Bayesian optimisation tackles high-dimensional categorical and mixed search spaces.
problem Bayesian optimisation on high-dimensional categorical and mixed search spaces is challenging.
method Combining local optimisation with a tailored kernel design.
result Empirically outperforms current baselines in performance and computational costs.
The paper proves a unique conformal measure for Anosov groups and shows local mixing.
problem Proving the uniqueness of conformal measures for Anosov groups.
method Analogue of Sullivan's theorem for Anosov subgroups of semisimple groups.
result Uniqueness of conformal measures and local mixing for Anosov groups.
Frame flows on certain symmetric spaces mix exponentially.
problem Exponential mixing of frame flows in convex cocompact locally symmetric spaces.
method Generalized local non-integrability and non-concentration properties to apply Dolgopyat's method.
result Exponential mixing of frame flows proved for convex cocompact locally symmetric spaces.
The paper explores mixed curvature for Hermitian manifolds and its implications.
problem Investigating the properties of mixed curvature for Hermitian manifolds.
method Analyzing convex combinations of first Chern Ricci curvature and holomorphic sectional curvature.
result Compact Hermitian surfaces with constant mixed curvature are Kähler unless specific conditions are met.
New method stabilizes quantum ergodicity for mixed quantization and partial hyperbolicity.
problem Stabilizing quantum ergodicity for complex systems.
method Combines mixed quantization techniques with stable ergodicity results for partially hyperbolic systems.
result Establishes stable quantum ergodicity for spin Hamiltonians.
Bayesian framework mixes imperfect models for improved predictions.
problem Improving predictions of complex computational models in unknown domains.
method Local Bayesian Dirichlet mixing of imperfect models using the Dirichlet distribution.
result Global and local mixtures of models achieve excellent performance in prediction accuracy and uncertainty quantification.
Local invertibility of higher order tensor transforms on compact manifolds.
problem Invertibility of higher order tensor transforms on compact manifolds.
method Local invertibility of transverse and mixed ray transforms of tensors on compact Riemannian manifolds.
result Local invertibility of transverse and mixed ray transforms of tensors for specific dimensions.
SBMs learn manifold-like structures by mixing samples with a non-conservative field.
problem How SBMs learn data distributions on low-dimensional manifolds.
method Investigating linear approximations and subspaces of local feature vectors during diffusion.
result SBMs mix samples by a non-conservative field within the manifold, maintaining manifold-like structure.
Local invertibility of ray transforms on convex manifolds.
problem Invertibility of ray transforms on compact Riemannian manifolds with strictly convex boundary.
method Local invertibility results for transverse and mixed ray transforms of 1 and 1+1 tensors.
result Local invertibility of ray transforms near boundary points, leading to global results.
The variational autoencoder (VAE) is a generative model with continuous latent variables where a pair of probabilistic encoder (bottom-up) and decoder (top-down) is jointly learned by stochastic gradient variational Bayes. We first elaborate Gaussian VAE, approximating the local covariance matrix of the decoder as an o…
Study mixed commutator lengths in wreath products and their relation to general ranks.
problem Understanding mixed commutator lengths in wreath products and their relation to general ranks.
method Analyzing wreath products (G,N)=(Z≀Γ,⨁ΓZ) and determining mixed commutator lengths in terms of general rank. result Mixed commutator lengths and ordinary commutator lengths coincide under certain conditions.
Puzzle Mix optimizes mixup by leveraging saliency and local statistics.
problem Overfitting and adversarial vulnerability of deep networks.
method Puzzle Mix alternates between multi-label and saliency-based objectives for optimal mixing masks.
result Puzzle Mix outperforms other mixup methods in generalization and adversarial robustness.
Mixed membership factorization is a popular approach for analyzing data sets that have within-sample heterogeneity. In recent years, several algorithms have been developed for mixed membership matrix factorization, but they only guarantee estimates from a local optimum. Here, we derive a global optimization (GOP) algor…
In the paper we develop a framework for the alternative way of the study of a local geometry of almost cosymplectic manifolds with Kahlerian leaves. The main idea is to apply the concept of a geometry and analysis of CR manifolds. Locally the almost cosymplectic manifold is modeled on the 'mixed' space RxCn. There is g…
We construct examples of nondegenerate CR manifolds with Levi form of signature (p,q), 2≤p≤q, which are compact, not locally CR flat, and admit essential CR vector fields. We also construct an example of a noncompact nondegenerate CR manifold with signature (1,n−1) which is not locally CR flat and admits …
Rapid mixing of Langevin dynamics on Riemannian manifolds
problem Mixing time of Langevin dynamics on Riemannian manifolds
method Relation between Langevin processes in domain and image
result Achievable polynomial mixing times
A new SSL method improves medical image classification using global latent mixing.
problem Costly annotation of large-scale medical image data sets.
method Linear mixing of labeled and unlabeled data in both input and latent space.
result Improved performance in semi-supervised classification of thoracic disease and skin lesion.
