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Modern time series forecasting methods, such as Transformer and its variants, have shown strong ability in sequential data modeling. To achieve high performance, they usually rely on redundant or unexplainable structures to model complex…
In estimating an unknown parameter of a quantum state the quantum Fisher information (QFI) is a pivotal quantity, which depends on the state and its derivate with respect to the unknown parameter. We prove the continuity property for the…
Granger causality analysis, as one of the most popular time series causality methods, has been widely used in the economics, neuroscience. However, unobserved confounders is a fundamental problem in the observational studies, which is still…
Strong gravitational lensed quasars (QSOs) have emerged as powerful and novel cosmic probes as they can deliver crucial cosmological information, such as a measurement of the Hubble constant, independent of other probes. Although the…
Canonical Correlation Analysis (CCA) and its regularised versions have been widely used in the neuroimaging community to uncover multivariate associations between two data modalities (e.g., brain imaging and behaviour). However, these…
A key goal of unsupervised learning is to go beyond density estimation and sample generation to reveal the structure inherent within observed data. Such structure can be expressed in the pattern of interactions between explanatory latent…
The intense radiation emitted by luminous quasars dramatically alters the ionization state of their surrounding IGM. This so-called proximity effect extends out to tens of Mpc, and manifests as large coherent regions of enhanced…
We report the result of a faint quasar survey in a one square degree field. The aim is to test the Y-K/g-z and J-K/i-Y color selection criteria for quasars at faint magnitude, to obtain a complete sample of quasars based on deep optical and…
Causal discovery from observational data underpins applications in finance, climate modeling, and machine learning. Constraint-based causal discovery reduces structure learning to a sequence of conditional independence (CI) tests, where…
This paper proposes a new subspace learning method, named Quantized Fisher Discriminant Analysis (QFDA), which makes use of both machine learning and information theory. There is a lack of literature for combination of machine learning and…
Many real-world decision-making tasks require learning causal relationships between a set of variables. Traditional causal discovery methods, however, require that all variables are observed, which is often not feasible in practical…
We describe the algorithm for selecting quasar candidates for optical spectroscopy in the Sloan Digital Sky Survey. Quasar candidates are selected via their non-stellar colors in "ugriz" broad-band photometry, and by matching unresolved…
This paper develops the inferential theory for latent factor models estimated from large dimensional panel data with missing observations. We propose an easy-to-use all-purpose estimator for a latent factor model by applying principal…
Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables…
We investigate the distribution of companion galaxies around quasars using {\em Hubble Space Telescope} ({\em HST}) Advanced Camera for Surveys Wide Field Camera (ACS/WFC) archival images. Our master sample contains 532 quasars which have…
Quasars at the redshift frontier (z > 7.0) are fundamental probes of black hole (BH) growth and evolution but notoriously difficult to identify. At these redshifts, machine learning-based selection methods have proven to be efficient, but…
Fourier feature approximations have been successfully applied in the literature for scalable Gaussian Process (GP) regression. In particular, Quadrature Fourier Features (QFF) derived from Gaussian quadrature rules have gained popularity in…
Every organism in an environment, whether biological, robotic or virtual, must be able to predict certain aspects of its environment in order to survive or perform whatever task is intended. It needs a model that is capable of estimating…
The power spectrum of transmitted flux in the Ly$\alpha$ forest in spectra of distant quasars gives us an information about matter power spectrum on the smallest spatial scales which is very important for testing of different models of dark…
We develop a field-level posterior for cosmological data by marginalizing over initial conditions and noise in a general forward model. While our focus is on large-scale structure data, the results generalize to any weakly non-Gaussian…