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Researcher profile

Ping Ma

Ping Ma contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Machine LearningMethodologymath.STStatistics TheoryApplicationsComputationcond-mat.mes-hallcond-mat.mtrl-sciphysics.app-phphysics.optics

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Published work

8 published item(s)

preprint2026arXiv

Wahkon: A Statistically Principled Deep RKHS Superposition Network

Deep learning excels at prediction but often lacks finite-sample guarantees and calibrated uncertainty; RKHS (Reproducing Kernel Hilbert Space)-based methods provide those guarantees but struggle to adapt in high dimensions. We propose Wahkon, a deep RKHS superposition network that unifies Kolmogorov's superposition principle with RKHS regularization in the smoothing-spline tradition of Wahba. This yields a finite-dimensional deep representer theorem that makes training tractable and provides explicit layerwise complexity control. We show the penalized estimator is exactly the MAP (maximum a posteriori) estimate under a hierarchical Gaussian-process prior, extending the spline/GP duality to deep compositions. Using metric-entropy arguments, we establish minimax-optimal convergence rates under mild smoothness and clarify how depth and width trade off with regularity. Empirically, Wahkon outperforms multilayer perceptrons, Neural Tangent Kernels, and Kolmogorov--Arnold Networks across simulation benchmarks and a single-cell CITE-seq study. By unifying Kolmogorov's superposition principle with RKHS regularization, Wahkon delivers accuracy, interpretability, and statistical rigor in a single framework.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

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.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

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.

0 citations0 reviewsNo code linkedOpen access