arXiv subjects

Jiashun Jin

Publications and source records attributed to Jiashun Jin.

At least 19 recordsLinked to original sources

arXiv2026

Optimal estimators and tests for reciprocal effects

The $p_1$ model plays a fundamental role in modeling directed networks, where the reciprocal effect parameter $ρ$ is of special interest in practice. However, due to nonlinear factors in this model, how to estimate $ρ$ efficiently is a long-standing open problem. We tackle the problem by the cycle count approach. The challenge is, due to the nonlinear factors in the model, for any given type of generalized cycles, the expected count is a complicated function of many parameters in the model, so it is unclear how to use cycle counts to estimate $ρ$. However, somewhat surprisingly, we discover that, among many types of generalized cycles with the same length, we can carefully pick a pair of them such that in the ratio between the expected cycle counts of the two types, the non-linear factors cancel out nicely with each other, and as a result, the ratio equals to $\mathrm{exp}(ρ)$ exactly. Therefore, though the expected count of cycles of any type is not tractable, the ratio between the expected cycle counts of a (carefully chosen) pair of generalized cycles may have an utterly simple form. We study to what extent such pairs exist, and use our discovery to derive both an estimate for $ρ$ and a testing procedure for testing $ρ= ρ_0$. In a setting where we allow a wide range of reciprocal effects and a wide variety of network sparsity and degree heterogeneity, we show that our estimator achieves the optimal rate and our test achieves the optimal phase transition. Technically, first, motivated by what we observe on real networks, we do not want to impose strong conditions on reciprocal effects, network sparsity, and degree heterogeneity. Second, our proposed statistic is a type of $U$-statistic, the analysis of which involves complex combinatorics and is error-prone. For these reasons, our analysis is long and delicate.

math.ST↗

arXiv2026

The Gold Rush in AI4Math: Where Are We Now?

Recent advances in artificial intelligence (AI) have sparked growing interest in its use for mathematical research. While some view this as a major opportunity for discovery, others have raised concerns about its impact on traditional research practices. Despite extensive debate, empirical evidence on how AI is actually being used in mathematics remains limited. To address this gap, we collected all 32,944 arXiv submissions posted between March 1 and August 20, 2026, whose primary or secondary categories included Mathematics. We identified 3,575 submissions that explicitly disclosed author use of AI, of which 1,712 involved at least one substantive mathematical contribution. Our analysis reveals several broad patterns. First, disclosed AI use increased sharply over the study period, with substantive use growing from 1.39% of Mathematics submissions in March to 14.09% through August 20. Second, substantive AI use is highly uneven across fields: Combinatorics has the largest number of such papers, while Metric Geometry has the highest substantive-use rate. Third, substantive AI use is geographically concentrated: under weighted author counts, the United States and China together account for about two-thirds of the recognized country weight. Fourth, AI is already being applied to open research problems: among 717 named open-problem records associated with substantive use, 71% are labeled as fully resolved based on the authors' descriptions, with proofs of the conjectured statement more common than counterexamples or disproofs. Finally, AI-system use is also highly concentrated, with OpenAI systems appearing most frequently, followed by Anthropic. Together, these findings suggest that AI-assisted mathematics is expanding rapidly but remains at an early and uneven stage of adoption.

stat.AP↗

arXiv2026

A New Impossibility Region for the $5\times5$ Symmetric Nonnegative Inverse Eigenvalue Problem

We present a new impossibility region for the $5\times5$ symmetric nonnegative inverse eigenvalue problem. The region lies in the low-trace regime and, to the best of our knowledge, has not been identified previously. The proof uses a suitable diagonal shift to transform the problem to a critical high-trace boundary and then reduces a complementary commuting matrix to a weighted five-cycle. The characteristic polynomial and spectral identities of this five-cycle provide the main tools for deriving the resulting contradiction.

math.RA↗

arXiv2026

Counting Cycles with AI: Counting Cycles with AI: Computationally Efficient Equivalent Forms with Applications

