arXiv subjects

Ping Ma

Publications and source records attributed to Ping Ma.

At least 37 records · Page 2Linked to original sources

arXiv2024

Knowledge Distillation of LLM for Automatic Scoring of Science Education Assessments

This study proposes a method for knowledge distillation (KD) of fine-tuned Large Language Models (LLMs) into smaller, more efficient, and accurate neural networks. We specifically target the challenge of deploying these models on resource-constrained devices. Our methodology involves training the smaller student model (Neural Network) using the prediction probabilities (as soft labels) of the LLM, which serves as a teacher model. This is achieved through a specialized loss function tailored to learn from the LLM's output probabilities, ensuring that the student model closely mimics the teacher's performance. To validate the performance of the KD approach, we utilized a large dataset, 7T, containing 6,684 student-written responses to science questions and three mathematical reasoning datasets with student-written responses graded by human experts. We compared accuracy with state-of-the-art (SOTA) distilled models, TinyBERT, and artificial neural network (ANN) models. Results have shown that the KD approach has 3% and 2% higher scoring accuracy than ANN and TinyBERT, respectively, and comparable accuracy to the teacher model. Furthermore, the student model size is 0.03M, 4,000 times smaller in parameters and x10 faster in inferencing than the teacher model and TinyBERT, respectively. The significance of this research lies in its potential to make advanced AI technologies accessible in typical educational settings, particularly for automatic scoring.

cs.CL↗

arXiv2024

Non-Destructive Peat Analysis using Hyperspectral Imaging and Machine Learning

Peat, a crucial component in whisky production, imparts distinctive and irreplaceable flavours to the final product. However, the extraction of peat disrupts ancient ecosystems and releases significant amounts of carbon, contributing to climate change. This paper aims to address this issue by conducting a feasibility study on enhancing peat use efficiency in whisky manufacturing through non-destructive analysis using hyperspectral imaging. Results show that shot-wave infrared (SWIR) data is more effective for analyzing peat samples and predicting total phenol levels, with accuracies up to 99.81%.

cs.CV↗

arXiv2023

Leverage classifier: Another look at support vector machine

Support vector machine (SVM) is a popular classifier known for accuracy, flexibility, and robustness. However, its intensive computation has hindered its application to large-scale datasets. In this paper, we propose a new optimal leverage classifier based on linear SVM under a nonseparable setting. Our classifier aims to select an informative subset of the training sample to reduce data size, enabling efficient computation while maintaining high accuracy. We take a novel view of SVM under the general subsampling framework and rigorously investigate the statistical properties. We propose a two-step subsampling procedure consisting of a pilot estimation of the optimal subsampling probabilities and a subsampling step to construct the classifier. We develop a new Bahadur representation of the SVM coefficients and derive unconditional asymptotic distribution and optimal subsampling probabilities without giving the full sample. Numerical results demonstrate that our classifiers outperform the existing methods in terms of estimation, computation, and prediction.

stat.ME↗

arXiv2023

Optimal Sampling Designs for Multi-dimensional Streaming Time Series with Application to Power Grid Sensor Data

The Internet of Things (IoT) system generates massive high-speed temporally correlated streaming data and is often connected with online inference tasks under computational or energy constraints. Online analysis of these streaming time series data often faces a trade-off between statistical efficiency and computational cost. One important approach to balance this trade-off is sampling, where only a small portion of the sample is selected for the model fitting and update. Motivated by the demands of dynamic relationship analysis of IoT system, we study the data-dependent sample selection and online inference problem for a multi-dimensional streaming time series, aiming to provide low-cost real-time analysis of high-speed power grid electricity consumption data. Inspired by D-optimality criterion in design of experiments, we propose a class of online data reduction methods that achieve an optimal sampling criterion and improve the computational efficiency of the online analysis. We show that the optimal solution amounts to a strategy that is a mixture of Bernoulli sampling and leverage score sampling. The leverage score sampling involves auxiliary estimations that have a computational advantage over recursive least squares updates. Theoretical properties of the auxiliary estimations involved are also discussed. When applied to European power grid consumption data, the proposed leverage score based sampling methods outperform the benchmark sampling method in online estimation and prediction. The general applicability of the sampling-assisted online estimation method is assessed via simulation studies.