Uniform volume estimate for Kähler metrics in big cohomology classes.
problem Estimating volume for singular Kähler metrics in big cohomology classes.
method Generalized mixed energy estimate for functions in complex Sobolev space to big cohomology classes.
result Uniform non-collapsing volume estimate for local Kähler metrics.
In this paper, we present smooth examples of degenerate hyperbolic and mixed type Monge-Ampere equations in the plane, which do not admit a local C^3 solution.
Develops a contraction framework for MCMC mixing rates.
problem Proving mixing-time bounds for MCMC algorithms.
method Global and local contraction coefficients under Eγ-divergence. result Explicit global contraction coefficients for Gaussian smoothing.
MixCIT tests conditional independence for mixed data types efficiently and reliably.
problem Testing conditional independence for mixed data types, especially when at least one is continuous.
method Graph-based test statistic comparing kernel similarities, debiased local-polynomial approach for continuous variables.
result Unified, efficient, and statistically guaranteed solution across heterogeneous data types.
Study shows mixing of flows on specific geometric spaces.
problem Mixing of one-parameter diagonal flows on Anosov homogeneous spaces.
method Proves local mixing for flows on $Γackslash G$ with deviations in transverse subspaces.
result Local mixing of flows on $Γackslash G$ for various directions.
Solves Christoffel-Minkowski problem for axially symmetric bodies.
problem Necessary and sufficient conditions for mixed area measures of axially symmetric convex bodies.
method Introduced a new method to transform mixed area measures and mixed volumes of axially symmetric bodies, refining Firey's classification and improving estimates.
result Complete solution to the mixed Christoffel-Minkowski problem for axially symmetric bodies without regularity assumptions.
Study on mixed Killing vector fields on Cigar Ricci-Bourguignon solitons.
problem Characterizing mixed Killing vector fields on Cigar Ricci-Bourguignon solitons.
method Analyzing the condition LVLVg=fLVg and using rigidity phenomena. result Dimension of complete mixed Killing fields is 5 and a basis is explicitly determined.
A new method for efficient inference in sequential latent-variable models.
problem Computational challenges in integrating subject-specific random effects.
method Anchored variational inference framework to approximate posterior distributions.
result The method achieves accurate estimation with significant computational gains.
Develops a functional generalization of Eldan's stochastic localization for optimization and privacy.
problem Sampling under non-Euclidean geometries and optimization in differential privacy.
method Functional generalization of Eldan's stochastic localization, incorporating log-Laplace transform.
result Improves query complexities in zeroth-order differential private convex optimization.
In this paper, we give a new sharp generalization bound of lp-MKL which is a generalized framework of multiple kernel learning (MKL) and imposes lp-mixed-norm regularization instead of l1-mixed-norm regularization. We utilize localization techniques to obtain the sharp learning rate. The bound is characterized by the d…
In mix-game which is an extension of minority game, there are two groups of agents; group1 plays the majority game, but the group2 plays the minority game. This paper studies the change of the average winnings of agents and volatilities vs. the change of mixture of agents in mix-game model. It finds that the correlatio…
Abelian covers of hyperbolic 3-manifolds are ubiquitous. We prove the local mixing theorem of the frame flow for abelian covers of closed hyperbolic 3-manifolds. We obtain a classification theorem for measures invariant under the horospherical subgroup. We also describe applications to the prime geodesic theorem as…
In this paper we study the equidistribution of expanding horospheres in infinite volume geometrically finite rank one locally symmetric manifolds and apply it to the orbital counting problem in apollonian sphere packing.
We introduce a new method of calculating intersections on \bar{M}_{g,n}, using localization of equivariant cohomology. As an application, we give a proof of Mirzakhani's recursion relation for calculating intersections of mixed psi and kappa_1 classes.
We prove the existence of C^{\infty} local solutions to a class of mixed type Monge-Ampere equations in the plane. More precisely, the equation changes type to finite order across two smooth curves intersecting transversely at a point. Existence of C^{\infty} global solutions to a corresponding class of linear mixed ty…
Paper proves inequalities on Hermitian manifolds with applications to bounded solutions.
problem Establishing mixed Hessian inequalities on Hermitian manifolds.
method Weak convergence theorem of complex Hessian operators and general mixed Hessian inequality.
result Existence of bounded solutions of complex Hessian equations.
