This study assesses risk concentration in MDB portfolios using Monte Carlo simulations.
problem Risk concentration in MDB portfolios of a few borrowers.
method Realistic MDB portfolio simulations and Monte Carlo analysis.
result Current risk adjustments may be overly conservative.
Deep learning method improves risk assessment for small loan portfolios.
problem Measuring name concentration risk in small loan portfolios.
method Deep learning approach using Monte Carlo simulations with importance sampling.
result New method outperforms existing analytical methods for small portfolios.
New assumptions and algorithm solve offline two-player zero-sum Markov games.
problem Solving offline two-player zero-sum Markov games under insufficient assumptions.
method Proposed unilateral concentration assumption and pessimism-type algorithm.
result Algorithm efficiently learns Nash equilibrium under unilateral concentration.
Mean exit times concentrate near equators and minimal hypersurfaces in high dimensions.
problem Understanding mean exit times on spheres and manifolds.
method Analyzing Brownian motion on spheres and manifolds with minimal hypersurfaces.
result Mean exit times concentrate near equators and minimal hypersurfaces in high dimensions.
Sharp stability result for maps near infinitely concentrated minimisers.
problem Stability of maps near minimisers with infinite concentration.
method Dynamic approach to deform maps into harmonic maps, controlling topology changes.
result Sharp quantitative estimates on map distance to infinitely concentrated minimisers.
We present a methodology to extract the backbone of complex networks based on the weight and direction of links, as well as on nontopological properties of nodes. We show how the methodology can be applied in general to networks in which mass or energy is flowing along the links. In particular, the procedure enables us…
The study provides a criterion for diffeomorphism via long-time Ricci flow.
problem Understanding conditions for diffeomorphism in geometric flows.
method Long-time Ricci flow criterion for diffeomorphism.
result Affirmative answer to manifold diffeomorphism in dimension 4.
Expanding on techniques of concentration of measure, we develop a quantitative framework for modeling liquidity risk using convex risk measures. The fundamental objects of study are curves of the form (ρ(λX))λ≥0, where ρ is a convex risk measure and X a random variable, and we call such a curve a \emph{liqu…
Paper addresses DP in bandits, focusing on zCDP and providing private algorithms.
problem Privacy concerns in recommender systems using user-sensitive data.
method Formalizes and compares different DP adaptations to bandits, proposes private algorithms for various bandit settings.
result Private algorithms ensure negligible privacy costs compared to non-private regret.
Spike-and-Slab Deep Learning (SS-DL) is a fully Bayesian alternative to Dropout for improving generalizability of deep ReLU networks. This new type of regularization enables provable recovery of smooth input-output maps with unknown levels of smoothness. Indeed, we show that the posterior distribution concentrates at t…
Greedy algorithm achieves sublinear regret for various distributions.
problem Efficient performance of greedy algorithms in linear contextual bandit problems.
method Introduced Local Anti-Concentration (LAC) condition to ensure sublinear regret.
result Greedy algorithm achieves O(polylogT) cumulative expected regret. Quantum neural networks converge to Gaussian processes as they grow.
problem Understanding the convergence of quantum neural networks to Gaussian processes.
method Analyzing Haar random unitary and orthogonal deep QNNs, considering input states, measurement observables, and non-independence of unitary matrix entries.
result Quantum neural networks outputs converge to Gaussian processes in the limit of large Hilbert space dimension.
Max-sliced Wasserstein metric reduces high-dimensional data to 1D for better estimation.
problem Curse of dimensionality in optimal transport.
method Introduces max-sliced Wasserstein metric to reduce high-dimensional problems to 1D.
result Uniform ratio bounds of empirical measures on RKHS concentrate uniformly fast at parametric rates.
Study on signed graphs with random signs, focusing on community detection.
problem Community detection in signed stochastic block models.
method Strong concentration inequalities for adjacency and Laplacian matrices, applied to signed Laplacian matrix.
result The sign of the first eigenvector of the Laplacian matrix defines a weakly consistent estimator for balanced community detection.
Study on estimating distances between covariance operators and Gaussian processes.
problem Estimating distances between covariance operators and Gaussian processes.
method Riemannian distances, concentration results for Hilbert space-valued random variables, RKHS covariance and cross-covariance operators.
result Both distances converge in the Hilbert-Schmidt norm and can be consistently and efficiently estimated.
