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.
Non-convex regularizers usually improve the performance of sparse estimation in practice. To prove this fact, we study the conditions of sparse estimations for the sharp concave regularizers which are a general family of non-convex regularizers including many existing regularizers. For the global solutions of the regul…
The study finds necessary and sufficient conditions for -hypersurfaces to have nowhere -regular parallel sets.
The paper explores -regularity for real analytic maps and its relation to Milnor fibrations.
The outcome of Jacobian singular values regularization was studied for supervised learning problems. It also was shown that Jacobian conditioning regularization can help to avoid the ``mode-collapse'' problem in Generative Adversarial Networks. In this paper, we try to answer the following question: Can information abo…
Classifies local boundary conditions for Dirac-type operators on manifolds.
Modelling statistical relationships beyond the conditional mean is crucial in many settings. Conditional density estimation (CDE) aims to learn the full conditional probability density from data. Though highly expressive, neural network based CDE models can suffer from severe over-fitting when trained with the maximum …
Paper introduces a differentiable regularizer for condition number to improve neural network stability.
Proposes a new method for selecting regularization parameters in sparse precision matrix estimation.
Derives spacetime regularity under specific curvature conditions.
The paper analyzes Tikhonov regularization in Hilbert scales for statistical inverse problems.
We study the regularity of the solutions of second order boundary value problems on manifolds with boundary and bounded geometry. We first show that the regularity property of a given boundary value problem is equivalent to the uniform regularity of the natural family of associated boundary value …
A regular F-manifold is an F-manifold (with Euler field) (M, \circ, e, E), such that the endomorphism {\mathcal U}(X) := E \circ X of TM is regular at any p\in M. We prove that the germ ((M,p), \circ, e, E) is uniquely determined (up to isomorphism) by the conjugacy class of {\mathcal U}_{p} : T_{p}M \rightarrow T_{p}M…
Unified framework for understanding and optimizing training acceleration.
The paper extends completeness notions to low-regularity spacetimes.
IRKSN algorithm achieves sparse recovery with wider applicability conditions.
The study shows that certain graphs are regular at boundary points.
In this paper we prove that every definable set has a definable triangulation which is locally Lipschitz and weakly bi-Lipschitz on the natural simplicial stratification of the simplicial complex. We also distinguish a class T of regularity conditions and give a universal construction of a definable triangulation with …
In this paper we describe the notion of a weak lipschitzianity of a mapping on a stratification. We also distinguish a class of regularity conditions that are in some sense invariant under definable, locally Lipschitz and weakly bi-Lipschitz homeomorphisms. This class includes the Whitney (B) condition and the …
We consider the learning algorithms under general source condition with the polynomial decay of the eigenvalues of the integral operator in vector-valued function setting. We discuss the upper convergence rates of Tikhonov regularizer under general source condition corresponding to increasing monotone index function. T…
This paper studies least-square regression penalized with partly smooth convex regularizers. This class of functions is very large and versatile allowing to promote solutions conforming to some notion of low-complexity. Indeed, they force solutions of variational problems to belong to a low-dimensional manifold (the so…
We propose a simple yet highly effective method that addresses the mode-collapse problem in the Conditional Generative Adversarial Network (cGAN). Although conditional distributions are multi-modal (i.e., having many modes) in practice, most cGAN approaches tend to learn an overly simplified distribution where an input…
Curvature formulas on regular graphs identified bone idle edges and graphs.
New learning rates derived for Tikhonov-regularized problems without kernel assumptions.
In this work, we study data preconditioning, a well-known and long-existing technique, for boosting the convergence of first-order methods for regularized loss minimization. It is well understood that the condition number of the problem, i.e., the ratio of the Lipschitz constant to the strong convexity modulus, has a h…
Curve shortening flow's regularity depends on initial conditions after a certain time.
The aim of this note is to present an alternative proof for an already known result relative to the solvability of the Dirichlet problem in Riemannian manifolds (see remark 0.1). In particular, we discuss the p-regularity (regularity relative to the p-laplacian) of domains of the form I = O-K, where O is a regular doma…
We formulate a principle for classification with the knowledge of the marginal distribution over the data points (unlabeled data). The principle is cast in terms of Tikhonov style regularization where the regularization penalty articulates the way in which the marginal density should constrain otherwise unrestricted co…
Entropy-regularized NPG converges linearly with linear function approximation.
We propose and study a general framework for regularized Markov decision processes (MDPs) where the goal is to find an optimal policy that maximizes the expected discounted total reward plus a policy regularization term. The extant entropy-regularized MDPs can be cast into our framework. Moreover, under our framework, …
Study uses property elicitation to understand how fairness regularizers affect optimal decisions.
The paper defines conditions for Gaussian process sample path regularity.
Conditional Asian options are recent market innovations, which offer cheaper and long-dated alternatives to regular Asian options. In contrast with payoffs from regular Asian options which are based on average asset prices, the payoffs from conditional Asian options are determined only by average prices above certain t…
Unified framework for estimating high-dimensional conditional factor models.
The paper tackles safe reinforcement learning with convex regularization.
New method for fitting graphical models with latent variables using regularized conditional likelihood.
DG algorithms often fail to generalize well in limited domains, highlighting necessary vs. sufficient conditions.
We study a hybrid conditional gradient - smoothing algorithm (HCGS) for solving composite convex optimization problems which contain several terms over a bounded set. Examples of these include regularization problems with several norms as penalties and a norm constraint. HCGS extends conditional gradient methods to cas…
Unique solution found for financial system risk.
In this article we introduce local gauge conditions under which many curvature tensors appearing in conformal geometry, such as the Weyl, Cotton, Bach, and Fefferman-Graham obstruction tensors, become elliptic operators. The gauge conditions amount to fixing an -harmonic coordinate system and normalizing the determi…
Study rates of convergence for approximate solutions to linear ill-posed problems in Hilbert scales.
Study Dirac operators on finite warped cylinders with gauge fields.
The paper examines how gradient descent stabilizes low-rank matrix factorization in noisy conditions.
We give sufficient conditions for a parametrised family of probability measures on a Riemannian manifold with boundary to be represented by random maps of class . The conditions allow for the probability densities to approach zero towards the boundary of the manifold. We also formulate two obstructions to regular …
Study on the smoothness of solutions to a specific type of stochastic differential equation.
Regularized LAEs learn principal components efficiently.
Characterizes graphs with Lin-Lu-Yau curvature at least one and explores bone-idle graphs.
By performing required evaluations, we show that in the Finsleroid-regular space the Landsberg-space condition just degenerates to the Berwald-space condition (at any dimension number ). Simple and clear expository representations are obtained. Due comparisons with the Finsleroid-Finsler space are indicated. Key…
In this paper, we prove a Morse index theorem for the index form of regular Lagrangian system with selfadjoint boundary condition.