arXiv subjects

Meng Huang

Publications and source records attributed to Meng Huang.

At least 37 records · Page 2Linked to original sources

arXiv2022

Unveiling interpretable development-specific gene signatures in the developing human prefrontal cortex with ICGS

In this paper, to unveil interpretable development-specific gene signatures in human PFC, we propose a novel gene selection method, named Interpretable Causality Gene Selection (ICGS), which adopts a Bayesian Network (BN) to represent causality between multiple gene variables and a development variable. The proposed ICGS method combines the positive instances-based contrastive learning with a Variational AutoEncoder (VAE) to obtain this optimal BN structure and use a Markov Blanket (MB) to identify gene signatures causally related to the development variable. Moreover, the differential expression genes (DEGs) are used to filter redundant genes before gene selection. In order to identify gene signatures, we apply the proposed ICGS to the human PFC single-cell transcriptomics data. The experimental results demonstrate that the proposed method can effectively identify interpretable development-specific gene signatures in human PFC. Gene ontology enrichment analysis and ASD-related gene analysis show that these identified gene signatures reveal the key biological processes and pathways in human PFC and have more potential for neurodevelopment disorder cure. These gene signatures are expected to bring important implications for understanding PFC development heterogeneity and function in humans.

q-bio.NC↗

arXiv2022

Affine phase retrieval for sparse signals via $\ell_1$ minimization

Affine phase retrieval is the problem of recovering signals from the magnitude-only measurements with a priori information. In this paper, we use the $\ell_1$ minimization to exploit the sparsity of signals for affine phase retrieval, showing that $O(k\log(en/k))$ Gaussian random measurements are sufficient to recover all $k$-sparse signals by solving a natural $\ell_1$ minimization program, where $n$ is the dimension of signals. For the case where measurements are corrupted by noises, the reconstruction error bounds are given for both real-valued and complex-valued signals. Our results demonstrate that the natural $\ell_1$ minimization program for affine phase retrieval is stable.

cs.IT↗

arXiv2022

No existence of linear algorithm for Fourier phase retrieval

Fourier phase retrieval, which seeks to reconstruct a signal from its Fourier magnitude, is of fundamental importance in fields of engineering and science. In this paper, we give a theoretical understanding of algorithms for Fourier phase retrieval. Particularly, we show if there exists an algorithm which could reconstruct an arbitrary signal ${\mathbf x}\in {\mathbb C}^N$ in $ \mbox{Poly}(N) \log(1/ε)$ time to reach $ε$-precision from its magnitude of discrete Fourier transform and its initial value $x(0)$, then $\mathcal{ P}=\mathcal{NP}$. This demystifies the phenomenon that, although almost all signals are determined uniquely by their Fourier magnitude with a prior conditions, there is no algorithm with theoretical guarantees being proposed over the past few decades. Our proofs employ the result in computational complexity theory that Product Partition problem is NP-complete in the strong sense.

cs.IT↗

arXiv2022

Strong convexity of affine phase retrieval

The recovery of a signal from the intensity measurements with some entries being known in advance is termed as {\em affine phase retrieval}. In this paper, we prove that a natural least squares formulation for the affine phase retrieval is strongly convex on the entire space under some mild conditions, provided the measurements are complex Gaussian random vecotrs and the measurement number $m \gtrsim d \log d$ where $d$ is the dimension of signals. Based on the result, we prove that the simple gradient descent method for the affine phase retrieval converges linearly to the target solution with high probability from an arbitrary initial point. These results show an essential difference between the affine phase retrieval and the classical phase retrieval, where the least squares formulations for the classical phase retrieval are non-convex.

cs.IT↗

arXiv2022

Nearly optimal bounds for the global geometric landscape of phase retrieval

The phase retrieval problem is concerned with recovering an unknown signal $\bf{x} \in \mathbb{R}^n$ from a set of magnitude-only measurements $y_j=|\langle \bf{a}_j,\bf{x} \rangle|, \; j=1,\ldots,m$. A natural least squares formulation can be used to solve this problem efficiently even with random initialization, despite its non-convexity of the loss function. One way to explain this surprising phenomenon is the benign geometric landscape: (1) all local minimizers are global; and (2) the objective function has a negative curvature around each saddle point and local maximizer. In this paper, we show that $m=O(n \log n)$ Gaussian random measurements are sufficient to guarantee the loss function of a commonly used estimator has such benign geometric landscape with high probability. This is a step toward answering the open problem given by Sun-Qu-Wright, in which the authors suggest that $O(n \log n)$ or even $O(n)$ is enough to guarantee the favorable geometric property.

