Explicit formula derived for Slepian process boundary non-crossing probabilities.
problem Calculating boundary non-crossing probabilities for Slepian processes.
method Derived explicit formula and approximation formula for general continuous boundaries.
result Easy to implement formulas for boundary non-crossing probabilities.
The study counts non-crossing permutations on surfaces of any genus.
problem Counting non-crossing permutations on surfaces of any genus.
method Polygon diagrams and arc diagrams are used to represent non-crossing permutations. The count of these diagrams exhibits interesting polynomial behavior, with leading coefficients related to intersection numbers on moduli spaces.
result The count of polygon diagrams is almost polynomial in the number of points, with leading coefficients related to intersection numbers on moduli spaces.
Let Wi={Wi(ti),ti∈R+},i=1,2,…,d are independent Wiener processes. W={W(t),t∈R+d} be the additive Wiener field define as the sum of Wi. For any trend f in $\kHC$ (the reproducing kernel Hilbert Space of W), we derive upper and lower bounds for the boundary non-crossing proba…
A scalable PyTorch framework for non-crossing quantile regression.
problem Non-crossing quantile regression to avoid impossible negative probability densities.
method CJQR-ALM combining Augmented Lagrangian Method, differentiable pinball loss, and L-BFGS optimization.
result Achieves near-zero crossing rates on large datasets within minutes.
Proposes a non-crossing deep neural network quantile regression method.
problem Quantile crossing in nonparametric quantile regression.
method Non-crossing constraints via rectified linear unit penalty function.
result Established non-asymptotic upper bounds for excess risk.
Proposes a deep learning method to ensure non-crossing quantiles in conditional distributions.
problem Non-crossing quantiles issue in deep learning QR models.
method Generic deep learning algorithm enforcing quantile monotonicity.
result Ensures non-crossing quantiles up to machine precision.
Deep neural networks enforce non-crossing quantile regression curves.
problem Estimating quantile regression curves without crossing.
method Penalized deep ReQU neural networks with a non-crossing penalty.
result Established non-asymptotic risk and error bounds for the estimated QRP.
Introduces NQ network for non-crossing quantile learning.
problem Quantile crossing issue in distributional learning.
method Non-negative activation functions ensure monotonic distributions.
result Effective for distributional reinforcement learning and causal effect estimation.
Study on Gaussian ensemble of matrix products with mixed moments computed.
problem Understanding the statistical properties of matrix products of Gaussian matrices.
method Analysis of a multi-Wishart ensemble and enumeration of non-crossing pairings.
result Mixed moments of the product matrix are computed and found to be weighted by Fuss-Catalan numbers at large N. Study on bit threads and their locking properties in holographic spacetimes.
problem Understanding the conditions under which regions can be locked in holographic spacetimes.
method Investigation of different density bounds and their implications on the locking of regions.
result Non-crossing regions can be locked under the most stringent bound, but crossing regions cannot.
Paper improves wind power forecasting with constrained quantile regression.
problem Improving probabilistic forecasting of wind power.
method Combines support vector machines and nonlinear quantile regression with non-crossing constraints.
result Proposed approach leads to significantly better performance in probabilistic forecasting.
Diagonal complexes generalize associahedra to surfaces, providing models for ribbon graphs and tautological bundles.
problem Generalizing associahedra to surfaces with marked points.
method Defining cell complexes and their barycentric subdivisions on surfaces, proving homotopy equivalences and contraction properties.
result Homotopy equivalence of diagonal complexes to ribbon graph spaces and tautological bundles.
This work connects Cramér distance to QR-DQN for DRL.
problem Improving performance in DRL by capturing full distribution of returns.
method Proves Cramér distance's equivalence to 1-Wasserstein distance and proposes a low-complexity algorithm to compute Cramér distance.
result Cramér distance and quantile regression losses yield collinear gradients under non-crossing constraints.
Regular representation of measures on manifolds with boundary.
problem Representing probability densities on manifolds near boundaries.
method Sufficient conditions for Ck random maps, obstructions to representability. result Conditions for regular representation of measures near boundaries.
RNA structures show that a significant portion of bases do not form hydrogen bonds.
problem Understanding the unpaired bases in RNA secondary structures.
method Comparing random words in free groups to RNA sequences, analyzing word lengths.
result The expected fraction of unpaired bases converges to a constant λ2. In the present paper we define dual monoids for all Artin-Tits groups and we prove that for the type A~n we get a (quasi)-Garside structure. Such a structure provides normal forms for the Artin-Tits group elements and allows to solve some questions such as to determine the centralizer of a power of the Coxeter…
Probability versions of Li-Yau inequalities for manifolds with boundary.
problem Establishing Li-Yau inequalities for manifolds with non-convex boundaries.
method Stochastic analysis and Bakry-Emery curvature-dimension approach.
result Explicit probability versions of Li-Yau inequalities for manifolds with boundary.
