Related papers: Smoothing spline primordial power spectrum reconst…
In areas such as kernel smoothing and non-parametric regression there is emphasis on smooth interpolation and smooth statistical models. Splines are known to have optimal smoothness properties in one and higher dimensions. It is shown, with…
The integration of Symmetric Positive Definite (SPD) matrices into deep learning has historically relied on fixed algebraic Riemannian metrics. Analogous to hand-crafted features in classical machine learning, these static formulations…
Full Stokes filter-polarimeters are key instruments for investigating the rapid evolution of magnetic structures on the solar surface. To this end, the image quality is routinely improved using a-posteriori image reconstruction methods. We…
In paper I of this series (Yang et al. 2017, ApJ), we proposed an analytical method of blind separation ({\bf ABS}) to extract the cosmic magnification signal in galaxy number distribution and reconstruct the weak lensing power spectrum.…
Features in the primordial power spectrum have been suggested as an explanation for glitches in the angular power spectrum of temperature anisotropies measured by the WMAP satellite. However, these glitches might just as well be artifacts…
We study the morphology of convergence maps by perturbatively reconstructing their Minkowski Functionals (MFs). We present a systematics study using a set of three generalised skew-spectra as a function of source redshift and smoothing…
Intensity mapping is a promising technique for surveying the large scale structure of our Universe from $z=0$ to $z \sim 150$, using the brightness temperature field of spectral lines to directly observe previously unexplored portions of…
The Cosmic Microwave Background Radiation (CMBR) holds information about almost all the fundamental cosmological parameters, and by performing a likelihood analysis of high precision CMBR fluctuation data, these parameters can be inferred.…
We investigate constraints on power spectra of the primordial curvature and tensor perturbations with priors based on single-field slow-roll inflation models. We stochastically draw the Hubble slow-roll parameters and generate the…
The observables of the perturbed universe, CMB anisotropy and large structures, depend on a set of cosmological parameters, as well as, the assumed nature of primordial perturbations. In particular, the shape of the primordial power…
A new computational scheme for the nonlinear cosmological matter power spectrum (PS) is presented. Our method is based on evolution equations in time, which can be cast in a form extremely convenient for fast numerical evaluations. A…
Detecting slender, overlapping structures remains a challenge in computational microscopy. While recent coordinate-based approaches improve detection, they often produce less accurate splines than pixel-based methods. We introduce a…
We reconstruct the primordial power spectrum $P_{\mathcal{R}}(k)$ from the BOSS DR 12 LRG and eBOSS DR 16 QSO catalogs with a non-parametric Bayesian method. The $P_{\mathcal{R}}(k)$ is reconstructed by linearly interpolating $N$ knots in…
Using the temperature data from Planck we search for departures from a power-law primordial power spectrum, employing Bayesian model-selection and posterior probabilities. We parametrize the spectrum with $n$ knots located at arbitrary…
Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…
We propose a new, likelihood-free approach to inferring the primordial matter power spectrum and cosmological parameters from arbitrarily complex forward models of galaxy surveys where all relevant statistics can be determined from…
We propose a flexible nonparametric regression method for ultrahigh-dimensional data. As a first step, we propose a fast screening method based on the favored smoothing bandwidth of the marginal local constant regression. Then, an iterative…
Smoothing splines have been used pervasively in nonparametric regressions. However, the computational burden of smoothing splines is significant when the sample size $n$ is large. When the number of predictors $d\geq2$, the computational…
In the cosmic microwave background or galaxy density maps, missing fluctuations in masked regions can be reconstructed from fluctuations in the surrounding unmasked regions if the original fluctuations are sufficiently smooth. One…
We present Neural Splines, a technique for 3D surface reconstruction that is based on random feature kernels arising from infinitely-wide shallow ReLU networks. Our method achieves state-of-the-art results, outperforming recent neural…