Related papers: A Regularized Free Form Estimator for Dark Energy
The concepts of sparsity, and regularised estimation, have proven useful in many high-dimensional statistical applications. Dynamic factor models (DFMs) provide a parsimonious approach to modelling high-dimensional time series, however, it…
We use the framework of a recently proposed model of reduced relativistic gas (RRG) to obtain the bounds for $\Omega$'s of Dark Matter and Dark Energy (in the present case, a cosmological constant), taking into consideration an arbitrary…
Standard regularization methods that are used to compute solutions to ill-posed inverse problems require knowledge of the forward model. In many real-life applications, the forward model is not known, but training data is readily available.…
The response envelope model provides substantial efficiency gains over the standard multivariate linear regression by identifying the material part of the response to the model and by excluding the immaterial part. In this paper, we propose…
In this paper we discuss the numerical solution of elliptic distributed optimal control problems with state or control constraints when the control is considered in the energy norm. As in the unconstrained case we can relate the…
We present a general framework for studying regularized estimators; such estimators are pervasive in estimation problems wherein "plug-in" type estimators are either ill-defined or ill-behaved. Within this framework, we derive, under…
We propose a convex variational approach to compute localized density matrices for both zero temperature and finite temperature cases, by adding an entry-wise $\ell_1$ regularization to the free energy of the quantum system. Based on the…
Estimation of quantum states is one of the most important steps in any quantum information processing experiment. A naive reconstruction of the density matrix from experimental measurements can often give density matrices which are not…
In this paper we propose a new class of iterative regularization methods for solving ill-posed linear operator equations. The prototype of these iterative regularization methods is in the form of second order evolution equation with a…
Image tokenizers play a central role in modern generative models, where the structure of the latent space critically determines the downstream generation performance. A key but underexplored property of effective latent representations is…
We propose a new Dark Energy parametrization based on the dynamics of a scalar field. We use an equation of state $w=(x-1)/(x+1)$, with $x=E_k/V$, the ratio of kinetic energy $E_k=\dot\phi^2/2$ and potential $V$. The eq. of motion gives…
We present $N$-body simulations which are fully compatible with general relativity, with dark energy consistently included at both the background and perturbation level. We test our approach for dark energy parameterised as both a fluid,…
Low-rank modeling has a lot of important applications in machine learning, computer vision and social network analysis. While the matrix rank is often approximated by the convex nuclear norm, the use of nonconvex low-rank regularizers has…
Allowing for greater low-redshift flexibility through parametrizations such as CPL can lead to apparent deviations from $\Lambda$CDM, with the latter lying at roughly the $2\sigma$ level from the best-fit model. This motivates an…
The highly anisotropic nature of the Lyman-alpha (Ly$\alpha$) forest data introduces a complex survey window function that complicates the measurement of the three-dimensional power spectrum ($P_{\mathrm{3D}}$). In this paper, we present…
It is an efficient and effective strategy to utilize the nuclear norm approximation to learn low-rank matrices, which arise frequently in machine learning and computer vision. So the exploration of nuclear norm minimization problems is…
For high-dimensional sparse parameter estimation problems, Log-Sum Penalty (LSP) regularization effectively reduces the sampling sizes in practice. However, it still lacks theoretical analysis to support the experience from previous…
The evolution of dark energy density is a crucial quantity in understanding the nature of dark energy. Often, the quantity is described by the so-called equation of state, that is the ratio of dark energy pressure to its density. In this…
Inspired by ideas taken from the machine learning literature, new regularization techniques have been recently introduced in linear system identification. In particular, all the adopted estimators solve a regularized least squares problem,…
In various scientific and engineering applications, there is typically an approximate model of the underlying complex system, even though it contains both aleatoric and epistemic uncertainties. In this paper, we present a principled method…