arXiv subjects

Sifan Liu

Publications and source records attributed to Sifan Liu.

At least 37 records · Page 2Linked to original sources

arXiv2024

Cooperative Cell-Free ISAC Networks: Joint BS Mode Selection and Beamforming Design

Owing to the promising ability of saving hardware cost and spectrum resources, integrated sensing and communication (ISAC) is regarded as a revolutionary technology for future sixth-generation (6G) networks. The mono-static ISAC systems considered in most of existing works can only achieve limited sensing performance due to the single observation angle and easily blocked transmission links, which motivates researchers to investigate cooperative ISAC networks. In order to further improve the degrees of freedom (DoFs) of cooperative ISAC networks, the transmitter-receiver selection, i.e., base station (BS) mode selection problem, is meaningful to be studied. However, to our best knowledge, this crucial problem has not been extensively studied in existing works. In this paper, we consider the joint BS mode selection, transmit beamforming, and receive filter designs for cooperative cell-free ISAC networks, where multi-BSs cooperatively serve communication users and detect targets. An efficient joint beamforming design algorithm and three different heuristic BS mode selection methods are proposed to solve the non-convex NP-hard problem. Simulation results demonstrates the advantages of cooperative ISAC networks, the importance of BS mode selection, and the effectiveness of proposed algorithms.

cs.IT↗

arXiv2023

Langevin Quasi-Monte Carlo

Langevin Monte Carlo (LMC) and its stochastic gradient versions are powerful algorithms for sampling from complex high-dimensional distributions. To sample from a distribution with density $π(θ)\propto \exp(-U(θ)) $, LMC iteratively generates the next sample by taking a step in the gradient direction $\nabla U$ with added Gaussian perturbations. Expectations w.r.t. the target distribution $π$ are estimated by averaging over LMC samples. In ordinary Monte Carlo, it is well known that the estimation error can be substantially reduced by replacing independent random samples by quasi-random samples like low-discrepancy sequences. In this work, we show that the estimation error of LMC can also be reduced by using quasi-random samples. Specifically, we propose to use completely uniformly distributed (CUD) sequences with certain low-discrepancy property to generate the Gaussian perturbations. Under smoothness and convexity conditions, we prove that LMC with a low-discrepancy CUD sequence achieves smaller error than standard LMC. The theoretical analysis is supported by compelling numerical experiments, which demonstrate the effectiveness of our approach.

stat.CO↗

arXiv2023

Black-box Selective Inference via Bootstrapping

Conditional selective inference requires an exact characterization of the selection event, which is often unavailable except for a few examples like the lasso. This work addresses this challenge by introducing a generic approach to estimate the selection event, facilitating feasible inference conditioned on the selection event. The method proceeds by repeatedly generating bootstrap data and running the selection algorithm on the new datasets. Using the outputs of the selection algorithm, we can estimate the selection probability as a function of certain summary statistics. This leads to an estimate of the distribution of the data conditioned on the selection event, which forms the basis for conditional selective inference. We provide a theoretical guarantee assuming both asymptotic normality of relevant statistics and accurate estimation of the selection probability. The applicability of the proposed method is demonstrated through a variety of problems that lack exact characterizations of selection, where conditional selective inference was previously infeasible.

stat.ME↗

arXiv2023

An Exact Sampler for Inference after Polyhedral Model Selection

Inference after model selection presents computational challenges when dealing with intractable conditional distributions. Markov chain Monte Carlo (MCMC) is a common method for sampling from these distributions, but its slow convergence often limits its practicality. In this work, we introduce a method tailored for selective inference in cases where the selection event can be characterized by a polyhedron. The method transforms the variables constrained by a polyhedron into variables within a unit cube, allowing for efficient sampling using conventional numerical integration techniques. Compared to MCMC, the proposed sampling method is highly accurate and equipped with an error estimate. Additionally, we introduce an approach to use a single batch of samples for hypothesis testing and confidence interval construction across multiple parameters, reducing the need for repetitive sampling. Furthermore, our method facilitates fast and precise computation of the maximum likelihood estimator based on the selection-adjusted likelihood, enhancing the reliability of MLE-based inference. Numerical results demonstrate the superior performance of the proposed method compared to alternative approaches for selective inference.