Study the geometry of lightlike loci on mixed type surfaces in Lorentz-Minkowski 3-space.
problem Characterize the differential geometric properties of lightlike loci on mixed type surfaces.
method Define a frame field and lightlike ruled surfaces along the lightlike locus, analyze their singularities and intersections.
result Establish a relationship between the singularities of lightlike ruled surfaces and the differential geometric properties of the lightlike locus.
Bayesian optimization tackles mixed discrete-continuous problems with Gaussian processes.
problem Optimizing problems with both discrete and continuous variables using costly simulations.
method Relaxing discrete variables into continuous latent variables, using Bayesian optimization, and incorporating compatibility constraints with Lagrangians.
result Comparative analysis of different mixed Bayesian optimization approaches.
We investigate the problem of calculating the Fredholm index of a geometric Dirac operator subject to local (e.g. Dirichlet and Neumann) and non-local (APS) boundary conditions posed on the strata of a manifold with corners. The boundary strata of the manifold with corners can intersect in higher codimension. To calcul…
Study proves projective Anosov subgroups lead to mixing flows in specific spaces.
problem Understanding mixing properties of flows on specific geometric spaces.
method Constructing non-empty domain of discontinuity in homogeneous space, using spectral estimates for transfer operators.
result Exponential mixing, spectral gap, and meromorphic continuation of zeta functions established.
Two algorithms learn Gaussian graphical models from Glauber dynamics trajectories, achieving optimal performance.
problem Learning Gaussian graphical models from a single trajectory of a dependent stochastic process.
method Two algorithms based on dueling-neighborhood search and local statistics built from the update sequence of Glauber dynamics.
result Achieve κ−2 dependence of the information-theoretic lower bounds, mixing-free and signal-optimal. Common perpendiculars equidistribute in negatively curved spaces.
problem Equidistribution of common perpendiculars in negatively curved spaces.
method Analyzing the Bowen-Margulis measure and geodesic flow properties.
result Lebesgue measures of common perpendiculars equidistribute to the Bowen-Margulis measure.
Study shows a universal local obstruction to the Samuelson condition for tangent Lagrangian 2-webs.
problem Obstruction to the Samuelson condition for tangent Lagrangian 2-webs.
method Local analysis of tangent lines and their intersection maps.
result A universal local phenomenon produces a nonzero mixed derivative, obstructing the Samuelson condition.
Algorithm recovers graph from Glauber dynamics trajectory without mixing.
problem Learning Gaussian graphical models from a single Glauber dynamics trajectory.
method Three components: conditional variance estimation, pairwise influence test, robust median aggregation.
result Polynomial-time recovery of conditional independence graph from a single trajectory.
A new model improves clustering by reducing redundancy in mixture of local EPCAs.
problem Redundancy in traditional mixture models causes ambiguity in clustering.
method Introduced a repulsiveness-encouraging prior and a DPP for diversity in DEPCAM model.
result The method reduces model redundancy and improves clustering performance.
Characterizes continuity of monotone functionals in mixed topology.
problem Continuity of monotone functionals in mixed topology.
method Characterization through lower semicontinuity and dual representations.
result Continuity in mixed topology is equivalent to dual representation in terms of countably additive measures.
NUTS mixing time scales as d^(1/4) for Gaussian distributions.
problem Improving the efficiency of the No-U-Turn Sampler (NUTS) for Gaussian distributions.
method Coupling argument leveraging geometric structure of Gaussian concentration, uniformity analysis of NUTS transitions.
result The mixing time of NUTS scales as d^(1/4) for Gaussian distributions, up to logarithmic factors.
Study on robustness of unsupervised representation learning in slightly misspecified settings.
problem Identify nonlinear representation learning in slightly misspecified settings.
method Formalize and investigate Independent Component Analysis (ICA) with observations generated by a mixing function close to a local isometry.
result Approximate identifiability of nonlinear ICA with almost isometric mixing functions.
The paper improves SMC algorithm for multi-modal distributions by proving variance bounds.
problem Problems with SMC on multi-modal distributions, especially in terms of mixing time.
method Proves variance bounds for SMC on multi-modal distributions using soft decomposition.
result Bounds on SMC variance depend on local rather than global mixing times.
QR-MIX models joint state-action values as a distribution to handle randomness in MARL.
problem Randomness in rewards and observations leads to randomness in long-term returns in MARL.
method QR-MIX uses quantile regression and combines it with QMIX and IQN to model joint state-action values as a distribution.
result QR-MIX outperforms QMIX in the StarCraft Multi-Agent Challenge (SMAC) environment.
The theory of monotone Riemannian metrics on the state space of a quantum system was established by Denes Petz in 1996. In a recent paper he argued that the scalar curvature of a statistically relevant - monotone - metric can be interpreted as an average statistical uncertainty. The present paper contributes to this su…