Proves density and mass theorems for specific initial data sets.
problem Initial data sets with boundary in spacetime.
method Harmonic asymptotics and dominant energy condition.
result Spacetime positive mass theorem for initial data sets with apparent horizon boundary.
The paper proves density and positive mass theorems for incomplete manifolds.
problem Proving density and positive mass theorems for manifolds with incomplete ends.
method Using harmonic asymptotics and quantitative positive mass theorem improvements.
result Improved quantitative positive mass theorem in dimensions 3 to 7.
Derives spectral density function for symplectic manifolds.
problem Calculating spectral density functions on symplectic manifolds.
method Explicit local formula derivation for spectral density function.
result Explicit formula for spectral density function.
Derives stability for curvature measure near constant density, proving dual Minkowski problem solutions.
problem Stability of curvature measure near constant density
method Derives stability result for curvature measure, proves existence and uniqueness of solutions to dual Minkowski problem.
result Existence and uniqueness of solutions to dual Minkowski problem for positive indices, stability result for curvature measure.
The paper introduces a new energy density function and proves Liouville type theorems for various maps.
problem Proving Liouville type theorems for holomorphic, harmonic, and pluri-harmonic maps.
method Introducing a new energy density function and deriving Hessian estimates.
result No non-constant holomorphic map exists between certain Hermitian manifolds with specific curvature conditions.
Proves positive mass theorem for non-spin weighted manifolds.
problem Proving the positive mass theorem for non-spin weighted manifolds.
method Establishing density theorem and generalizing Geroch conjecture.
result Proves positive weighted mass theorem for non-spin weighted manifolds.
We find an upper bound for geodesic distances associated to monotone Riemannian metrics on positive definite matrices and density matrices.
Study identifies high-density anomalies in normal data regions.
problem Detecting anomalies in normal data regions.
method Introduces non-parametric algorithmic frameworks for unsupervised detection.
result IPP framework yields the best detection results.
We create efficient coresets for kernel density estimates.
problem Efficiently summarize kernel density estimates for large datasets.
method Construct polynomial-time coresets of size O(sqrt(d)/ε√log(1/ε)) for kernel density estimates.
result Near-optimal coresets with polynomial dependence on 1/ε and logarithmic dependence on 1/ε.
Copulas reveal strong positive dependencies in stock demand fluctuations due to volume imbalances.
problem Analyzing dependencies of stock demands using local volume fluctuations.
method Copula analysis of empirical data to model dependence structures.
result Large local fluctuations of signed traded volumes increase positive dependencies in demand but slightly lower negative ones.
A new imputation method estimates missing values by matching observed marginals from masked data.
problem Missing values in data undermine statistical and machine learning analysis.
method Estimates a distribution from masked observations using positive semi-definite kernel density estimation.
result The method yields both single and multiple imputations from the same fitted density, with statistical consistency and fast adaptive excess risk.
The study of harmonic maps into non-positively curved spaces proves a Bochner formula.
problem Understanding harmonic maps in non-positively curved spaces.
method Expanding domain variation and Bochner formulas in terms of curvature.
result Harmonic maps from spaces of non-negative Ricci curvature into non-positively curved spaces have subharmonic energy density.
Given a nonlinear model, a probabilistic forecast may be obtained by Monte Carlo simulations. At a given forecast horizon, Monte Carlo simulations yield sets of discrete forecasts, which can be converted to density forecasts. The resulting density forecasts will inevitably be downgraded by model mis-specification. In o…
Survival MDN uses invertible functions to speed up survival analysis models.
problem Training neural ODEs for survival analysis is computationally expensive.
method Survival MDN applies an invertible positive function to MDN outputs.
result Survival MDN outperforms or matches other models on concordance, Brier score, and log-likelihood.
We model messaging activities as a hierarchical doubly stochastic point process with three main levels, and develop an iterative algorithm for inferring actors' relative latent positions from a stream of messaging activity data. Each of the message-exchanging actors is modeled as a process in a latent space. The actors…
On a closed manifold of dimension greater than one, every smooth weak Riemannian metric on the space of smooth positive probability densities, that is invariant under the action of the diffeomorphism group, is a multiple of the Fisher--Rao metric.