This paper presents a unified approach based on Wasserstein distance to derive concentration bounds for empirical estimates for two broad classes of risk measures defined in the paper. The classes of risk measures introduced include as special cases well known risk measures from the finance literature such as condition…
Bayesian inference for Levy density with Gibbs posterior in discrete sampling.
problem Inference on Levy density for financial models with jumps.
method Gibbs posterior framework using a loss function for intractable likelihood.
result Gibbs posterior achieves nearly optimal rate of convergence under certain conditions.
The portfolio optimization problem in which the variances of the return rates of assets are not identical is analyzed in this paper using the methodology of statistical mechanical informatics, specifically, replica analysis. We define two characteristic quantities of an optimal portfolio, namely, minimal investment ris…
The problem is sequence prediction in the following setting. A sequence x1,..., xn,... of discrete-valued observations is generated according to some unknown probabilistic law (measure) mu. After observing each outcome, it is required to give the conditional probabilities of the next observation. The measure mu belongs…
This article introduces proximal planar vortex 1-cycles, resembling the structure of vortex atoms introduced by William Thomson (Lord Kelvin) in 1867 and recent work on the proximity of sets that overlap either spatially or descriptively. Vortex cycles resemble Thomson's model of a vortex atom, inspired by P.G. Tait's …
New inequality for ternary variables improves on existing measures.
problem Analyzing excess losses and weighted majority votes with ternary random variables.
method Developed a split-kl inequality and its PAC-Bayes extension.
result Outperforms existing inequalities in certain regimes.
Theory for algebraic data on categories via concentration structures.
problem Defining algebraic structures on categories.
method Introducing concentration structures and concentration monoids.
result Every group can be represented as a concentration monoid of a trivial category.
Paper addresses concentration of distances for fractional quasi p-norms, identifying conditions for concentration and anti-concentration.
problem Understanding concentration of distances for fractional quasi p-norms in high dimensions.
method Analyzes conditions for concentration and anti-concentration of distances for fractional quasi p-norms.
result Identifies conditions for concentration and anti-concentration of fractional quasi p-norms, ruling out some approaches and specifying conditions for control.
Study Finsler metric measure manifolds' concentration properties.
problem Understanding concentration properties in Finsler metric measure manifolds.
method Established relationships with observable diameter, isoperimetric inequalities, and first eigenvalue.
result Derived a Cheng type upper bound estimate for the first closed eigenvalue.
New method improves missing mass concentration bounds.
problem Missing mass concentration problem
method New method of estimating concentration of heterogenic sums
result Slightly improved state-of-the-art bounds
Surfaces in 3-manifolds concentrate at curvature critical points.
problem Understanding concentration of surfaces in 3-manifolds.
method Proving surfaces concentrate at critical points of scalar curvature.
result Simply connected H-surfaces concentrate at curvature critical points.
Sharp concentration bounds for i.i.d. variables.
problem Controlling the tail probabilities of independent variables.
method Extension of Sanov's theorem using large deviations and information theory.
result Matching concentration and anti-concentration bounds for i.i.d. samples of any size.
We survey recent results related to the concentration of eigenfunctions. We also prove some new results concerning ball-concentration, as well as showing that eigenfunctions saturating lower bounds for L1-norms must also, in a measure theoretical sense, have extreme concentration near a geodesic.
A new model CDTM improves text classification by concentrating document topics.
problem Unsupervised text classification with diverse topic distributions.
method Imposes an exponential entropy penalty on document topic distribution to encourage concentration.
result More coherent topics and concentrated, sparse document-topic distributions.
Simplified proof of Gaussian concentration inequality using covariance.
problem Gaussian concentration inequality proof
method Covariance representation based on characteristic functions
result Elementary proof of Gaussian concentration inequality
Study provides bounds for estimating intrinsic dimension using Gaussian kernels.
problem Estimating intrinsic dimension from data.
method Finite-sample concentration and anti-concentration bounds for Gaussian kernel sums.
result Explicit dependence on sample size, bandwidth, and geometric parameters.
Developed concentrated liquidity in n-dimensional AMM with polar coordinates in Rust.
problem Risk of stacking too many stablecoin pools.
method Building concentrated liquidity positions with ticks in polar coordinates in Rust.
result Hedging risk of stacking stablecoin pools.