stat.ML↗

arXiv2022

Smoothing splines approximation using Hilbert curve basis selection

Smoothing splines have been used pervasively in nonparametric regressions. However, the computational burden of smoothing splines is significant when the sample size $n$ is large. When the number of predictors $d\geq2$, the computational cost for smoothing splines is at the order of $O(n^3)$ using the standard approach. Many methods have been developed to approximate smoothing spline estimators by using $q$ basis functions instead of $n$ ones, resulting in a computational cost of the order $O(nq^2)$. These methods are called the basis selection methods. Despite algorithmic benefits, most of the basis selection methods require the assumption that the sample is uniformly-distributed on a hyper-cube. These methods may have deteriorating performance when such an assumption is not met. To overcome the obstacle, we develop an efficient algorithm that is adaptive to the unknown probability density function of the predictors. Theoretically, we show the proposed estimator has the same convergence rate as the full-basis estimator when $q$ is roughly at the order of $O[n^{2d/\{(pr+1)(d+2)\}}\quad]$, where $p\in[1,2]$ and $r\approx 4$ are some constants depend on the type of the spline. Numerical studies on various synthetic datasets demonstrate the superior performance of the proposed estimator in comparison with mainstream competitors.

stat.ME↗

arXiv2022

An optimal transport approach for selecting a representative subsample with application in efficient kernel density estimation

Subsampling methods aim to select a subsample as a surrogate for the observed sample. Such methods have been used pervasively in large-scale data analytics, active learning, and privacy-preserving analysis in recent decades. Instead of model-based methods, in this paper, we study model-free subsampling methods, which aim to identify a subsample that is not confined by model assumptions. Existing model-free subsampling methods are usually built upon clustering techniques or kernel tricks. Most of these methods suffer from either a large computational burden or a theoretical weakness. In particular, the theoretical weakness is that the empirical distribution of the selected subsample may not necessarily converge to the population distribution. Such computational and theoretical limitations hinder the broad applicability of model-free subsampling methods in practice. We propose a novel model-free subsampling method by utilizing optimal transport techniques. Moreover, we develop an efficient subsampling algorithm that is adaptive to the unknown probability density function. Theoretically, we show the selected subsample can be used for efficient density estimation by deriving the convergence rate for the proposed subsample kernel density estimator. We also provide the optimal bandwidth for the proposed estimator. Numerical studies on synthetic and real-world datasets demonstrate the performance of the proposed method is superior.

stat.ML↗

arXiv2021

Managing dataset shift by adversarial validation for credit scoring

Dataset shift is common in credit scoring scenarios, and the inconsistency between the distribution of training data and the data that actually needs to be predicted is likely to cause poor model performance. However, most of the current studies do not take this into account, and they directly mix data from different time periods when training the models. This brings about two problems. Firstly, there is a risk of data leakage, i.e., using future data to predict the past. This can result in inflated results in offline validation, but unsatisfactory results in practical applications. Secondly, the macroeconomic environment and risk control strategies are likely to be different in different time periods, and the behavior patterns of borrowers may also change. The model trained with past data may not be applicable to the recent stage. Therefore, we propose a method based on adversarial validation to alleviate the dataset shift problem in credit scoring scenarios. In this method, partial training set samples with the closest distribution to the predicted data are selected for cross-validation by adversarial validation to ensure the generalization performance of the trained model on the predicted samples. In addition, through a simple splicing method, samples in the training data that are inconsistent with the test data distribution are also involved in the training process of cross-validation, which makes full use of all the data and further improves the model performance. To verify the effectiveness of the proposed method, comparative experiments with several other data split methods are conducted with the data provided by Lending Club. The experimental results demonstrate the importance of dataset shift in the field of credit scoring and the superiority of the proposed method.