Researchers derive a formula for Brownian motion transition probability in a specific octant.
problem Computing default probabilities and credit valuation adjustments in structural credit models.
method Semi-analytic formula derived using separation of variables in spherical coordinates, followed by numerical methods to solve the resulting eigenvalue problem.
result A solution to the transition probability problem expressed as an expansion into special functions and an eigenvalue.
A new machine learning method calculates failure probability efficiently and accurately.
problem Computing the probability of failure for complex systems.
method Penalized Profile Support Vector Machine with adaptive sampling and clustering.
result The method minimizes model evaluations while preserving decision boundary geometry.
Sharp boundaries for detecting dense subhypergraphs established.
problem Detecting dense subhypergraphs in random hypergraphs.
method Established sharp detection boundaries for known and unknown edge probabilities.
result Sharp detectable regions differ significantly from graph counterparts.
The Martin boundary of certain groups is stable under specific conditions.
problem Stability of Martin boundaries in relatively hyperbolic groups.
method Extending Floyd-Ancona inequalities, defining spectral degenerescence, and proving stability criteria.
result The Martin boundary of admissible symmetric finitely supported probability measures on geometrically finite Kleinian groups of dimension at most 5 is always strongly stable.
Investigates methods to regularize quantile regression for accurate predictions.
problem Improving accuracy and fairness in quantile regression predictions.
method Various regularization techniques including expected pinball loss, monotonicity constraints, and rate constraints.
result Deep lattice networks can maintain non-crossing quantiles and improve calibration and fairness.
Study Hofer's metric in compact Lie groups using group invariant convex geometry.
problem Hofer's metric in compact Lie groups and its geodesics.
method Group invariant convex geometry, functional and matrix analysis.
result Existence and characterization of geodesics in compact Lie groups.
The paper explores geometry of probability measures and barycenter maps.
problem Understanding the space of probability measures and their barycenter.
method Information geometry, Fisher metric, dualistic structures, divergences, geodesics.
result Recent developments in the geometry of probability measures and barycenter.
Detects dense subhypergraphs in heterogeneous random hypergraphs.
problem Testing for the existence of a dense subhypergraph in heterogeneous random hypergraphs.
method Established detection boundaries and constructed asymptotically powerful and adaptive tests.
result Developed tests for distinguishing between null and alternative hypotheses.
Method estimates posterior model for boundary value problems with uncertain constraints.
problem Estimating posterior probability model for stochastic boundary value problems with uncertain constraints.
method Probabilistic learning inference using Kullback-Leibler divergence and MCMC.
result Method successfully estimates posterior probability measure with constraints.
Novel method estimates quantile planes over arbitrary predictor spaces.
problem Joint estimation of linear quantile planes in arbitrary predictor domains.
method Parametrization using scalar, vector and function valued parameters; Bayesian methodology with Gaussian process priors.
result Posterior consistency under mild conditions; superior accuracy and coverage compared to existing methods.
Characterizes Martin boundaries of certain hyperbolic groups.
problem Understanding the Martin boundaries of specific groups.
method Topological characterization using Green's function and random walks.
result Martin boundary matches CAT (0) boundary in some cases.
Study optimal transport on simplex boundary, proving transport map and potential regularity.
problem Regularity of transport map and potential on simplex boundary.
method Boundary regularity results for optimal transport maps, exploiting simplex symmetries.
result Regularity properties of transport map and its convex potential.
The study connects the Furstenberg-Poisson boundary to CAT(0) cube complexes under specific conditions.
problem Understanding the Furstenberg-Poisson boundary in CAT(0) cube complexes.
method Analyzing a random walk on a group acting on a CAT(0) cube complex.
result The Roller boundary of a CAT(0) cube complex is the Furstenberg-Poisson boundary for a specific random walk.
A new method tracks retinal vessels more accurately than existing methods.
problem Tracking retinal vessels accurately in spherical images.
method Computing cusp-free, crossing-preserving geodesics on spherical positions and orientations.
result Crossing-preserving tracking shows clear advantages over non-crossing-preserving tracking.
Global EQG sums boundary states over manifold diffeomorphism classes.
problem Summing boundary states over manifold diffeomorphism classes.
method Formulated as classical statistical physics, weights determined by general principles.
result Hartle-Hawking state as a probability measure.
