Neue Begründung der Theorie quadratischer Formen von unendlichvielen Veränderlichen.

By Von Herrn E. Hdlinger. 1909

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Citations in the corpus

Dropout Inference in Bayesian Neural Networks with Alpha-divergences (2017, methodology): “Black-box α -divergence minimisation (Hern´andez-Lobato et al., 2016; Li & Turner, 2016; Minka, 2005) is a class of approximate inference methods extending on VI, approximating EP’s energy function (Minka, 2001) as well as the Hellinger distance (Hellinger, 1909).”
Human-level performance in 3D multiplayer games with population-based reinforcement learning (2018, methodology): “Comparing these behaviour fingerprints using the Hellinger distance (25) we found that the human behaviour was most similar to the FTW agent after 200K games of training.”
On Measures of Entropy and Information (2015, background): “The name originates form that of the corresponding integral in the continuous case [53].”
On Measures of Entropy and Information (1961, unknown): “Pearson divergence ( χ 2 -divergence, chi square divergence, Pearson chi square divergence, Kagan divergence, quadratic divergence, least squares) [4] Pearson ( A ; B ) := = Neyman divergence (inverse Pearson chi square divergence) [13, 39] Neyman ( A ; B ) := Pearson ( B ; A ) The dual of the…”
InfoLM: A New Metric to Evaluate Summarization & Data2Text Generation (2021, background): “From Table 1 we note special cases of α-Divergences: (i) Kullback-Leiber (KL) is recovered by letting α → 1, (ii) Hellinger distance (Hellinger 1909) follows by choosing α = 0.”
Learned lessons in credit card fraud detection from a practitioner perspective (2014, methodology): “HDDT (Cieslak & Chawla, 2008) is a decision tree that uses Hellinger distance (Hellinger, 1909) as splitting criteria that is able to deal with skewed distribution.”
Fifty years of pulsar candidate selection: from simple filters to a new principled real-time classification approach (2016, methodology): “The key feature of the GH-VFDT, is its use of the skew-insensitive Hellinger distance measure (Hellinger 1909; Nikulin 2001) to evaluate split points during learning.”
How Generalizable Is Your Experiment? An Index for Comparing Experimental Samples and Populations (2014, methodology): “However, the definitions of b (or the Hellinger distance, η ¼ ffiffiffiffiffiffiffiffiffiffiffi 1 b p ; Hellinger, 1909; see Online Appendix) could just as easily be used as measures of similarity or distance in propensity score analyses in quasi-experiments.”
Analyzing concept drift and shift from sample data (2018, methodology): “Webb et al. (2016) use Hellinger distance (Hellinger 1909; Hoens et al. 2011) for this purpose.”
An introduction to domain adaptation and transfer learning (2018, methodology): “The length of the geodesic along the statistical manifold, called the Hellinger distance, can be used as a measure of domain discrepancy [96,54].”
Aitchison’s Compositional Data Analysis 40 Years on: A Reappraisal (2022, methodology): “The square root transformation maps the proportions onto the multidimensional unit sphere in the positive orthant [84], and the Euclidean distances are then the same as the Hellinger distances, named after Ernst Hellinger [54].”
Objective Priors: An Introduction for Frequentists (2011, background): “Also, β = 1/2 gives the Bhattacharyya– Hellinger (Bhattacharyya, 1943; Hellinger, 1909) distance, and β = −1 leads to the chi-square distance (Clarke and Sun, 1997, 1999).”
TX-Ray: Quantifying and Explaining Model-Knowledge Transfer in (Un-)Supervised NLP (2019, methodology): “We use Hellinger distance H [14] and neuron distribution length l to quantify differences between discrete feature probability distribu-”
Bayes linear spaces (2010, background): “…variance constitute a Hilbert space (Witting, 1985; Small and Leish, 1994; Berlinet and Thomas-Agnan, 2004), which is relevant in statistical modelling; metric spaces are obtained defining distances such as Hellinger-Matusita (Hellinger, 1909; Matusita, 1955) or those based on Fisher-information.”
Optimal Entropy-Transport problems and a new Hellinger–Kantorovich distance between positive measures (2015, background): “13) provides an equivalent formulation of the Hellinger-Kakutani distance [20, 22], see also Example E.”