arXiv subjects

Fang Tian

Publications and source records attributed to Fang Tian.

14 recordsLinked to original sources

arXiv2026

Editable XAI: Toward Bidirectional Human-AI Alignment with Co-Editable Explanations of Interpretable Attributes

While Explainable AI (XAI) helps users understand AI decisions, misalignment in domain knowledge can lead to disagreement. This inconsistency hinders understanding, and because explanations are often read-only, users lack the control to improve alignment. We propose making XAI editable, allowing users to write rules to improve control and gain deeper understanding through the generation effect of active learning. We developed CoExplain, leveraging a neural network for universal representation and symbolic rules for intuitive reasoning on interpretable attributes. CoExplain explains the neural network with a faithful proxy decision tree, parses user-written rules as an equivalent neural network graph, and collaboratively optimizes the decision tree. In a user study (N=43), CoExplain and manually editable XAI improved user understanding and model alignment compared to read-only XAI. CoExplain was easier to use with fewer edits and less time. This work contributes Editable XAI for bidirectional AI alignment, improving understanding and control.

cs.HC↗

arXiv2025

On the number of linear uniform hypergraphs with linear girth constraint

For an integer $r\geqslant 3$, a hypergraph on vertex set $[n]$ is $r$-uniform if each edge is a set of $r$ vertices, and is said to be linear if every two distinct edges share at most one vertex. Given a family $\mathcal{H}$ of linear $r$-uniform hypergraphs,let $Forb_r^L(n,\mathcal{H})$ be the set of linear $r$-uniform hypergraphs on vertex set $[n]$, which does not contain any member from $\mathcal{H}$ as a subgraph. An $r$-uniform linear cycle of length $\ell$, denoted by $C_\ell^r$, is a linear $r$-uniform hypergraph on $(r-1)\ell$ vertices whose edges can be ordered as $\boldsymbol{e}_1,\ldots,\boldsymbol{e}_\ell$ such that $|\boldsymbol{e}_i\cap \boldsymbol{e}_j|=1$ if $j=i\pm 1$ (indices taken modulo $\ell$) and $|\boldsymbol{e}_i\cap \boldsymbol{e}_j|=0$ otherwise. The linear girth of a linear $r$-uniform hypergraph is the smallest integer $\ell$ such that it contains a $C_\ell^r$. Let $Forb_L(n,r,\ell)=Forb_r^L(n,\mathcal{H})$ when $\mathcal{H}=\{C_i^r:\, 3\leqslant i\leqslant \ell\}$, that is, $Forb_L(n,r,\ell)$ is the set of all linear $r$-uniform hypergraphs on $[n]$ with linear girth greater than $\ell$. For integers $r\geqslant 3$ and $\ell\geqslant 4$, Balogh and Li [On the number of linear hypergraphs of large girth, J. Graph Theory, 93(1) (2020), 113-141] showed that $|Forb_L(n,r,\ell)|= 2^{O(n^{1+1/\lfloor \ell/2\rfloor})}$ based on the graph container method. It is natural to obtain $|Forb_L(n,r,\ell)|\geqslant 2^{c\cdot n^{1+1/\ell}}$ for some constant $c$ by probabilistic deletion method. Combined with the known results that $|Forb_L(n,r,3)|= 2^{o (n^{2})}$ and $|Forb_L(n,3,4)|= 2^{\Theta (n^{3/2})}$, by analyzing the random greedy high linear girth linear $r$-uniform hypergraph process, we show $|Forb_L(n,r,\ell)|\geqslant 2^{n^{1+1/(\ell-1)-O(\log\log n/\log n)}}$ for every pair of fixed integers $r,\ell\geqslant 4$, or $r= 3$ and $\ell\geqslant 5$.

