arXiv subjects

Chuan Bi

Publications and source records attributed to Chuan Bi.

7 recordsLinked to original sources

arXiv2024

Semi-Confirmatory Factor Analysis for High-Dimensional Data with Interconnected Community Structures

Confirmatory factor analysis (CFA) is a statistical method for identifying and confirming the presence of latent factors among observed variables through the analysis of their covariance structure. Compared to alternative factor models, CFA offers interpretable common factors with enhanced specificity and a more adaptable approach to covariance structure modeling. However, the application of CFA has been limited by the requirement for prior knowledge about "non-zero loadings" and by the lack of computational scalability (e.g., it can be computationally intractable for hundreds of observed variables). We propose a data-driven semi-confirmatory factor analysis (SCFA) model that attempts to alleviate these limitations. SCFA automatically specifies "non-zero loadings" by learning the network structure of the large covariance matrix of observed variables, and then offers closed-form estimators for factor loadings, factor scores, covariances between common factors, and variances between errors using the likelihood method. Therefore, SCFA is applicable to high-throughput datasets (e.g., hundreds of thousands of observed variables) without requiring prior knowledge about "non-zero loadings". Through an extensive simulation analysis benchmarking against standard packages, SCFA exhibits superior performance in estimating model parameters with a much-reduced computational time. We illustrate its practical application through factor analysis on two high-dimensional RNA-seq gene expression datasets.

stat.ME↗

arXiv2023

Evaluating the effects of high-throughput structural neuroimaging predictors on whole-brain functional connectome outcomes via network-based vector-on-matrix regression

The joint analysis of multimodal neuroimaging data is critical in the field of brain research because it reveals complex interactive relationships between neurobiological structures and functions. In this study, we focus on investigating the effects of structural imaging (SI) features, including white matter micro-structure integrity (WMMI) and cortical thickness, on the whole brain functional connectome (FC) network. To achieve this goal, we propose a network-based vector-on-matrix regression model to characterize the FC-SI association patterns. We have developed a novel multi-level dense bipartite and clique subgraph extraction method to identify which subsets of spatially specific SI features intensively influence organized FC sub-networks. The proposed method can simultaneously identify highly correlated structural-connectomic association patterns and suppress false positive findings while handling millions of potential interactions. We apply our method to a multimodal neuroimaging dataset of 4,242 participants from the UK Biobank to evaluate the effects of whole-brain WMMI and cortical thickness on the resting-state FC. The results reveal that the WMMI on corticospinal tracts and inferior cerebellar peduncle significantly affect functional connections of sensorimotor, salience, and executive sub-networks with an average correlation of 0.81 (p<0.001).

stat.ME↗

arXiv2023

Improving CNN-base Stock Trading By Considering Data Heterogeneity and Burst

In recent years, there have been quite a few attempts to apply intelligent techniques to financial trading, i.e., constructing automatic and intelligent trading framework based on historical stock price. Due to the unpredictable, uncertainty and volatile nature of financial market, researchers have also resorted to deep learning to construct the intelligent trading framework. In this paper, we propose to use CNN as the core functionality of such framework, because it is able to learn the spatial dependency (i.e., between rows and columns) of the input data. However, different with existing deep learning-based trading frameworks, we develop novel normalization process to prepare the stock data. In particular, we first empirically observe that the stock data is intrinsically heterogeneous and bursty, and then validate the heterogeneity and burst nature of stock data from a statistical perspective. Next, we design the data normalization method in a way such that the data heterogeneity is preserved and bursty events are suppressed. We verify out developed CNN-based trading framework plus our new normalization method on 29 stocks. Experiment results show that our approach can outperform other comparing approaches.

q-fin.ST↗

arXiv2021

Solution of Non-negative Least Squares Inverse Problems Using a Span of Regularized Solutions, with Application to Magnetic Resonance Relaxometry

We present a fundamentally new regularization method for the solution of the Fredholm integral equation of the first kind, in which we incorporate solutions corresponding to a range of Tikhonov regularizers into the end result. This method identifies solutions within a much larger function space, spanned by this set of regularized solutions, than is available to conventional regularizaton methods. Each of these solutions is regularized to a different extent. In effect, we combine the stability of solutions with greater degrees of regularization with the resolution of those that are less regularized. In contrast, current methods involve selection of a single, or in some cases several, regularization parameters that define an optimal degree of regularization. Because the identified solution is within the span of a set of differently-regularized solutions, we call this method \textit{span of regularizations}, or SpanReg. We demonstrate the performance of SpanReg through a non-negative least squares analysis employing a Gaussian basis, and demonstrate the improved recovery of bimodal Gaussian distribution functions as compared to conventional methods. We also demonstrate that this method exhibits decreased dependence of the end result on the optimality of regularization parameter selection. We further illustrate the method with an application to myelin water fraction mapping in the human brain from experimental magnetic resonance imaging relaxometry data. We expect SpanReg to be widely applicable as an effective new method for regularization of inverse problems.

stat.ME↗

arXiv2021

Integral Representation of Hydraulic Permeability

In this paper, we show that the permeability of a porous {material} and that of a bubbly fluid are limiting cases of the complexified version of the two-fluid models posed in {Lipton_Avellaneda_1990}. We assume the viscosity of the inclusion fluid is $z\mu_1$ and the viscosity of the hosting fluid is $\mu_1\in \mathbb{R}^+$, $z\in\mathbb{C}$. The proof is carried out by the construction of solutions for large $|z|$ and small $|z|$ with an iteration process and the analytic continuation. Moreover, we also show that for a fixed microstructure, the permeabilities of these three cases share the same integral representation formula (IRF) in Equation (99) with different values of contrast parameter $s:=1/(z-1)$, as long as $s$ is outside the interval $[-\frac{2E_2^2}{1+2E_2^2},-\frac{1}{1+2E_1^2}]$, where the positive constants $E_1$ and $E_2$ are the extension constants that depend only on the geometry of the periodic pore space of the material.

math.AP↗

arXiv2020

Quantum-Inspired Classical Algorithm for Slow Feature Analysis

Recently, there has been a surge of interest for quantum computation for its ability to exponentially speed up algorithms, including machine learning algorithms. However, Tang suggested that the exponential speed up can also be done on a classical computer. In this paper, we proposed an algorithm for slow feature analysis, a machine learning algorithm that extracts the slow-varying features, with a run time O(polylog(n)poly(d)). To achieve this, we assumed necessary preprocessing of the input data as well as the existence of a data structure supporting a particular sampling scheme. The analysis of algorithm borrowed results from matrix perturbation theory, which was crucial for the algorithm's correctness. This work demonstrates the possible application and extent for which quantum-inspired computation can be used.

cs.DM↗

arXiv2020

Quantum-Inspired Classical Algorithm for Principal Component Regression

This paper presents a sublinear classical algorithm for principal component regression. The algorithm uses quantum-inspired linear algebra, an idea developed by Tang. Using this technique, her algorithm for recommendation systems achieved runtime only polynomially slower than its quantum counterpart. Her work was quickly adapted to solve many other problems in sublinear time complexity. In this work, we developed an algorithm for principal component regression that runs in time polylogarithmic to the number of data points, an exponential speed up over the state-of-the-art algorithm, under the mild assumption that the input is given in some data structure that supports a norm-based sampling procedure. This exponential speed up allows for potential applications in much larger data sets.

cs.LG↗