cs.IT↗

arXiv2021

Performance bound of the intensity-based model for noisy phase retrieval

The aim of noisy phase retrieval is to estimate a signal $\mathbf{x}_0\in \mathbb{C}^d$ from $m$ noisy intensity measurements $b_j=\left\lvert \langle \mathbf{a}_j,\mathbf{x}_0 \rangle \right\rvert^2+η_j, \; j=1,\ldots,m$, where $\mathbf{a}_j \in \mathbb{C}^d$ are known measurement vectors and $η=(η_1,\ldots,η_m)^\top \in \mathbb{R}^m$ is a noise vector. A commonly used model for estimating $\mathbf{x}_0$ is the intensity-based model $\widehat{\mathbf{x}}:=\mbox{argmin}_{\mathbf{x} \in \mathbb{C}^d} \sum_{j=1}^m \big(\left\lvert \langle \mathbf{a}_j,\mathbf{x} \rangle \right\rvert^2-b_j \big)^2$. Although one has already developed many efficient algorithms to solve the intensity-based model, there are very few results about its estimation performance. In this paper, we focus on the estimation performance of the intensity-based model and prove that the error bound satisfies $\min_{θ\in \mathbb{R}}\|\widehat{\mathbf{x}}-e^{iθ}\mathbf{x}_0\|_2 \lesssim \min\Big\{\frac{\sqrt{\|η\|_2}}{{m}^{1/4}}, \frac{\|η\|_2}{\| \mathbf{x}_0\|_2 \cdot \sqrt{m}}\Big\}$ under the assumption of $m \gtrsim d$ and $\mathbf{a}_j, j=1,\ldots,m,$ being Gaussian random vectors. We also show that the error bound is sharp. For the case where $\mathbf{x}_0$ is a $s$-sparse signal, we present a similar result under the assumption of $m \gtrsim s \log (ed/s)$. To the best of our knowledge, our results are the first theoretical guarantees for the intensity-based model and its sparse version. Our proofs employ Mendelson's small ball method which can deliver an effective lower bound on a nonnegative empirical process.

cs.IT↗

arXiv2021

The global landscape of phase retrieval I: perturbed amplitude models

A fundamental task in phase retrieval is to recover an unknown signal $\vx\in \Rn$ from a set of magnitude-only measurements $y_i=\abs{\nj{\va_i,\vx}}, \; i=1,\ldots,m$. In this paper, we propose two novel perturbed amplitude models (PAMs) which have non-convex and quadratic-type loss function. When the measurements $ \va_i \in \Rn$ are Gaussian random vectors and the number of measurements $m\ge Cn$, we rigorously prove that the PAMs admit no spurious local minimizers with high probability, i.e., the target solution $ \vx$ is the unique global minimizer (up to a global phase) and the loss function has a negative directional curvature around each saddle point. Thanks to the well-tamed benign geometric landscape, one can employ the vanilla gradient descent method to locate the global minimizer $\vx$ (up to a global phase) without spectral initialization. We carry out extensive numerical experiments to show that the gradient descent algorithm with random initialization outperforms state-of-the-art algorithms with spectral initialization in empirical success rate and convergence speed.

math.NA↗

arXiv2021

The global landscape of phase retrieval II: quotient intensity models

A fundamental problem in phase retrieval is to reconstruct an unknown signal from a set of magnitude-only measurements. In this work we introduce three novel quotient intensity-based models (QIMs) based a deep modification of the traditional intensity-based models. A remarkable feature of the new loss functions is that the corresponding geometric landscape is benign under the optimal sampling complexity. When the measurements $ a_i\in \Rn$ are Gaussian random vectors and the number of measurements $m\ge Cn$, the QIMs admit no spurious local minimizers with high probability, i.e., the target solution $ x$ is the unique global minimizer (up to a global phase) and the loss function has a negative directional curvature around each saddle point. Such benign geometric landscape allows the gradient descent methods to find the global solution $x$ (up to a global phase) without spectral initialization.

