Entropy asymmetry affects regularization in ERM, leading to biased solutions.
problem Analyzing the impact of relative entropy asymmetry in ERM regularization.
method Examined Type-I and Type-II ERM-RER, comparing their solutions and properties.
result Type-II ERM-RER regularization introduces a strong bias against training data.
In this paper, we propose a generalized scale mixture family of distributions, namely the Power Exponential Scale Mixture (PESM) family, to model the sparsity inducing priors currently in use for sparse signal recovery (SSR). We show that the successful and popular methods such as LASSO, Reweighted ℓ1 and Reweigh…
We study almost-calibrated, O(n)-equivariant Lagrangian mean curvature flow in Cn, and prove structural theorems about the Type I and Type II blowups of finite-time singularities. In particular, we prove that any Type I blowup of such a flow must be a special Lagrangian pair of transversely intersecting p…
Despite the great success of deep neural networks, the adversarial attack can cheat some well-trained classifiers by small permutations. In this paper, we propose another type of adversarial attack that can cheat classifiers by significant changes. For example, we can significantly change a face but well-trained neural…
New framework for robust hypothesis testing using Sinkhorn uncertainty sets.
problem Non-convex robust hypothesis testing problem.
method Exact mixed-integer exponential conic reformulation and convex approximation.
result Satisfactory testing performance and computational efficiency.
Sparse linear (or generalized linear) models combine a standard likelihood function with a sparse prior on the unknown coefficients. These priors can conveniently be expressed as a maximization over zero-mean Gaussians with different variance hyperparameters. Standard MAP estimation (Type I) involves maximizing over bo…
New algorithm controls type I error in NP classification under label noise.
problem Label noise affects NP classification methods, reducing power.
method Proposes a label-noise-adjusted Neyman-Pearson algorithm.
result Improves power while controlling type I error under desired level.
We systematically analyse the necessary and sufficient conditions for the preservation of supersymmetry for bosonic geometries of the form R^{1,9-d} \times M_d, in the common NS-NS sector of type II string theory and also type I/heterotic string theory. The results are phrased in terms of the intrinsic torsion of G-str…
Numerical simulations show stability of Type-II singularities in noncompact hypersurfaces.
problem Stability of Type-II singularities in noncompact hypersurfaces with rotationally-symmetric perturbations.
method Adaptation of the overlap method to include angular dependence.
result MCF of noncompact hypersurfaces with angular dependence behaves similarly to rotationally-symmetric perturbations, developing Type-II or Type-I singularities.
Local singularity analysis for Ricci flows with applications to bounded scalar curvature.
problem Understanding the nature of singularities in Ricci flows.
method Local singularity analysis, introducing Type I and Type II singular points, and proving curvature blow-up rates.
result Ricci curvature must blow up at least at a Type I rate near singular points of a Ricci flow.
Proves product metrics are Yamabe metrics under small flat torus conditions.
problem Yamabe metrics on product spaces with small flat tori.
method Extends earlier results to Type~I and Type~II Yamabe constants, Q-curvature problems, and isoperimetric-ratio type problems. result Product metrics are Yamabe metrics for sufficiently small flat tori.
We provide a condition for spatial curves which rules out the development of a type I singularity. The condition is that after the last time for which an inflection point develops, if the torsion is ever everywhere non-negative, the curve cannot develop a type I singularity.
A list of possible holonomy groups contained the exceptional, non-compact Lie group G2∗ was provided by Fino and Kath. The classification is due to the corresponding holonomy algebras and divided into Type I, II and III, depending on the dimension of the socle being 1,2 or 3, respectively. It was also sh…
In this paper we investigate the singularities of Lagrangian mean curvature flows in Cm by means of smooth singularity models. Type I singularities can only occur at certain times determined by invariants in the cohomology of the initial data. In the type II case, these smooth singularity models are asympto…
In this paper, we study the dividend strategies for a shareholder with non-constant discount rate in a diffusion risk model. We assume that the dividends can only be paid at a bounded rate and restrict ourselves to the Markov strategies. This is a time inconsistent control problem. The extended HJB equation is given an…
Most existing binary classification methods target on the optimization of the overall classification risk and may fail to serve some real-world applications such as cancer diagnosis, where users are more concerned with the risk of misclassifying one specific class than the other. Neyman-Pearson (NP) paradigm was introd…
We show that a rescale limit at any degenerate singularity of Ricci flow in dimension 3 is a steady gradient soliton. In particular, we give a geometric description of type I and type II singularities.
