Journal on Mathematical Analysis 29
Jordan, R., Kinderlehrer, D., Otto, F.: The variational formulation of the Fokker–Planck equation · 1998
Earlier work this paper cites.
Hiroshima Mathematical Journal 29
Matsuzoe, H.: Geometry of contrast functions and conformal geometry · 1999
Earlier work this paper cites.
American Mathematical Society (2003)
Villani, C.: Topics in Optimal Transportation · 2003
Earlier work this paper cites.
Neural Computation 16
Zhang, J.: Divergence function, duality, and convex analysis · 2004
Earlier work this paper cites.
Journal of Machine Learning Research 6
Banerjee, A., Merugu, S., Dhillon, I.S., Ghosh, J.: Clustering with bregman divergences · 2005
Earlier work this paper cites.
In: Proceedings of the Second International Symposium on Information Geometry and Its Applications, Tokyo, Japan, vol. 1216, p. 5867 (2005)
Zhang, J.: Referential duality and representational duality on statistical manifolds · 2005
Earlier work this paper cites.
Translations of mathematical monographs. American Mathematical Society (2007)
Amari, S., Nagaoka, H., Harada, D.: Methods of Information Geometry · 2007
Earlier work this paper cites.
Springer (2008)
Ambrosio, L., Gigli, N., Savaré, G.: Gradient flows: In Metric Spaces and in the Space of Probability Measures · 2008
Cited alongside, same era.
Springer (2008)
Villani, C.: Optimal Transport: Old and New · 2008
Cited alongside, same era.
In: Journal of Physics: Conference Series, vol. 201, p. 012003. IOP Publishing (2010)
Naudts, J.: The q q -exponential family in statistical physics · 2010
Cited alongside, same era.
Communications in Mathematical Physics 307
Adams, S., Dirr, N., Peletier, M.A., Zimmer, J.: From a large-deviations principle to the Wasserstein gradient flow: a new micro-macro passage · 2011
Cited alongside, same era.
Entropy 13
Amari, S.i., Ohara, A.: Geometry of q q -exponential family of probability distributions · 2011
Cited alongside, same era.
Journal of Functional Analysis 262
Léonard, C.: From the Schrödinger problem to the Monge-Kantorovich problem · 2012
Cited alongside, same era.
Annals of Finance 11
Wong, T.K.L.: Optimization of relative arbitrage · 2015
Later among the works it cites.
In: AIP Conference Proceedings, vol. 1641, pp. 130–146. AIP (2015)
Zhang, J.: Reference duality and representation duality in information geometry · 2015
Later among the works it cites.
Springer (2016)
Amari, S.i.: Information Geometry and Its Applications · 2016
Later among the works it cites.
Mathematics and Financial Economics 10
Pal, S., Wong, T.K.L.: The geometry of relative arbitrage · 2016
Later among the works it cites.
Springer (2017)
Ay, N., Jost, J., Lê, H., Schwachhöfer, L.: Information geometry · 2017
Closest in time.
Indian Journal of Pure and Applied Mathematics 48
Pal, S.: Embedding optimal transports in statistical manifolds · 2017
Closest in time.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
In: Modelling and Optimisation of Flows on Networks, pp. 1–155. Springer (2013)
Ambrosio, L., Gigli, N.: A user’s guide to optimal transport · 2013
Cited alongside, same era.
arXiv preprint arXiv:1308.5376 (2013)
Pal, S., Wong, T.K.L.: Energy, entropy, and arbitrage · 2013
Cited alongside, same era.
Springer (2014)
Calin, O., Udrişte, C.: Geometric modeling in probability and statistics · 2014
Cited alongside, same era.
IEEE Transactions on Information Theory 60
Van Erven, T., Harremos, P.: Rényi divergence and Kullback-Leibler divergence · 2014
Cited alongside, same era.
Entropy 17
Ay, N., Amari, S.i.: A novel approach to canonical divergences within information geometry · 2015
Cited alongside, same era.
arXiv preprint arXiv:1508.05216 (2015)
Chizat, L., Peyré, G., Schmitzer, B., Vialard, F.X.: Unbalanced optimal transport: geometry and kantorovich formulation · 2015
Cited alongside, same era.
Wong, T.K.L.: On portfolios generated by optimal transport · 2017
Closest in time.
To appear in Information Geometry
Amari, S.i., Karakida, R., Oizumi, M.: Information geometry connecting Wasserstein distance and Kullback–Leibler divergence via the entropy-relaxed transportation problem (2018) · 2018
Closest in time.
arXiv preprint arXiv:1805.08380 (2018)
Chen, Y., Li, W.: Natural gradient in Wasserstein statistical manifold · 2018
Closest in time.
arXiv preprint arXiv:1806.11363 (2018)
Felice, D., Ay, N.: Towards a canonical divergence within information geometry · 2018
Closest in time.
arXiv preprint arXiv:1807.07095 (2018)
Li, W., Montufar, G.: Ricci curvature for parametric statistics via optimal transport · 2018
Closest in time.
To appear in Information Geometry
Naudts, J., Zhang, J.: Rho–tau embedding and gauge freedom in information geometry (2018) · 2018
Closest in time.
The Annals of Probability 46
Pal, S., Wong, T.K.L.: Exponentially concave functions and a new information geometry · 2018
Closest in time.
arXiv preprint arXiv:1807.05649 (2018)
Pal, S., Wong, T.K.L.: Multiplicative Schrödinger problem and the Dirichlet transport · 2018
Closest in time.