cs.LG↗

arXiv2021

Best Subset Selection: Statistical Computing Meets Quantum Computing

With the rapid development of quantum computers, quantum algorithms have been studied extensively. However, quantum algorithms tackling statistical problems are still lacking. In this paper, we propose a novel non-oracular quantum adaptive search (QAS) method for the best subset selection problems. QAS performs almost identically to the naive best subset selection method but reduces its computational complexity from $O(D)$ to $O(\sqrt{D}\log_2D)$, where $D=2^p$ is the total number of subsets over $p$ covariates. Unlike existing quantum search algorithms, QAS does not require the oracle information of the true solution state and hence is applicable to various statistical learning problems with random observations. Theoretically, we prove QAS attains any arbitrary success probability $q \in (0.5, 1)$ within $O(\log_2D)$ iterations. When the underlying regression model is linear, we propose a quantum linear prediction method that is faster than its classical counterpart. We further introduce a hybrid quantum-classical strategy to avoid the capacity bottleneck of existing quantum computing systems and boost the success probability of QAS by majority voting. The effectiveness of this strategy is justified by both theoretical analysis and extensive empirical experiments on quantum and classical computers.

stat.ME↗

arXiv2021

Large-scale optimal transport map estimation using projection pursuit

This paper studies the estimation of large-scale optimal transport maps (OTM), which is a well-known challenging problem owing to the curse of dimensionality. Existing literature approximates the large-scale OTM by a series of one-dimensional OTM problems through iterative random projection. Such methods, however, suffer from slow or none convergence in practice due to the nature of randomly selected projection directions. Instead, we propose an estimation method of large-scale OTM by combining the idea of projection pursuit regression and sufficient dimension reduction. The proposed method, named projection pursuit Monge map (PPMM), adaptively selects the most ``informative'' projection direction in each iteration. We theoretically show the proposed dimension reduction method can consistently estimate the most ``informative'' projection direction in each iteration. Furthermore, the PPMM algorithm weakly convergences to the target large-scale OTM in a reasonable number of steps. Empirically, PPMM is computationally easy and converges fast. We assess its finite sample performance through the applications of Wasserstein distance estimation and generative models.

stat.ML↗

arXiv2021

A Review on Modern Computational Optimal Transport Methods with Applications in Biomedical Research

Optimal transport has been one of the most exciting subjects in mathematics, starting from the 18th century. As a powerful tool to transport between two probability measures, optimal transport methods have been reinvigorated nowadays in a remarkable proliferation of modern data science applications. To meet the big data challenges, various computational tools have been developed in the recent decade to accelerate the computation for optimal transport methods. In this review, we present some cutting-edge computational optimal transport methods with a focus on the regularization-based methods and the projection-based methods. We discuss their real-world applications in biomedical research.

stat.ML↗

arXiv2021

Sufficient dimension reduction for classification using principal optimal transport direction

Sufficient dimension reduction is used pervasively as a supervised dimension reduction approach. Most existing sufficient dimension reduction methods are developed for data with a continuous response and may have an unsatisfactory performance for the categorical response, especially for the binary-response. To address this issue, we propose a novel estimation method of sufficient dimension reduction subspace (SDR subspace) using optimal transport. The proposed method, named principal optimal transport direction (POTD), estimates the basis of the SDR subspace using the principal directions of the optimal transport coupling between the data respecting different response categories. The proposed method also reveals the relationship among three seemingly irrelevant topics, i.e., sufficient dimension reduction, support vector machine, and optimal transport. We study the asymptotic properties of POTD and show that in the cases when the class labels contain no error, POTD estimates the SDR subspace exclusively. Empirical studies show POTD outperforms most of the state-of-the-art linear dimension reduction methods.

