New Bianchi-convex sets generalize Ricci flow maximum principle.
problem Generalizing maximum principle for Ricci flow.
method Introducing Bianchi-convex sets.
result Hamilton's maximum principle extended to Bianchi-convex sets.
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48 results for “maximum convexity”
Shortfall from Maximum Convexityq-fin.ST
Proposes a new volatility measure for LETFs.
problem Leveraged Exchange Traded Funds (LETFs) returns do not follow normal distribution and independence.
method Introduces Shortfall from Maximum Convexity (SMC) as a new measure of realized volatility.
result SMC provides a more intuitive interpretation and more statistical information than standard deviation.
New guarantees for MRLEs in prediction accuracy.
problem Prediction accuracy in high-dimensional statistics.
method Derive guarantees for MRLEs in Kullback-Leibler divergence under convex parametrization and positive homogeneity.
result MRLEs are broadly consistent in prediction regardless of model conditions.
Given a monotone convex function on the space of essentially bounded random variables with the Lebesgue property (order continuity), we consider its extension preserving the Lebesgue property to as big solid vector space of random variables as possible. We show that there exists a maximum such extension, with explicit …
Convex hypersurfaces evolve to spheres under a specific flow.
problem Volume preserving nonhomogeneous mean curvature flow of convex hypersurfaces.
method Monotonicity of isoperimetric ratio, inner and outer radius control, maximum principle arguments.
result Closed convex hypersurfaces converge to round spheres.
Paper develops MRCs for supervised classification using generalized maximum entropy.
problem Developing robust classifiers for decision problems.
method Generalized maximum entropy principle applied to minimax risk classifiers.
result Learning techniques for determining MRCs with performance guarantees.
The paper solves a thermodynamics problem about crystal shape.
problem Understanding if minimizing free energy with convex potential and mass constraint generates a convex crystal.
method Utilized a stability theorem, convexity, and a new maximum principle approach to prove a three-dimensional convexity theorem.
result Completely settled the Almgren problem in under generic conditions.
Paper proves convex domains have one maximum for semi-stable solutions.
problem Analyzing critical points of semi-stable solutions on convex domains.
method Relating critical points to an auxiliary function and using topological degree.
result Positive, semi-stable solutions have exactly one non-degenerate critical point.
Uniqueness of convex self-similar solutions shown for a specific curvature flow.
problem Uniqueness of strictly convex closed self-similar solutions to the Gauss curvature flow.
method Introduced a Pogorelov type computation and applied the strong maximum principle.
result Uniqueness of strictly convex closed smooth self-similar solutions to the -Gauss curvature flow with .
Geometric approach solves maximum likelihood for Cauchy-like distributions.
problem Estimating center and scatter robustly from heavy-tailed data.
method Geodesic convexity and symmetry spaces of noncompact type.
result Efficient numerical solution for robust estimates of location and spread.
New principle for harmonic maps helps study higher-dimensional submanifolds.
problem Understanding unboundedness of totally geodesic projections in higher codimension.
method Introducing a flexible notion of convexity and applying it to harmonic and conformal maps.
result New maximum principle for harmonic maps applicable to various geometric settings.
New framework inscribes maximum volume ellipsoid for structured matrix factorization.
problem Structured matrix factorization with columns in unit simplex.
method Maximum volume inscribed ellipsoid (MVIE) via facet enumeration and convex optimization.
result MVIE framework guarantees exact recovery under certain conditions.
Paper relaxes convexity assumptions in mean curvature flow results.
problem Relaxing convexity assumptions in mean curvature flow results.
method Proves a generalized Harnack inequality and uses maximum principle.
result Characterizes family of shrinking spheres for ancient solutions.
Ancient mean curvature flows confined to slabs, halfspaces, or full space.
problem Characterizing ancient solutions of mean curvature flow.
method Bi-halfspace theorem derived from a parabolic Omori-Yau maximum principle.
result Compact convex ancient mean curvature flows are confined to specific regions.
The paper extends flow theory with free boundaries, proving key bounds and theorems.
problem Mean convex mean curvature flow with free boundary conditions.
method Triple-approximation scheme combining maximum principle and various theorems.
result A priori bound on the ratio of second fundamental form to mean curvature.
Solves indirect supervision problems with linear methods.
problem Structured prediction with indirect supervision.
method Solves linear system to estimate sufficient statistics, then uses convex optimization for parameter estimation.
result Effective in learning with privacy constraints and from count-based annotations.
