arXiv research

New image restoration method using localized patches and external databases.

The paper classifies and analyzes the stability of elastic curves with fixed endpoints.

The extension of the classical Bayesian penalized spline method to inference on vector-valued functions is considered, with an emphasis on characterizing the suitability of the method for general application.We show that the standard quadratic penalty is exactly analogous to the energy of a stretched string, with the p…

This paper studies the convergence of penalized energy to harmonic maps in Riemannian manifolds.

Regularizes 3D inverse scattering with tangent-point energy for better solutions.

By introducing a shape manifold as a solution set to solve inverse obstacle scattering problems we allow the reconstruction of general, not necessarily star-shaped curves. The bending energy is used as a stabilizing term in Tikhonov regularization to gain independence of the parametrization. Moreover, we discuss how se…

We study the problem of finding the one-dimensional structure in a given data set. In other words we consider ways to approximate a given measure (data) by curves. We consider an objective functional whose minimizers are a regularization of principal curves and introduce a new functional which allows for multiple curve…

The paper explores MMPR to select diverse models for scientific insight.

Study on elastic curves pinned at the boundary, focusing on minimizers and their interaction with obstacles.

Gradient flow on diffeomorphisms for image registration, with well-posedness proven.

We consider the Willmore functional on graphs, with an additional penalization of the area where the curvature is non-zero. Interpreting the penalization parameter as a Lagrange multiplier, this corresponds to the Willmore functional with a constraint on the area where the graph is flat. Sending the penalization parame…

We prove a Gamma-convergence result for a family of bending energies defined on smooth surfaces in $\mathbb{R}^3$ equipped with a director field. The energies strongly penalize the deviation of the director from the surface unit normal and control the derivatives of the director. Such type of energies for example arise…

Poisson variational autoencoders introduce a metabolic cost term that penalizes high baseline activity.

TPBS models improve robustness to overfitting with localized Dirichlet energy regularization.

We investigate the elastic behavior of knotted loops of springy wire. To this end we minimize the classic bending energy $E_{\text{bend}}=\intκ^2$ together with a small multiple of ropelength $\mathcal R=\text{length}/\text{thickness}$ in order to penalize selfintersection. Our main objective is to characterize elastic…

We characterize the value of swing contracts in continuous time as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation with suitable boundary conditions. The case of contracts with penalties is straightforward, and in that case only a terminal condition is needed. Conversely, the case of contracts with …

MAP inference for general energy functions remains a challenging problem. While most efforts are channeled towards improving the linear programming (LP) based relaxation, this work is motivated by the quadratic programming (QP) relaxation. We propose a novel MAP relaxation that penalizes the Kullback-Leibler divergence…

Volatility is a key measure of risk in financial analysis. The high volatility of one financial asset today could affect the volatility of another asset tomorrow. These lagged effects among volatilities - which we call volatility spillovers - are studied using the Vector AutoRegressive (VAR) model. We account for the p…

We develop a maximum penalized quasi-likelihood estimator for estimating in a nonparametric way the diffusion function of a diffusion process, as an alternative to more traditional kernel-based estimators. After developing a numerical scheme for computing the maximizer of the penalized maximum quasi-likelihood function…

Paper estimates differences in multi-attribute Gaussian graphical models using non-convex penalties.

In this paper we study nonconvex penalization using Bernstein functions. Since the Bernstein function is concave and nonsmooth at the origin, it can induce a class of nonconvex functions for high-dimensional sparse estimation problems. We derive a threshold function based on the Bernstein penalty and give its mathemati…

A new Branch-and-Bound solver tackles L0-penalized problems with flexible loss functions.

In this work we establish the equivalence of algorithmic regularization and explicit convex penalization for generic convex losses. We introduce a geometric condition for the optimization path of a convex function, and show that if such a condition is satisfied, the optimization path of an iterative algorithm on the un…

In this paper we study nonconvex penalization using Bernstein functions whose first-order derivatives are completely monotone. The Bernstein function can induce a class of nonconvex penalty functions for high-dimensional sparse estimation problems. We derive a thresholding function based on the Bernstein penalty and di…

Penalized estimation can conduct variable selection and parameter estimation simultaneously. The general framework is to minimize a loss function subject to a penalty designed to generate sparse variable selection. The majorization-minimization (MM) algorithm is a computational scheme for stability and simplicity, and …

New algorithm reduces costs in wind energy systems by minimizing decision changes.

The paper develops a deep neural network estimator for weakly dependent processes with various loss functions.

This paper introduces a gradient analysis framework to improve language model performance by rewarding good examples and penalizing bad ones.

Early-stopped aggregation improves computational efficiency in adaptive statistical inference.

New method avoids surface self-collision in geometric optimization.

In this paper, we propose a one-pass algorithm on MapReduce for penalized linear regression \[f_λ(α, β) = \|Y - α\mathbf{1} - Xβ\|_2^2 + p_λ(β)\] where $α$ is the intercept which can be omitted depending on application; $β$ is the coefficients and $p_λ$ is the penalized function with penalizing parameter $λ$. $f_λ(α, β…

We extend the analysis of investment strategies derived from penalized quantile regression models, introducing alternative approaches to improve state\textendash of\textendash art asset allocation rules. First, we use a post\textendash penalization procedure to deal with overshrinking and concentration issues. Second, …

The paper develops adaptive deep learning methods for nonlinear time series models.

New method for inference on strongly identified functionals even when nuisance functions are weakly identified.

We consider a Canham-Helfrich-type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes. It consists of minimizing the sum of the Canham-Helfrich energy, in which the bending rigidities and spontaneous curvatures…

Unified analysis of multi-attribute graph learning with non-convex penalties.

In this paper the robust utility maximization problem for a market model based on Lévy processes is analyzed. The interplay between the form of the utility function and the penalization function required to have a well posed problem is studied, and for a large class of utility functions it is proved that the dual probl…

Improved convergence rates for MLE in mixture models using penalized log-likelihood.

Existing methods for sparse channel estimation typically provide an estimate computed as the solution maximizing an objective function defined as the sum of the log-likelihood function and a penalization term proportional to the l1-norm of the parameter of interest. However, other penalization terms have proven to have…

Optimal control problems on Riemannian manifolds are solved by penalizing constraint violations.

Paper develops PGMM framework for debiased inference on nonparametric IV estimators.

In this paper, we study the performance of extremum estimators from the perspective of generalization ability (GA): the ability of a model to predict outcomes in new samples from the same population. By adapting the classical concentration inequalities, we derive upper bounds on the empirical out-of-sample prediction e…

For every $\;b>1\;$ fixed, we explicitly construct $1$-dimensional families of embedded constrained Willmore tori parametrized by their conformal class $\;(a,b)$\; with $\; a \sim_b 0^+\;$ deforming the homogenous torus \;$f^b$ of conformal class \;$(0,b).$ The variational vector field at $f^b$ is hereby given by a non…

We give improved constants for data dependent and variance sensitive confidence bounds, called empirical Bernstein bounds, and extend these inequalities to hold uniformly over classes of functionswhose growth function is polynomial in the sample size n. The bounds lead us to consider sample variance penalization, a nov…

The paper develops methods to reduce deployment risk under dynamic covariate shifts.

The standard approach for dealing with the ill-posedness of the training problem in machine learning and/or the reconstruction of a signal from a limited number of measurements is regularization. The method is applicable whenever the problem is formulated as an optimization task. The standard strategy consists in augme…

Develops a fast algorithm for high-dimensional LASSO penalized quantile regression.

Flexible empirical Bayes for large-scale multiple linear regression.