arXiv subjects

Haoming Shi

Publications and source records attributed to Haoming Shi.

6 recordsLinked to original sources

arXiv2026

Tight Bandwidth Lower Bounds and Optimal Constructions of Locally Repairable Convertible Codes in the Global Split Regime

Erasure coding is a key technique for providing fault tolerance in modern distributed storage systems. In practice, as storage systems evolve, the parameters of the deployed erasure code may need to be adjusted to accommodate changes in storage scale, reliability requirements, and disk failure rates. Such adaptation is achieved through code conversion, which transforms data encoded by an initial code into data encoded by a final code. Convertible codes are designed to carry out this transformation efficiently while preserving desirable code properties. In this work, we study code conversion between systematic optimal-distance locally repairable codes (LRCs) in the global split regime, using read bandwidth as the conversion-efficiency metric. Specifically, we focus on the parameter range $g^I,g^F \leq r$, where the numbers of initial and final global parity nodes are at most the local information dimension $r$. Over this entire parameter range, we derive lower bounds on the read bandwidth of stable optimal-distance locally repairable convertible codes (LRCCs) via an information-theoretic approach, without imposing any linearity assumption on the initial codes, the final codes, or the conversion procedure. We then develop constructions based on MDS array codes with prescribed repair or alignment properties. Depending on the relative sizes of $g^I$ and $g^F$, we handle the construction separately in the three cases $g^F=g^I$, $g^F>g^I$, and $g^F<g^I$, and show that each attains the corresponding lower bound. This yields a complete characterization of the optimal read bandwidth for stable optimal-distance LRCCs over the entire parameter range $g^I,g^F\le r$.

cs.IT↗

arXiv2026

Transfer Learning for Robust Structured Regression with Bi-level Source Detection

High-dimensional data in modern applications, such as COVID-19 mortality, often span multiple domains. Leveraging auxiliary information from source domains to improve performance in a target domain motivates the use of transfer learning. However, a practical issue that has been overlooked is data contamination, which induces heterogeneity and can significantly degrade transfer learning performance. To address this challenge, we propose a novel approach that tackles transfer learning under data contamination within a structured regression setting. By employing the robust L2E criterion, we develop the TransL2E method that accounts for contamination in both target and source data while effectively transferring relevant information. Beyond robust estimation, TransL2E introduces a data-driven bi-level source detection mechanism, operating at both individual and cohort levels, which possesses multiple advantages over existing source detection approaches. Comprehensive simulation studies and a real data application demonstrate the superior performance of TransL2E in both robust estimation and structure recovery in the presence of data limitation and contamination.

stat.ME↗

arXiv2026

Asymptotic Optimism for Tensor Regression Models with Applications to Neural Network Compression

We study rank selection for low-rank tensor regression under random covariates design. Under a Gaussian random-design model and some mild conditions, we derive population expressions for the expected training-testing discrepancy (optimism) for both CP and Tucker decomposition. We further demonstrate that the optimism is minimized at the true tensor rank for both CP and Tucker regression. This yields a prediction-oriented rank-selection rule that aligns with cross-validation and extends naturally to tensor-model averaging. We also discuss conditions under which under- or over-ranked models may appear preferable, thereby clarifying the scope of the method. Finally, we showcase its practical utility on a real-world image regression task and extend its application to tensor-based compression of neural network, highlighting its potential for model selection in deep learning.

