A definition for elliptical tempered stable distribution, based on the characteristic function, have been explained which involve a unique spectral measure. This definition provides a framework for creating a connection between infinite divisible distribution, and particularly elliptical tempered stable distribution, w…
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48 results for “infinitely divisible distributions”
We connect shift-invariant characteristic kernels to infinitely divisible distributions on . Characteristic kernels play an important role in machine learning applications with their kernel means to distinguish any two probability measures. The contribution of this paper is two-fold. First, we show, usi…
In this paper, we study the risk bounds for samples independently drawn from an infinitely divisible (ID) distribution. In particular, based on a martingale method, we develop two deviation inequalities for a sequence of random variables of an ID distribution with zero Gaussian component. By applying the deviation ineq…
Spectral methods learn flexible topic models with topic correlations.
problem Learning topic models with arbitrary topic correlations.
method Flexible topic model using Normalized Infinitely Divisible (NID) distributions, learned via spectral methods.
result Improved perplexity on real datasets compared to baseline.
New framework resolves central limit behavior in differential privacy.
problem Choosing appropriate privacy metrics in hypothesis testing.
method Infinitely divisible limit experiments and Le Cam's theory.
result Characterizes all limiting baseline trade-off functions in differential privacy.
This a free translation with additional explanations of {\em Processus à Accroissement Independants Chapitre I: La Décomposition de Paul Lévy}, by J.L. Bretagnolle, in {\em Ecole d'Eté de Probabilités}, Lecture Notes in Mathematics 307, Springer 1973. The Lévy-Khintchine representation of infinitely divisible distribut…
As a corollary of work of Ozsvath and Szabo [math.GT/0301149], it is shown that the classical concordance group of algebraically slice knots has an infinite cyclic summand and in particular is not a divisible group.
Horse racing odds match random division statistics.
problem Understanding the distribution of horses' winning abilities.
method Comparing horse racing data with the 'randomly broken stick' problem.
result Horses' winning abilities are exponentially distributed.
Information theory provides principled ways to analyze different inference and learning problems such as hypothesis testing, clustering, dimensionality reduction, classification, among others. However, the use of information theoretic quantities as test statistics, that is, as quantities obtained from empirical data, p…
Probability Weighting Meets Heavy Tails: An Econometric Framework for Behavioral Asset Pricingq-fin.MF
Econometric framework integrates heavy-tailed distributions with behavioral probability weighting for better asset pricing.
problem Underestimation of Value-at-Risk by traditional models in asset pricing.
method Developed an econometric framework combining heavy-tailed Student's distributions with behavioral probability weighting.
result Student's specifications outperform Gaussian models in 88.4% of cases, reducing underestimation of Value-at-Risk by 16.5 percentage points.
We analyze the Levy processes produced by means of two interconnected classes of non stable, infinitely divisible distribution: the Variance Gamma and the Student laws. While the Variance Gamma family is closed under convolution, the Student one is not: this makes its time evolution more complicated. We prove that -- a…
Algorithm learns fair division from noisy feedback in uncertain markets.
problem Learning fair division in uncertain markets with noisy feedback.
method Wrapper algorithms using dual averaging to learn item and agent values from bandit feedback.
result Asymptotically achieves optimal Nash social welfare in linear Fisher markets.
New examples of hyperbolic manifolds with convex projective structures.
problem Finding new examples of hyperbolic manifolds with convex projective structures.
method Generalized Dehn filling and real projective structures.
result Infinitely many hyperbolic manifolds with cusps admit properly convex real projective structures.
Researchers infer gene activity in dividing cells, accounting for protein inheritance and division history.
problem Inferring protein production kinetics in dividing cells due to protein inheritance and division history.
method Adapted conditional normalizing flows to approximate intractable likelihoods from simulated data.
result Glc3 gene is mostly inactive under stress, with brief and transient expression.
A new distributed algorithm for fitting sparse additive models with feature division and decorrelation.
problem Fitting high-dimensional sparse additive models efficiently and accurately.
method Divide, decorrelate, and conquer approach.
result Effective and efficient recovery of sparsity patterns and statistical inference for each component.
From division to extensionmath.CV
A new proof of an extension theorem with bounded generators.
problem Extension theorems in complex analysis.
method Skoda-type division theorem with bounded generators.
result The new division theorem allows to be 1 in the norm of the datum.