Cycle count statistics are fundamental tools in statistics and engineering, with applications in motif counting, channel coding, and statistical inference of network and matrix data. However, how to compute high-order cycle count statistics efficiently is still an open problem. In this paper, we aim to derive Computationally Efficient Equivalent Forms (CEEF) for cycle count statistics of any given order, where we express each cycle count statistic equivalently as a linear combination of finitely many terms. Using the CEEF, we provide a much more efficient way to compute the cycle count statistics. The CEEF problem has no known general solution and requires delicate combinatorial arguments together with extensive calculations. While this task is hard to accomplish by humans alone, it provides an ideal setting in which Artificial Intelligence (AI) can be useful. We solve the problem by combining several theorems we derive with powerful coding skills of modern AI systems. Our results leverage graph-theoretic arguments and yield new formulas for general cases that were previously unknown. We find that, although AI cannot solve the problem independently, it becomes highly effective when guided by humans through theorems we derive as well as a clear derivation strategy, step-by-step instructions, and carefully-written prompts. We consider several statistical applications, including spiked matrix testing, estimation of weak spike eigenvalues, and pairwise network comparison. For each problem, we demonstrate that optimal statistical performance is achieved by using high-order cycle count statistics, and our CEEF formulas make their computation feasible on large-scale data sets.

cs.CL↗

arXiv2026

Subgraph counting estimation for the $β$-model in sparse networks

The $β$-model is popular for characterizing the commonly observed degree heterogeneity phenomenon in real-world networks. In this study, we develop a cycle counting approach to estimate $n$ node-specific parameters in the $β$-model for moderate or extremely sparse networks. Our proposed estimators, called \emph{Cycle Counting Ratio (CCR) Estimator}, are based on the log-ratios of two network cycle counting statistics with explicit expressions and therefore easy to compute. We focus on conditions to guarantee statistical properties of the single estimator for each node. Under the very weak conditions that $\max_t θ_t \to 0$ and $θ_t \|θ\|_1 \to \infty$, we show that the CCR estimator is consistent and achieves the minimax rate in terms of the mean squared error, which is the squared signal-to-noise ratio for $\hatβ_t$ up to a constant factor. Here, $\hatβ_t$ is the CCR estimator of the node-specific parameter $β_t$, $θ_t = \exp(β_t)$ and $θ=(θ_1, \ldots, θ_n)$. Even if the whole network density is close to the Erdős-Rényi lower bound $\log n/n$, the CCR estimator for the single parameter $β_t$ is still consistent as long as $θ_t \|θ\|_1 \to \infty$. To the best of our knowledge, this is the first time to derive the minimax rate and consistency result under such weak conditions. Under a slight stronger condition, we further establish its uniform consistency and asymptotic normality, whose asymptotic variance is $θ_t \|θ\|_1$. Numerical studies and an application to a sparse network data set demonstrate our theoretical findings.

stat.ME↗

arXiv2025

A Comparison of DeepSeek and Other LLMs

Recently, DeepSeek has been the focus of attention in and beyond the AI community. An interesting problem is how DeepSeek compares to other large language models (LLMs). There are many tasks an LLM can do, and in this paper, we use the task of "predicting an outcome using a short text" for comparison. We consider two settings, an authorship classification setting and a citation classification setting. In the first one, the goal is to determine whether a short text is written by human or AI. In the second one, the goal is to classify a citation to one of four types using the textual content. For each experiment, we compare DeepSeek with $4$ popular LLMs: Claude, Gemini, GPT, and Llama. We find that, in terms of classification accuracy, DeepSeek outperforms Gemini, GPT, and Llama in most cases, but underperforms Claude. We also find that DeepSeek is comparably slower than others but with a low cost to use, while Claude is much more expensive than all the others. Finally, we find that in terms of similarity, the output of DeepSeek is most similar to those of Gemini and Claude (and among all $5$ LLMs, Claude and Gemini have the most similar outputs). In this paper, we also present a fully-labeled dataset collected by ourselves, and propose a recipe where we can use the LLMs and a recent data set, MADStat, to generate new data sets. The datasets in our paper can be used as benchmarks for future study on LLMs.

cs.CL↗

arXiv2025

STAR-Net: An Interpretable Model-Aided Network for Remote Sensing Image Denoising