math.CO↗

arXiv2025

Subgraphs in random graphs with specified degrees and forbidden edges

Let $G$ be a uniformly chosen simple (labelled) random graph with given degree sequence $\boldsymbol{d}$ and let $X,Y,L$ be edge-disjoint graphs on the same vertex set as $G$. We investigate the probability that $X \subseteq G$ and that $G \cap Y = \emptyset$ both conditioned on the event $G \cap L = \emptyset$. We improve upon known bounds of these probabilities and extend them to a wider range of degree sequences through a more precise edge switching argument. Notably, a few vertices of linear degree are permitted provided that the subgraph $X$ does not have an edge incident with them. Further, the graph $L$ is permitted to contain many edges (we provide an example where $L$ is a spanning $r$-regular subgraph with $r = o(n)$). We provide the same analysis when $G$ is a simple (labelled) bipartite random graph with a given degree sequence $(\boldsymbol{s},\boldsymbol{t})$. Our work extends the results of Gao and Ohapkin (2023) and McKay (1981, 2010).

math.CO↗

arXiv2024

High-dimensional multiple imputation (HDMI) for partially observed confounders including natural language processing-derived auxiliary covariates

Multiple imputation (MI) models can be improved by including auxiliary covariates (AC), but their performance in high-dimensional data is not well understood. We aimed to develop and compare high-dimensional MI (HDMI) approaches using structured and natural language processing (NLP)-derived AC in studies with partially observed confounders. We conducted a plasmode simulation study using data from opioid vs. non-steroidal anti-inflammatory drug (NSAID) initiators (X) with observed serum creatinine labs (Z2) and time-to-acute kidney injury as outcome. We simulated 100 cohorts with a null treatment effect, including X, Z2, atrial fibrillation (U), and 13 other investigator-derived confounders (Z1) in the outcome generation. We then imposed missingness (MZ2) on 50% of Z2 measurements as a function of Z2 and U and created different HDMI candidate AC using structured and NLP-derived features. We mimicked scenarios where U was unobserved by omitting it from all AC candidate sets. Using LASSO, we data-adaptively selected HDMI covariates associated with Z2 and MZ2 for MI, and with U to include in propensity score models. The treatment effect was estimated following propensity score matching in MI datasets and we benchmarked HDMI approaches against a baseline imputation and complete case analysis with Z1 only. HDMI using claims data showed the lowest bias (0.072). Combining claims and sentence embeddings led to an improvement in the efficiency displaying the lowest root-mean-squared-error (0.173) and coverage (94%). NLP-derived AC alone did not perform better than baseline MI. HDMI approaches may decrease bias in studies with partially observed confounders where missingness depends on unobserved factors.

stat.ME↗

arXiv2022

A note on the random triadic process

For a fixed integer $r\geqslant 3$, let $\mathbb{H}_r(n,p)$ be a random $r$-uniform hypergraph on the vertex set $[n]$, where each $r$-set is an edge randomly and independently with probability $p$. The random $r$-generalized triadic process starts with a complete bipartite graph $K_{r-2,n-r+2}$ on the same vertex set, chooses two distinct vertices $x$ and $y$ uniformly at random and iteratively adds $\{x,y\}$ as an edge if there is a subset $Z$ with size $r-2$, denoted as $Z=\{z_1,\cdots,z_{r-2}\}$, such that $\{x,z_i\}$ and $\{y,z_i\}$ for $1\leqslant i\leqslant r-2$ are already edges in the graph and $\{x,y, z_1,\cdots,z_{r-2}\}$ is an edge in $\mathbb{H}_r(n,p)$. The random triadic process is an abbreviation for the random $3$-generalized triadic process. Kor\'{a}ndi et al. proved a sharp threshold probability for the propagation of the random triadic process, that is, if $p= cn^{ - \frac 12}$ for some positive constant $c$, with high probability, the triadic process reaches the complete graph when $c> \frac 12$ and stops at $O(n^{\frac 32})$ edges when $c< \frac 12$. In this note, we consider the final size of the random $r$-generalized triadic process when $p=o( n^{- \frac 12}\log^{ \alpha(3-r)} n)$ with a constant $\alpha> \frac 12$. We show that the generated graph of the process essentially behaves like $\mathbb{G}(n,p)$. The final number of added edges in the process, with high probability, equals $ \frac {1}{2}n^{2}p(1\pm o(1))$ provided that $p=\omega(n^{-2})$. The results partially complement the ones on the case of $r=3$.