Polyak step size GD reaches final radius of convergence after log iterations.
problem Statistical and computational complexities of Polyak step size GD.
method Generalized smoothness and Lojasiewicz conditions, stability of gradients.
result Polyak step size GD reaches final statistical radius of convergence after logarithmic number of iterations.
In this paper, we consider a concentration of measure problem on Riemannian manifolds with boundary. We study concentration phenomena of non-negative 1-Lipschitz functions with Dirichlet boundary condition around zero, which is called boundary concentration phenomena. We first examine relation between boundary concen…
Study on volume of tubes and concentration in Riemannian geometry.
problem Understanding concentration loci in Riemannian manifolds and their relation to tube volumes.
method Provided a general formula for tube volumes, specialized to totally geodesic submanifolds, and investigated concentration loci.
result Explicitly proved concentration for codimension one cases and explored characterizations in Wasserstein and Box distances.
This paper deals with chain graphs under the Andersson-Madigan-Perlman (AMP) interpretation. In particular, we present a constraint based algorithm for learning an AMP chain graph a given probability distribution is faithful to. Moreover, we show that the extension of Meek's conjecture to AMP chain graphs does not hold…
Polluting fine dusts in South Korea which are mainly consisted of biomass burning and fugitive dust blown from dust belt is significant problem these days. Predicting concentrations of fine dust particles in Seoul is challenging because they are product of complicate chemical reactions among gaseous pollutants and also…
We study concentration phenomena of eigenfunctions of the Laplacian on closed Riemannian manifolds. We prove that the volume measure of a closed manifold concentrates around nodal sets of eigenfunctions exponentially. Applying the method of Colding and Minicozzi we also prove restricted exponential concentration inequa…
A limit point p of a discrete group of Mobius transformations acting on S^n is called a concentration point if for any sufficiently small connected open neighborhood U of p, the set of translates of U contains a local basis for the topology of S^n at p. For the case of Fuchsian groups (n = 1), every concentration point…
New approach to concentration inequalities for unbounded state space dynamical systems.
problem Concentration inequalities for unbounded state space dynamical systems.
method Functional analytic framework, transport-entropy inequality.
result Exponential concentration inequalities for sampling from stationary distribution.
Q-learning for average cost MDPs gets a concentration bound.
problem Finding bounds for Q-learning in average cost MDPs.
method Derives a concentration bound using shortest path problem equivalence.
result Numerical comparison with relative value iteration shows the bound's effectiveness.
Sharp concentration results for sums of heavy-tailed random variables.
problem Analyzing sums of independent heavy-tailed random variables.
method Using concentration inequalities and large deviation principles for distributions satisfying specific tail bounds.
result Sharp concentration inequalities and large deviation results for sums of heavy-tailed random variables.
New bound improves on weighted majority vote risk estimation.
problem Improving risk estimation for weighted majority vote.
method Novel Chebyshev-Cantelli inequality and PAC-Bayes-Bennett inequality.
result New bounds improve on existing methods.
The paper reviews and improves concentration inequalities for statistical inference.
problem Analyzing statistical inference in various settings with high-dimensional data.
method Review and improvement of concentration inequalities for different types of random variables and statistical measures.
result Fresh new results and improved bounds with sharper constants.
Study analyzes impact of concentrated liquidity on trading fees and provider returns.
problem Impact of concentrated liquidity on trading fees and provider returns.
method Comparison of average liquidity provider returns before and after concentrated liquidity introduction; quantification of fundamental strategies performance.
result Concentrated liquidity strategies outperform in certain trading pairs and market conditions.
In this paper, we study the Lévy-Milman concentration phenomenon of 1-Lipschitz maps into infinite dimensional metric spaces. Our main theorem asserts that the concentration to an infinite dimensional ℓp-ball with the ℓq-distance function for 1≤p<q≤+∞ is equivalent to the concentration to the…
This work explores the characteristics of financial contagion in networks whose links distributions approaches a power law, using a model that defines banks balance sheets from information of network connectivity. By varying the parameters for the creation of the network, several interbank networks are built, in which …
We give concentration bounds for martingales that are uniform over finite times and extend classical Hoeffding and Bernstein inequalities. We also demonstrate our concentration bounds to be optimal with a matching anti-concentration inequality, proved using the same method. Together these constitute a finite-time versi…