Related papers: Gaussian regression and power spectral density est…
When training a machine learning model with observational data, it is often encountered that some values are systemically missing. Learning from the incomplete data in which the missingness depends on some covariates may lead to biased…
The current accelerated expansion of the Universe remains ones of the most intriguing topics in modern cosmology, driving the search for innovative statistical techniques. Recent advancements in machine learning have significantly enhanced…
Recent cosmological observations, including the latest Dark Energy Spectroscopic Instrument (DESI) data releases DR1 and DR2, have renewed interest in the possibility that dark energy may exhibit dynamical behavior rather than being a…
The stochastic gradient descent (SGD) algorithm has been widely used in statistical estimation for large-scale data due to its computational and memory efficiency. While most existing works focus on the convergence of the objective function…
We analyze a practical algorithm for sparse PCA on incomplete and noisy data under a general non-random sampling scheme. The algorithm is based on a semidefinite relaxation of the $\ell_1$-regularized PCA problem. We provide theoretical…
In compressive sensing, sparse signals are recovered from underdetermined noisy linear observations. One of the interesting problems which attracted a lot of attention in recent times is the support recovery or sparsity pattern recovery…
Compressive Sensing (CS) is a new paradigm for the efficient acquisition of signals that have sparse representation in a certain domain. Traditionally, CS has provided numerous methods for signal recovery over an orthonormal basis. However,…
Density regression characterizes the conditional density of the response variable given the covariates, and provides much more information than the commonly used conditional mean or quantile regression. However, it is often computationally…
We propose a robust inferential procedure for assessing uncertainties of parameter estimation in high-dimensional linear models, where the dimension $p$ can grow exponentially fast with the sample size $n$. Our method combines the…
MICROSCOPE's space test of the weak equivalence principle (WEP) is based on the minute measurement of the difference of accelerations experienced by two test masses as they orbit the Earth. A detection of a violation of the WEP would appear…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…
Weak lensing mass-mapping is a useful tool to access the full distribution of dark matter on the sky, but because of intrinsic galaxy ellipticies and finite fields/missing data, the recovery of dark matter maps constitutes a challenging…
Spatial fields in the Earth and environmental sciences are often available at multiple scales or resolutions. While coarse-scale data (e.g., from global circulation models) are often abundant, they lack the local detail provided by…
Gaussian process (GP) regression provides a flexible, nonparametric framework for probabilistic modeling, yet remains computationally demanding in large-scale applications. For one-dimensional data, state space (SS) models achieve…
Efficient information processing is crucial for both living organisms and engineered systems. The mutual information rate, a core concept of information theory, quantifies the amount of information shared between the trajectories of input…
We wish to estimate conditional density using Gaussian Mixture Regression model with logistic weights and means depending on the covariate. We aim at selecting the number of components of this model as well as the other parameters by a…
Modeling sequential data has become more and more important in practice. Some applications are autonomous driving, virtual sensors and weather forecasting. To model such systems, so called recurrent models are frequently used. In this paper…
Public health data are often spatially dependent, but standard spatial regression methods can suffer from bias and invalid inference when the independent variable is associated with spatially-correlated residuals. This could occur if, for…
Most compressed sensing algorithms do not account for the effect of saturation in noisy compressed measurements, though saturation is an important consequence of the limited dynamic range of existing sensors. The few algorithms that handle…
Computing accurate estimates of the Fourier transform of analog signals from discrete data points is important in many fields of science and engineering. The conventional approach of performing the discrete Fourier transform of the data…