Spectrahedral Regressionmath.OC
Spectrahedral regression fits convex functions via a non-convex optimization problem.
problem Fitting convex functions to data sets.
method Fitting a spectrahedral function (maximum eigenvalue of an affine matrix expression) to the data via an alternating minimization algorithm.
result The alternating minimization algorithm converges geometrically to a small ball around the optimal parameter.
We consider geometric flow equations for contracting and expanding normal velocities, including powers of the Gauss curvature, of the mean curvature, and of the norm of the second fundamental form, and ask whether - after appropriate rescaling - closed strictly convex surfaces converge to spheres. To prove this, many a…
Maximum Variance Unfolding is one of the main methods for (nonlinear) dimensionality reduction. We study its large sample limit, providing specific rates of convergence under standard assumptions. We find that it is consistent when the underlying submanifold is isometric to a convex subset, and we provide some simple e…
Optimizes MMD learning for generative models with theoretical guarantees.
problem Theoretical guarantees for optimizing non-convex MMD objectives.
method Analyzes MMD optimization landscape for specific distributions.
result Gradient-based methods globally minimize MMD objective for certain distributions.
Study proves radial symmetry in convex cones using subharmonic functions.
problem Proving radial symmetry in convex cones with boundary conditions.
method Using maximum principle and integral identities for subharmonic functions.
result Proves radial symmetry and Serrin-type results for partially overdetermined problems.
The paper extends convexity results for translating solitons in higher dimensions.
problem Characterizing translating solitons in higher-dimensional spaces.
method Generalization of Spruck-Xiao and Spruck-Sun's convexity results for -homogeneous curvature functions.
result Characterizations of grim reaper cylinders under curvature constraints.
We study the asymptotic behavior of smooth, origin-symmetric, strictly convex bodies under the centro-affine normal flows. By means of a stability version of the Blaschke-Santaló inequality, we obtain regularity of the solutions provided that initial convex bodies have almost maximum Mahler volume. We prove that suitab…
Convex optimization models predict outputs from inputs via optimization problems.
problem Predicting outputs from inputs using convex optimization models.
method Proposed a heuristic for learning parameters of convex optimization models from datasets.
result Demonstrated the effectiveness of the proposed method on three model classes.
Study convexity of geodesics and balls in Outer space.
problem Convexity properties of geodesics and balls in Outer space.
method Introduced balanced folding paths and used them to show weak convexity of out-going balls.
result Weak convexity of out-going balls in Outer space.
New theorems for translating solitons restrict their shapes.
problem No halfspace theorems for self-translating solitons.
method Distance functions and Omori-Yau maximum principle.
result Properly immersed complete self-translating solitons must obey a bi-halfspace theorem.
We study a robust maximization problem from terminal wealth and consumption under a convex constraints on the portfolio. We state the existence and the uniqueness of the consumption-investment strategy by studying the associated quadratic backward stochastic differential equation (BSDE in short). We characterize the op…
SNEPPPs use squared neural networks to efficiently model Poisson point processes.
problem Efficiently modeling Poisson point processes with flexibility.
method Parameterizing intensity function with squared norm of a two-layer neural network.
result Closed-form integration of intensity function for quadratic time computation.
Study on Cheeger constant in specific hyperbolic 3-manifolds.
problem Analyzing Cheeger constant in convex co-compact hyperbolic 3-manifolds.
method Examining Cheeger constant as a functional in the space of specific hyperbolic 3-manifolds.
result Global maximum of Cheeger constant is uniquely attained at the Fuchsian locus.
The paper solves a maximum entropy sampling problem with efficient algorithms and performance guarantees.
problem Selecting the most informative principal submatrix from a covariance matrix.
method Derive a novel convex integer program, develop efficient sampling algorithms with approximation bounds, and analyze local search algorithms.
result Efficient algorithms with near-optimal performance guarantees for solving MESP and A-MESP.
Study asymptotic behavior of Weingarten surfaces at infinity.
problem Understanding the behavior of Weingarten surfaces at infinity.
method Derive asymptotic expansion and solve Dirichlet problem.
result Established maximum principle and solved Dirichlet problem.
Paper learns Markov models from data with low-rank optimization.
problem Learning Markov models from a single trajectory with latent structure.
method Two maximum likelihood estimation methods: convex with nuclear-norm regularization and nonconvex with rank constraint. Novel DC programming algorithm for nonconvex estimator.
result Accurate estimation of full transition model with trajectory length proportional to state space.
