New algorithm for tensor factorization with outlying slabs.
problem Factoring low-rank tensors with outlying slabs in real-world data.
method Group-sparsity promoting formulation and alternating optimization framework.
result Proposed algorithm converges and performs well on various real-world data.
This paper categorizes and analyzes existing outlying aspect mining methods.
problem Finding unique features in data objects that differ from others.
method Grouping and analyzing existing outlying aspect mining approaches in three categories.
result Comparison of strengths, weaknesses, and time complexities of different techniques.
Efficient tests detect outlying sequences without knowing their distributions.
problem Detecting outlying sequences among multiple distributions without prior knowledge.
method Distribution clustering-based tests with linear complexity and exponential consistency.
result Tests are computationally efficient and perform similarly to existing methods.
Paper introduces a fast density estimator for efficient outlying aspects mining.
problem Efficiently searching for feature subsets that describe how a query stands out from a dataset.
method Proposes a simple and efficient density estimator that replaces the kernel density estimator in existing outlying aspects miners.
result The new density estimator enables systematic search of large datasets with thousands of dimensions.
The paper constructs unstable and outlying CMC spheres in specific manifolds.
problem Stability of CMC spheres in certain manifolds.
method Non-linear ODE method to construct CMC surfaces in Riemannian manifolds with symmetry.
result Existence of unstable CMC spheres, indicating the stability condition cannot be removed.
Researchers prove existence of convex translators in slab regions in all dimensions.
problem Existence of translating solutions in slab regions.
method Proof in all dimensions n≥2; slab width πsecθ; convexity and regularity results for symmetrical translators. result Existence of convex translators in specific slab regions.
Develops generic spike-and-slab priors for high-dimensional linear regression.
problem Bayesian high-dimensional linear regression challenges.
method Proposes a class of generic spike-and-slab priors and a unified framework for theoretical assessment.
result Achieves nearly-optimal posterior contraction rate and model selection consistency under general conditions.
Spike-and-slab priors are improved for high-dimensional Bayesian regression.
problem Prohibitive computational costs for existing samplers in high-dimensional settings.
method Proposes Scalable Spike-and-Slab (S3) for high-dimensional Bayesian regression. result Improves computational cost to max{n2pt,np} per iteration, demonstrating significant speed-ups and quality gains. Study characterizes X-ray transform kernel for periodic slabs and related manifolds.
problem Characterizing the kernel of X-ray transform for tensor fields on periodic slabs.
method Characterization of the kernel for L2-regular m-tensors on [0,1]imesTn. result Kernel characterization extends to more general manifolds, including the Möbius strip.
Paper proposes a new method for Bayesian linear regression using spike-and-slab priors.
problem Identifying predictors with similar relationships in linear regression models.
method Hierarchical Bayesian models with spike-and-slab priors and a Gibbs sampler.
result The proposed method outperforms previous methods in simulations and real data analysis.
Study minimal annuli in a slab, estimating their area.
problem Estimating the area of minimal annuli in a slab.
method Organized minimal annuli based on winding number, deduced convexity of length function, compared to catenoid waist area.
result Deduced convexity of length function and estimated area of minimal annuli.
2D simply connected translating solitons in slabs are convex and have entropy < 3.
problem Characterizing 2D translating solitons in slabs with entropy constraints.
method Analyzing the properties of translating solitons in slabs with entropy constraints.
result 2D simply connected translating solitons in slabs are convex and have entropy < 3.
The study restricts surfaces in a specific geometry to certain configurations, proving no annular ends can be contained in horizontal slabs.
problem Properly embedded surfaces with constant mean curvature in a specific geometric setting.
method Proof of geometric restrictions using slab and halfspace theorems.
result Surfaces with constant mean curvature are confined to specific configurations, including graphs over simply connected domains.
Ancient solution found in 3D space with specific symmetry properties.
problem Finding ancient solutions with specific symmetry and geometric constraints in 3D space.
method Constructed a compact, convex ancient solution with O(1)imesO(n) symmetry in a slab of width π. result The only compact, convex, O(n)-invariant ancient solution in a slab of width π. Consider a non-planar orientable minimal surface S in a slab which is possibly with genus or with more than two boundary components. We show that there exists a catenoidal waist W in the slab whose flux has the same vertical component as S such that Area(S)>= Area(W), provided the intersections of S with horizontal pla…
New algorithms improve Bayesian linear regression with spike-and-slab priors.
problem Efficiently sampling from Bayesian linear regression models with sparsity-inducing priors.
method Design of two sampling algorithms: Gibbs sampling and Stochastic Localization.
result Stochastic Localization sampler shows significant advantage for poorly designed data matrices.