We study the homotopical minimal periods for maps on infra-solvmanifolds of type (R) using the density of the homotopical minimal period set in the natural numbers. This extends the result of [10] from flat manifolds to infra-solvmanifolds of type (R). Applying our main result we will list all possible maps on infra-so…
Paper estimates diameter for Minkowski problem solutions.
problem Estimating diameter of solutions to Minkowski problem.
method Uniform diameter estimate for Lp dual Minkowski problem. result Uniform diameter estimate for planar Lp dual Minkowski problem. Paper proposes a new approach to optimal transport for vector and matrix densities.
problem Optimal transport for vector and matrix densities with positivity and action transitivity constraints.
method Gauge-theoretic approach using semi-direct product groups of diffeomorphisms and gauge transformations.
result Bures-type metrics on semi-direct product groups relate to Wasserstein-type metrics on vector and matrix densities via Riemannian submersions.
Graph Laplace operators uniquely identify metrics and densities on manifolds.
problem Identifying Riemannian metrics and sampling densities from graph Laplace operators.
method Analyzing intrinsic and extrinsic graph Laplace operators on compact Riemannian manifolds.
result Graph Laplace operators uniquely determine metrics and densities under certain conditions.
The paper classifies biharmonic quadratic maps between spheres, proving their energy density properties.
problem Classifying non-harmonic biharmonic quadratic forms between spheres.
method Proving non-harmonic biharmonic quadratic forms have constant energy density and classifying them.
result Non-harmonic biharmonic quadratic forms have constant energy density (m+1)/2. Paper proposes a new softmax loss for better performance in Positive and Unlabeled data tasks.
problem Current softmax losses and sampling schemes have drawbacks in Positive and Unlabeled learning.
method Proposes Relaxed Softmax (RS) loss and a new negative sampling scheme.
result New training objective drives uplifts in performance on textual and recommendation datasets.
New method estimates travel times more accurately with fewer components.
problem Dynamic number of travel time modes and skewed distributions.
method Gamma mixture densities with sparse estimation and recursive algorithm.
result Improved travel time estimation with fewer components and better fitting accuracy.
Meta-learning method improves PU classification performance.
problem Improving binary classifiers from PU data in unseen tasks.
method Adapts model to PU data using related tasks and neural networks.
result Proposed method outperforms existing methods on synthetic and real-world datasets.
We compute the analytic expression of the probability distributions F{FTSE100,+} and F{FTSE100,-} of the normalized positive and negative FTSE100 (UK) index daily returns r(t). Furthermore, we define the alpha re-scaled FTSE100 daily index positive returns r(t)^alpha and negative returns (-r(t))^alpha that we call, aft…
Random groups with high density have Property (T).
problem Determining the conditions for Property (T) in random groups.
method Analyzing k-gonal random groups and their limits. result Property (T) holds with high probability for high densities.
Bipartite graphs with more edges than a threshold have positive curvature.
problem Determining the curvature of bipartite graphs based on edge density.
method Using a new formula for Lin--Lu--Yau curvature, the study establishes conditions for bipartite graphs to have positive curvature.
result Bipartite graphs with more edges than the specified threshold have positive Lin--Lu--Yau curvature.
Extended Moser's theorem to manifolds with corners.
problem Diffeomorphism group action on smooth densities.
method Based on Banyaga's 1974 paper, with cohomological interpretation.
result Moser's theorem proven for simplices.
This paper presents a method for efficient density estimation in nonlinear systems.
problem Accurate representation of non-Gaussian distributions in nonlinear dynamical systems is challenging.
method Uses Seminonparametric (SNP) densities with probabilists' Hermite polynomial basis and Monte Carlo approximation for maximum likelihood estimation.
result Demonstrates that the method can accurately capture non-Gaussian density structure and compute quantiles using fewer samples than raw Monte Carlo.
Two deep learning models improve indoor location prediction from WiFi fingerprints.
problem Indoor location prediction from WiFi fingerprints.
method Convolutional mixture density recurrent neural network and VAE-based semi-supervised learning model.
result Proposed models outperform existing methods in real-world datasets.
In terms of the stock exchange returns, we compute the analytic expression of the probability distributions F{DAX,+} and F{DAX,-} of the normalized positive and negative DAX (Germany) index daily returns r(t). Furthermore, we define the alpha re-scaled DAX daily index positive returns r(t)^alpha and negative returns (-…
New method connects leverage scores and kernel density, revealing a decreasing relationship.
problem Understanding the relationship between leverage scores and kernel density.
method Introducing regularized Christoffel functions to study leverage scores for kernel methods.
result Quantitatively describes a decreasing relation between leverage score and population density for a broad class of kernels.