math.NA↗

arXiv2021

Linear convergence of randomized Kaczmarz method for solving complex-valued phaseless equations

A randomized Kaczmarz method was recently proposed for phase retrieval, which has been shown numerically to exhibit empirical performance over other state-of-the-art phase retrieval algorithms both in terms of the sampling complexity and in terms of computation time. While the rate of convergence has been studied well in the real case where the signals and measurement vectors are all real-valued, there is no guarantee for the convergence in the complex case. In fact, the linear convergence of the randomized Kaczmarz method for phase retrieval in the complex setting is left as a conjecture by Tan and Vershynin. In this paper, we provide the first theoretical guarantees for it. We show that for random measurements $\mathbf{a}_j \in \mathbb{C}^n, j=1,\ldots,m $ which are drawn independently and uniformly from the complex unit sphere, or equivalent are independent complex Gaussian random vectors, when $m \ge Cn$ for some universal positive constant $C$, the randomized Kaczmarz scheme with a good initialization converges linearly to the target solution (up to a global phase) in expectation with high probability. This gives a positive answer to that conjecture.

math.NA↗

arXiv2021

"Let Your Characters Tell Their Story": A Dataset for Character-Centric Narrative Understanding

When reading a literary piece, readers often make inferences about various characters' roles, personalities, relationships, intents, actions, etc. While humans can readily draw upon their past experiences to build such a character-centric view of the narrative, understanding characters in narratives can be a challenging task for machines. To encourage research in this field of character-centric narrative understanding, we present LiSCU -- a new dataset of literary pieces and their summaries paired with descriptions of characters that appear in them. We also introduce two new tasks on LiSCU: Character Identification and Character Description Generation. Our experiments with several pre-trained language models adapted for these tasks demonstrate that there is a need for better models of narrative comprehension.

cs.CL↗

arXiv2021

Uniqueness and stability for the solution of a nonlinear least squares problem

In this paper, we focus on the nonlinear least squares: $\mbox{min}_{\mathbf{x} \in \mathbb{H}^d}\| |A\mathbf{x}|-\mathbf{b}\|$ where $A\in \mathbb{H}^{m\times d}$, $\mathbf{b} \in \mathbb{R}^m$ with $\mathbb{H} \in \{\mathbb{R},\mathbb{C} \}$ and consider the uniqueness and stability of solutions. Such problem arises, for instance, in phase retrieval and absolute value rectification neural networks. For the case where $\mathbf{b}=|A\mathbf{x}_0|$ for some $\mathbf{x}_0\in \mathbb{H}^d$, many results have been developed to characterize the uniqueness and stability of solutions. However, for the case where $\mathbf{b} \neq |A\mathbf{x}_0| $ for any $\mathbf{x}_0\in \mathbb{H}^d$, there is no existing result for it to the best of our knowledge. In this paper, we first focus on the uniqueness of solutions and show for any matrix $A\in \mathbb{H}^{m \times d}$ there always exists a vector $\mathbf{b} \in \mathbb{R}^m$ such that the solution is not unique. But, in real case, such ``bad'' vectors $\mathbf{b}$ are negligible, namely, if $\mathbf{b} \in \mathbb{R}_{+}^m$ does not lie in some measure zero set, then the solution is unique. We also present some conditions under which the solution is unique. For the stability of solutions, we prove that the solution is never uniformly stable. But if we restrict the vectors $\mathbf{b}$ to any convex set then it is stable.

math.NA↗

arXiv2021

Precoder Design and Power Allocation for Downlink MIMO-NOMA via Simultaneous Triangularization

