arXiv subjects

Yicheng Li

Publications and source records attributed to Yicheng Li.

52 records · Page 3Linked to original sources

arXiv2024

Emergence of collective spectral features in finite arrays of dielectric rods

Periodic optical structures, such as diffraction grating and numerous photonic crystals, are one of the staples of modern nanophotonics for the manipulation of electromagnetic radiation. The array of subwavelength dielectric rods is one of the simplest platforms, which, despite its simplicity exhibits extraordinary wave phenomena, such as diffraction anomalies and narrow reflective resonances. Despite the well-documented properties of infinite periodic systems, the behavior of these diffractive effects in systems incorporating a finite number of elements is studied to a far lesser extent. Here we study theoretically and numerically the evolution of collective spectral features in finite arrays of dielectric rods. We develop an analytical model of light scattering by a finite array of circular rods based on the coupled dipoles approximation and analyze the spectral features of finite arrays within the developed model. Finally, we validate the results of the analytical model using full-wave numerical simulations.

physics.optics↗

arXiv2024

Sensor Network Localization via Riemannian Conjugate Gradient and Rank Reduction: An Extended Version

This paper addresses the Sensor Network Localization (SNL) problem using received signal strength. The SNL is formulated as an Euclidean Distance Matrix Completion (EDMC) problem under the unit ball sample model. Using the Burer-Monteiro factorization type cost function, the EDMC is solved by Riemannian conjugate gradient with Hager-Zhang line search method on a quotient manifold. A "rank reduction" preprocess is proposed for proper initialization and to achieve global convergence with high probability. Simulations on a synthetic scene show that our approach attains better localization accuracy and is computationally efficient compared to several baseline methods. Characterization of a small local basin of attraction around the global optima of the s-stress function under Bernoulli sampling rule and incoherence matrix completion framework is conducted for the first time. Theoretical result conjectures that the Euclidean distance problem with a structure-less sample mask can be effectively handled using spectral initialization followed by vanilla first-order methods. This preliminary analysis, along with the aforementioned numerical accomplishments, provides insights into revealing the landscape of the s-stress function and may stimulate the design of simpler algorithms to tackle the non-convex formulation of general EDMC problems.

eess.SP↗

arXiv2024

Mixed Distillation Helps Smaller Language Model Better Reasoning

While large language models (LLMs) have demonstrated exceptional performance in recent natural language processing (NLP) tasks, their deployment poses substantial challenges due to high computational and memory demands in real-world applications. Recent studies have focused on enhancing smaller models through knowledge distillation from LLMs, yielding promising results. However, these models often struggle to match the performance of LLMs, especially in tasks that require reasoning. In this work, we introduce Mixed Distillation (MD) framework, which capitalizes on the strengths of Program of Thought (PoT) and Chain of Thought (CoT) capabilities within LLMs, combining multiple prompting techniques and distilling these capabilities into smaller models. Our experimental results show that MD significantly enhances the single-path and multi-path reasoning ability of smaller models in various tasks. In terms of accuracy and generality of reasoning tasks, the model generated by it exceeds the comprehensive performance of two individually distilled models. Notably, LLaMA2-7B and CodeLlama-7B using MD achieved remarkable improvements of (84.5%) and (85.5%), respectively, outperforming GPT-3.5-Turbo by (2.5%) and (3.5%), on the SVAMP benchmark.

cs.CL↗

arXiv2024

Optimal Rates of Kernel Ridge Regression under Source Condition in Large Dimensions

Motivated by the studies of neural networks (e.g.,the neural tangent kernel theory), we perform a study on the large-dimensional behavior of kernel ridge regression (KRR) where the sample size $n \asymp d^γ$ for some $γ> 0$. Given an RKHS $\mathcal{H}$ associated with an inner product kernel defined on the sphere $\mathbb{S}^{d}$, we suppose that the true function $f_ρ^{*} \in [\mathcal{H}]^{s}$, the interpolation space of $\mathcal{H}$ with source condition $s>0$. We first determined the exact order (both upper and lower bound) of the generalization error of kernel ridge regression for the optimally chosen regularization parameter $λ$. We then further showed that when $0 1$, KRR is not minimax optimal (a.k.a. he saturation effect). Our results illustrate that the curves of rate varying along $γ$ exhibit the periodic plateau behavior and the multiple descent behavior and show how the curves evolve with $s>0$. Interestingly, our work provides a unified viewpoint of several recent works on kernel regression in the large-dimensional setting, which correspond to $s=0$ and $s=1$ respectively.