cs.LG↗

arXiv2021

Minimax Nonparametric Two-sample Test under Smoothing

We consider the problem of comparing probability densities between two groups. A new probabilistic tensor product smoothing spline framework is developed to model the joint density of two variables. Under such a framework, the probability density comparison is equivalent to testing the presence/absence of interactions. We propose a penalized likelihood ratio test for such interaction testing and show that the test statistic is asymptotically chi-square distributed under the null hypothesis. Furthermore, we derive a sharp minimax testing rate based on the Bernstein width for nonparametric two-sample tests and show that our proposed test statistics is minimax optimal. In addition, a data-adaptive tuning criterion is developed to choose the penalty parameter. Simulations and real applications demonstrate that the proposed test outperforms the conventional approaches under various scenarios.

stat.ME↗

arXiv2020

LowCon: A design-based subsampling approach in a misspecified linear modeL

We consider a measurement constrained supervised learning problem, that is, (1) full sample of the predictors are given; (2) the response observations are unavailable and expensive to measure. Thus, it is ideal to select a subsample of predictor observations, measure the corresponding responses, and then fit the supervised learning model on the subsample of the predictors and responses. However, model fitting is a trial and error process, and a postulated model for the data could be misspecified. Our empirical studies demonstrate that most of the existing subsampling methods have unsatisfactory performances when the models are misspecified. In this paper, we develop a novel subsampling method, called "LowCon", which outperforms the competing methods when the working linear model is misspecified. Our method uses orthogonal Latin hypercube designs to achieve a robust estimation. We show that the proposed design-based estimator approximately minimizes the so-called "worst-case" bias with respect to many possible misspecification terms. Both the simulated and real-data analyses demonstrate the proposed estimator is more robust than several subsample least squares estimators obtained by state-of-the-art subsampling methods.

stat.ME↗

arXiv2020

An Asympirical Smoothing Parameters Selection Approach for Smoothing Spline ANOVA Models in Large Samples

Large samples have been generated routinely from various sources. Classic statistical models, such as smoothing spline ANOVA models, are not well equipped to analyze such large samples due to expensive computational costs. In particular, the daunting computational costs of selecting smoothing parameters render smoothing spline ANOVA models impractical. In this article, we develop an asympirical, i.e., asymptotic and empirical, smoothing parameters selection approach for smoothing spline ANOVA models in large samples. The idea of this approach is to use asymptotic analysis to show that the optimal smoothing parameter is a polynomial function of the sample size and an unknown constant. The unknown constant is then estimated through empirical subsample extrapolation. The proposed method significantly reduces the computational costs of selecting smoothing parameters in high-dimensional and large samples. We show smoothing parameters chosen by the proposed method tend to the optimal smoothing parameters that minimise a specific risk function. In addition, the estimator based on the proposed smoothing parameters achieves the optimal convergence rate. Extensive simulation studies demonstrate the numerical advantage of the proposed method over competing methods in terms of relative efficacies and running time. On an application to molecular dynamics data with nearly one million observations, the proposed method has the best prediction performance.

stat.ME↗

arXiv2020

More efficient approximation of smoothing splines via space-filling basis selection

We consider the problem of approximating smoothing spline estimators in a nonparametric regression model. When applied to a sample of size $n$, the smoothing spline estimator can be expressed as a linear combination of $n$ basis functions, requiring $O(n^3)$ computational time when the number of predictors $d\geq 2$. Such a sizable computational cost hinders the broad applicability of smoothing splines. In practice, the full sample smoothing spline estimator can be approximated by an estimator based on $q$ randomly-selected basis functions, resulting in a computational cost of $O(nq^2)$. It is known that these two estimators converge at the identical rate when $q$ is of the order $O\{n^{2/(pr+1)}\}$, where $p\in [1,2]$ depends on the true function $η$, and $r > 1$ depends on the type of spline. Such $q$ is called the essential number of basis functions. In this article, we develop a more efficient basis selection method. By selecting the ones corresponding to roughly equal-spaced observations, the proposed method chooses a set of basis functions with a large diversity. The asymptotic analysis shows our proposed smoothing spline estimator can decrease $q$ to roughly $O\{n^{1/(pr+1)}\}$, when $d\leq pr+1$. Applications on synthetic and real-world datasets show the proposed method leads to a smaller prediction error compared with other basis selection methods.