Study finds existence and non-existence of large stable CMC spheres in asymptotically flat 3-manifolds.
problem Existence and non-existence of large stable CMC spheres in asymptotically flat 3-manifolds.
method Extends Lyapunov-Schmidt analysis to 'far-off-center' regime and general Schwarzschild asymptotics.
result Sharp existence and non-existence results for large stable CMC spheres.
This paper speeds up OCSSVM training using SMO.
problem Training One-Class Slab SVMs is slow.
method Uses updated SMO to divide large problems into smaller, analytically solvable subproblems.
result Training OCSSVMs scales better with large datasets.
Finite entropy translating solitons in slabs have quantized entropy and unique structure.
problem Finite entropy translating solitons in slabs with finite genus and finite entropy.
method Analyzing wing numbers and using Morse theory for minimal surfaces.
result Entropy of these solitons is quantized into integer steps and unique structure proven.
The paper defines and proves properties of minimal surfaces in a specific space.
problem Conditions for minimal surfaces in a special space to be graphs.
method Introduced generalized slabs and proved properties of minimal surfaces inside them.
result Minimal surfaces in generalized slabs have multi-graph ends, and under certain conditions, are entire graphs.
The paper extends and applies a new shrinkage prior in Bayesian factor analysis.
problem Estimating the number of factors in sparse Bayesian factor analysis.
method Introduces and extends a generalized cumulative shrinkage process (CUSP) prior.
result Exchangeable spike-and-slab shrinkage priors imply increasing shrinkage as the column index increases.
A new GP-LVM with spike and slab priors for latent dimension selection.
problem Selecting the number of latent variables in GP-LVM.
method Spike and slab prior for latent variables, efficient variational inference.
result The new model provides a principled approach for latent dimension selection.
We study stable immersed capillary hypersurfaces in a domain B which is either a half-space or a slab in the Euclidean space Rn+1. We prove that such a hypersurface Σ is rotationally symmetric in the following cases: (1) n=2, B is a slab and Σ has genus zero, (2) n≥2, $\mathc…
Study uses machine learning to recommend best solvers for slab transport problems.
problem Auto-selecting the best solvers for transport problems in uniform slabs.
method Three solvers (Richardson, diffusion synthetic acceleration, nonlinear diffusion acceleration) and five machine learning algorithms (linear discriminant analysis, K-nearest neighbors, support vector machine, random forest, neural networks) were tested.
result Random forest and K-nearest neighbors showed potential as best solvers for classification problems.
New algorithms sample spike-and-slab priors efficiently in high dimensions.
problem Sampling from spike-and-slab priors in high-dimensional settings.
method Provably efficient algorithms for posterior sampling with sublinear measurement count.
result First provable algorithms for spike-and-slab posterior sampling without strong SNR assumptions.
Model for EEG source localization with spatio-temporal structure.
problem Solving MMV problems with spatio-temporal sparsity patterns.
method Generalized spike and slab prior with Expectation Propagation.
result Demonstrated viability of the proposed model and inference scheme.
A fast and scalable method for variable selection in high-dimensional Gaussian processes.
problem Inefficient variable selection in high-dimensional Gaussian processes.
method Developed a fast and scalable variational inference algorithm for spike and slab Gaussian processes.
result Consistently outperforms vanilla and sparse variational GPs while retaining similar runtimes.
Study on stable CMC surfaces in slabs with boundary conditions.
problem Characterizing and proving properties of stable CMC surfaces in slabs.
method Analyzing stable constant mean curvature (CMC) hypersurfaces in product spaces with free boundary conditions.
result No stable CMC surface connects boundary components of a slab with width greater than a certain limit.
Kaczmarz++ accelerates convergence for ill-conditioned systems.
problem Solving ill-conditioned linear systems efficiently.
method Adaptive momentum acceleration, Tikhonov-regularized projections, and memoization.
result Kaczmarz++ converges faster than Krylov methods on ill-conditioned systems.
We apply the spike-and-slab Restricted Boltzmann Machine (ssRBM) to texture modeling. The ssRBM with tiled-convolution weight sharing (TssRBM) achieves or surpasses the state-of-the-art on texture synthesis and inpainting by parametric models. We also develop a novel RBM model with a spike-and-slab visible layer and bi…
New robust PCA algorithm for matrices with both sparse and outlying elements.
problem Simultaneous sparse and outlying corruption in matrices.
method Sparse approximation of a sparsely corrupted column to distinguish inliers from outliers.
result Robust PCA algorithm can handle both sparse and outlying corruptions.
