Related papers: A Regularized Free Form Estimator for Dark Energy
In this paper, we develop a relative error bound for nuclear norm regularized matrix completion, with the focus on the completion of full-rank matrices. Under the assumption that the top eigenspaces of the target matrix are incoherent, we…
The understanding of the accelerated expansion of the Universe poses one of the most fundamental questions in physics and cosmology today. Whether or not the acceleration is driven by some form of dark energy, and in the absence of a…
The current paper provides a comprehensive examination of a dark energy cosmological model in the classical regime, in which a generic scalar field is regarded as a dark energy source. Einstein's field equations are solved in model…
The response of a nucleus to an electromagnetic probe is a key quantity to simulate photabsorption or photodeexcitation processes. For large calculations at the scale of the entire mass table, this response can be estimated by linear…
We describe two fitting schemes that aim to represent the high-density part of realistic equations of state for numerical simulations such as neutron star oscillations. The low-density part of the equation of state is represented by an…
We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…
A Maximum Likelihood recursive state estimator is derived for non-linear and non-Gaussian state-space models. The estimator combines a particle filter to generate the conditional density and the Expectation Maximization algorithm to compute…
An adaptive regularization strategy for stabilizing Newton-like iterations on a coarse mesh is developed in the context of adaptive finite element methods for nonlinear PDE. Existence, uniqueness and approximation properties are known for…
We develop a method for computing exact one-loop quantum corrections to the energies of static classical backgrounds in renormalizable quantum field theories. We use a continuum density of states formalism to construct a regularized Casimir…
Based on a suite of state-of-the-art high-resolution $N$-body simulations, we revisit the so-called halofit model (Smith et al. 2003) as an accurate fitting formula for the nonlinear matter power spectrum. While the halofit model has been…
When classical particle filtering algorithms are used for maximum likelihood parameter estimation in nonlinear state-space models, a key challenge is that estimates of the likelihood function and its derivatives are inherently noisy. The…
From the statistical learning perspective, complexity control via explicit regularization is a necessity for improving the generalization of over-parameterized models. However, the impressive generalization performance of neural networks…
Regularization plays an important role in solving ill-posed problems by adding extra information about the desired solution, such as sparsity. Many regularization terms usually involve some vector norm, e.g., $L_1$ and $L_2$ norms. In this…
We study the problem of finding structured low-rank matrices using nuclear norm regularization where the structure is encoded by a linear map. In contrast to most known approaches for linearly structured rank minimization, we do not (a) use…
Approximate dynamic programming has been used successfully in a large variety of domains, but it relies on a small set of provided approximation features to calculate solutions reliably. Large and rich sets of features can cause existing…
In this paper, we present a novel optimization algorithm designed specifically for estimating state-space models to deal with heavy-tailed measurement noise and constraints. Our algorithm addresses two significant limitations found in…
For electrical impedance tomography (EIT), most practical reconstruction methods are based on linearizing the underlying non-linear inverse problem. Recently, it has been shown that the linearized problem still contains the exact shape…
The power method is one of the most fundamental tools for extracting top principal components from data through low-rank matrix approximation. Yet, when the target rank is large, the cost of matrix multiplication associated with this…
We compare current and forecasted constraints on dynamical dark energy models from Type Ia supernovae and the cosmic microwave background using figures of merit based on the volume of the allowed dark energy parameter space. For a…
Regression by composition provides a flexible framework for constructing conditional distributions through sequential group actions. However, when multiple flows act on the same distribution, the model becomes non-identifiable, leading to…