stat.CO↗

arXiv2020

Asymptotic Analysis of Sampling Estimators for Randomized Numerical Linear Algebra Algorithms

The statistical analysis of Randomized Numerical Linear Algebra (RandNLA) algorithms within the past few years has mostly focused on their performance as point estimators. However, this is insufficient for conducting statistical inference, e.g., constructing confidence intervals and hypothesis testing, since the distribution of the estimator is lacking. In this article, we develop an asymptotic analysis to derive the distribution of RandNLA sampling estimators for the least-squares problem. In particular, we derive the asymptotic distribution of a general sampling estimator with arbitrary sampling probabilities. The analysis is conducted in two complementary settings, i.e., when the objective of interest is to approximate the full sample estimator or is to infer the underlying ground truth model parameters. For each setting, we show that the sampling estimator is asymptotically normally distributed under mild regularity conditions. Moreover, the sampling estimator is asymptotically unbiased in both settings. Based on our asymptotic analysis, we use two criteria, the Asymptotic Mean Squared Error (AMSE) and the Expected Asymptotic Mean Squared Error (EAMSE), to identify optimal sampling probabilities. Several of these optimal sampling probability distributions are new to the literature, e.g., the root leverage sampling estimator and the predictor length sampling estimator. Our theoretical results clarify the role of leverage in the sampling process, and our empirical results demonstrate improvements over existing methods.

math.ST↗

arXiv2019

Plasmonic Ferroelectric Modulators

Integrated ferroelectric plasmonic modulators featuring large bandwidths, broad optical operation range, resilience to high temperature and ultracompact footprint are introduced. Measurements show a modulation bandwidth of 70 GHz and a temperature stability up to 250°C. Mach-Zehnder interferometer modulators with 10-$μ$m-long phase shifters were operated at 116 Gbit/s PAM-4 and 72 Gbit/s NRZ. Wide and open eye diagrams with extinction ratios beyond 15 dB were found. The fast and robust devices are apt to an employment in industrial environments.

physics.app-ph↗

arXiv2019

Waveguide-integrated van der Waals heterostructure photodetector at telecom band with high speed and high responsivity

Intensive efforts have been devoted to exploit novel optoelectronic devices based on two-dimensional (2D) transition-metal dichalcogenides (TMDCs) owing to their strong light-matter interaction and distinctive material properties. In particular, photodetectors featuring both high-speed and high-responsivity performance are of great interest for a vast number of applications such as high-data-rate interconnects operated at standardized telecom wavelengths. Yet, the intrinsically small carrier mobilities of TMDCs become a bottleneck for high-speed application use. Here, we present high-performance vertical van der Waals heterostructure-based photodetectors integrated on a silicon photonics platform. Our vertical MoTe2/graphene heterostructure design minimizes the carrier transit path length in TMDCs and enables a record-high measured bandwidth of at least 24GHz under a moderate bias voltage of -3 volts. Applying a higher bias or employing thinner MoTe2 flakes boosts the bandwidth even to 50GHz. Simultaneously, our device reaches a high external responsivity of 0.2A/W for incident light at 1300nm, benefiting from the integrated waveguide design. Our studies shed light on performance trade-offs and present design guidelines for fast and efficient devices. The combination of 2D heterostructures and integrated guided-wave nano photonics defines an attractive platform to realize high-performance optoelectronic devices, such as photodetectors, light-emitting devices and electro-optic modulators.

cond-mat.mes-hall↗