stat.ME↗

arXiv2023

Conditional Quasi-Monte Carlo with Constrained Active Subspaces

Conditional Monte Carlo or pre-integration is a powerful tool for reducing variance and improving the regularity of integrands when using Monte Carlo and quasi-Monte Carlo (QMC) methods. To select the variable to pre-integrate, one must consider both the variable's importance and the tractability of the conditional expectation. For integrals over a Gaussian distribution, any linear combination of variables can potentially be pre-integrated. Liu and Owen (2022) propose to select the linear combination based on an active subspace decomposition of the integrand. However, pre-integrating the selected direction might be intractable. In this work, we address this issue by finding the active subspace subject to constraints such that pre-integration can be easily carried out. The proposed algorithm also provides a computationally-efficient alternative to dimension reduction for pre-integrated functions. The method is applied to examples from computational finance, density estimation, and computational chemistry, and is shown to achieve smaller errors than previous methods.

stat.CO↗

arXiv2023

Selective Inference with Distributed Data

As datasets grow larger, they are often distributed across multiple machines that compute in parallel and communicate with a central machine through short messages. In this paper, we focus on sparse regression and propose a new procedure for conducting selective inference with distributed data. Although many distributed procedures exist for point estimation in the sparse setting, few options are available for estimating uncertainties or conducting hypothesis tests based on the estimated sparsity. We solve a generalized linear regression on each machine, which then communicates a selected set of predictors to the central machine. The central machine uses these selected predictors to form a generalized linear model (GLM). To conduct inference in the selected GLM, our proposed procedure bases approximately-valid selective inference on an asymptotic likelihood. The proposal seeks only aggregated information, in relatively few dimensions, from each machine which is merged at the central machine for selective inference. By reusing low-dimensional summary statistics from local machines, our procedure achieves higher power while keeping the communication cost low. This method is also applicable as a solution to the notorious p-value lottery problem that arises when model selection is repeated on random splits of data.

stat.ME↗

arXiv2022

Joint BS-RIS-User Association and Beamforming Design for RIS-assisted Cellular Networks

Reconfigurable intelligent surface (RIS) is a revolutionary technology for sixth-generation (6G) networks owing to its ability to manipulate wireless environments. As a frequency-selective device, RIS can only effectively shape the propagation of signals within a certain frequency band. Due to this frequency-selective property, the deployment of RIS in cellular networks will introduce a complicated base station (BS)-RIS-user association issue since adjacent BSs operate at different frequency bands. In this paper, with the consideration of the frequency-selective characteristics of RIS, we aim to jointly optimize BS-RIS-user association, active beamforming at BSs, and passive beamforming of RIS to maximize the sum-rate of a RIS-assisted cellular network. We first leverage $l_0$-norm to efficiently integrate BS-RIS-user association with active and passive beamforming. Then, we adopt fractional programming (FP) and block coordinate descent (BCD) methods to deal with logarithmic and fractional parts and decouple the joint association and beamforming design problem into several sub-problems. Efficient algorithms which combine $l_0$-norm approximation, majorization-minimization (MM), and alternating direction method of multipliers (ADMM) are developed to alternately solve the sub-problems. Extensive simulation results illustrate the importance of BS-RIS-user association optimization in RIS-assisted cellular networks and verify the effectiveness of the proposed joint association and beamforming design algorithm.

cs.IT↗

arXiv2022

Global and Individualized Community Detection in Inhomogeneous Multilayer Networks

In network applications, it has become increasingly common to obtain datasets in the form of multiple networks observed on the same set of subjects, where each network is obtained in a related but different experiment condition or application scenario. Such datasets can be modeled by multilayer networks where each layer is a separate network itself while different layers are associated and share some common information. The present paper studies community detection in a stylized yet informative inhomogeneous multilayer network model. In our model, layers are generated by different stochastic block models, the community structures of which are (random) perturbations of a common global structure while the connecting probabilities in different layers are not related. Focusing on the symmetric two block case, we establish minimax rates for both global estimation of the common structure and individualized estimation of layer-wise community structures. Both minimax rates have sharp exponents. In addition, we provide an efficient algorithm that is simultaneously asymptotic minimax optimal for both estimation tasks under mild conditions. The optimal rates depend on the parity of the number of most informative layers, a phenomenon that is caused by inhomogeneity across layers. The method is extended to handle multiple and potentially asymmetric community cases. We demonstrate its effectiveness on both simulated examples and a real multi-modal single-cell dataset.