Study finds finitely many non-congruent polygonal domains with same Steklov spectrum.
problem Inverse Steklov problem on convex polygons.
method Analysis of Steklov eigenvalues and isoperimetric bounds.
result For almost all convex polygonal domains, there exist at most finitely many non-congruent domains with the same Steklov spectrum.
We simplify inference for TPP models with latent structures.
problem Intractable marginalization in TPP models with latent structures.
method Approximate inference over latent variables using a tight upper bound on the approximation gap.
result Improved results for models like Survival Analysis.
Convex functions defined on metric spaces are pulled back to subharmonic ones by harmonic mapsmath.MG
Harmonic maps pull convex functions on metric spaces to subharmonic ones.
problem Understanding how convex functions behave under harmonic maps on metric spaces.
method Proving subharmonicity of pullbacks of convex functions by harmonic maps in metric spaces.
result The pullback of a convex function by a harmonic map is subharmonic in metric spaces.
Study centers of convex polyhedrons that are independent of parameters.
problem Characterize centers of convex polyhedrons that are independent of parameters.
method Investigate centers defined by Riesz potential and Poisson's integral, providing necessary and sufficient conditions for independence.
result Necessary and sufficient condition for existence of centers independent of parameters.
Convex optimization method infers latent structure in random dot product graphs.
problem Inferring latent probability matrix of random dot product graphs.
method Conic programming with nuclear norm regularization.
result Asymptotic consistency of probability estimates and recovery of latent structure.
Classifies ancient solutions to curvature flows on the sphere.
problem Classifying ancient solutions to curvature flows on the sphere.
method Geometric techniques including maximum principle, rigidity result, and Alexandrov reflection argument.
result Any convex, quasi-ancient solution must be stationary or a family of shrinking geodesic spheres.
A nearly tight convex relaxation for sparse Naive Bayes features.
problem Feature selection in large-scale Naive Bayes classification.
method Proposes a convex relaxation for the combinatorial maximum-likelihood problem of feature selection in Naive Bayes.
result The convex relaxation bounds become tight as marginal feature contributions decrease, providing a nearly optimal solution.
This paper formulates and studies a stochastic maximum principle for forward-backward stochastic Volterra integral equations (FBSVIEs in short), while the control area is assumed to be convex. Then a linear quadratic (LQ in short) problem for backward stochastic Volterra integral equations (BSVIEs in short) is present …
New method improves MMD estimation without convexity assumptions.
problem Lack of theoretical guarantees for MMD estimation algorithms.
method Preconditioned gradient descent (PGD) scheme for MMD optimization.
result PGD scheme converges globally under specific conditions.
Bayesian inference becomes tractable with log-concave priors and targets.
problem Transforming samples from a prior to a posterior distribution efficiently.
method Optimal transport theory and convex optimization.
result Log-concave priors and targets allow for efficient Bayesian inference.
New estimator learns graph of Ising models efficiently and optimally.
problem Learning the graph of an Ising model from samples.
method Interaction screening approach using convex optimization.
result Estimator recovers graph with logarithmic samples in p and exponential in coupling-intensity and node-degree.
A number of discrete and continuous optimization problems in machine learning are related to convex minimization problems under submodular constraints. In this paper, we deal with a submodular function with a directed graph structure, and we show that a wide range of convex optimization problems under submodular constr…
Gradient estimates for hyperbolic space CMC equation solved.
problem Gradient estimates for solutions to constant mean curvature equation in hyperbolic space.
method Maximum principles theory of Φ-functions.
result Gradient estimates obtained for bounded strictly convex domains.
Reconstructs power grid dynamics from PMU measurements.
problem Reconstructing dynamic state matrix of power transmission grids.
method Maximum likelihood based convex estimators adapting to prior information.
result Fully data-driven method that works in near real-time.
We consider convex hypersurfaces for which the ratio of principal curvatures at each point is bounded by a function of the maximum principal curvature with limit 1 at infinity. We prove that the ratio of circumradius to inradius is bounded by a function of the circumradius with limit 1 at zero. We apply this result to …
Maximal open subset found for product of CAT(-1) spaces.
problem Maximal open subset in horofunction compactification of product spaces.
method Maximal open subset found in horofunction compactification of product spaces.
result Maximal open subset compactifies diagonal action of infinite quasi-convex group.