Remote sensing image (RSI) denoising is an important topic in the field of remote sensing. Despite the impressive denoising performance of RSI denoising methods, most current deep learning-based approaches function as black boxes and lack integration with physical information models, leading to limited interpretability. Additionally, many methods may struggle with insufficient attention to non-local self-similarity in RSI and require tedious tuning of regularization parameters to achieve optimal performance, particularly in conventional iterative optimization approaches. In this paper, we first propose a novel RSI denoising method named sparse tensor-aided representation network (STAR-Net), which leverages a low-rank prior to effectively capture the non-local self-similarity within RSI. Furthermore, we extend STAR-Net to a sparse variant called STAR-Net-S to deal with the interference caused by non-Gaussian noise in original RSI for the purpose of improving robustness. Different from conventional iterative optimization, we develop an alternating direction method of multipliers (ADMM)-guided deep unrolling network, in which all regularization parameters can be automatically learned, thus inheriting the advantages of both model-based and deep learning-based approaches and successfully addressing the above-mentioned shortcomings. Comprehensive experiments on synthetic and real-world datasets demonstrate that STAR-Net and STAR-Net-S outperform state-of-the-art RSI denoising methods.

cs.CV↗

arXiv2025

Fitting networks with a cancellation trick

The degree-corrected block model (DCBM), latent space model (LSM), and $β$-model are all popular network models. We combine their modeling ideas and propose the logit-DCBM as a new model. Similar as the $β$-model and LSM, the logit-DCBM contains nonlinear factors, where fitting the parameters is a challenging open problem. We resolve this problem by introducing a cancellation trick. We also propose R-SCORE as a recursive community detection algorithm, where in each iteration, we first use the idea above to update our parameter estimation, and then use the results to remove the nonlinear factors in the logit-DCBM so the renormalized model approximately satisfies a low-rank model, just like the DCBM. Our numerical study suggests that R-SCORE significantly improves over existing spectral approaches in many cases. Also, theoretically, we show that the Hamming error rate of R-SCORE is faster than that of SCORE in a specific sparse region, and is at least as fast outside this region.

stat.ME↗

arXiv2025

Network Goodness-of-Fit for the block-model family

The block-model family has four popular network models (SBM, DCBM, MMSBM, and DCMM). A fundamental problem is, how well each of these models fits with real networks. We propose GoF-MSCORE as a new Goodness-of-Fit (GoF) metric for DCMM (the broadest one among the four), with two main ideas. The first is to use cycle count statistics as a general recipe for GoF. The second is a novel network fitting scheme. GoF-MSCORE is a flexible GoF approach, and we further extend it to SBM, DCBM, and MMSBM. This gives rise to a series of GoF metrics covering each of the four models in the block-model family. We show that for each of the four models, if the assumed model is correct, then the corresponding GoF metric converges to $N(0, 1)$ as the network sizes diverge. We also analyze the powers and show that these metrics are optimal in many settings. In comparison, many other GoF ideas face challenges: they may lack a parameter-free limiting null, or are non-optimal in power, or face an analytical hurdle. Note that a parameter-free limiting null is especially desirable as many network models have a large number of unknown parameters. The limiting nulls of our GoF metrics are always $N(0,1)$, which are parameter-free as desired. For 12 frequently-used real networks, we use the proposed GoF metrics to show that DCMM fits well with almost all of them. We also show that SBM, DCBM, and MMSBM do not fit well with many of these networks, especially when the networks are relatively large. To complement with our study on GoF, we also show that the DCMM is nearly as broad as the rank-$K$ network model. Based on these results, we recommend the DCMM as a promising model for undirected networks.

math.ST↗

arXiv2024

Optimal Network Pairwise Comparison

We are interested in the problem of two-sample network hypothesis testing: given two networks with the same set of nodes, we wish to test whether the underlying Bernoulli probability matrices of the two networks are the same or not. We propose Interlacing Balance Measure (IBM) as a new two-sample testing approach. We consider the {\it Degree-Corrected Mixed-Membership (DCMM)} model for undirected networks, where we allow severe degree heterogeneity, mixed-memberships, flexible sparsity levels, and weak signals. In such a broad setting, how to find a test that has a tractable limiting null and optimal testing performances is a challenging problem. We show that IBM is such a test: in a broad DCMM setting with only mild regularity conditions, IBM has $N(0,1)$ as the limiting null and achieves the optimal phase transition. While the above is for undirected networks, IBM is a unified approach and is directly implementable for directed networks. For a broad directed-DCMM (extension of DCMM for directed networks) setting, we show that IBM has $N(0, 1/2)$ as the limiting null and continues to achieve the optimal phase transition. We have also applied IBM to the Enron email network and a gene co-expression network, with interesting results.