cs.LG↗

arXiv2023

Estimating Photometric Redshift from Mock Flux for CSST Survey by using Weighted Random Forest

Accurate estimation of photometric redshifts (photo-$z$) is crucial in studies of both galaxy evolution and cosmology using current and future large sky surveys. In this study, we employ Random Forest (RF), a machine learning algorithm, to estimate photo-$z$ and investigate the systematic uncertainties affecting the results. Using galaxy flux and color as input features, we construct a mapping between input features and redshift by using a training set of simulated data, generated from the Hubble Space Telescope Advanced Camera for Surveys (HST-ACS) and COSMOS catalogue, with the expected instrumental effects of the planned China Space Station Telescope (CSST). To improve the accuracy and confidence of predictions, we incorporate inverse variance weighting and perturb the catalog using input feature errors. Our results show that weighted RF can achieve a photo-$z$ accuracy of $\rm σ_{NMAD}=0.025$ and an outlier fraction of $\rm η=2.045\%$, significantly better than the values of $\rm σ_{NMAD}=0.043$ and $\rm η=6.45\%$ obtained by the widely used Easy and Accurate Zphot from Yale (EAZY) software which uses template-fitting method. Furthermore, we have calculated the importance of each input feature for different redshift ranges and found that the most important input features reflect the approximate position of the break features in galaxy spectra, demonstrating the algorithm's ability to extract physical information from data. Additionally, we have established confidence indices and error bars for each prediction value based on the shape of the redshift probability distribution function, suggesting that screening sources with high confidence can further reduce the outlier fraction.

astro-ph.CO↗

arXiv2023

On the Asymptotic Learning Curves of Kernel Ridge Regression under Power-law Decay

The widely observed 'benign overfitting phenomenon' in the neural network literature raises the challenge to the 'bias-variance trade-off' doctrine in the statistical learning theory. Since the generalization ability of the 'lazy trained' over-parametrized neural network can be well approximated by that of the neural tangent kernel regression, the curve of the excess risk (namely, the learning curve) of kernel ridge regression attracts increasing attention recently. However, most recent arguments on the learning curve are heuristic and are based on the 'Gaussian design' assumption. In this paper, under mild and more realistic assumptions, we rigorously provide a full characterization of the learning curve: elaborating the effect and the interplay of the choice of the regularization parameter, the source condition and the noise. In particular, our results suggest that the 'benign overfitting phenomenon' exists in very wide neural networks only when the noise level is small.

cs.LG↗

arXiv2023

Kernel interpolation generalizes poorly

One of the most interesting problems in the recent renaissance of the studies in kernel regression might be whether the kernel interpolation can generalize well, since it may help us understand the `benign overfitting henomenon' reported in the literature on deep networks. In this paper, under mild conditions, we show that for any $\varepsilon>0$, the generalization error of kernel interpolation is lower bounded by $Ω(n^{-\varepsilon})$. In other words, the kernel interpolation generalizes poorly for a large class of kernels. As a direct corollary, we can show that overfitted wide neural networks defined on the sphere generalize poorly.

cs.LG↗

arXiv2023

On the Optimality of Misspecified Kernel Ridge Regression

In the misspecified kernel ridge regression problem, researchers usually assume the underground true function $f_ρ^{*} \in [\mathcal{H}]^{s}$, a less-smooth interpolation space of a reproducing kernel Hilbert space (RKHS) $\mathcal{H}$ for some $s\in (0,1)$. The existing minimax optimal results require $\|f_ρ^{*}\|_{L^{\infty}}<\infty$ which implicitly requires $s > α_{0}$ where $α_{0}\in (0,1)$ is the embedding index, a constant depending on $\mathcal{H}$. Whether the KRR is optimal for all $s\in (0,1)$ is an outstanding problem lasting for years. In this paper, we show that KRR is minimax optimal for any $s\in (0,1)$ when the $\mathcal{H}$ is a Sobolev RKHS.

