arXiv research

The study restricts surfaces in a specific geometry to certain configurations, proving no annular ends can be contained in horizontal slabs.

Study minimal annuli in a slab, estimating their area.

Spike-and-slab priors are improved for high-dimensional Bayesian regression.

We prove, in all dimensions $n\geq 2$, that there exists a convex translator lying in a slab of width $π\secθ$ in $\mathbb{R}^{n+1}$ (and in no smaller slab) if and only if $θ\in[0,\fracπ{2}]$. We also obtain convexity and regularity results for translators which admit appropriate symmetries and study the asymptotics a…

Spike-and-slab priors are popular Bayesian solutions for high-dimensional linear regression problems. Previous theoretical studies on spike-and-slab methods focus on specific prior formulations and use prior-dependent conditions and analyses, and thus can not be generalized directly. In this paper, we propose a class o…

Paper proposes a new method for Bayesian linear regression using spike-and-slab priors.

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.

We construct a compact, convex ancient solution of mean curvature flow in $\mathbb R^{n+1}$ with $O(1)\times O(n)$ symmetry that lies in a slab of width $π$. We provide detailed asymptotics for this solution and show that, up to rigid motions, it is the only compact, convex, $O(n)$-invariant ancient solution that lies …

This paper speeds up OCSSVM training using SMO.

Finite entropy translating solitons in slabs have quantized entropy and unique structure.

The paper extends and applies a new shrinkage prior in Bayesian factor analysis.

We study stable immersed capillary hypersurfaces in a domain $\mathcal B$ which is either a half-space or a slab in the Euclidean space $\Bbb R^{n+1}.$ We prove that such a hypersurface $Σ$ is rotationally symmetric in the following cases: (1) $n=2$, $\mathcal B$ is a slab and $Σ$ has genus zero, (2) $n\geq 2$, $\mathc…

The X-ray transform on the periodic slab $[0,1]\times\mathbb T^n$, $n\geq0$, has a non-trivial kernel due to the symmetry of the manifold and presence of trapped geodesics. For tensor fields gauge freedom increases the kernel further, and the X-ray transform is not solenoidally injective unless $n=0$. We characterize t…

New algorithms sample spike-and-slab priors efficiently in high dimensions.

A fast and scalable method for variable selection in high-dimensional Gaussian processes.

Unlike $\mathbb{R}^{3}$, the homogeneous spaces $\mathbb{E}(-1,τ)$ have a great variety of entire vertical minimal graphs. In this paper we explore conditions which guarantees that a minimal surface in $\mathbb{E}(-1,τ)$ is such a graph. More specifically: we introduce the definition of a generalized slab in $\mathbb{E…

In this work we show that $2$-dimensional, simply connected, translating solitons of the mean curvature flow embedded in a slab of $\mathbb{R}^3$ with entropy strictly less than $3$ must be mean convex and thus, thanks to a result by J. Spruck and L. Xiao, are convex. Recently, such $2$-dimensional convex translating s…

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…

In this work, we address the problem of solving a series of underdetermined linear inverse problems subject to a sparsity constraint. We generalize the spike-and-slab prior distribution to encode a priori correlation of the support of the solution in both space and time by imposing a transformed Gaussian process on the…

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…

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.

The paper constructs ancient solutions to curvature flows in bounded and unbounded regions.

A new method discovers equations from data using Bayesian and kernel techniques.

The paper confirms isoperimetric conjectures on cubes and Gaussian slabs.

We are interested in solving the multiple measurement vector (MMV) problem for instances, where the underlying sparsity pattern exhibit spatio-temporal structure motivated by the electroencephalogram (EEG) source localization problem. We propose a probabilistic model that takes this structure into account by generalizi…

Bayesian SPCA method tackles orthogonality constraint with spike and slab prior.

Bayesian $l_0$-regularized least squares is a variable selection technique for high dimensional predictors. The challenge is optimizing a non-convex objective function via search over model space consisting of all possible predictor combinations. Spike-and-slab (a.k.a. Bernoulli-Gaussian) priors are the gold standard f…

The Gaussian process latent variable model (GP-LVM) is a popular approach to non-linear probabilistic dimensionality reduction. One design choice for the model is the number of latent variables. We present a spike and slab prior for the GP-LVM and propose an efficient variational inference procedure that gives a lower …

The study proves optimal isoperimetric regions in manifolds with density.

Bayesian neural network achieves nearly optimal performance in Besov space.

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…

We consider factoring low-rank tensors in the presence of outlying slabs. This problem is important in practice, because data collected in many real-world applications, such as speech, fluorescence, and some social network data, fit this paradigm. Prior work tackles this problem by iteratively selecting a fixed number …

We consider the problem of object recognition with a large number of classes. In order to overcome the low amount of labeled examples available in this setting, we introduce a new feature learning and extraction procedure based on a factor model we call spike-and-slab sparse coding (S3C). Prior work on S3C has not prio…

In this article, we propose a new class of priors for Bayesian inference with multiple Gaussian graphical models. We introduce fully Bayesian treatments of two popular procedures, the group graphical lasso and the fused graphical lasso, and extend them to a continuous spike-and-slab framework to allow self-adaptive shr…

We consider the problem of using a factor model we call {\em spike-and-slab sparse coding} (S3C) to learn features for a classification task. The S3C model resembles both the spike-and-slab RBM and sparse coding. Since exact inference in this model is intractable, we derive a structured variational inference procedure …

The use of L1 regularisation for sparse learning has generated immense research interest, with successful application in such diverse areas as signal acquisition, image coding, genomics and collaborative filtering. While existing work highlights the many advantages of L1 methods, in this paper we find that L1 regularis…

We study stable constant mean curvature (CMC) hypersurfaces $Σ$ in slabs in a product space $M\times\r,$ where $M$ is an orientable Riemannian manifold. We obtain a characterization of stable cylinders and prove that if $Σ$ is not a cylinder then it is locally a vertical graph. Moreover, in case $M$ is $\h^n,\r^n$ or $…

Paper proposes new Bayesian neural network models for efficient learning.

We show that under certain curvature conditions of the ambient space an entire Killing graph of constant mean curvature lying inside a slab must be a totally geodesic slice.

The study proves that certain minimal hypersurfaces in 4D space must be planes.

The use of machine learning algorithms to address classification problems is on the rise in many research areas. The current study is aimed at testing the potential of using such algorithms to auto-select the best solvers for transport problems in uniform slabs. Three solvers are used in this work: Richardson, diffusio…

Exact inference in the linear regression model with spike and slab priors is often intractable. Expectation propagation (EP) can be used for approximate inference. However, the regular sequential form of EP (R-EP) may fail to converge in this model when the size of the training set is very small. As an alternative, we …

Bayesian GAMs improve predictive performance for high-dimensional data.

Improved Thompson Sampling for high-dimensional sparse bandits.

IDS improves sparse linear bandits by balancing information and regret.

Proposes a flexible MGP model for dynamic, sparse correlations.