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Shi Li

Publications and source records attributed to Shi Li.

At least 55 records · Page 3Linked to original sources
arXiv2025

Exploring Neural Ordinary Differential Equations as Interpretable Healthcare classifiers

Deep Learning has emerged as one of the most significant innovations in machine learning. However, a notable limitation of this field lies in the ``black box" decision-making processes, which have led to skepticism within groups like healthcare and scientific communities regarding its applicability. In response, this study introduces a interpretable approach using Neural Ordinary Differential Equations (NODEs), a category of neural network models that exploit the dynamics of differential equations for representation learning. Leveraging their foundation in differential equations, we illustrate the capability of these models to continuously process textual data, marking the first such model of its kind, and thereby proposing a promising direction for future research in this domain. The primary objective of this research is to propose a novel architecture for groups like healthcare that require the predictive capabilities of deep learning while emphasizing the importance of model transparency demonstrated in NODEs.

cs.LG↗
arXiv2025

An Optimization Algorithm for Multimodal Data Alignment

In the data era, the integration of multiple data types, known as multimodality, has become a key area of interest in the research community. This interest is driven by the goal to develop cutting edge multimodal models capable of serving as adaptable reasoning engines across a wide range of modalities and domains. Despite the fervent development efforts, the challenge of optimally representing different forms of data within a single unified latent space a crucial step for enabling effective multimodal reasoning has not been fully addressed. To bridge this gap, we introduce AlignXpert, an optimization algorithm inspired by Kernel CCA crafted to maximize the similarities between N modalities while imposing some other constraints. This work demonstrates the impact on improving data representation for a variety of reasoning tasks, such as retrieval and classification, underlining the pivotal importance of data representation.

cs.LG↗
arXiv2025

A Collection of Innovations in Medical AI for patient records in 2024

The field of Artificial Intelligence in healthcare is evolving at an unprecedented pace, driven by rapid advancements in machine learning and the recent breakthroughs in large language models. While these innovations hold immense potential to transform clinical decision making, diagnostics, and patient care, the accelerating speed of AI development has outpaced traditional academic publishing cycles. As a result, many scholarly contributions quickly become outdated, failing to capture the latest state of the art methodologies and their real world implications. This paper advocates for a new category of academic publications an annualized citation framework that prioritizes the most recent AI driven healthcare innovations. By systematically referencing the breakthroughs of the year, such papers would ensure that research remains current, fostering a more adaptive and informed discourse. This approach not only enhances the relevance of AI research in healthcare but also provides a more accurate reflection of the fields ongoing evolution.

cs.CY↗
arXiv2024

Energy Efficient Offloading Policies in Multi-Access Edge Computing Systems with Task Handover

The rapid growth of mobile devices and the increasing complexity of tasks have made energy efficiency a critical challenge in Multi-Access Edge Computing (MEC) systems. This paper explores energy-efficient offloading strategies in large-scale MEC systems with heterogeneous mobile users, diverse network components, and frequent task handovers to capture user mobility. The problem is inherently complex due to the system's scale, task and resource diversity, and the need to maintain real-time performance. Traditional optimization approaches are often computationally infeasible for such scenarios. To tackle these challenges, we model the offloading problem using the restless multi-armed bandit (RMAB) framework and develop two scalable online policies that prioritize resources based on their marginal costs. The proposed policies dynamically adapt to the system's heterogeneity and mobility while ensuring near-optimal energy efficiency. Through extensive numerical simulations, we demonstrate that the policies significantly outperform baseline methods in power conservation and show robust performance under non-exponentially distributed task lifespans. These results highlight the practical applicability and scalability of our approach in dynamic MEC environments.

cs.DC↗
arXiv2024

Simultaneously Approximating All Norms for Massively Parallel Correlation Clustering

We revisit the simultaneous approximation model for the correlation clustering problem introduced by Davies, Moseley, and Newman[DMN24]. The objective is to find a clustering that minimizes given norms of the disagreement vector over all vertices. We present an efficient algorithm that produces a clustering that is simultaneously a $63.3$-approximation for all monotone symmetric norms. This significantly improves upon the previous approximation ratio of $6348$ due to Davies, Moseley, and Newman[DMN24], which works only for $\ell_p$-norms. To achieve this result, we first reduce the problem to approximating all top-$k$ norms simultaneously, using the connection between monotone symmetric norms and top-$k$ norms established by Chakrabarty and Swamy [CS19]. Then we develop a novel procedure that constructs a $12.66$-approximate fractional clustering for all top-$k$ norms. Our $63.3$-approximation ratio is obtained by combining this with the $5$-approximate rounding algorithm by Kalhan, Makarychev, and Zhou[KMZ19]. We then demonstrate that with a loss of $ε$ in the approximation ratio, the algorithm can be adapted to run in nearly linear time and in the MPC (massively parallel computation) model with poly-logarithmic number of rounds. By allowing a further trade-off in the approximation ratio to $(359+ε)$, the number of MPC rounds can be reduced to a constant.