cs.LG↗

arXiv2023

Development of a Hardware-in-the-loop Testbed for Laboratory Performance Verification of Flexible Building Equipment in Typical Commercial Buildings

The goals of reducing energy costs, shifting electricity peaks, increasing the use of renewable energy, and enhancing the stability of the electric grid can be met in part by fully exploiting the energy flexibility potential of buildings and building equipment. The development of strategies that exploit these flexibilities could be facilitated by publicly available high-resolution datasets illustrating how control of HVAC systems in commercial buildings can be used in different climate zones to shape the energy use profile of a building for grid needs. This article presents the development and integration of a Hardware-In-the-Loop Flexible load Testbed (HILFT) that integrates physical HVAC systems with a simulated building model and simulated occupants with the goal of generating datasets to verify load flexibility of typical commercial buildings. Compared to simulation-only experiments, the hardware-in-the-loop approach captures the dynamics of the physical systems while also allowing efficient testing of various boundary conditions. The HILFT integration in this article is achieved through the co-simulation among various software environments including LabVIEW, MATLAB, and EnergyPlus. Although theoretically viable, such integration has encountered many real-world challenges, such as: 1) how to design the overall data infrastructure to ensure effective, robust, and efficient integration; 2) how to avoid closed-loop hunting between simulated and emulated variables; 3) how to quantify system response times and minimize system delays; and 4) how to assess the overall integration quality. Lessons-learned using the examples of an AHU-VAV system, an air-source heat pump system, and a water-source heat pump system are presented.

eess.SY↗

arXiv2022

A non-local gradient based approach of infinity Laplacian with $Γ$-convergence

We propose an infinity Laplacian method to address the problem of interpolation on an unstructured point cloud. In doing so, we find the labeling function with the smallest infinity norm of its gradient. By introducing the non-local gradient, the continuous functional is approximated with a discrete form. The discrete problem is convex and can be solved efficiently with the split Bregman method. Experimental results indicate that our approach provides consistent interpolations and the labeling functions obtained are globally smooth, even in the case of extreme low sampling rate. More importantly, convergence of the discrete minimizer to the optimal continuous labeling function is proved using $Γ$-convergence and compactness, which guarantees the reliability of the infinity Laplacian method in various potential applications.

math.NA↗

arXiv2021

On Post-Selection Inference in A/B Tests

When interpreting A/B tests, we typically focus only on the statistically significant results and take them by face value. This practice, termed post-selection inference in the statistical literature, may negatively affect both point estimation and uncertainty quantification, and therefore hinder trustworthy decision making in A/B testing. To address this issue, in this paper we explore two seemingly unrelated paths, one based on supervised machine learning and the other on empirical Bayes, and propose post-selection inferential approaches that combine the strengths of both. Through large-scale simulated and empirical examples, we demonstrate that our proposed methodologies stand out among other existing ones in both reducing post-selection biases and improving confidence interval coverage rates, and discuss how they can be conveniently adjusted to real-life scenarios.

stat.AP↗

arXiv2020

An Integrated Enhancement Solution for 24-hour Colorful Imaging

The current industry practice for 24-hour outdoor imaging is to use a silicon camera supplemented with near-infrared (NIR) illumination. This will result in color images with poor contrast at daytime and absence of chrominance at nighttime. For this dilemma, all existing solutions try to capture RGB and NIR images separately. However, they need additional hardware support and suffer from various drawbacks, including short service life, high price, specific usage scenario, etc. In this paper, we propose a novel and integrated enhancement solution that produces clear color images, whether at abundant sunlight daytime or extremely low-light nighttime. Our key idea is to separate the VIS and NIR information from mixed signals, and enhance the VIS signal adaptively with the NIR signal as assistance. To this end, we build an optical system to collect a new VIS-NIR-MIX dataset and present a physically meaningful image processing algorithm based on CNN. Extensive experiments show outstanding results, which demonstrate the effectiveness of our solution.

eess.IV↗

arXiv2019

Estimating and Forecasting the Smoking-Attributable Mortality Fraction for Both Genders Jointly in Over 60 Countries