stat.ML↗

arXiv2025

New Constructions of Optimal $(r,\delta)$-LRCs via Algebraic Function Fields

Constructing optimal $(r,\delta)$-LRCs that attain the Singleton-type bound is an active and important research direction, particularly due to their practical applications in distributed storage systems. In this paper, we focus on the construction of optimal $(r,\delta)$-LRCs with flexible minimum distances, especially for the case $\delta \geq 3$. We first extend a general framework -- originally proposed by Li \textit{et al.} (IEEE Trans. Inf. Theory, vol. 65, no. 1, 2019) and Ma and Xing (J. Comb. Theory Ser. A., vol. 193, 2023) -- for constructing optimal $r$-LRCs via automorphism groups of elliptic function fields to the case of $(r,\delta)$-LRCs. This newly extended general framework relies on certain conditions concerning the group law of elliptic curves. By carefully selecting elliptic function fields suitable for this framework, we arrive at several families of explicit $q$-ary optimal $(r,3)$-LRCs and $(2,\delta)$-LRCs with lengths slightly less than $q + 2\sqrt{q}$. Next, by employing automorphism groups of hyperelliptic function fields of genus $2$, we develop a framework for constructing optimal $(r,3)$-LRCs and obtain a family of explicit $q$-ary optimal $(4,3)$-LRCs with code lengths slightly below $q+4\sqrt{q}$. We then consider the construction of optimal $(r,\delta)$-LRCs via hyperelliptic function fields of arbitrary genus $g \geq 2$, yielding a class of explicit $q$-ary optimal $(g+1-g',g+1+g')$-LRCs for $0 \leq g' \leq g-1$ with lengths up to $q + 2g\sqrt{q}$. Finally, applying certain superelliptic curves derived from modified Norm-Trace curves, we construct two families of explicit optimal $(r,\delta)$-LRCs with even longer code lengths and more flexible parameters. Notably, many of the newly constructed optimal $(r,\delta)$-LRCs attain the largest known lengths among existing constructions with flexible minimum distances.

cs.IT↗

arXiv2025

Robust Spatiotemporal Epidemic Modeling with Integrated Adaptive Outlier Detection

In epidemic modeling, outliers can distort parameter estimation and ultimately lead to misguided public health decisions. Although there are existing robust methods that can mitigate this distortion, the ability to simultaneously detect outliers is equally vital for identifying potential disease hotspots. In this work, we introduce a robust spatiotemporal generalized additive model (RST-GAM) to address this need. We accomplish this with a mean-shift parameter to quantify and adjust for the effects of outliers and rely on adaptive Lasso regularization to model the sparsity of outlying observations. We use univariate polynomial splines and bivariate penalized splines over triangulations to estimate the functional forms and a data-thinning approach for data-adaptive weight construction. We derive a scalable proximal algorithm to estimate model parameters by minimizing a convex negative log-quasi-likelihood function. Our algorithm uses adaptive step-sizes to ensure global convergence of the resulting iterate sequence. We establish error bounds and selection consistency for the estimated parameters and demonstrate our model's effectiveness through numerical studies under various outlier scenarios. Finally, we demonstrate the practical utility of RST-GAM by analyzing county-level COVID-19 infection data in the United States, highlighting its potential to inform public health decision-making.

stat.ME↗

arXiv2025

Bounds and Optimal Constructions of Generalized Merge-Convertible Codes for Code Conversion into LRCs

Error-correcting codes are essential for ensuring fault tolerance in modern distributed data storage systems. However, in practice, factors such as the failure rates of storage devices can vary significantly over time, resulting in changes to the optimal code parameters. To reduce storage cost while maintaining efficiency, Maturana and Rashmi introduced a theoretical framework known as code conversion, which enables dynamic adjustment of code parameters according to device performance. In this paper, we focus exclusively on the bounds and constructions of generalized merge-convertible codes. First, we establish a new lower bound on the access cost when the final code is an $(r,\delta)$-LRC. This bound unifies and generalizes all previously known bounds for merge conversion, where the initial and final codes are either LRCs or MDS codes. We then construct a family of access-optimal MDS convertible codes by leveraging subgroups of the automorphism group of a rational function field. It is worth noting that our construction is also per-symbol read access-optimal. Next, we further extend our MDS-based construction to design access-optimal convertible codes for the conversion between $(r,\delta)$-LRCs with parameters that have not been previously reported. Finally, using the parity-check matrix approach, we present a construction of access-optimal convertible codes that enable merge conversion from MDS codes to an $(r,\delta)$-LRC. To the best of our knowledge, this is the first explicit optimal construction of code conversion between MDS codes and LRCs. All of our constructions are performed over finite fields whose sizes grow linearly with the code length.

cs.IT↗