In this paper, we consider the downlink precoder design for two-user power-domain multiple-input multiple-output (MIMO) non-orthogonal multiple access (NOMA) systems. The proposed precoding scheme is based on simultaneous triangularization and decomposes the MIMO-NOMA channels of the two users into multiple single-input single-output NOMA channels, assuming low-complexity self-interference cancellation at the users. In contrast to the precoding schemes based on simultaneous diagonalization (SD), the proposed scheme avoids inverting the MIMO channels of the users, thereby enhancing the ergodic rate performance. Furthermore, we develop a power allocation algorithm based on the convex-concave procedure, and exploit it to obtain the ergodic achievable rate region of the proposed MIMO-NOMA scheme. Our results illustrate that the proposed scheme outperforms baseline precoding schemes based on SD and orthogonal multiple access for a wide range of user rates and performs close to the dirty paper coding upper bound. The ergodic rate region can further be improved by utilizing a hybrid scheme based on time sharing between the proposed MIMO-NOMA scheme and point-to-point MIMO.

cs.IT↗

arXiv2021

Solving phase retrieval with random initial guess is nearly as good as by spectral initialization

The problem of recovering a signal $\mathbf{x}\in \mathbb{R}^n$ from a set of magnitude measurements $y_i=|\langle \mathbf{a}_i, \mathbf{x} \rangle |, \; i=1,\ldots,m$ is referred as phase retrieval, which has many applications in fields of physical sciences and engineering. In this paper we show that the smoothed amplitude flow model for phase retrieval has benign geometric structure under the optimal sampling complexity. In particular, we show that when the measurements $\mathbf{a}_i\in \mathbb{R}^n$ are Gaussian random vectors and the number of measurements $m\ge Cn$, our smoothed amplitude flow model has no spurious local minimizers with high probability, ie., the target solution $\mathbf{x}$ is the unique global minimizer (up to a global phase) and the loss function has a negative directional curvature around each saddle point. Due to this benign geometric landscape, the phase retrieval problem can be solved by the gradient descent algorithms without spectral initialization. Numerical experiments show that the gradient descent algorithm with random initialization performs well even comparing with state-of-the-art algorithms with spectral initialization in empirical success rate and convergence speed.

cs.IT↗

arXiv2020

Fermi liquid behavior and colossal magnetoresistance in layered MoOCl2

A characteristic of a Fermi liquid is the T^2 dependence of its resistivity, sometimes referred to as the Baber law. However, for most metals, this behavior is only restricted to very low temperatures, usually below 20 K. Here, we experimentally demonstrate that for the single-crystal van der Waals layered material MoOCl2, the Baber law holds in a wide temperature range up to ~120 K, indicating that the electron-electron scattering plays a dominant role in this material. Combining with the specific heat measurement, we find that the modified Kadowaki-Woods ratio of the material agrees well with many other strongly correlated metals. Furthermore, in the magneto-transport measurement, a colossal magneto-resistance is observed, which reaches ~350% at 9 T and displays no sign of saturation. With the help of first-principles calculations, we attribute this behavior to the presence of open orbits on the Fermi surface. We also suggest that the dominance of electron-electron scattering is related to an incipient charge density wave state of the material. Our results establish MoOCl2 as a strongly correlated metal and shed light on the underlying physical mechanism, which may open a new path for exploring the effects of electron-electron interaction in van der Waals layered structures.

cond-mat.mtrl-sci↗

arXiv2019

Almost Everywhere Generalized Phase Retrieval

The aim of generalized phase retrieval is to recover $\mathbf{x}\in \mathbb{F}^d$ from the quadratic measurements $\mathbf{x}^*A_1\mathbf{x},\ldots,\mathbf{x}^*A_N\mathbf{x}$, where $A_j\in \mathbf{H}_d(\mathbb{F})$ and $\mathbb{F}=\mathbb{R}$ or $\mathbb{C}$. In this paper, we study the matrix set $\mathcal{A}=(A_j)_{j=1}^N$ which has the almost everywhere phase retrieval property. For the case $\mathbb{F}=\mathbb{R}$, we show that $N\geq d+1$ generic matrices with prescribed ranks have almost everywhere phase retrieval property. We also extend this result to the case where $A_1,\ldots,A_N$ are orthogonal matrices and hence establish the almost everywhere phase retrieval property for the fusion frame phase retrieval. For the case where $\mathbb{F}=\mathbb{C}$, we obtain similar results under the assumption of $N\geq 2d$. We lower the measurement number $d+1$ (resp. $2d$) with showing that there exist $N=d$ (resp. $2d-1$) matrices $A_1,\ldots, A_N\in \mathbf{H}_d(\mathbb{R})$ (resp. $\mathbf{H}_d(\mathbb{C})$) which have the almost everywhere phase retrieval property. Our results are an extension of almost everywhere phase retrieval from the standard phase retrieval to the general setting and the proofs are often based on some new ideas about determinant variety.

