Related papers: A Regularized Free Form Estimator for Dark Energy
Within the statistical and machine learning literature, regularization techniques are often used to construct sparse (predictive) models. Most regularization strategies only work for data where all predictors are treated identically, such…
Complex phenomena in engineering and the sciences are often modeled with computationally intensive feed-forward simulations for which a tractable analytic likelihood does not exist. In these cases, it is sometimes necessary to estimate an…
We investigate the generalizability of deep learning based on the sensitivity to input perturbation. We hypothesize that the high sensitivity to the perturbation of data degrades the performance on it. To reduce the sensitivity to…
We consider discrete default intensity based and logit type reduced form models for conditional default probabilities for corporate loans where we develop simple closed form approximations to the maximum likelihood estimator (MLE) when the…
A review on spatially flat D-dimensional Friedmann-Robertson-Walker (FRW) model of the universe has been performed. Some standard parameterizations of the equation of state parameter of the Dark Energy models are proposed and the…
We provide a model-independent reconstruction of dark energy from $z=0$ to $ \gtrsim 10^5$. We parameterise the model by a perfect fluid with a series of physically well-motivated bins in energy-density, such that the equation of state is…
We investigate a dynamical reconstruction of the dark energy equation of state parameter by assuming that it satisfies a law of motion described by an autonomous second-order differential equation, with the limit of the cosmological…
Reinforcement learning (RL) methods have been shown to be capable of learning intelligent behavior in rich domains. However, this has largely been done in simulated domains without adequate focus on the process of building the simulator. In…
f(R) gravity is one of the simplest generalizations of general relativity, which may explain the accelerated cosmic expansion without introducing a cosmological constant. Transformed into the Einstein frame, a new scalar degree of freedom…
Estimating a low rank matrix from its linear measurements is a problem of central importance in contemporary statistical analysis. The choice of tuning parameters for estimators remains an important challenge from a theoretical and…
Adaptive nuclear-norm penalization is proposed for low-rank matrix approximation, by which we develop a new reduced-rank estimation method for the general high-dimensional multivariate regression problems. The adaptive nuclear norm of a…
The de-facto standard approach of promoting sparsity by means of $\ell_1$-regularization becomes ineffective in the presence of simplex constraints, i.e.,~the target is known to have non-negative entries summing up to a given constant. The…
Sparsity and rank functions are important ways of regularizing under-determined linear systems. Optimization of the resulting formulations is made difficult since both these penalties are non-convex and discontinuous. The most common remedy…
In this letter we propose a test to detect the linearity of the dark energy equation of state, and apply it to two different Type Ia Supernova (SN Ia) data sets, Union2.1 and SNLS3. We find that: a. current SN Ia data are well described by…
Constraining the dark energy equation of state, $w_x(z)$, is one of the main issues of current and future cosmological surveys. In practice, this requires making assumptions about the evolution of $w_x$ with redshift $z$, which can be…
In this work, we investigate the regularized solutions and their finite element solutions to the inverse source problems governed by partial differential equations, and establish the stochastic convergence and optimal finite element…
We present a novel approach to image restoration that leverages ideas from localized structured prediction and non-linear multi-task learning. We optimize a penalized energy function regularized by a sum of terms measuring the distance…
This review summarizes recent attempts to reconstruct the expansion history of the Universe and to probe the nature of dark energy. Reconstruction methods can be broadly classified into parametric and non-parametric approaches. It is…
It has been repeatedly stated that maximum likelihood (ML) estimates of exponents of power-law distributions can only be reliably obtained for exponents smaller than minus one. The main argument that power laws are otherwise not…
Estimating the values of unknown parameters from corrupted measured data faces a lot of challenges in ill-posed problems. In such problems, many fundamental estimation methods fail to provide a meaningful stabilized solution. In this work,…