cs.DS↗
arXiv2024

Approximating Unrelated Machine Weighted Completion Time Using Iterative Rounding and Computer Assisted Proofs

We revisit the unrelated machine scheduling problem with the weighted completion time objective. It is known that independent rounding achieves a 1.5 approximation for the problem, and many prior algorithms improve upon this ratio by leveraging strong negative correlation schemes. On each machine $i$, these schemes introduce strong negative correlation between events that some pairs of jobs are assigned to $i$, while maintaining non-positive correlation for all pairs. Our algorithm deviates from this methodology by relaxing the pairwise non-positive correlation requirement. On each machine $i$, we identify many groups of jobs. For a job $j$ and a group $B$ not containing $j$, we only enforce non-positive correlation between $j$ and the group as a whole, allowing $j$ to be positively-correlated with individual jobs in $B$. This relaxation suffices to maintain the 1.5-approximation, while enabling us to obtain a much stronger negative correlation within groups using an iterative rounding procedure: at most one job from each group is scheduled on $i$. We prove that the algorithm achieves a $(1.36 + ε)$-approximation, improving upon the previous best approximation ratio of $1.4$ due to Harris. While the improvement may not be substantial, the significance of our contribution lies in the relaxed non-positive correlation condition and the iterative rounding framework. Due to the simplicity of our algorithm, we are able to derive a closed form for the weighted completion time our algorithm achieves with a clean analysis. Unfortunately, we could not provide a good analytical analysis for the quantity; instead, we rely on a computer assisted proof.

cs.DS↗
arXiv2024

Polylogarithmic Approximation for Robust s-t Path

The paper revisits the robust $s$-$t$ path problem, one of the most fundamental problems in robust optimization. In the problem, we are given a directed graph with $n$ vertices and $k$ distinct cost functions (scenarios) defined over edges, and aim to choose an $s$-$t$ path such that the total cost of the path is always provable no matter which scenario is realized. With the view of each cost function being associated with an agent, our goal is to find a common $s$-$t$ path minimizing the maximum objective among all agents, and thus create a fair solution for them. The problem is hard to approximate within $o(\log k)$ by any quasi-polynomial time algorithm unless $\mathrm{NP} \subseteq \mathrm{DTIME}(n^{\mathrm{poly}\log n})$, and the best approximation ratio known to date is $\widetilde{O}(\sqrt{n})$ which is based on the natural flow linear program. A longstanding open question is whether we can achieve a polylogarithmic approximation even when a quasi-polynomial running time is allowed. We give the first polylogarithmic approximation for robust $s$-$t$ path since the problem was proposed more than two decades ago. In particular, we introduce a $O(\log n \log k)$-approximate algorithm running in quasi-polynomial time. The algorithm is built on a novel linear program formulation for a decision-tree-type structure which enables us to get rid of the $Ω(\max\{k,\sqrt{n}\})$ integrality gap of the natural flow LP. Further, we also consider some well-known graph classes, e.g., graphs with bounded treewidth, and show that the polylogarithmic approximation can be achieved polynomially on these graphs. We hope the new proposed techniques in the paper can offer new insights into the robust $s$-$t$ path problem and related problems in robust optimization.

cs.DS↗
arXiv2024

Machine Learning in Short-Reach Optical Systems: A Comprehensive Survey

In recent years, extensive research has been conducted to explore the utilization of machine learning algorithms in various direct-detected and self-coherent short-reach communication applications. These applications encompass a wide range of tasks, including bandwidth request prediction, signal quality monitoring, fault detection, traffic prediction, and digital signal processing (DSP)-based equalization. As a versatile approach, machine learning demonstrates the ability to address stochastic phenomena in optical systems networks where deterministic methods may fall short. However, when it comes to DSP equalization algorithms, their performance improvements are often marginal, and their complexity is prohibitively high, especially in cost-sensitive short-reach communications scenarios such as passive optical networks (PONs). They excel in capturing temporal dependencies, handling irregular or nonlinear patterns effectively, and accommodating variable time intervals. Within this extensive survey, we outline the application of machine learning techniques in short-reach communications, specifically emphasizing their utilization in high-bandwidth demanding PONs. Notably, we introduce a novel taxonomy for time-series methods employed in machine learning signal processing, providing a structured classification framework. Our taxonomy categorizes current time series methods into four distinct groups: traditional methods, Fourier convolution-based methods, transformer-based models, and time-series convolutional networks. Finally, we highlight prospective research directions within this rapidly evolving field and outline specific solutions to mitigate the complexity associated with hardware implementations. We aim to pave the way for more practical and efficient deployment of machine learning approaches in short-reach optical communication systems by addressing complexity concerns.