The paper explores how supervision level affects both statistical accuracy and computational efficiency in weakly supervised binary classification.
problem The impact of label flip probability on statistical and computational efficiency in weakly supervised binary classification.
method Information-theoretic and computational boundaries were established to characterize the relationship between supervision level and performance.
result The gap between statistical and computational boundaries narrows as the supervision level increases, indicating improved computational efficiency with more supervision.
Study critical exponents on hyperbolic surfaces with long boundaries using Weil-Petersson measures.
problem Analyzing critical exponents on hyperbolic surfaces with long boundaries.
method Using spine graph construction and comparing normalized Weil-Petersson and Kontsevich measures.
result Asymptotic convergence-in-mean result of normalized Weil-Petersson measures to normalized Kontsevich measures.
New bounds on multi-armed bandit probabilities for exponential families.
problem Analyzing probabilities of crossing boundaries in exponential families.
method Developed a concentration inequality for exponential families of dimension K.
result Extended results to arbitrary finite dimension K, including logarithmic boundary functions.
The interplay between computational efficiency and statistical accuracy in high-dimensional inference has drawn increasing attention in the literature. In this paper, we study computational and statistical boundaries for submatrix localization. Given one observation of (one or multiple non-overlapping) signal submatrix…
Let S be a non-exceptional oriented surface of finite type. We discuss the action of subgroups of the mapping class group of S on the CAT(0)-boundary of the completion of Teichmueller space with respect to the Weil-Petersson metric. We show that the set of invariant Borel probability measures for the Weil-Petersson flo…
Shallow neural nets classify objects perfectly if their distribution is linearly separable.
problem Designing efficient neural networks for classification.
method Constructed shallow sigmoid-type neural networks.
result Achieves 100% accuracy for datasets following a linear separability condition.
Deep neural operators learn complex probabilistic models efficiently.
problem Learning complex probabilistic models with global Lipschitz conditions.
method Deep neural-operator framework under global Lipschitz conditions.
result Explicit network-size bounds for universal approximation of probabilistic models.
We derive a new equation for the optimal investment boundary of a general irreversible investment problem under exponential Lévy uncertainty. The problem is set as an infinite time-horizon, two-dimensional degenerate singular stochastic control problem. In line with the results recently obtained in a diffusive setting,…
A fast method for pricing swaptions in Gaussian models.
problem Pricing swaptions in multi-factor Gaussian term structure models efficiently.
method Approximating exercise boundary by a hyperplane and simplifying multi-dimensional integration.
result Our method is superior to previous methods in accuracy and speed.
Machine learning infers time-reversible dynamics from data.
problem Learn time-reversible dynamics constrained by initial and final conditions.
method Machine learning algorithms solve boundary value problems for deterministic and stochastic dynamics.
result Inferred time-reversible dynamics for various types of systems.
BDSG generates samples on distribution boundaries, improving anomaly detection.
problem Difficulty in capturing multimodal supports and approximating distribution tails.
method Invertible Residual Network (IResNet) and Residual Flow (ResFlow) for density estimation; compound loss function for boundary samples.
result Competitive performance on synthetic and multimodal data compared to existing methods.
Study on hyperbolic manifolds and their boundary data, focusing on volume functions.
problem Determining the hyperbolic metric from boundary data of convex co-compact hyperbolic manifolds.
method Analysis of volume functions and their relation to boundary data, using first variations.
result New connections with physics and probability theory, with open questions remaining.
Paper proposes a method to estimate truncated density models using Score Matching.
problem Estimating parameters of truncated probability densities.
method Score Matching with a novel weight function derived from Stein discrepancy.
result The proposed method minimizes a weighted Fisher divergence and corrects outlier-trimming bias.
Let M1 and M2 be two n-dimensional smooth manifolds with boundary. Suppose we glue M1 and M2 along some boundary components (which are, therefore, diffeomorphic). Call the result N. If we have a group G acting continuously on M1, and also acting continuously on M2, such that the actions are comp…
TailGAN uses GANs to detect anomalies near data distribution tails.
problem Anomaly detection near data distribution tails with current GAN limitations.
method TailGAN leverages GANs with maximum entropy regularization to generate and detect anomalies near data distribution tails.
result TailGAN achieves competitive performance on various datasets compared to existing methods.
This study improves audit sampling by using sequential procedures with statistical guarantees.
problem Improving audit efficiency and reliability with statistical methods.
method Formulated as a sequential testing problem, defining null and alternative hypotheses, stopping and decision rules, and exact boundary conditions.
result Exact design yields ex ante control of decision error probabilities, and simulation-based implementation approximates this design.