arXiv subjects

Jiayi Lian

Publications and source records attributed to Jiayi Lian.

10 recordsLinked to original sources

arXiv2026

An Improved Pseudopolynomial Time Algorithm for Subset Sum

We investigate pseudo-polynomial time algorithms for Subset Sum. Given a multi-set $X$ of $n$ positive integers and a target $t$, Subset Sum asks whether some subset of $X$ sums to $t$. Bringmann proposes an $\tilde{O}(n + t)$-time algorithm [Bringmann SODA'17], and an open question has naturally arisen: can Subset Sum be solved in $O(n + w)$ time? Here $w$ is the maximum integer in $X$. We make a progress towards resolving the open question by proposing an $\tilde{O}(n + \sqrt{wt})$-time algorithm.

cs.DS↗

arXiv2025

Weakly Approximating Knapsack in Subquadratic Time

We consider the classic Knapsack problem. Let $t$ and $\mathrm{OPT}$ be the capacity and the optimal value, respectively. If one seeks a solution with total profit at least $\mathrm{OPT}/(1 + \varepsilon)$ and total weight at most $t$, then Knapsack can be solved in $\tilde{O}(n + (\frac{1}{\varepsilon})^2)$ time [Chen, Lian, Mao, and Zhang '24][Mao '24]. This running time is the best possible (up to a logarithmic factor), assuming that $(\min,+)$-convolution cannot be solved in truly subquadratic time [Künnemann, Paturi, and Schneider '17][Cygan, Mucha, Węgrzycki, and Włodarczyk '19]. The same upper and lower bounds hold if one seeks a solution with total profit at least $\mathrm{OPT}$ and total weight at most $(1 + \varepsilon)t$. Therefore, it is natural to ask the following question. If one seeks a solution with total profit at least $\mathrm{OPT}/(1+\varepsilon)$ and total weight at most $(1 + \varepsilon)t$, can Knsapck be solved in $\tilde{O}(n + (\frac{1}{\varepsilon})^{2-δ})$ time for some constant $δ> 0$? We answer this open question affirmatively by proposing an $\tilde{O}(n + (\frac{1}{\varepsilon})^{7/4})$-time algorithm.

cs.DS↗

arXiv2025

Bridging the Data Gap in AI Reliability Research and Establishing DR-AIR, a Comprehensive Data Repository for AI Reliability

Artificial intelligence (AI) technology and systems have been advancing rapidly. However, ensuring the reliability of these systems is crucial for fostering public confidence in their use. This necessitates the modeling and analysis of reliability data specific to AI systems. A major challenge in AI reliability research, particularly for those in academia, is the lack of readily available AI reliability data. To address this gap, this paper focuses on conducting a comprehensive review of available AI reliability data and establishing DR-AIR: a data repository for AI reliability. Specifically, we introduce key measurements and data types for assessing AI reliability, along with the methodologies used to collect these data. We also provide a detailed description of the currently available datasets with illustrative examples. Furthermore, we outline the setup of the DR-AIR repository and demonstrate its practical applications. This repository provides easy access to datasets specifically curated for AI reliability research. We believe these efforts will significantly benefit the AI research community by facilitating access to valuable reliability data and promoting collaboration across various academic domains within AI. We conclude our paper with a call to action, encouraging the research community to contribute and share AI reliability data to further advance this critical field of study.

stat.AP↗

arXiv2025

A Note on Deterministic FPTAS for Partition

We consider the Partition problem and propose a deterministic FPTAS (Fully Polynomial-Time Approximation Scheme) that runs in $\widetilde{O}(n + 1/\varepsilon)$-time. This is the best possible (up to a polylogarithmic factor) assuming the Strong Exponential Time Hypothesis~[Abboud, Bringmann, Hermelin, and Shabtay'22]. Prior to our work, only a randomized algorithm can achieve a running time of $\widetilde{O}(n + 1/\varepsilon)$~[Chen, Lian, Mao and Zhang '24], while the best deterministic algorithm runs in $\widetilde{O}(n+1/\varepsilon^{5/4})$ time~[Deng, Jin and Mao '23] and [Wu and Chen '22].

cs.DS↗

arXiv2025

A Nearly Quadratic-Time FPTAS for Knapsack

We investigate the classic Knapsack problem and propose a fully polynomial-time approximation scheme (FPTAS) that runs in $\widetilde{O}(n + (1/\varepsilon)^2)$ time. This improves upon the $\widetilde{O}(n + (1/\varepsilon)^{11/5})$-time algorithm by Deng, Jin, and Mao [\textit{Proceedings of the 2023 Annual ACM-SIAM Symposium on Discrete Algorithms, 2023}]. Our algorithm is the best possible (up to a polylogarithmic factor) conditioned on the conjecture that $(\min, +)$-convolution has no truly subquadratic-time algorithm, since this conjecture implies that Knapsack has no $O((n + 1/\varepsilon)^{2-δ})$-time FPTAS for any constant $δ> 0$.