eess.SP↗
arXiv2024

Online Load and Graph Balancing for Random Order Inputs

Online load balancing for heterogeneous machines aims to minimize the makespan (maximum machine workload) by scheduling arriving jobs with varying sizes on different machines. In the adversarial setting, where an adversary chooses not only the collection of job sizes but also their arrival order, the problem is well-understood and the optimal competitive ratio is known to be $Θ(\log m)$ where $m$ is the number of machines. In the more realistic random arrival order model, the understanding is limited. Previously, the best lower bound on the competitive ratio was only $Ω(\log \log m)$. We significantly improve this bound by showing an $Ω( \sqrt {\log m})$ lower bound, even for the restricted case where each job has a unit size on two machines and infinite size on the others. On the positive side, we propose an $O(\log m/\log \log m)$-competitive algorithm, demonstrating that better performance is possible in the random arrival model.

cs.DS↗
arXiv2023

Handling Correlated Rounding Error via Preclustering: A 1.73-approximation for Correlation Clustering

We consider the classic Correlation Clustering problem: Given a complete graph where edges are labelled either $+$ or $-$, the goal is to find a partition of the vertices that minimizes the number of the \pedges across parts plus the number of the \medges within parts. Recently, Cohen-Addad, Lee and Newman [CLN22] presented a 1.994-approximation algorithm for the problem using the Sherali-Adams hierarchy, hence breaking through the integrality gap of 2 for the classic linear program and improving upon the 2.06-approximation of Chawla, Makarychev, Schramm and Yaroslavtsev [CMSY15]. We significantly improve the state-of-the-art by providing a 1.73-approximation for the problem. Our approach introduces a preclustering of Correlation Clustering instances that allows us to essentially ignore the error arising from the {\em correlated rounding} used by [CLN22]. This additional power simplifies the previous algorithm and analysis. More importantly, it enables a new {\em set-based rounding} that complements the previous roundings. A combination of these two rounding algorithms yields the improved bound.

cs.DS↗
arXiv2023

Nearly-Linear Time LP Solvers and Rounding Algorithms for Scheduling Problems

We study nearly-linear time approximation algorithms for non-preemptive scheduling problems in two settings: the unrelated machine setting, and the identical machine with job precedence constraints setting, under the well-studied objectives such as makespan and weighted completion time. For many problems, we develop nearly-linear time approximation algorithms with approximation ratios matching the current best ones achieved in polynomial time. Our main technique is linear programming relaxation. For the unrelated machine setting, we formulate mixed packing and covering LP relaxations of nearly-linear size, and solve them approximately using the nearly-linear time solver of Young. For the makespan objective, we develop a rounding algorithm with $(2+ε)$-approximation ratio. For the weighted completion time objective, we prove the LP is as strong as the rectangle LP used by Im and Li, leading to a nearly-linear time $(1.45 + ε)$-approximation for the problem. For problems in the identical machine with precedence constraints setting, the precedence constraints can not be formulated as packing or covering constraints. To achieve the nearly-linear running time, we define a polytope for the constraints, and leverage the multiplicative weight update (MWU) method with an oracle which always returns solutions in the polytope.

cs.DS↗
arXiv2023

Degrees and Network Design: New Problems and Approximations

While much of network design focuses mostly on cost (number or weight of edges), node degrees have also played an important role. They have traditionally either appeared as an objective, to minimize the maximum degree (e.g., the Minimum Degree Spanning Tree problem), or as constraints which might be violated to give bicriteria approximations (e.g., the Minimum Cost Degree Bounded Spanning Tree problem). We extend the study of degrees in network design in two ways. First, we introduce and study a new variant of the Survivable Network Design Problem where in addition to the traditional objective of minimizing the cost of the chosen edges, we add a constraint that the $\ell_p$-norm of the node degree vector is bounded by an input parameter. This interpolates between the classical settings of maximum degree (the $\ell_{\infty}$-norm) and the number of edges (the $\ell_1$-degree), and has natural applications in distributed systems and VLSI design. We give a constant bicriteria approximation in both measures using convex programming. Second, we provide a polylogrithmic bicriteria approximation for the Degree Bounded Group Steiner problem on bounded treewidth graphs, solving an open problem from [Kortsarz and Nutov, Discret. Appl. Math. 2022] and [Guo et al., Algorithmica 2022].