stat.ME↗

arXiv2024

Improved Algorithm and Bounds for Successive Projection

Given a $K$-vertex simplex in a $d$-dimensional space, suppose we measure $n$ points on the simplex with noise (hence, some of the observed points fall outside the simplex). Vertex hunting is the problem of estimating the $K$ vertices of the simplex. A popular vertex hunting algorithm is successive projection algorithm (SPA). However, SPA is observed to perform unsatisfactorily under strong noise or outliers. We propose pseudo-point SPA (pp-SPA). It uses a projection step and a denoise step to generate pseudo-points and feed them into SPA for vertex hunting. We derive error bounds for pp-SPA, leveraging on extreme value theory of (possibly) high-dimensional random vectors. The results suggest that pp-SPA has faster rates and better numerical performances than SPA. Our analysis includes an improved non-asymptotic bound for the original SPA, which is of independent interest.

cs.LG↗

arXiv2024

Recent Advances in Text Analysis

Text analysis is an interesting research area in data science and has various applications, such as in artificial intelligence, biomedical research, and engineering. We review popular methods for text analysis, ranging from topic modeling to the recent neural language models. In particular, we review Topic-SCORE, a statistical approach to topic modeling, and discuss how to use it to analyze MADStat - a dataset on statistical publications that we collected and cleaned. The application of Topic-SCORE and other methods on MADStat leads to interesting findings. For example, $11$ representative topics in statistics are identified. For each journal, the evolution of topic weights over time can be visualized, and these results are used to analyze the trends in statistical research. In particular, we propose a new statistical model for ranking the citation impacts of $11$ topics, and we also build a cross-topic citation graph to illustrate how research results on different topics spread to one another. The results on MADStat provide a data-driven picture of the statistical research in $1975$--$2015$, from a text analysis perspective.

stat.AP↗

arXiv2023

Subject clustering by IF-PCA and several recent methods

Subject clustering (i.e., the use of measured features to cluster subjects, such as patients or cells, into multiple groups) is a problem of great interest. In recent years, many approaches were proposed, among which unsupervised deep learning (UDL) has received a great deal of attention. Two interesting questions are (a) how to combine the strengths of UDL and other approaches, and (b) how these approaches compare to one other. We combine Variational Auto-Encoder (VAE), a popular UDL approach, with the recent idea of Influential Feature PCA (IF-PCA), and propose IF-VAE as a new method for subject clustering. We study IF-VAE and compare it with several other methods (including IF-PCA, VAE, Seurat, and SC3) on $10$ gene microarray data sets and $8$ single-cell RNA-seq data sets. We find that IF-VAE significantly improves over VAE, but still underperforms IF-PCA. We also find that IF-PCA is quite competitive, which slightly outperforms Seurat and SC3 over the $8$ single-cell data sets. IF-PCA is conceptually simple and permits delicate analysis. We demonstrate that IF-PCA is capable of achieving the phase transition in a Rare/Weak model. Comparatively, Seurat and SC3 are more complex and theoretically difficult to analyze (for these reasons, their optimality remains unclear).

stat.ME↗

arXiv2023

Phase transition for detecting a small community in a large network

How to detect a small community in a large network is an interesting problem, including clique detection as a special case, where a naive degree-based $χ^2$-test was shown to be powerful in the presence of an Erdős-Renyi background. Using Sinkhorn's theorem, we show that the signal captured by the $χ^2$-test may be a modeling artifact, and it may disappear once we replace the Erdős-Renyi model by a broader network model. We show that the recent SgnQ test is more appropriate for such a setting. The test is optimal in detecting communities with sizes comparable to the whole network, but has never been studied for our setting, which is substantially different and more challenging. Using a degree-corrected block model (DCBM), we establish phase transitions of this testing problem concerning the size of the small community and the edge densities in small and large communities. When the size of the small community is larger than $\sqrt{n}$, the SgnQ test is optimal for it attains the computational lower bound (CLB), the information lower bound for methods allowing polynomial computation time. When the size of the small community is smaller than $\sqrt{n}$, we establish the parameter regime where the SgnQ test has full power and make some conjectures of the CLB. We also study the classical information lower bound (LB) and show that there is always a gap between the CLB and LB in our range of interest.