cs.DS↗

arXiv2024

Approximating Partition in Near-Linear Time

We propose an $\widetilde{O}(n + 1/\eps)$-time FPTAS (Fully Polynomial-Time Approximation Scheme) for the classical Partition problem. This is the best possible (up to a polylogarithmic factor) assuming SETH (Strong Exponential Time Hypothesis) [Abboud, Bringmann, Hermelin, and Shabtay'22]. Prior to our work, the best known FPTAS for Partition runs in $\widetilde{O}(n + 1/\eps^{5/4})$ time [Deng, Jin and Mao'23, Wu and Chen'22]. Our result is obtained by solving a more general problem of weakly approximating Subset Sum.

cs.DS↗

arXiv2023

Faster Algorithms for Bounded Knapsack and Bounded Subset Sum Via Fine-Grained Proximity Results

We investigate pseudopolynomial-time algorithms for Bounded Knapsack and Bounded Subset Sum. Recent years have seen a growing interest in settling their fine-grained complexity with respect to various parameters. For Bounded Knapsack, the number of items $n$ and the maximum item weight $w_{\max}$ are two of the most natural parameters that have been studied extensively in the literature. The previous best running time in terms of $n$ and $w_{\max}$ is $O(n + w^3_{\max})$ [Polak, Rohwedder, Wegrzycki '21]. There is a conditional lower bound of $O((n + w_{\max})^{2-o(1)})$ based on $(\min,+)$-convolution hypothesis [Cygan, Mucha, Wegrzycki, Wlodarczyk '17]. We narrow the gap significantly by proposing a $\tilde{O}(n + w^{12/5}_{\max})$-time algorithm. Note that in the regime where $w_{\max} \approx n$, our algorithm runs in $\tilde{O}(n^{12/5})$ time, while all the previous algorithms require $Ω(n^3)$ time in the worst case. For Bounded Subset Sum, we give two algorithms running in $\tilde{O}(nw_{\max})$ and $\tilde{O}(n + w^{3/2}_{\max})$ time, respectively. These results match the currently best running time for 0-1 Subset Sum. Prior to our work, the best running times (in terms of $n$ and $w_{\max}$) for Bounded Subset Sum is $\tilde{O}(n + w^{5/3}_{\max})$ [Polak, Rohwedder, Wegrzycki '21] and $\tilde{O}(n + μ_{\max}^{1/2}w_{\max}^{3/2})$ [implied by Bringmann '19 and Bringmann, Wellnitz '21], where $μ_{\max}$ refers to the maximum multiplicity of item weights.

cs.DS↗

arXiv2023

On Block Cholesky Decomposition for Sparse Inverse Covariance Estimation

The modified Cholesky decomposition is popular for inverse covariance estimation, but often needs pre-specification on the full information of variable ordering. In this work, we propose a block Cholesky decomposition (BCD) for estimating inverse covariance matrix under the partial information of variable ordering, in the sense that the variables can be divided into several groups with available ordering among groups, but variables within each group have no orderings. The proposed BCD model provides a unified framework for several existing methods including the modified Cholesky decomposition and the Graphical lasso. By utilizing the partial information on variable ordering, the proposed BCD model guarantees the positive definiteness of the estimated matrix with statistically meaningful interpretation. Theoretical results are established under regularity conditions. Simulation and case studies are conducted to evaluate the proposed BCD model.

stat.ME↗

arXiv2021

Statistical Perspectives on Reliability of Artificial Intelligence Systems

Artificial intelligence (AI) systems have become increasingly popular in many areas. Nevertheless, AI technologies are still in their developing stages, and many issues need to be addressed. Among those, the reliability of AI systems needs to be demonstrated so that the AI systems can be used with confidence by the general public. In this paper, we provide statistical perspectives on the reliability of AI systems. Different from other considerations, the reliability of AI systems focuses on the time dimension. That is, the system can perform its designed functionality for the intended period. We introduce a so-called SMART statistical framework for AI reliability research, which includes five components: Structure of the system, Metrics of reliability, Analysis of failure causes, Reliability assessment, and Test planning. We review traditional methods in reliability data analysis and software reliability, and discuss how those existing methods can be transformed for reliability modeling and assessment of AI systems. We also describe recent developments in modeling and analysis of AI reliability and outline statistical research challenges in this area, including out-of-distribution detection, the effect of the training set, adversarial attacks, model accuracy, and uncertainty quantification, and discuss how those topics can be related to AI reliability, with illustrative examples. Finally, we discuss data collection and test planning for AI reliability assessment and how to improve system designs for higher AI reliability. The paper closes with some concluding remarks.

cs.SE↗

arXiv2020

Investigating the Robustness of Artificial Intelligent Algorithms with Mixture Experiments

Artificial intelligent (AI) algorithms, such as deep learning and XGboost, are used in numerous applications including computer vision, autonomous driving, and medical diagnostics. The robustness of these AI algorithms is of great interest as inaccurate prediction could result in safety concerns and limit the adoption of AI systems. In this paper, we propose a framework based on design of experiments to systematically investigate the robustness of AI classification algorithms. A robust classification algorithm is expected to have high accuracy and low variability under different application scenarios. The robustness can be affected by a wide range of factors such as the imbalance of class labels in the training dataset, the chosen prediction algorithm, the chosen dataset of the application, and a change of distribution in the training and test datasets. To investigate the robustness of AI classification algorithms, we conduct a comprehensive set of mixture experiments to collect prediction performance results. Then statistical analyses are conducted to understand how various factors affect the robustness of AI classification algorithms. We summarize our findings and provide suggestions to practitioners in AI applications.

stat.ML↗