27 citations · 32 across the 10 of their papers we have counts for
10 papers
Scales of Fréchet means and Karcher quasi-arithmetic means
Frank Nielsen
In this paper, we first prove that any interior point of an open interval of the real line can be interpreted as Fréchet means with respect to corresponding metric distances, thus…
Two tales for a geometric Jensen--Shannon divergence
Frank Nielsen
The geometric Jensen--Shannon divergence (G-JSD) gained popularity in machine learning and information sciences thanks to its closed-form expression between Gaussian distributions.…
Hilbert geometry of the symmetric positive-definite bicone: Application to the geometry of the extended Gaussian family
Jacek Karwowski, Frank Nielsen
The extended Gaussian family is the closure of the Gaussian family obtained by completing the Gaussian family with the counterpart elements induced by degenerate covariance or dege…
Geometric Jensen-Shannon Divergence Between Gaussian Measures On Hilbert Space
Minh Ha Quang, Frank Nielsen
This work studies the Geometric Jensen-Shannon divergence, based on the notion of geometric mean of probability measures, in the setting of Gaussian measures on an infinite-dimensi…
Curved representational Bregman divergences and their applications
Frank Nielsen
By analogy to the terminology of curved exponential families in statistics, we define curved Bregman divergences as Bregman divergences restricted to non-affine parameter subspaces…
Adaptive -nearest neighbor classifier based on the local estimation of the shape operator
Alexandre Luís Magalhães Levada, Frank Nielsen, Michel Ferreira Cardia Haddad
The -nearest neighbor (-NN) algorithm is one of the most popular methods for nonparametric classification. However, a relevant limitation concerns the definition of the numbe…
A Rate-Distortion View of Uncertainty Quantification
Ifigeneia Apostolopoulou, Benjamin Eysenbach, Frank Nielsen +1
In supervised learning, understanding an input's proximity to the training data can help a model decide whether it has sufficient evidence for reaching a reliable prediction. While…
Approximation and bounding techniques for the Fisher-Rao distances between parametric statistical models
Frank Nielsen
The Fisher-Rao distance between two probability distributions of a statistical model is defined as the Riemannian geodesic distance induced by the Fisher information metric. In ord…
Partial k-means to avoid outliers, mathematical programming formulations, complexity results
Nicolas Dupin, Frank Nielsen
A well-known bottleneck of Min-Sum-of-Square Clustering (MSSC, the celebrated -means problem) is to tackle the presence of outliers. In this paper, we propose a Partial clusteri…
Sinkhorn AutoEncoders
Giorgio Patrini, Rianne van den Berg, Patrick Forré +5
Optimal transport offers an alternative to maximum likelihood for learning generative autoencoding models. We show that minimizing the p-Wasserstein distance between the generator…