math.ST↗

arXiv2022

Mixed Membership Estimation for Social Networks

In economics and social science, network data are regularly observed, and a thorough understanding of the network community structure facilitates the comprehension of economic patterns and activities. Consider an undirected network with $n$ nodes and $K$ communities. We model the network using the Degree-Corrected Mixed-Membership (DCMM) model, where for each node $i$, there exists a membership vector $π_i = (π_i(1), π_i(2), \ldots, π_i(K))'$, where $π_i(k)$ is the weight that node $i$ puts in community $k$, $1 \leq k \leq K$. In comparison to the well-known stochastic block model (SBM), the DCMM permits both severe degree heterogeneity and mixed memberships, making it considerably more realistic and general. We present an efficient approach, Mixed-SCORE, for estimating the mixed membership vectors of all nodes and the other DCMM parameters. This approach is inspired by the discovery of a delicate simplex structure in the spectral domain. We derive explicit error rates for the Mixed-SCORE algorithm and demonstrate that it is rate-optimal over a broad parameter space. Our findings provide a novel statistical tool for network community analysis, which can be used to understand network formations, extract nodal features, identify unobserved covariates in dyadic regressions, and estimate peer effects. We applied Mixed-SCORE to a political blog network, two trade networks, a co-authorship network, and a citee network, and obtained interpretable results.

stat.ME↗

arXiv2022

Co-citation and Co-authorship Networks of Statisticians

We collected and cleaned a large data set on publications in statistics. The data set consists of the coauthor relationships and citation relationships of 83, 331 papers published in 36 representative journals in statistics, probability, and machine learning, spanning 41 years. The data set allows us to construct many different networks, and motivates a number of research problems about the research patterns and trends, research impacts, and network topology of the statistics community. In this paper we focus on (i) using the citation relationships to estimate the research interests of authors, and (ii) using the coauthor relationships to study the network topology. Using co-citation networks we constructed, we discover a "statistics triangle", reminiscent of the statistical philosophy triangle (Efron, 1998). We propose new approaches to constructing the "research map" of statisticians, as well as the "research trajectory" for a given author to visualize his/her research interest evolvement. Using co-authorship networks we constructed, we discover a multi-layer community tree and produce a Sankey diagram to visualize the author migrations in different sub-areas. We also propose several new metrics for research diversity of individual authors. We find that "Bayes", "Biostatistics", and "Nonparametric" are three primary areas in statistics. We also identify 15 sub-areas, each of which can be viewed as a weighted average of the primary areas, and identify several underlying reasons for the formation of co-authorship communities. We also find that the research interests of statisticians have evolved significantly in the 41-year time window we studied: some areas (e.g., biostatistics, high-dimensional data analysis, etc.) have become increasingly more popular.

cs.DL↗

arXiv2022

The SCORE normalization, especially for highly heterogeneous network and text data

SCORE was introduced as a spectral approach to network community detection. Since many networks have severe degree heterogeneity, the ordinary spectral clustering (OSC) approach to community detection may perform unsatisfactorily. SCORE alleviates the effect of degree heterogeneity by introducing a new normalization idea in the spectral domain and makes OSC more effective. SCORE is easy to use and computationally fast. It adapts easily to new directions and sees an increasing interest in practice. In this paper, we review the basics of SCORE, the adaption of SCORE to network mixed membership estimation and topic modeling, and the application of SCORE in real data, including two datasets on the publications of statisticians. We also review the theoretical 'ideology' underlying SCORE. We show that in the spectral domain, SCORE converts a simplicial cone to a simplex, and provides a simple and direct link between the simplex and network memberships. SCORE attains an exponential rate and a sharp phase transition in community detection, and achieves optimal rates in mixed membership estimation and topic modeling.

cs.SI↗

arXiv2022

Allocation of COVID-19 Testing Budget on a Commute Network of Counties

The screening testing is an effective tool to control the early spread of an infectious disease such as COVID-19. When the total testing capacity is limited, we aim to optimally allocate testing resources among n counties. We build a (weighted) commute network on counties, with the weight between two counties a decreasing function of their traffic distance. We introduce a network-based disease model, in which the number of newly confirmed cases of each county depends on the numbers of hidden cases of all counties on the network. Our proposed testing allocation strategy first uses historical data to learn model parameters and then decides the testing rates for all counties by solving an optimization problem. We apply the method on the commute networks of Massachusetts, USA and Hubei, China and observe its advantages over testing allocation strategies that ignore the network structure. Our approach can also be extended to study the vaccine allocation problem.

stat.ME↗