cs.DS↗
arXiv2022

Online Unrelated-Machine Load Balancing and Generalized Flow with Recourse

We consider the online unrelated-machine load balancing problem with recourse, where the algorithm is allowed to re-assign prior jobs. We give a $(2+ε)$-competitive algorithm for the problem with $O_ε(\log n)$ amortized recourse per job. This is the first $O(1)$-competitive algorithm for the problem with reasonable recourse, and the competitive ratio nearly matches the long-standing best-known offline approximation guarantee. We also show an $O(\log\log n/\log\log\log n)$-competitive algorithm for the problem with $O(1)$ amortized recourse. The best-known bounds from prior work are $O(\log\log n)$-competitive algorithms with $O(1)$ amortized recourse due to [GKS14], for the special case of the restricted assignment model. Along the way, we design an algorithm for the online generalized network flow problem (also known as network flow problem with gains) with recourse. In the problem, any edge $uv$ in the network has a gain parameter $γ_{uv} > 0$ and $θ$-units of flow sent across $uv$ from $u$'s side becomes $γ_{uv} θ$ units of flow on the $v$'th side. In the online problem, there is one sink, and sources come one by one. Upon arrival of a source, we need to send 1 unit flow from the source. A recourse occurs if we change the flow value of an edge. We give an online algorithm for the problem with recourse at most $O(1/ε)$ times the optimum cost for the instance with capacities scaled by $\frac{1}{1+ε}$. The $(1+ε)$-factor improves upon the corresponding $(2+ε)$-factor of [GKS14], which only works for the ordinary network flow problem. As an immediate corollary, we also give an improved algorithm for the online $b$-matching problem with reassignment costs.

cs.DS↗
arXiv2022

Improved Approximations for Unrelated Machine Scheduling

We revisit two well-studied scheduling problems in the unrelated machines setting where each job can have a different processing time on each machine. For minimizing total weighted completion time we give a 1.45-approximation, which improves upon the previous 1.488-approximation [Im and Shadloo SODA 2020]. The key technical ingredient in this improvement lies in a new rounding scheme that gives strong negative correlation with less restrictions. For minimizing $L_k$-norms of machine loads, inspired by [Kalaitzis et al. SODA 2017], we give better approximation algorithms. In particular we give a $\sqrt {4/3}$-approximation for the $L_2$-norm which improves upon the former $\sqrt 2$-approximations due to [Azar-Epstein STOC 2005] and [Kumar et al. JACM 2009].

cs.DS↗
arXiv2022

Polynomial Integrality Gap of Flow LP for Directed Steiner Tree

In the Directed Steiner Tree (DST) problem, we are given a directed graph $G=(V,E)$ on $n$ vertices with edge-costs $c \in \mathbb{R}_{\geq 0}^E$, a root vertex $r \in V$, and a set $K \subseteq V \setminus \{r\}$ of $k$ terminals. The goal is to find a minimum-cost subgraph of $G$ that contains a path from $r$ to every terminal $t \in K$. DST has been a notorious problem for decades as there is a large gap between the best-known polynomial-time approximation ratio of $O(k^ε)$ for any constant $ε> 0$, and the best quasi-polynomial-time approximation ratio of $O\left(\frac{\log^2 k}{\log \log k}\right)$. Towards understanding this gap, we study the integrality gap of the standard flow LP relaxation for the problem. We show that the LP has an integrality gap of $Ω(n^{0.0418})$. Previously, the integrality gap of the LP is only known to be $Ω\left(\frac{\log^2n}{\log\log n}\right)$ [Halperin~et~al., SODA'03 \& SIAM J.~Comput.] and $Ω(\sqrt{k})$ [Zosin-Khuller, SODA'02] in some instance with $\sqrt{k}=O\left(\frac{\log n}{\log \log n}\right)$. Our result gives the first known lower bound on the integrality gap of this standard LP that is polynomial in $n$, the number of vertices. Consequently, we rule out the possibility of developing a poly-logarithmic approximation algorithm for the problem based on the flow LP relaxation.

cs.DS↗
arXiv2022

Nested Active-Time Scheduling

The active-time scheduling problem considers the problem of scheduling preemptible jobs with windows (release times and deadlines) on a parallel machine that can schedule up to $g$ jobs during each timestep. The goal in the active-time problem is to minimize the number of active steps, i.e., timesteps in which at least one job is scheduled. In this way, the active time models parallel scheduling when there is a fixed cost for turning the machine on at each discrete step. This paper presents a 9/5-approximation algorithm for a special case of the active-time scheduling problem in which job windows are laminar (nested). This result improves on the previous best 2-approximation for the general case.

cs.DS↗