The study examines conjugation curvature in a specific group, finding elements with various curvatures.
problem Analyzing conjugation curvature in a particular group structure.
method Examined elements in BS(1,n), calculated word length, and used density results. result Found elements with positive, negative, and zero conjugation curvature.
This paper proposes using contextualized word representations for better concept taxonomies.
problem Current taxonomy learning systems define concepts as single words, limiting their semantic understanding.
method Defines concepts as synsets, learns density-based approximations of contextualized word representations, and measures similarity and hypernymy.
result Contextualized word representations can improve the accuracy of concept taxonomies.
We propose a method for nonparametric density estimation that exhibits robustness to contamination of the training sample. This method achieves robustness by combining a traditional kernel density estimator (KDE) with ideas from classical M-estimation. We interpret the KDE based on a radial, positive semi-definite ke…
The implicit function theorem is proven for Lipschitz mappings into metric spaces.
problem Proving the implicit function theorem for mappings into arbitrary metric spaces.
method Metric change of variables and positive upper density.
result There exists a local diffeomorphism and a projection map satisfying the theorem.
The paper studies curvature bounds for manifolds with density.
problem Curvature bounds for Riemannian manifolds with density.
method Develops new tools for studying weighted sectional curvature bounds, including a weighted Rauch comparison theorem and a modified convexity notion.
result Improves results for spaces of positive weighted sectional curvature and symmetry.
The Fisher-Rao metric on smooth densities is studied on compact manifolds.
problem Characterizing the Fisher-Rao metric on smooth densities.
method Analyzing geodesics, curvature, and completeness of the Fisher-Rao metric.
result Geodesics and curvature of the Fisher-Rao metric are determined.
Fold maps associated to geodesic random walks on curved spaces.
problem Understanding the behavior of geodesic random walks on curved surfaces.
method Analyzing mappings from the unit tangent sphere to a manifold with non-positive curvature.
result For odd powers of the unit tangent sphere, these mappings are fold maps.
DEDPUL improves PU learning by estimating proportions and classifying unlabeled data.
problem Analog to supervised binary classification with only positive samples clean and unlabeled mixtures of positive and negative.
method Applies a post-processing procedure to any classifier trained to distinguish positive and unlabeled data, estimating proportions alongside classification.
result Outperforms state-of-the-art in both proportion estimation and PU classification.
UMNNs improve density estimation and variational inference without constraints.
problem Creating expressive invertible transformations without constraints.
method Proposed UMNN architecture enforcing monotonicity with a free-form neural network.
result UMNNs enhance autoregressive flows for density estimation and variational inference.
We investigate the position of the Buchen-Kelly density in a family of entropy maximising densities which all match European call option prices for a given maturity observed in the market. Using the Legendre transform which links the entropy function and the cumulant generating function, we show that it is both the uni…
We study the asymptotic behaviour of the partial density function associated to sections of a positive hermitian line bundle that vanish to a particular order along a fixed divisor Y. Assuming the data in question is invariant under an S1-action (locally around Y) we prove that this density function has a distri…
The paper constructs hyperbolic elements in multiple spaces.
problem Constructing hyperbolic elements in multiple Gromov-hyperbolic spaces.
method Explicit construction under minimal conditions.
result Set of simultaneously hyperbolic elements has strictly positive density.
We compute the analytic expression of the probability distributions F{AEX,+} and F{AEX,-} of the normalized positive and negative AEX (Netherlands) index daily returns r(t). Furthermore, we define the αre-scaled AEX daily index positive returns r(t)^αand negative returns (-r(t))^αthat we call, after normalization, the …
Paper proposes approximate Stein classes for efficient truncated density estimation.
problem Difficulties in estimating truncated density models due to intractable normalising constants and boundary conditions.
method Adapts score matching to solve the problem, introduces approximate Stein classes and a novel discrepancy measure, TKSD.
result TKSD does not require a fixed weighting function and can be evaluated using only boundary samples, leading to improved accuracy.
Hierarchical nucleation patterns emerge in deep neural network layers.
problem Understanding the generation of meaningful representations in deep neural networks.
method Analysis of the probability density of ImageNet dataset across hidden layers.
result Density peaks in subsequent layers mirror the semantic hierarchy of concepts, resembling nucleation process.
Paper generalizes PU classification for class prior shift and asymmetric error scenarios.
problem Bottlenecks in binary classification from PU data due to test marginal distribution and equal error penalties.
method Analysis of Bayes optimal classifier, risk minimization framework, and density ratio estimation framework.
result PU classification under class prior shift is equivalent to PU classification with asymmetric error.