Related papers: The Shapes of Things to Come: Probability Density …
Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…
This paper describes how to specify probability models for data analysis via a backward induction procedure. The new approach yields coherent, prior-free uncertainty assessment. After presenting some intuition-building examples, the new…
We study the geometry of germs of definable (semialgebraic or subanalytic) sets over a $p$-adic field from the metric, differential and measure geometric point of view. We prove that the local density of such sets at each of their points…
The probability density function (PDF) associated with a given set of samples is approximated by a piecewise-linear polynomial constructed with respect to a binning of the sample space. The kernel functions are a compactly supported basis…
A generalized Kullback-Leibler relative entropy is introduced starting with the symmetric Jackson derivative of the generalized overlap between two probability distributions. The generalization retains much of the structure possessed by the…
Finite mixture models that allow for a broad range of potentially non-elliptical cluster distributions is an emerging methodological field. Such methods allow for the shape of the clusters to match the natural heterogeneity of the data,…
Wide conditions are provided to guarantee asymptotic unbiasedness and L^2-consistency of the introduced estimates of the Kullback-Leibler divergence for probability measures in R^d having densities w.r.t. the Lebesgue measure. These…
New model equations are derived for dynamics of self-aggregation of finite-size particles. Differences from standard Debye-Huckel and Keller-Segel models are: a) the mobility $\mu$ of particles depends on the locally-averaged particle…
Information Geometry generalizes to infinite dimension by modeling the tangent space of the relevant manifold of probability densities with exponential Orlicz spaces. We review here several properties of the exponential manifold on a…
We investigate how quantum coherence can be distributed among the several off-diagonal elements of an arbitrary density matrix. An easily computable quantity that captures this variability notion is proposed and it is argued that it…
We tackle the problem of high-dimensional nonparametric density estimation by taking the class of log-concave densities on $\mathbb{R}^p$ and incorporating within it symmetry assumptions, which facilitate scalable estimation algorithms and…
We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we…
We consider some general facts concerning convergence P_{n}-Q_{n}\to 0 as n\to \infty, where P_{n} and Q_{n} are probability measures in a complete separable metric space. The main point is that the sequences {P_{n}} and {Q_{n}} are not…
We consider the evolution of a quantity advected by a compressible flow and subject to diffusion. When this quantity is scalar it can be, for instance, the temperature of the flow or the concentration of some pollutants. Because of the…
Probability density estimation is a core problem of statistics and signal processing. Moment methods are an important means of density estimation, but they are generally strongly dependent on the choice of feasible functions, which severely…
The estimation of probability densities based on available data is a central task in many statistical applications. Especially in the case of large ensembles with many samples or high-dimensional sample spaces, computationally efficient…
The empirical measure of an interacting particle system is a purely atomic random probability measure. In the limit as the number of particles grows to infinity, we show for McKean-Vlasov systems with common noise that this measure becomes…
This work establishes computable bounds between f-divergences for probability measures within a generalized quasi-$\varepsilon_{(M,m)}$-neighborhood framework. We make the following key contributions. (1) a unified characterization of local…
A coordinate system is constructed for a general accelerating observer in 1+1 dimensions, and is used to determine the particle density of the massless Dirac vacuum for that observer. Equations are obtained for the spatial distribution and…
We make quantitative improvements to recently obtained results on the structure of the image of a large difference set under certain quadratic forms and other homogeneous polynomials. Previous proofs used deep results of Benoist-Quint on…