math.FA↗

arXiv2019

Adiabatic and Nonadiabatic Energy Dissipation during Scattering of Vibrationally Excited CO from Au(111)

A high-dimensional potential energy surface (PES) for CO interaction with the Au(111) surface is developed using a machine-learning algorithm. Including both molecular and surface coordinates, this PES enables the simulation of the recent experiment on scattering of vibrationally excited CO from Au(111). Trapping in a physisorption well is observed to increase with decreasing incidence energy. While energy dissipation of physisorbed CO is slow, due to weak coupling with both the phonons and electron-hole pairs, its access to the chemisorption well facilitates fast vibrational relaxation of CO through nonadiabatic coupling with surface electron-hole pairs.

physics.chem-ph↗

arXiv2019

The estimation performance of nonlinear least squares for phase retrieval

Suppose that $\mathbf{y}=\lvert A\mathbf{x_0}\rvert+η$ where $\mathbf{x_0} \in \mathbb{R}^d$ is the target signal and $η\in \mathbb{R}^m$ is a noise vector. The aim of phase retrieval is to estimate $\mathbf{x_0}$ from $\mathbf{y}$. A popular model for estimating $\mathbf{x_0} $ is the nonlinear least square $ \widehat{\mathbf{x}}:={\rm argmin}_{\mathbf{x}} \| \lvert A \mathbf{x}\rvert-\mathbf{y}\|_2$. One already develops many efficient algorithms for solving the model, such as the seminal error reduction algorithm. In this paper, we present the estimation performance of the model with proving that $\|\widehat{\mathbf{x}}-\mathbf{x_0} \|\lesssim {\|η\|_2}/{\sqrt{m}}$ under the assumption of $A$ being a Gaussian random matrix. We also prove the reconstruction error ${\|η\|_2}/{\sqrt{m}}$ is sharp. For the case where $\mathbf{x_0}$ is sparse, we study the estimation performance of both the nonlinear Lasso of phase retrieval and its unconstrained version. Our results are non-asymptotic, and we do not assume any distribution on the noise $η$. To the best of our knowledge, our results represent the first theoretical guarantee for the nonlinear least square and for the nonlinear Lasso of phase retrieval.

cs.IT↗

arXiv2018

On DC based Methods for Phase Retrieval

In this paper, we develop a new computational approach which is based on minimizing the difference of two convex functionals (DC) to solve a broader class of phase retrieval problems. The approach splits a standard nonlinear least squares minimizing function associated with the phase retrieval problem into the difference of two convex functions and then solves a sequence of convex minimization sub-problems. For each subproblem, the Nesterov's accelerated gradient descent algorithm or the Barzilai-Borwein (BB) algorithm is used. In the setting of sparse phase retrieval, a standard $\ell_1$ norm term is added into the minimization mentioned above. The subproblem is approximated by a proximal gradient method which is solved by the shrinkage-threshold technique directly without iterations. In addition, a modified Attouch-Peypouquet technique is used to accelerate the iterative computation. These lead to more effective algorithms than the Wirtinger flow (WF) algorithm and the Gauss-Newton (GN) algorithm and etc.. A convergence analysis of both DC based algorithms shows that the iterative solutions is convergent linearly to a critical point and will be closer to a global minimizer than the given initial starting point. Our study is a deterministic analysis while the study for the Wirtinger flow (WF) algorithm and its variants, the Gauss-Newton (GN) algorithm, the trust region algorithm is based on the probability analysis. In particular, the DC based algorithms are able to retrieve solutions using a number $m$ of measurements which is about twice of the number $n$ of entries in the solution with high frequency of successes. When $m\approx n$, the $\ell_1$ DC based algorithm is able to retrieve sparse signals.

cs.IT↗