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We study how the formalism of the Hierarchical Reference Theory (HRT) can be extended to inhomogeneous systems. HRT is a liquid state theory which implements the basic ideas of Wilson momentum shell renormalization group (RG) to microscopic…
In this paper we consider the problem of exact recovery of a fixed sparse vector with the measurement matrices sequentially arriving along with corresponding measurements. We propose an extension of the iterative hard thresholding (IHT)…
We present the marginal unbiased score expansion (MUSE) method, an algorithm for generic high-dimensional hierarchical Bayesian inference. MUSE performs approximate marginalization over arbitrary non-Gaussian latent parameter spaces,…
Evaluating the statistical dimension is a common tool to determine the asymptotic phase transition in compressed sensing problems with Gaussian ensemble. Unfortunately, the exact evaluation of the statistical dimension is very difficult and…
Size distortion can occur if an asymptotic testing procedure requiring diverging sample sizes, is implemented to data with very small sample sizes. In this paper, we consider one-sample and two-sample tests for mean vectors when data are…
Hidden Markov models (HMMs) are characterized by an unobservable Markov chain and an observable process -- a noisy version of the hidden chain. Decoding the original signal from the noisy observations is one of the main goals in nearly all…
We present a framework using the Quantized Tensor Train (QTT) decomposition to accurately and efficiently solve volume and boundary integral equations in three dimensions. We describe how the QTT decomposition can be used as a hierarchical…
Reconstructing cosmological initial conditions (ICs) from late-time observations is a difficult task, which relies on the use of computationally expensive simulators alongside sophisticated statistical methods to navigate multi-million…
It has been a long history in testing whether a mean vector with a fixed dimension has a specified value. Some well-known tests include the Hotelling $T^2$-test and the empirical likelihood ratio test proposed by Owen [Biometrika 75 (1988)…
A framework for estimation and hypothesis testing of functional restrictions against general alternatives is proposed. The parameter space is a reproducing kernel Hilbert space (RKHS). The null hypothesis does not necessarily define a…
In the context of large samples, a small number of individuals might spoil basic statistical indicators like the mean. It is difficult to detect automatically these atypical individuals, and an alternative strategy is using robust…
We propose a high dimensional mean test framework for shrinking random variables, where the underlying random variables shrink to zero as the sample size increases. By pooling observations across overlapping subsets of dimensions, we…
We consider Bayesian estimation of a hierarchical linear model (HLM) from partially observed data, assumed to be missing at random, and small sample sizes. A vector of continuous covariates $C$ includes cluster-level partially observed…
Compressed sensing (CS) is on recovery of high dimensional signals from their low dimensional linear measurements under a sparsity prior and digital quantization of the measurement data is inevitable in practical implementation of CS…
This article presents general procedures for constructing, estimating, and testing Hilbert space multi-dimensional (HSM) models, which are based on quantum probability theory. HSM models can be applied to collections of K different…
We propose a novel algorithm for large-scale regression problems named histogram transform ensembles (HTE), composed of random rotations, stretchings, and translations. First of all, we investigate the theoretical properties of HTE when the…
An extreme-point symmetric mode decomposition (ESMD) method is proposed to improve the Hilbert-Huang Transform (HHT) through the following prospects: (1) The sifting process is implemented by the aid of 1, 2, 3 or more inner interpolating…
Hierarchical Bayesian models can be especially useful in precision medicine settings, where clinicians are interested in estimating the patient-level latent variables associated with an individual's current health state and its trajectory.…
A general asynchronous alternating iterative model is designed, for which convergence is theoretically ensured both under classical spectral radius bound and, then, for a classical class of matrix splittings for $\mathsf H$-matrices. The…
Invariant coordinate selection (ICS) is a dimension reduction method, used as a preliminary step for clustering and outlier detection. It has been primarily applied to multivariate data. This work introduces a coordinate-free definition of…