Related papers: Generalized L$_p$-norm joint inversion of gravity …
Recent advances show that two-dimensional linear discriminant analysis (2DLDA) is a successful matrix based dimensionality reduction method. However, 2DLDA may encounter the singularity issue theoretically and the sensitivity to outliers.…
We propose a generic framework based on a new stochastic variance-reduced gradient descent algorithm for accelerating nonconvex low-rank matrix recovery. Starting from an appropriate initial estimator, our proposed algorithm performs…
This paper describes a new efficient conjugate subgradient algorithm which minimizes a convex function containing a least squares fidelity term and an absolute value regularization term. This method is successfully applied to the inversion…
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…
Inspired by the remarkable success of large neural networks, there has been significant interest in understanding the generalization performance of over-parameterized models. Substantial efforts have been invested in characterizing how…
Overparameterized models may have many interpolating solutions; implicit regularization refers to the hidden preference of a particular optimization method towards a certain interpolating solution among the many. A by now established line…
We analyze nonlinearly preconditioned gradient methods for solving smooth minimization problems. We introduce a generalized smoothness property, based on the notion of abstract convexity, that is broader than Lipschitz smoothness and…
We present a fast algorithm for the total variation regularization of the $3$-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved…
The \(L_1/L_2\) norm ratio has gained significant attention as a measure of sparsity due to three merits: sharper approximation to the \(L_0\) norm compared to the \(L_1\) norm, being parameter-free and scale-invariant, and exceptional…
In this paper, we study large-scale convex optimization algorithms based on the Newton method applied to regularized generalized self-concordant losses, which include logistic regression and softmax regression. We first prove that our new…
We study the Sobolev IPM problem for measures supported on a graph metric space, where critic function is constrained to lie within the unit ball defined by Sobolev norm. While Le et al. (2025) achieved scalable computation by relating…
We present a simplified and unified analysis of the Johnson-Lindenstrauss (JL) lemma, a cornerstone of dimensionality reduction for managing high-dimensional data. Our approach simplifies understanding and unifies various constructions…
In this paper, we propose a novel uniform generalization bound on the time and inverse temperature for stochastic gradient Langevin dynamics (SGLD) in a non-convex setting. While previous works derive their generalization bounds by uniform…
We present a general variational framework for the training of freeform nonlinearities in layered computational architectures subject to some slope constraints. The regularization that we add to the traditional training loss penalizes the…
The near-surface environment is often too complex to enable inference of hydrological and environmental variables using one geophysical data type alone. Joint inversion and coupled inverse modeling involving numerical flow- and transport…
Neural networks are predominantly trained using gradient-based methods, yet in many applications their final predictions remain far from the accuracy attainable within the model's expressive capacity. We introduce Linearized Subspace…
We consider linear inverse problems where the solution is assumed to have a sparse expansion on an arbitrary pre-assigned orthonormal basis. We prove that replacing the usual quadratic regularizing penalties by weighted l^p-penalties on the…
We study the fundamental problem of learning an unknown object from data using a prescribed model class. We introduce a unified framework that accommodates objects in arbitrary Hilbert spaces, general (possibly vector-valued) random linear…
Complexifying space time has many interesting applications, from the construction of higher dimensional unification, to provide a useful framework for quantum gravity and to better define some local symmetries that suffer singularities in…
We consider structured optimisation problems defined in terms of the sum of a smooth and convex function, and a proper, l.s.c., convex (typically non-smooth) one in reflexive variable exponent Lebesgue spaces $L_{p(\cdot)}(\Omega)$. Due to…