We formulate statistical watermarking as hypothesis testing and establish near-optimal bounds.
problem Statistical watermarking in the context of hypothesis testing.
method Formulated as a hypothesis testing problem, using coupling of output tokens and rejection regions.
result Established nearly matching upper and lower bounds on the number of i.i.d. tokens required for small Type I and Type II errors.
The paper defines new types of positivity and proves properties of Schur forms for vector bundles.
problem Defining and characterizing new types of positivity for vector bundles.
method Introducing and characterizing two types of strongly decomposable positivity, proving properties of Schur forms.
result Schur forms of strongly decomposable positive vector bundles are positive or weakly positive, answering a question of Griffiths.
FactTest assesses LLM factuality with Type I error control.
problem Lack of rigorous factuality verification for LLMs.
method Formulates factuality testing as hypothesis testing, ensuring Type I and II error control.
result Improves model accuracy by over 40% in abstaining from unknown questions.
Curve Shortening Flow preserves circularity for convex projections.
problem Understanding the behavior of curves under Curve Shortening Flow.
method Contradiction argument and analysis of tangent flows.
result Smooth curves with convex projections become asymptotically circular under Curve Shortening Flow.
Study on pseudo-Riemannian metrics on Lie groups, finding new non-Einstein examples.
problem Characterizing and finding non-Einstein pseudo-Riemannian metrics on Lie groups.
method Analyzing left invariant metrics, using double extension process, and constructing examples.
result Construction of infinitely many new explicit examples of non-Einstein pseudo-Riemannian metrics on Lie groups.
DP synthetic data may inflate statistical test results, caution advised.
problem Inflated Type I errors in statistical tests on DP-synthetic data.
method Evaluation of Mann-Whitney U test, t-test, chi-squared test, and median test on DP-synthetic data generated from real-world and simulated datasets using various DP-synthetic data generation methods.
result A large portion of evaluation results showed inflated Type I errors, especially at low privacy levels.
Constructs two types of Eguchi-Hanson metrics with negative scalar curvature.
problem Creating metrics with negative scalar curvature.
method Constructed two types of Eguchi-Hanson metrics.
result Found metrics with negative scalar curvature.
The paper examines translating solitons and their relation to Lagrangian mean curvature flows with zero Maslov class.
problem Understanding the behavior of Lagrangian translating solitons near Type II singularities.
method Analyzes necessary conditions for blow-up limits and applies to open questions.
result Provides a necessary condition for blow-up limits of Lagrangian mean curvature flows with zero Maslov class.
ERM with f-divergence regularization yields unique solution.
problem Optimizing empirical risk with f-divergence. method Mild conditions on f lead to unique optimal measure. result Equivalence of ERM-fDR to different f-divergence regularization. Gaussian graphical model is a graphical representation of the dependence structure for a Gaussian random vector. It is recognized as a powerful tool in different applied fields such as bioinformatics, error-control codes, speech language, information retrieval and others. Gaussian graphical model selection is a statist…
WHOMP optimizes randomized controlled trials by minimizing subgroup bias.
problem Minimizing subgroup bias in randomized controlled trials.
method Wasserstein Homogeneity Partition (WHOMP) method.
result WHOMP optimally minimizes type I and type II errors in trials.
The paper tackles data misappropriation in LLMs by embedding watermarks and testing for their presence.
problem Detecting data misappropriation in LLMs trained on copyrighted data.
method Embedding watermarks, formulating as hypothesis testing, developing statistical framework, constructing test statistics, determining optimal thresholds, controlling errors, establishing asymptotic optimality.
result The proposed statistical testing framework effectively detects data misappropriation in LLMs.
Study detects signals in spiked Wigner models using log likelihood ratio.
problem Detecting signals in rank-one spiked Wigner models with non-Gaussian noise.
method Proved asymptotic normality of log likelihood ratio and computed error thresholds.
result Optimal signal-to-noise ratio threshold for reliable detection.
Study ancient solutions on noncompact steady Ricci solitons, proving types of ancient solutions.
problem Classify ancient solutions on noncompact steady gradient Ricci solitons.
method Apply Perelman's L-geodesic theory to analyze blow-down solutions. result Prove that compact split ancient solutions are of type I.
We consider an ancient solution g(⋅,t) of the Ricci flow on a compact surface that exists for t∈(−∞,T) and becomes spherical at time t=T. We prove that the metric g(⋅,t) is either a family of contracting spheres, which is a type I ancient solution, or a Rosenau solution, which is a type II ancie…
Study shows different behaviors of noncompact hypersurfaces under mean curvature flow.
problem Analyzing stability of noncompact hypersurfaces with curvature blowup.
method Numerical overlap method to construct global solutions.
result Existence of near and far classes of initial data leading to distinct behaviors.
