Related papers: A Regularized Free Form Estimator for Dark Energy
We present a formalism for the numerical implementation of general theories of dark energy, combining the computational simplicity of the equation of state for perturbations approach with the generality of the effective field theory…
Estimating equations arise in a wide range of statistical applications, including longitudinal and clustered data analysis, survival analysis, econometrics, and semiparametric inference. In high-dimensional settings, adding…
The most commonly used form of regularization typically involves defining the penalty function as a L1 or L2 norm. However, numerous alternative approaches remain untested in practical applications. In this study, we apply ten different…
This paper studies the matrix completion problem under arbitrary sampling schemes. We propose a new estimator incorporating both max-norm and nuclear-norm regularization, based on which we can conduct efficient low-rank matrix recovery…
We present a simple mechanism which can mimic dark energy with an equation of state w < -1 as deduced from the supernova data. We imagine that the universe is accelerating under the control of a quintessence field, which is moving up a very…
Standard maximum likelihood estimation cannot be applied to discrete energy-based models in the general case because the computation of exact model probabilities is intractable. Recent research has seen the proposal of several new…
We show that the distance measures (such as the luminosity and angular diameter distances) are linear functionals of the equation-of-state function w(z) of the dark energy to a fair degree of accuracy in the regimes of interest. That is,…
We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…
Reconstructing gamma-ray spectra from detector measurements is an ill-posed inverse problem. Standard methods, such as Folding Iteration with Compton Subtraction (FICS), provide point estimates but lack calibrated uncertainties and may bias…
A comparative study of various parametrizations of the dark energy equation of state $w(z)$ and its variation with the redshift is made. Astrophysical constraints from 'integrated tracking' are laid down to test the physical viability and…
Many statistical estimands can expressed as continuous linear functionals of a conditional expectation function. This includes the average treatment effect under unconfoundedness and generalizations for continuous-valued and personalized…
When working with quantum states, analysis of the final quantum state generated through probabilistic measurements is essential. This analysis is typically conducted by constructing the density matrix from either partial or full tomography…
We develop a formalism to characterize the redshift evolution of the dark energy potential. Our formalism makes use of quantities similar to the Horizon-flow parameters in inflation and is general enough that can deal with multiscalar…
Method of moment estimators exhibit appealing statistical properties, such as asymptotic unbiasedness, for nonconvex problems. However, they typically require a large number of samples and are extremely sensitive to model misspecification.…
To address the challenges of reliable statistical inference in high-dimensional models, we introduce the Synthetic-data Regularized Estimator (SRE). Unlike traditional regularization methods, the SRE regularizes the complex target model via…
Estimating the free energy in molecular simulation requires, implicitly or explicitly, counting how many times the system is observed in a finite region. If the simulation is biased by an external potential, the weight of the configurations…
We develop an efficient sampling and free energy calculation technique within the adaptive biasing potential (ABP) framework. By mollifying the density of states we obtain an approximate free energy and an adaptive bias potential that is…
A new efficient numerical algorithm for interacting fermion systems is proposed and examined in detail. The ground state is expressed approximately by a linear combination of numerically chosen basis states in a truncated Hilbert space. Two…
The widely used nuclear norm heuristic for rank minimization problems introduces a regularization parameter which is difficult to tune. We have recently proposed a method to approximate the regularization path, i.e., the optimal solution as…
This paper provides a new regularization method which is particularly suitable for linear exponentially ill-posed problems. Under logarithmic source conditions (which have a natural interpretation in terms of Sobolev spaces in the…