A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
The study finds necessary and sufficient conditions for -hypersurfaces to have nowhere -regular parallel sets.
Proves regularity for multiple membrane solutions.
A new algorithm speeds up EEG source localization using regularization.
Paper proves smoothness of solutions to a complex geometric problem.
New regularization controls neural network generalization error and sparsifies input dimensions.
We prove a estimate for solutions of complex Monge-Ampère equations on compact Kähler manifolds with possibly nonempty boundary, in a degenerate cohomology class. This strengthens previous estimates of Phong-Sturm. As applications we deduce the local regularity of geodesic rays in the space of Kähle…
A neural network solves logistic regression with regularization efficiently.
We prove a estimate for solutions of a class of fully nonlinear equations introduced by Chen-He. As an application, we prove the regularity of geodesics in the space of volume forms.
We show the optimal regularity of geodesics in nef and big cohomology class on Kähler manifolds away from the non-Kähler locus, assuming sufficiently regular initial data. As a special case, we prove the regularity of geodesics of Kähler metrics on compact Kähler varieties away from the singular loc…
Compressed Sensing using regularization is among the most powerful and popular sparsification technique in many applications, but why has it not been used to obtain sparse deep learning model such as convolutional neural network (CNN)? This paper is aimed to provide an answer to this question and to show how t…
Proposes a method to adapt models in nonstationary environments using ℓ1 regularization.
New neural network training method uses bi-fidelity data to reduce errors.
In a recent work (arXiv:0910.2517), for nonlinear models with sparse underlying linear structures, we studied the error bounds of -regularized estimation. In this note, we show that -regularized estimation in some important cases can achieve the same order of error bounds as those in the aforementioned …
We propose an inference method to estimate sparse interactions and biases according to Boltzmann machine learning. The basis of this method is regularization, which is often used in compressed sensing, a technique for reconstructing sparse input signals from undersampled outputs. regularization impedes the …
We prove that any two Kahler potentials on a compact Kahler manifold can be connected by a geodesic segment of C^{1,1} regularity. This follows from an a priori interior real Hessian bound for solutions of the nondegenerate complex Monge-Ampere equation, which is independent of a positive lower bound for the right hand…
We first obtain the interior -regularity and solvability for the degenerate real Monge-Ampère equation in a bounded, -smooth and strictly convex domain in (), assuming that the boundary data is only globally , and the -th root of the nonnegative right-hand side is globally…
Deep neural network with l_1-regularization achieves nearly optimal risk bounds.
It is known that a tube over a Kahler submanifold in a complex form is a Hopf hypersurface. In some sense the reverse statement is true: a connected compact generic immersed C^(2n-1) regular Hopf hypersurface in the complex projective plane is a tube iver an irreducible algebraic variety. In the complex hyperbolic spac…
The paper improves ALO for -regularized models.
The paper extends NSGPs with -regularization for sparsity and solves the resulting R-NSGP regression problem.
We investigate the learning rate of multiple kernel learning (MKL) with and elastic-net regularizations. The elastic-net regularization is a composition of an -regularizer for inducing the sparsity and an -regularizer for controlling the smoothness. We focus on a sparse setting where the total …
The paper analyzes -LinR for Ising model selection using statistical mechanics.
Study on eigenvalues of complex Hessian operator on pseudoconvex manifolds.
The -regularized models are widely used for sparse regression or classification tasks. In this paper, we propose the orthant-wise passive descent algorithm (OPDA) for optimizing -regularized models, as an improved substitute of proximal algorithms, which are the standard tools for optimizing the models nowada…
In this paper we consider the task of estimating the non-zero pattern of the sparse inverse covariance matrix of a zero-mean Gaussian random vector from a set of iid samples. Note that this is also equivalent to recovering the underlying graph structure of a sparse Gaussian Markov Random Field (GMRF). We present two no…
Multi-task feature learning aims to identity the shared features among tasks to improve generalization. It has been shown that by minimizing non-convex learning models, a better solution than the convex alternatives can be obtained. Therefore, a non-convex model based on the capped- regularization wa…
The optimization of the variance supplemented by a budget constraint and an asymmetric regularizer is carried out analytically by the replica method borrowed from the theory of disordered systems. The asymmetric regularizer allows us to penalize short and long positions differently, so the present treatment in…
In this paper, we prove a estimate for solutions of complex Monge-Ampère equations on compact almost Hermitian manifolds. Using this estimate, we show existence of solutions to the degenerate Monge-Ampère equations, the corresponding Dirichlet problems and the singular Monge-Ampère equatio…
Study tail risk in high-frequency finance using -regularized regression.
Study geometric properties and topology of curves on a sphere with curvature constraints.
Feature selection and regularization are becoming increasingly prominent tools in the efforts of the reinforcement learning (RL) community to expand the reach and applicability of RL. One approach to the problem of feature selection is to impose a sparsity-inducing form of regularization on the learning method. Recent …
In this paper, the existence of C^1-umbilics with arbitrarily high indices is shown. This implies that more than C^1-regularity is required to prove Loewner's conjecture.
We analyze learning curves of RF models with convex regularization and derive precise asymptotic expressions.
Recent research has studied the role of sparsity in high dimensional regression and signal reconstruction, establishing theoretical limits for recovering sparse models from sparse data. This line of work shows that -regularized least squares regression can accurately estimate a sparse linear model from nois…
regularized logistic regression has now become a workhorse of data mining and bioinformatics: it is widely used for many classification problems, particularly ones with many features. However, regularization typically selects too many features and that so-called false positives are unavoidable. In this pape…
Unified framework for sparse logistic regression with nonconvex regularization.
Sharp curvature estimates lead to optimal regularity for Minkowski problems.
Method improves SINDy for noisy nonlinear systems.
The pseudo-likelihood method is one of the most popular algorithms for learning sparse binary pairwise Markov networks. In this paper, we formulate the regularized pseudo-likelihood problem as a sparse multiple logistic regression problem. In this way, many insights and optimization procedures for sparse logistic…
The Heston stochastic volatility process is a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order, degenerat…
Constructs surfaces that can be tiled by a finite set of rigid motion congruence classes of tiles.
We consider immersions admitting uniform graph representations over the affine tangent space over a ball of fixed radius r>0. We show that for sufficiently small C^0-norm of the graph functions, each graph function is smooth with small C^1-norm.
We establish short-time existence of the smooth solution to the fractional mean curvature flow when the initial set is bounded and C^{1,1}-regular. We provide the same result also for the volume preserving fractional mean curvature flow.
We introduce a proximal version of dual coordinate ascent method. We demonstrate how the derived algorithmic framework can be used for numerous regularized loss minimization problems, including regularization and structured output SVM. The convergence rates we obtain match, and sometimes improve, state-of-the-…
Study on regularity of optimal transport maps on convex domains with quadratic cost.
We prove the regularity for a class of abnormal length-minimizers in rank sub-Riemannian structures. As a consequence of our result, all length-minimizers for rank sub-Riemannian structures of step up to are of class .
Study sparse function recovery from indirect noisy observations using -regularization.
Sparse regularization such as regularization is a quite powerful and widely used strategy for high dimensional learning problems. The effectiveness of sparse regularization has been supported practically and theoretically by several studies. However, one of the biggest issues in sparse regularization is that i…