math.ST↗

arXiv2022

Pre-integration via Active Subspaces

Pre-integration is an extension of conditional Monte Carlo to quasi-Monte Carlo and randomized quasi-Monte Carlo. It can reduce but not increase the variance in Monte Carlo. For quasi-Monte Carlo it can bring about improved regularity of the integrand with potentially greatly improved accuracy. Pre-integration is ordinarily done by integrating out one of $d$ input variables to a function. In the common case of a Gaussian integral one can also pre-integrate over any linear combination of variables. We propose to do that and we choose the first eigenvector in an active subspace decomposition to be the pre-integrated linear combination. We find in numerical examples that this active subspace pre-integration strategy is competitive with pre-integrating the first variable in the principal components construction on the Asian option where principal components are known to be very effective. It outperforms other pre-integration methods on some basket options where there is no well established default. We show theoretically that, just as in Monte Carlo, pre-integration can reduce but not increase the variance when one uses scrambled net integration. We show that the lead eigenvector in an active subspace decomposition is closely related to the vector that maximizes a less computationally tractable criterion using a Sobol' index to find the most important linear combination of Gaussian variables. They optimize similar expectations involving the gradient. We show that the Sobol' index criterion for the leading eigenvector is invariant to the way that one chooses the remaining $d-1$ eigenvectors with which to sample the Gaussian vector.

math.NA↗

arXiv2021

Statistical Challenges in Tracking the Evolution of SARS-CoV-2

Genomic surveillance of SARS-CoV-2 has been instrumental in tracking the spread and evolution of the virus during the pandemic. The availability of SARS-CoV-2 molecular sequences isolated from infected individuals, coupled with phylodynamic methods, have provided insights into the origin of the virus, its evolutionary rate, the timing of introductions, the patterns of transmission, and the rise of novel variants that have spread through populations. Despite enormous global efforts of governments, laboratories, and researchers to collect and sequence molecular data, many challenges remain in analyzing and interpreting the data collected. Here, we describe the models and methods currently used to monitor the spread of SARS-CoV-2, discuss long-standing and new statistical challenges, and propose a method for tracking the rise of novel variants during the epidemic.

stat.AP↗

arXiv2021

BS-RIS-User Association and Beamforming Designs for RIS-aided Cellular Networks

Reconfigurable intelligent surface (RIS) has been regarded as a revolutionary and promising technology owing to its powerful feature of adaptively shaping wireless propagation environment. However, as a frequency-selective device, the RIS can only effectively provide tunable phase-shifts for signals within a certain frequency band. Thus, base-station (BS)-RIS-user association is an important issue to maximize the efficiency and ability of the RIS in cellular networks. In this paper, we consider a RIS-aided cellular network and aim to maximize the sum-rate of downlink transmissions by designing BS-RIS-user association as well as the active and passive beamforming of BSs and RIS, respectively. A dynamically successive access algorithm is developed to design the user association. During the dynamical access process, an iterative algorithm is proposed to alternatively obtain the active and passive beamforming. Finally, the optimal BS-RIS association is obtained by an exhaustive search method. Simulation results illustrate the significant performance improvement of the proposed BS-RIS-user association and beamforming design algorithm.

eess.SP↗

arXiv2021

Quasi-Newton Quasi-Monte Carlo for variational Bayes

Many machine learning problems optimize an objective that must be measured with noise. The primary method is a first order stochastic gradient descent using one or more Monte Carlo (MC) samples at each step. There are settings where ill-conditioning makes second order methods such as L-BFGS more effective. We study the use of randomized quasi-Monte Carlo (RQMC) sampling for such problems. When MC sampling has a root mean squared error (RMSE) of $O(n^{-1/2})$ then RQMC has an RMSE of $o(n^{-1/2})$ that can be close to $O(n^{-3/2})$ in favorable settings. We prove that improved sampling accuracy translates directly to improved optimization. In our empirical investigations for variational Bayes, using RQMC with stochastic L-BFGS greatly speeds up the optimization, and sometimes finds a better parameter value than MC does.

cs.LG↗

arXiv2021

How to reduce dimension with PCA and random projections?

In our "big data" age, the size and complexity of data is steadily increasing. Methods for dimension reduction are ever more popular and useful. Two distinct types of dimension reduction are "data-oblivious" methods such as random projections and sketching, and "data-aware" methods such as principal component analysis (PCA). Both have their strengths, such as speed for random projections, and data-adaptivity for PCA. In this work, we study how to combine them to get the best of both. We study "sketch and solve" methods that take a random projection (or sketch) first, and compute PCA after. We compute the performance of several popular sketching methods (random iid projections, random sampling, subsampled Hadamard transform, count sketch, etc) in a general "signal-plus-noise" (or spiked) data model. Compared to well-known works, our results (1) give asymptotically exact results, and (2) apply when the signal components are only slightly above the noise, but the projection dimension is non-negligible. We also study stronger signals allowing more general covariance structures. We find that (a) signal strength decreases under projection in a delicate way depending on the structure of the data and the sketching method, (b) orthogonal projections are more accurate, (c) randomization does not hurt too much, due to concentration of measure, (d) count sketch can be improved by a normalization method. Our results have implications for statistical learning and data analysis. We also illustrate that the results are highly accurate in simulations and in analyzing empirical data.