Bayesian l0-regularized least squares for high-dimensional predictors.
problem Optimizing a non-convex objective function over model space.
method Spike-and-slab priors with single Best Replacement (SBR) for scalability.
result SBR can find the spike-and-slab estimator, bridging Bayesian regularization and proximal updating.
A new score SiNNE improves OAM efficiency and accuracy.
problem Comparing outlier scores across subspaces of different dimensions.
method Introducing SiNNE, a new score independent of subspace dimensionality.
result SiNNE produces better or at least as good results as existing scores and significantly improves runtime.
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.
We study inference and learning based on a sparse coding model with `spike-and-slab' prior. As in standard sparse coding, the model used assumes independent latent sources that linearly combine to generate data points. However, instead of using a standard sparse prior such as a Laplace distribution, we study the applic…
Bayesian method selects sparse models efficiently with less bias.
problem Sparse model selection and regularization in Gaussian graphical models.
method Continuous spike-and-slab framework with EM algorithm for fast explorations.
result Efficient selection of sparse models with less bias compared to other methods.
We prove that the ends of a properly immersed simply or one connected minimal surface in H(2)xR contained in a slab of height less than πof H(2)xR, are multi-graphs. When such a surface is embedded then the ends are graphs. When embedded and simply connected, it is an entire graph.
Improved VB algorithm for high-dimensional logistic regression with theoretical guarantees.
problem Sparse high-dimensional logistic regression model selection.
method Spike and slab variational Bayes approximation.
result Optimal convergence rates in ℓ2 and prediction loss for sparse truths. Bayesian model tackles spatio-temporal underdetermined problems.
problem Solving underdetermined linear inverse problems with spatial and temporal sparsity constraints.
method Generalized spike-and-slab prior with transformed Gaussian process, expectation propagation algorithm, and approximations for scalability.
result Demonstrated effectiveness on synthetic and real data sets.
The outlying property detection problem is the problem of discovering the properties distinguishing a given object, known in advance to be an outlier in a database, from the other database objects. In this paper, we analyze the problem within a context where numerical attributes are taken into account, which represents…
The paper constructs ancient solutions to curvature flows in bounded and unbounded regions.
problem Understanding ancient solutions to curvature flows in bounded and unbounded regions.
method Constructing pancake-like and sausage-like ancient compact solutions.
result Ancient solutions to curvature flows in bounded and unbounded regions.
Method approximates covariance ellipsoid using random slabs or ellipsoids.
problem Approximating the covariance ellipsoid of a random vector.
method Constructing approximations using random slabs or ellipsoids generated from data.
result Approximations can be constructed with a sample size of N=c1dη−4log(2/η) or N=c1dη−2log(2/η) under minimal assumptions. The paper confirms isoperimetric conjectures on cubes and Gaussian slabs.
problem Isoperimetric inequalities on slabs and cubes.
method Analysis of weighted Riemannian manifolds and product spaces.
result The isoperimetric conjecture on the three-dimensional cube is confirmed for a new range of relative volumes.
A new method discovers equations from data using Bayesian and kernel techniques.
problem Discovering equations from data is hard due to sparsity and noise.
method Kernel regression for function estimation and Bayesian spike-and-slab prior for uncertainty quantification.
result KBASS method outperforms state-of-the-art methods on benchmark tasks.
Bayesian SPCA method tackles orthogonality constraint with spike and slab prior.
problem Bayesian SPCA method for high-dimensional data with orthogonality constraint.
method Parameter-expanded coordinate ascent variational inference (PX-CAVI) with spike and slab prior.
result PX-CAVI algorithm outperforms existing SPCA approaches in performance.
Bayesian neural network achieves nearly optimal performance in Besov space.
problem Bayesian neural networks in Besov space.
method Spike-and-slab prior and shrinkage prior for posterior convergence rate.
result The posterior convergence rate is nearly minimax and adaptive to unknown smoothness.
The study proves optimal isoperimetric regions in manifolds with density.
problem Finding optimal regions with minimal boundary area in manifolds with density.
method Proving existence of isoperimetric regions and using subgroup actions.
result Isoperimetric regions in product manifolds are slabs.
In this letter, we address sparse signal recovery using spike and slab priors. In particular, we focus on a Bayesian framework where sparsity is enforced on reconstruction coefficients via probabilistic priors. The optimization resulting from spike and slab prior maximization is known to be a hard non-convex problem, a…