math.CO↗

arXiv2022

On partial Steiner $(n,r,\ell)$-system process

For given integers $r$ and $\ell$ such that $2\leqslant\ell\leqslant r-1$, an $r$-uniform hypergraph $H$ is called a partial Steiner $(n,r,\ell)$-system, if every subset of size $\ell$ lies in at most one edge of $H$. In particular, partial Steiner $(n,r,2)$-systems are also called linear hypergraphs. The partial Steiner $(n,r,\ell)$-system process starts with an empty hypergraph on vertex set $[n]$ at time $0$, the $ \binom{n}{r}$ edges arrive one by one according to a uniformly chosen permutation, and each edge is added if and only if it does not overlap any of the previously-added edges in $\ell$ or more vertices. In this paper, we show with high probability, independent of $\ell$, the sharp threshold of connectivity in the algorithm is $ \frac{n}{r}\log n$ and the very edge which links the last isolated vertex with another vertex makes the partial Steiner $(n,r,\ell)$-system connected.

math.CO↗

arXiv2022

Large induced distance matchings in certain sparse random graphs

For a fixed integer $k\geqslant 2$, let $G\in \mathcal{G}(n,p)$ be a simple connected graph on $n\rightarrow\infty$ vertices with the expected degree $d=np$ satisfying $d\geqslant c$ and $d^{k-1}= o(n)$ for some large enough constant $c$. We show that the asymptotical size of any maximal collection of edges $M$ in $G$ such that no two edges in $M$ are within distance $k$, which is called a distance $k$-matching, is between $ \frac{(k-1)n\log d}{4d^{k-1}}$ and $ \frac{k n \log d}{2d^{k-1}}$. We also design a randomized greedy algorithm to generate one large distance $k$-matching in $G$ with asymptotical size $ \frac{kn\log d}{4d^{k-1}}$. Our results partially generalize the results on the size of the largest distance $k$-matchings from the case $k=2$ or $d=c$ for some large constant $c$.

math.CO↗

arXiv2022

Random $K_k$-removal algorithm

One interesting question is how a graph develops from some constrained random graph process, which is a fundamental mechanism in the formation and evolution of dynamic networks. The problem here is referred to the random $K_k$-removal algorithm. For a fixed integer $k\geqslant 3$, it starts with a complete graph on $n\rightarrow\infty$ vertices and iteratively removes the edges of an uniformly chosen $K_k$. This algorithm terminates once no $K_k$s remain and at the same time it generates one linear $k$-uniform hypergraph. For $k=3$, it was shown that the size in the final graph is $n^{3/2+o(1)}$. Less results are on the cases when $k\geqslant 4$. In this paper, we prove that the exact expected trajectories of various key parameters in the algorithm to some iteration such that the final size in the algorithm is at most $n^{2-1/(k(k-1)-2)+o(1)}$ for $k\geqslant 4$. We also show the bound is a natural barrier.

math.CO↗

arXiv2021

On the number of linear multipartite hypergraphs with given size

For any given integer $r\geqslant 3$, let $k=k(n)$ be an integer with $r\leqslant k\leqslant n$. A hypergraph is $r$-uniform if each edge is a set of $r$ vertices, and is said to be linear if two edges intersect in at most one vertex. Let $A_1,\ldots,A_k$ be a given $k$-partition of $[n]$ with $|A_i|=n_i\geqslant 1$. An $r$-uniform hypergraph $H$ is called {\it $k$-partite} if each edge $e$ satisfies $|e\cap A_i|\leqslant 1$ for $1\leqslant i\leqslant k$. In this paper, the number of linear $k$-partite $r$-uniform hypergraphs on $n\to\infty$ vertices is determined asymptotically when the number of edges is $m(n)=o(n^{\frac{4}{3}})$. For $k=n$, it is the number of linear $r$-uniform hypergraphs on vertex set $[n]$ with $m=o(n^{ \frac{4}{3}})$ edges.

math.CO↗

arXiv2019

Asymptotic enumeration of linear hypergraphs with given number of vertices and edges