New method uses CDMs to improve CI testing without distributional assumptions.
problem Testing conditional independence when the conditional distribution is unknown.
method Uses conditional diffusion models (CDMs) to approximate X∣Z and a classifier-based CMI estimator. result Proposed method performs better than GAN-based CI tests and controls type I and II errors.
Extends static vacuum metrics with specific boundary conditions.
problem Proving the existence of static vacuum metrics with prescribed boundary data.
method Introducing static regular types (I) and (II), showing local well-posedness, and confirming Bartnik's conjecture.
result Confirms Bartnik's static vacuum extension conjecture for a broad range of boundary conditions.
Study closed G2-structures with T3-symmetry, classifying them into types and deriving hypersymplectic structures.
problem Classify closed G2-structures with T3-symmetry and derive associated hypersymplectic structures.
method Decompose G2-structures into canonical forms, classify structures based on orbit isotropy, and derive hypersymplectic structures.
result Closed G2-structures with T3-symmetry are classified into two types, leading to specific hypersymplectic structures.
Study proves energy critical heat equation solutions are Type I blowups for n ≥ 7.
problem Analyzing blowup behavior of energy critical nonlinear heat equations.
method Reverse inner-outer gluing mechanism and bubbling behavior analysis.
result Proves all blowups are of Type I for n ≥ 7.
The Neyman-Pearson (NP) paradigm in binary classification seeks classifiers that achieve a minimal type II error while enforcing the prioritized type I error controlled under some user-specified level α. This paradigm serves naturally in applications such as severe disease diagnosis and spam detection, where people h…
New regularization method reduces support of empirical risk minimization solutions.
problem Regularization in empirical risk minimization with relative entropy.
method Introduces Type-II regularization, characterizes solutions, analyzes properties of relative entropy.
result Type-II regularization collapses solution support into reference measure's support.
In regression settings where explanatory variables have very low correlations and there are relatively few effects, each of large magnitude, we expect the Lasso to find the important variables with few errors, if any. This paper shows that in a regime of linear sparsity---meaning that the fraction of variables with a n…
Optimal classification rules control error rates in multiclass mixture models.
problem Classifying observations in multiclass mixture models while controlling error rates.
method Finding optimal classification rules by searching an optimal region in the observation space, using Maximum A Posteriori (MAP) rule and heuristic computation.
result The FDR-like optimal rule can be significantly less conservative than thresholded MAP rules.
Study curve shortening flow in high dimensions with boundary constraints.
problem Understanding the behavior of curves in high-dimensional spaces with boundary conditions.
method Used curvature and higher-derivative estimates, Stahl-type maximum principle, and blow-up analysis.
result Flow converges to a shrinking semicircle model or has only semicircle boundary singularities in low entropy regimes.
We study the Ricci flow on R4 starting at an SU(2)-cohomogeneity 1 metric g0 whose restriction to any hypersphere is a Berger metric. We prove that if g0 has no necks and is bounded by a cylinder, then the solution develops a global Type-II singularity and converges to the Bryant soliton when su…
Proposes tests for comparing high-dimensional manifold samples.
problem Determining if two manifold samples come from the same distribution.
method Integral Probability Metric (IPM) with neural network approximations.
result Tests achieve type-II risk in specific orders of n. This paper addresses the challenges in classifying textual data obtained from open online platforms, which are vulnerable to distortion. Most existing classification methods minimize the overall classification error and may yield an undesirably large type I error (relevant textual messages are classified as irrelevant)…
DP-SPRT improves privacy in sequential tests with near-optimal error rates.
problem Privacy constraints in sequential probability ratio tests.
method A wrapper for SPRT that uses a private mechanism to determine when to stop based on predefined intervals.
result DP-SPRT achieves near-optimal error rates and privacy guarantees.
Study homogeneous Lorentzian manifolds under reductive Lie groups, reducing descriptions to semisimple groups.
problem Characterize homogeneous Lorentzian manifolds under reductive Lie groups.
method Analyze manifolds M=G/L for connected reductive Lie groups G and reductive subgroup L; focus on totally reducible isotropy representations. result Homogeneous Lorentzian manifolds reduce to semisimple Lie groups, and are reductive.
Paper constructs flows converging to cones and foliations.
problem Understanding mean curvature flow convergence to cones and foliations.
method Constructs a family of mean curvature flows converging to cones and foliations under specific conditions.
result Flow converges to area minimizing, strictly stable hypercone and Hardt-Simon foliation of the cone.