Unique convex divisible domain found in Grassmannian.
problem Finding convex divisible domains in flag manifolds.
method Analyzing projective isomorphism and Lie groups.
result Only one convex divisible domain in Grassmannian.
Solves division problem for L. Hörmander's systems.
problem Division problem for L. Hörmander's overdetermined systems.
method Formulates and proves divisibility criterion, coherence theorem.
result Establishes effective divisibility criterion and extends coherence theorem.
Proves divisibility relations for symplectic curve polynomials.
problem Divisibility relations for symplectic curve polynomials.
method New proofs of divisibility relations for Oka and Alexander polynomials of symplectic curves.
result Proves Libgober's divisibility relations for symplectic curves.
funLOCI identifies clusters in functional data.
problem Identifying similar behavior in functional data.
method Divisive hierarchical clustering with additive model.
result funLOCI reduces the number of local clusters.
Uniform convexity in divisible domains leads to hyperbolic geometry.
problem Understanding the geometry of divisible convex sets in Finsler manifolds.
method Proving -uniform convexity of a specific Finsler metric.
result A strictly convex divisible domain induces a -uniformly convex Finsler metric.
Tropical division approximates polynomial division for neural networks.
problem Approximating polynomial division in max-plus semiring.
method Approximating Newton Polytope of dividend by divisor, then applying to neural networks.
result Minimizes a two-layer fully connected network for binary classification.
Paper tackles division difficulty, proposing new methods to improve accuracy.
problem Division is the most challenging arithmetic operation for both humans and computers.
method Proposes two novel approaches: Neural Reciprocal Unit (NRU) and Neural Multiplicative Reciprocal Unit (NMRU), and improves an existing division module.
result Improves division accuracy from 70.2% to 91.6%.
For each odd integer r greater than one and not divisible by three we give explicit examples of infinite families of simply and tangentially homotopy equivalent but pairwise non-homeomorphic closed homogeneous spaces with fundamental group isomorphic to Z/r. As an application we construct the first examples of manifold…
Adopting a zonal structure of electricity market requires specification of zones' borders. In this paper we use social welfare as the measure to assess quality of various zonal divisions. The social welfare is calculated by Market Coupling algorithm. The analyzed divisions are found by the usage of extended Locational …
Division algorithm for surface group rings yields standard complexes and cohomological dimensions.
problem Understanding cohomological dimensions of surface group actions.
method Division algorithm for group rings of surface groups.
result Some 2-complexes with surface fundamental groups are standard.
Geometrically explains divisibility of Euler classes for spin modules.
problem Divisibility of -theoretical Euler classes for spin modules.
method Geometric interpretation of divisibility using spin structures and Seiberg-Witten theory.
result Clarifies the role of reducibles in monopole equations.
The paper sets lower bounds on envy-free divisions in cake-cutting problems.
problem Finding the minimum number of envy-free divisions in cake-cutting problems.
method Analyzes two scenarios: classical and hybrid, with different constraints and allocations.
result Sharp bounds and examples for envy-free divisions in both scenarios.
New proof of divisibility property for certain algebraic varieties.
problem Divisibility property for LQEL varieties.
method Construction of Clifford algebra representations to Severi varieties.
result New proof of Russo's Divisibility Property for LQEL varieties.
The paper revisits Rokhlin's divisibility theorem and its significance.
problem Rokhlin's divisibility theorem on signatures of manifolds.
method Overview and retrace of Rokhlin's proof and further developments.
result Reaffirms the importance of Rokhlin's theorem in manifold theory.
Proves Skoda's Division Theorem using degeneration and positivity of direct image bundles.
problem Division Theorem in Skoda's context
method Degeneration approach inspired by B. Berndtsson and L. Lempert's extension theorem
result Simplified and extended proof of extension theorem
Under certain integrability and geometric conditions, we prove division theorems for the exact sequences of holomorphic vector bundles and improve the results in the case of Koszul complex. By introducing a singular Hermitian structure on the trivial bundle, our results recover Skoda's division theorem for holomorphic …
The paper explains the topological origin of the distinction between incidence theorems over division rings and fields.
problem Understanding the distinction between incidence theorems over division rings and fields.
method Extending the surface-graph approach to noncommutative settings, the paper analyzes the topological properties of graphs embedded on surfaces of different genera.
result Theorems associated with graphs on the sphere hold over any division ring, while those on surfaces of positive genus typically hold only if the ground ring is a field.