For $n\geq 3$, let $r=r(n)\geq 3$ be an integer. A hypergraph is $r$-uniform if each edge is a set of $r$ vertices, and is said to be linear if two edges intersect in at most one vertex. In this paper, the number of linear $r$-uniform hypergraphs on $n\to\infty$ vertices is determined asymptotically when the number of edges is $m(n)=o(r^{-3}n^{ \frac32})$. As one application, we find the probability of linearity for the independent-edge model of random $r$-uniform hypergraph when the expected number of edges is $o(r^{-3}n^{ \frac32})$. We also find the probability that a random $r$-uniform linear hypergraph with a given number of edges contains a given subhypergraph.

math.CO↗

arXiv2018

Social Vehicle Swarms: A Novel Perspective on Social-aware Vehicular Communication Architecture

Internet of vehicles is a promising area related to D2D communication and internet of things. We present a novel perspective for vehicular communications, social vehicle swarms, to study and analyze socially aware internet of vehicles with the assistance of an agent-based model intended to reveal hidden patterns behind superficial data. After discussing its components, namely its agents, environments, and rules, we introduce supportive technology and methods, deep reinforcement learning, privacy preserving data mining and sub-cloud computing, in order to detect the most significant and interesting information for each individual effectively, which is the key desire. Finally, several relevant research topics and challenges are discussed.

cs.CY↗

arXiv2017

Effect of sea quarks on single-spin asymmetries $A^{W^{\pm}}_{N}$ in transversely polarized pp collisions at RHIC

We calculate the single-spin asymmetries $A^{W^{\pm}}_{N}$ of $W^{\pm}$ bosons produced in transversely polarized pp collisions with the valence part of the up (u) and down (d) quark Sivers functions treated by an available parametrization and the light-cone quark spectator-diquark model respectively, while the sea part Sivers functions of u and d quarks treated as parametrization. Comparing our results with those from experimental data at RHIC, we find that the Sivers functions of sea quarks play an important role in the determination of the shapes of $A^{W^{\pm}}_{N}$. It is shown that $A^{W^{-}}_{N}$ is sensitive to u sea Sivers function, while $A^{W^{+}}_{N}$ to d sea Sivers function intuitively. The results show that the contributions of u and d sea Sivers functions are rather sizable and of the same sign, and their signs agree with that of d valence quarks and are opposite to that of u valence quarks.

hep-ph↗

arXiv2017

Effect of sea quarks on the single-spin asymmetries $A^{W^{\pm}}_{L}$ in polarized pp collisions at RHIC

We calculate the single-spin asymmetries $A^{W^{\pm}}_{L}$ of $W^{\pm}$ bosons produced in polarized pp collisions with the valence part of the up and down quark helicity distributions modeled by the light-cone quark-spectator-diquark model while the sea part helicity distributions of the up and down quarks treated as parametrization. Comparing our results with those from experimental data at RHIC, we find that the helicity distributions of sea quarks play an important role in the determination of the shapes of $A^{W^{\pm}}_{L}$. It is shown that $A^{W^{-}}_{L}$ is sensitive to $Δ\bar u$, while $A^{W^{+}}_{L}$ to $Δ\bar d$ intuitively. The experimental data of the polarized structure functions and the sum of helicities are also important to constrain the sizes of quark helicity distributions both for the sea part and the valence part of the nucleon.

hep-ph↗

arXiv2017

Combined analysis of jet substructure for Higgs decay to $b\bar{b}$ in vector boson associated production at the 13 TeV LHC

We study the Standard Model Higgs and vector boson associated production with large transvese momentum at the 13 TeV LHC, followed by Higgs decay to bottom quark pair. Using mass-drop tagging and filtering techiques, we obtained the cross section of signal and background. The background mainly come from $Vb\bar{b}$, $t\bar{t}$ and single top production. In order to suppress them further, we combined the mass-drop tagging and filtering analysis with $N$-subjettiness jet shape. After performing $N$-subjettiness identification, the significance can be enhanced to 3.52$σ$ with current integrated luminosity of $13.2 {\rm fb}^{-1}$. $H\to b\bar{b}$ decay channel is expected to reach 5$σ$ with $27\,{\rm fb}^{-1}$ at the 13 TeV LHC.

hep-ph↗