Related papers: A Regularized Free Form Estimator for Dark Energy

An important issue in cosmology is reconstructing the effective dark energy equation of state directly from observations. With so few physically motivated models, future dark energy studies cannot only be based on constraining a dark energy…

We investigate a top-down approach for modeling the dark energy where we fit the luminosity distances directly rather than indirectly fitting the equation of state.

In this paper, we study extended linear regression approaches for quantum state tomography based on regularization techniques. For unknown quantum states represented by density matrices, performing measurements under certain basis yields…

We consider model selection and estimation for partial spline models and propose a new regularization method in the context of smoothing splines. The regularization method has a simple yet elegant form, consisting of roughness penalty on…

We propose an adaptive finite element algorithm to approximate solutions of elliptic problems whose forcing data is locally defined and is approximated by regularization (or mollification). We show that the energy error decay is…

A basic aim of ongoing and upcoming cosmological surveys is to unravel the mystery of dark energy. In the absence of a compelling theory to test, a natural approach is to better characterize the properties of dark energy in search of clues…

The possibility of reconstructing the dark energy equation of state from variations in the fine structure constant is investigated for a class of models where the quintessence field is non-minimally coupled to the electromagnetic field. For…

It is well known that popular optimization techniques can lead to overfitting or even a lack of convergence altogether; thus, practitioners often utilize ad hoc regularization terms added to the energy functional. When carefully crafted,…

Modern applications require methods that are computationally feasible on large datasets but also preserve statistical efficiency. Frequently, these two concerns are seen as contradictory: approximation methods that enable computation are…

We revisit the idea of using varying couplings to probe the nature of dark energy, in particular by reconstructing its equation of state. We show that this method can be far superior to the standard methods (using type Ia supernovae or weak…

The present work is based upon a parametric reconstruction of the effective or total equation of state in a model for the universe with accelerated expansion. The constraints on the model parameters are obtained by maximum likelihood…

Exact free energy minimization is a convex optimization problem that is usually approximated with stochastic sampling methods. Deterministic approximations have been less successful because many desirable properties have been difficult to…

Over the past few years, trace regression models have received considerable attention in the context of matrix completion, quantum state tomography, and compressed sensing. Estimation of the underlying matrix from regularization-based…

In this paper, we explore a new type of smooth and well-behaved polynomial redshift function that can avoid a future singularity. Using this function, we have proposed different redshift parametrizations of the dark energy equation of…

In this paper, a novel linear formulation for power system state estimation that simultaneously treats conventional and synchrophasor measurements is proposed. A linear circuit model for conventional measurements is introduced to enable a…

Machine learning models suffer from overfitting, which is caused by a lack of labeled data. To tackle this problem, we proposed a framework of regularization methods, called density-fixing, that can be used commonly for supervised and…

This paper proposes an algorithm for computing regularized solutions to linear rational expectations models. The algorithm allows for regularization cross-sectionally as well as across frequencies. A variety of numerical examples illustrate…

In this paper, we introduce a new estimator for the emission densities of a nonparametric hidden Markov model. It is adaptive and minimax with respect to each state's regularity--as opposed to globally minimax estimators, which adapt to the…

This paper presents a general framework for estimating high-dimensional conditional latent factor models via constrained nuclear norm regularization. We establish large sample properties of the estimators and provide efficient algorithms…

This letter proposes to estimate low-rank matrices by formulating a convex optimization problem with non-convex regularization. We employ parameterized non-convex penalty functions to estimate the non-zero singular values more accurately…