Constructs projective plane over octonions, proving no higher real division algebras.
problem Existence of higher-dimensional real division algebras.
method Using Adams' solution of the Hopf invariant 1 problem, constructs projective plane over octonions.
result No higher-dimensional real division algebras exist.
Avoiding subtraction and division of stochastic signals using normalizing flows: NFdeconvolvestat.ML
A new method avoids noise amplification when subtracting or dividing stochastic signals.
problem Noise amplification when subtracting or dividing stochastic signals.
method Normalizing flows to approximate the distribution of the signal of interest.
result Normalizing flows can generate an approximation of the probability distribution over the signal of interest, avoiding subtraction or division.
Market incentivizes parties to share high-quality data for collaborative machine learning tasks.
problem Fair revenue distribution and data replication threats in collaborative machine learning markets.
method Introduces a novel payment division function robust to replication and customized output models.
result Validated assumptions and showed approximate satisfaction for commonly used models.
Dividing local Gaussian processes improve real-time prediction efficiency.
problem Efficient online prediction for large data sets.
method Iterative data-driven division of input space for sublinear computational complexity.
result Sublinear computational complexity in real-time prediction.
Envy-free classification ensures fairness in machine learning tasks.
problem Ensuring fairness in classification tasks.
method Analyzes the generalizability of envy-free classifiers, focusing on low Natarajan dimension families of deterministic classifiers.
result A small sample is sufficient to achieve almost envy-free classification guarantees.
Geodesic connectedness proved for statistical manifolds with divisible cubic forms.
problem Geodesic connectedness of affine connections on statistical manifolds with divisible cubic forms.
method Analogy with Hopf-Rinow theorem in Riemannian geometry, establishing geodesic completeness.
result Geodesic connectedness established for statistical manifolds with divisible cubic forms.
Paper introduces DACAL for high-resolution photo and video enhancement.
problem Photo and video enhancement with weak supervision.
method Divide-and-conquer adversarial learning approach with hierarchical decomposition.
result State-of-the-art performance in high-resolution photo and video enhancement.
Paper finds a divisibility property of first Pontrjagin classes for even-dimensional homotopy complex projective spaces.
problem Understanding the first Pontrjagin classes of homotopy complex projective spaces.
method Analyzing the difference of first Pontrjagin classes for even-dimensional manifolds homotopy equivalent to .
result The difference of the first Pontrjagin classes is divisible by 16 for even .
A new SBI framework for trawl processes efficiently estimates parameters from large datasets.
problem Challenges in estimating parameters of complex stochastic processes.
method Telescoping ratio estimation, Chebyshev polynomial approximations, amortized posterior inference.
result Accurate and efficient inference for intractable stochastic processes, even with limited data.
Study of characteristic numbers in 24-dimensional String manifolds.
problem Characterizing and understanding characteristic numbers of 24-dimensional String manifolds.
method Using Pontryagin numbers, integral basis of String cobordism group, and divisibility results.
result Established 2- and 3-primary divisibilities of characteristic numbers.
An open convex set in real projective space is called divisible if there exists a discrete group of projective automorphisms which acts co-compactly. There are many examples of such sets and a theorem of Benoist implies that many of these examples are strictly convex, have boundary, and have word hyperbolic divid…
The Jones polynomial's divisibility is analyzed via local moves on virtual links.
problem Divisibility of the Jones polynomial under local moves on virtual links.
method Developed a general decomposition for the Jones polynomial of virtual links and analyzed divisibility conditions for various local moves.
result Succinct divisibility conditions on the Jones polynomial of virtual links differing via local moves.
In this note we introduce a construction which assigns to an arbitrary manifold bundle its fiberwise orientation covering. This is used to show that the zeta classes of unoriented surface bundles are not divisible in the stable range.
Supersymmetry is deeply related to division algebras. Nonabelian Yang-Mills fields minimally coupled to massless spinors are supersymmetric if and only if the dimension of spacetime is 3, 4, 6 or 10. The same is true for the Green-Schwarz superstring. In both cases, supersymmetry relies on the vanishing of a certain tr…
Study shows non-symmetric convex sets have full boundary limits.
problem Understanding boundaries of non-symmetric convex sets.
method Proved using proximal limit set analysis.
result Proximal limit set equals full projective boundary for non-symmetric irreducible divisible convex sets.