math.ST↗

arXiv2020

Optimal Iterative Sketching with the Subsampled Randomized Hadamard Transform

Random projections or sketching are widely used in many algorithmic and learning contexts. Here we study the performance of iterative Hessian sketch for least-squares problems. By leveraging and extending recent results from random matrix theory on the limiting spectrum of matrices randomly projected with the subsampled randomized Hadamard transform, and truncated Haar matrices, we can study and compare the resulting algorithms to a level of precision that has not been possible before. Our technical contributions include a novel formula for the second moment of the inverse of projected matrices. We also find simple closed-form expressions for asymptotically optimal step-sizes and convergence rates. These show that the convergence rate for Haar and randomized Hadamard matrices are identical, and asymptotically improve upon Gaussian random projections. These techniques may be applied to other algorithms that employ randomized dimension reduction.

math.OC↗

arXiv2020

WeChat Neural Machine Translation Systems for WMT20

We participate in the WMT 2020 shared news translation task on Chinese to English. Our system is based on the Transformer (Vaswani et al., 2017a) with effective variants and the DTMT (Meng and Zhang, 2019) architecture. In our experiments, we employ data selection, several synthetic data generation approaches (i.e., back-translation, knowledge distillation, and iterative in-domain knowledge transfer), advanced finetuning approaches and self-bleu based model ensemble. Our constrained Chinese to English system achieves 36.9 case-sensitive BLEU score, which is the highest among all submissions.

cs.CL↗

arXiv2020

Ridge Regression: Structure, Cross-Validation, and Sketching

We study the following three fundamental problems about ridge regression: (1) what is the structure of the estimator? (2) how to correctly use cross-validation to choose the regularization parameter? and (3) how to accelerate computation without losing too much accuracy? We consider the three problems in a unified large-data linear model. We give a precise representation of ridge regression as a covariance matrix-dependent linear combination of the true parameter and the noise. We study the bias of $K$-fold cross-validation for choosing the regularization parameter, and propose a simple bias-correction. We analyze the accuracy of primal and dual sketching for ridge regression, showing they are surprisingly accurate. Our results are illustrated by simulations and by analyzing empirical data.

math.ST↗

arXiv2020

p-Value as the Strength of Evidence Measured by Confidence Distribution

The notion of p-value is a fundamental concept in statistical inference and has been widely used for reporting outcomes of hypothesis tests. However, p-value is often misinterpreted, misused or miscommunicated in practice. Part of the issue is that existing definitions of p-value are often derived from constructions under specific settings, and a general definition that directly reflects the evidence of the null hypothesis is not yet available. In this article, we first propose a general and rigorous definition of p-value that fulfills two performance-based characteristics. The performance-based definition subsumes all existing construction-based definitions of the p-value, and justifies their interpretations. The paper further presents a specific approach based on confidence distribution to formulate and calculate p-values. This specific way of computing p values has two main advantages. First, it is applicable for a wide range of hypothesis testing problems, including the standard one- and two-sided tests, tests with interval-type null, intersection-union tests, multivariate tests and so on. Second, it can naturally lead to a coherent interpretation of p-value as evidence in support of the null hypothesis, as well as a meaningful measure of degree of such support. In particular, it places a meaning of a large p-value, e.g. p-value of 0.8 has more support than 0.5. Numerical examples are used to illustrate the wide applicability and computational feasibility of our approach. We show that our proposal is effective and can be applied broadly, without further consideration of the form/size of the null space. As for existing testing methods, the solutions have not been available or cannot be easily obtained.

stat.ME↗

arXiv2019

Asymptotics for Sketching in Least Squares Regression

We consider a least squares regression problem where the data has been generated from a linear model, and we are interested to learn the unknown regression parameters. We consider "sketch-and-solve" methods that randomly project the data first, and do regression after. Previous works have analyzed the statistical and computational performance of such methods. However, the existing analysis is not fine-grained enough to show the fundamental differences between various methods, such as the Subsampled Randomized Hadamard Transform (SRHT) and Gaussian projections. In this paper, we make progress on this problem, working in an asymptotic framework where the number of datapoints and dimension of features goes to infinity. We find the limits of the accuracy loss (for estimation and test error) incurred by popular sketching methods. We show separation between different methods, so that SRHT is better than Gaussian projections. Our theoretical results are verified on both real and synthetic data. The analysis of SRHT relies on novel methods from random matrix theory that may be of independent interest.

math.ST↗