Smoking is one of the preventable threats to human health and is a major risk factor for lung cancer, upper aero-digestive cancer, and chronic obstructive pulmonary disease. Estimating and forecasting the smoking attributable fraction (SAF) of mortality can yield insights into smoking epidemics and also provide a basis for more accurate mortality and life expectancy projection. Peto et al. (1992) proposed a method to estimate the SAF using the lung cancer mortality rate as an indicator of exposure to smoking in the population of interest. Here we use the same method to estimate the all-age SAF (ASAF) for both genders for over 60 countries. We document a strong and cross-nationally consistent pattern of the evolution of the SAF over time. We use this as the basis for a new Bayesian hierarchical model to project future male and female ASAF from over 60 countries simultaneously. This gives forecasts as well as predictive distributions that can be used to find uncertainty intervals for any quantities of interest. We assess the model using out-of-sample predictive validation, and find that it provides good forecasts and well calibrated forecast intervals.

stat.AP↗

arXiv2019

Accounting for Smoking in Forecasting Mortality and Life Expectancy

Smoking is one of the main risk factors that has affected human mortality and life expectancy over the past century. Smoking accounts for a large part of the nonlinearities in the growth of life expectancy and of the geographic and sex differences in mortality. As Bongaarts (2006) and Janssen (2018) suggested, accounting for smoking could improve the quality of mortality forecasts due to the predictable nature of the smoking epidemic. We propose a new Bayesian hierarchical model to forecast life expectancy at birth for both sexes and for 69 countries with good data on smoking-related mortality. The main idea is to convert the forecast of the non-smoking life expectancy at birth (i.e., life expectancy at birth removing the smoking effect) into life expectancy forecast through the use of the age-specific smoking attributable fraction (ASSAF). We introduce a new age-cohort model for the ASSAF and a Bayesian hierarchical model for non-smoking life expectancy at birth. The forecast performance of the proposed method is evaluated by out-of-sample validation compared with four other commonly used methods for life expectancy forecasting. Improvements in forecast accuracy and model calibration based on the new method are observed.

stat.AP↗

arXiv2019

Moment bounds for large autocovariance matrices under dependence

The goal of this paper is to obtain expectation bounds for the deviation of large sample autocovariance matrices from their means under weak data dependence. While the accuracy of covariance matrix estimation corresponding to independent data has been well understood, much less is known in the case of dependent data. We make a step towards filling this gap, and establish deviation bounds that depend only on the parameters controlling the "intrinsic dimension" of the data up to some logarithmic terms. Our results have immediate impacts on high dimensional time series analysis, and we apply them to high dimensional linear VAR($d$) model, vector-valued ARCH model, and a model used in Banna et al. (2016).

math.ST↗

arXiv2018

Instance-level Human Parsing via Part Grouping Network

Instance-level human parsing towards real-world human analysis scenarios is still under-explored due to the absence of sufficient data resources and technical difficulty in parsing multiple instances in a single pass. Several related works all follow the "parsing-by-detection" pipeline that heavily relies on separately trained detection models to localize instances and then performs human parsing for each instance sequentially. Nonetheless, two discrepant optimization targets of detection and parsing lead to suboptimal representation learning and error accumulation for final results. In this work, we make the first attempt to explore a detection-free Part Grouping Network (PGN) for efficiently parsing multiple people in an image in a single pass. Our PGN reformulates instance-level human parsing as two twinned sub-tasks that can be jointly learned and mutually refined via a unified network: 1) semantic part segmentation for assigning each pixel as a human part (e.g., face, arms); 2) instance-aware edge detection to group semantic parts into distinct person instances. Thus the shared intermediate representation would be endowed with capabilities in both characterizing fine-grained parts and inferring instance belongings of each part. Finally, a simple instance partition process is employed to get final results during inference. We conducted experiments on PASCAL-Person-Part dataset and our PGN outperforms all state-of-the-art methods. Furthermore, we show its superiority on a newly collected multi-person parsing dataset (CIHP) including 38,280 diverse images, which is the largest dataset so far and can facilitate more advanced human analysis. The CIHP benchmark and our source code are available at http://sysu-hcp.net/lip/.

cs.CV↗