arXiv research

Total variation minimization clusters partially labeled data points.

Paper proposes a new method to minimize submodular functions with fewer calls to simpler oracles.

Improved DNN robustness to adversarial attacks using data-dependent activation and total variation minimization.

Optimal pre-processing reduces disparate impact by minimizing total variation distance.

Study variational properties of curves in half-plane with area constraints.

Characterizing the phase transitions of convex optimizations in recovering structured signals or data is of central importance in compressed sensing, machine learning and statistics. The phase transitions of many convex optimization signal recovery methods such as $\ell_1$ minimization and nuclear norm minimization are…

CV outperforms mean-variance for stock returns, minimizing risk and maximizing growth.

We examine the total mixed scalar curvature of a fixed distribution as a functional of a pseudo-Riemannian metric. We develop variational formulas for quantities of extrinsic geometry of the distribution to find the critical points of this action. Together with the arbitrary variations of the metric, we consider also v…

Unified federated learning via GTV minimization.

This paper deals with continuity preservation when minimizing generalized total variation with a $L^2$ fidelity term or a Dirichlet boundary condition. We extend several recent results in the two cases, mainly by showing comparison principles for the prescribed mean curvature problem satisfied by the level-sets of such…

Method uses TV minimization for semi-supervised learning on network data.

Network Lasso clusters sparse graph clusters efficiently.

Proposes a method to estimate discrete curvatures for image reconstruction.

New method optimizes non-linear functionals over probability measures.

New algorithms help machines forget old data efficiently.

In recent years, total variation (TV) and Euler's elastica (EE) have been successfully applied to image processing tasks such as denoising and inpainting. This paper investigates how to extend TV and EE to the supervised learning settings on high dimensional data. The supervised learning problem can be formulated as an…

New geometric insights reveal properties of adversarial training problems.

Network Lasso classifies partially labeled data with high-dimensional features.

In this paper, we establish the first variational formula and its Euler-Lagrange equation for the total $2p$-th mean curvature functional $\mathcal {M}_{2p}$ of a submanifold $M^n$ in a general Riemannian manifold $N^{n+m}$ for $p=0,1,...,[\frac{n}{2}]$. As an example, we prove that closed complex submanifolds in compl…

Study on free boundary minimal hypersurfaces in Schwarzschild space, proving zero Morse index for certain hypersurfaces.

Study calculates the renormalized area of catenoids in hyperbolic spaces.

Study variations of metrics on Riemannian submersions to preserve fiber geometry.

Optimized $\alpha$-posteriors reduce KL divergence from true posterior in parametric misspecification.

The conformal parameterisation of a minimal surface is harmonic. Therefore, a minimal surface is a critical point of both the energy functional and the area functional. In this paper, we compare the Morse index of a minimal surface as a critical point of the area functional with its Morse index as a critical point of t…

The area renormalization procedure gives an invariant of even-dimensional closed submanifolds in a conformal manifold, which we call the Graham-Witten energy, and it is a generalization of the classical Willmore energy. In this paper, we obtain an explicit formula for the second variation of this energy at minimal subm…

In this paper, we study a risk process modeled by a Brownian motion with drift (the diffusion approximation model). The insurance entity can purchase reinsurance to lower its risk and receive cash injections at discrete times to avoid ruin. Proportional reinsurance and excess-of-loss reinsurance are considered. The obj…

New optimal surfaces found in Heisenberg group defy Euclidean sphere optimality.

Ideas from the image processing literature have recently motivated a new set of clustering algorithms that rely on the concept of total variation. While these algorithms perform well for bi-partitioning tasks, their recursive extensions yield unimpressive results for multiclass clustering tasks. This paper presents a g…

The paper studies curves in Riemannian manifolds using total variation flow.

Total variation denoising improves image quality adaptively.

New method speeds up diffusion models without requiring complex assumptions.

New method trains Markov kernels for efficient sampling.

Polynomial-time algorithm forecasts TV-bounded sequences with optimal error rate.

Study on free-boundary CMC hypersurfaces in upper hemisphere, proving Morse index and eigenvalue bounds.

The paper proves conditions for minimal surfaces to be holomorphic and stable.

We present a graph-based variational algorithm for classification of high-dimensional data, generalizing the binary diffuse interface model to the case of multiple classes. Motivated by total variation techniques, the method involves minimizing an energy functional made up of three terms. The first two terms promote a …

We show a very simple and general total second variation formula for Perelman's $\mathcal{W}$-functional at arbitrary points in the space of Riemannian metrics. Moreover we perform a study of the properties of the variations of Kähler structures. We deduce a quite simple and general total second variation formula for P…

This work improves texture segmentation by automatically tuning hyperparameters for Total-Variation.

We decrease the $rms$ mean curvature and area of a variable surface with a fixed boundary by iterating a few times through a curvature-based variational algorithm. For a boundary with a known minimal surface, starting with a deliberately chosen non-minimal surface, we achieve up to 65 percent of the total possible decr…

This paper combines three techniques to reduce communications in distributed variational inequalities.

Paper relaxes differential privacy for correlated features, improving privacy-utility trade-off.

New algorithms minimize dynamic regret for strongly convex losses.

We derive variational formulas for the total Q-prime curvature under the deformation of strictly pseudoconvex domains in a complex manifold. We also show that the total Q-prime curvature agrees with the renormalized volume of such domains with respect to the complete Einstein-Kähler metric. In the appendix, by Rod Gove…

Diffusion models achieve nearly optimal distribution estimation in various spaces.

The paper derives oracle inequalities for estimators with fast and slow rates.

A method for disentangling discrete and continuous factors of data without using a discriminator network.

Two complementary approaches have been extensively used in signal and image processing leading to novel results, the sparse representation methodology and the variational strategy. Recently, a new sparsity based model has been proposed, the cosparse analysis framework, which may potentially help in bridging sparse appr…

Study minimal surfaces with finite curvature in a specific manifold.