arXiv subjects

Luhao Zhang

Publications and source records attributed to Luhao Zhang.

10 recordsLinked to original sources

arXiv2026

Conformal-DRO: Distributionally Robust Optimization with Conformalized Ambiguity Set

Data-driven distributionally robust optimization (DRO) typically treats the conditional outcome law as fixed and uses ambiguity sets to capture estimation error. This paper studies latent distributional heterogeneity, where each instance has an unobserved law but contributes only one observation, so uncertainty persists even if the mixture law is known. We propose Conformal-DRO, which uses nested conformal regions to construct an ambiguity set for the future latent law. Under exchangeability, the set covers this law with probability at least $1-\alpha$ in finite samples, without estimating underlying latent laws or their mixing mechanism. The conformal path induces a data-driven transport geometry, while $\alpha$ determines the radius. The worst-case problem reduces to a finite linear program over conformal shells and admits sparse adversarial solutions. The resulting robust value provides a finite-sample certificate for the selected decision's expected cost.

math.OC↗

arXiv2026

Integrating Feature Correlation in Differential Privacy with Applications in DP-ERM

Standard differential privacy imposes uniform privacy constraints across all features, overlooking the inherent distinction between sensitive and insensitive features in practice. In this paper, we introduce a relaxed definition of differential privacy that accounts for such heterogeneity, allowing certain features to be treated as insensitive even when correlated with sensitive ones. We propose a correlation-aware framework, $\textsf{CorrDP}$, which relaxes privacy for insensitive features while accounting for their correlations with sensitive features, with the correlations quantified using total variation distance. We design algorithms for differentially private empirical risk minimization (DP-ERM) under the $\textsf{CorrDP}$ framework, incorporating distance-dependent noise into gradients for improved theoretical utility guarantees. When the correlation distance is unknown, we estimate it from the dataset and show that it achieves a comparable privacy-utility guarantee. We perform experiments on synthetic and real-world datasets and show that $\textsf{CorrDP}$-based DP-ERM algorithms consistently outperform the standard DP framework in the presence of insensitive features.

cs.LG↗

arXiv2026

Schr\"odinger bridge with transport relaxation

Motivated by modern machine learning applications where we only have access to empirical measures constructed from finite samples, we relax the marginal constraints of the classical Schr\"odinger bridge problem by penalizing the transport cost between the bridge's marginals and the prescribed marginals. We derive a duality formula for this transport-relaxed bridge and demonstrate that it reduces to a finite-dimensional concave optimization problem when the prescribed marginals are discrete and the reference distribution is absolutely continuous. We establish the existence and uniqueness of solutions for both the primal and dual problems. Moreover, as the penalty blows up, we characterize the limiting bridge as the solution to a discrete Schr\"odinger bridge problem and identify a leading-order logarithmic divergence. Finally, we propose gradient ascent and Sinkhorn-type algorithms to numerically solve the transport-relaxed Schr\"odinger bridge, establishing a linear convergence rate for both algorithms.

math.PR↗

arXiv2025

SCoder: Iterative Self-Distillation for Bootstrapping Small-Scale Data Synthesizers to Empower Code LLMs

Existing code large language models (LLMs) often rely on large-scale instruction data distilled from proprietary LLMs for fine-tuning, which typically incurs high costs. In this paper, we explore the potential of small-scale open-source LLMs (e.g., 7B) as synthesizers for high-quality code instruction data construction. We first observe that the data synthesis capability of small-scale LLMs can be enhanced by training on a few superior data synthesis samples from proprietary LLMs. Building on this, we propose a novel iterative self-distillation approach to bootstrap small-scale LLMs, transforming them into powerful synthesizers that reduce reliance on proprietary LLMs and minimize costs. Concretely, in each iteration, to obtain diverse and high-quality self-distilled data, we design multi-checkpoint sampling and multi-aspect scoring strategies for initial data selection. Furthermore, to identify the most influential samples, we introduce a gradient-based influence estimation method for final data filtering. Based on the code instruction datasets from the small-scale synthesizers, we develop SCoder, a family of code generation models fine-tuned from DeepSeek-Coder. SCoder models achieve state-of-the-art code generation capabilities, demonstrating the effectiveness of our method.

cs.AI↗

arXiv2025

Lightweight Backbone Networks Only Require Adaptive Lightweight Self-Attention Mechanisms

Currently, lightweight hybrid backbone networks have partially alleviated the issue of computational saturation, but the imbalance in computational efficiencys between convolutional neural networks (CNNs) and attention mechanisms is becoming increasingly apparent. Specifically, although linear attention mechanisms and their variants have made progress in lightweight design, they still fail to meet the demands of hybrid models for long-sequence modeling. On the other hand, existing lightweight SoftMax attention computations typically reduce the feature map to a fixed size to decrease the number of sequences, thereby compressing the computational scale. However, the process of determining the feature map reduction ratio is cumbersome, and computational saturation issues still persist. To address this issue, this paper proposes a lightweight SoftMax attention mechanism with adaptive feature map sizes, named Fast Window Attention (FWA), which generates a small number of key sequences (Key and Value) through window aggregation for attention computation. Additionally, it explains the rationality of using ReLU to simulate SoftMax operations in lightweight global attention mechanisms. Finally, the paper designs a global-local feature fusion mechanism and combines it with GhostNet to propose a lightweight hybrid backbone network, LOLViT. Through visual tasks such as classification (ImageNet 1K), detection (COCO 2017), and segmentation (BDD100K), along with extensive ablation studies, it is demonstrated that LOLViT outperforms CNN models of the same level in both inference speed and model accuracy. Notably, the inference speed of LOLViT-X is 5x that of MobileViT-X.

cs.CV↗

arXiv2025

Design of a Wearable Parallel Electrical Impedance Imaging System for Healthcare

A wireless wearable Electrical Impedance Tomography (EIT) system has been developed utilizing the AD5933 chip to achieve real-time imaging of lung respiration. The system employs a voltage excitation method tailored to human impedance characteristics, injecting current by applying a known voltage and measuring the resulting current through the body. Additionally, specific measures have been implemented to effectively suppress signal oscillations and leakage currents caused by parasitic capacitances. To enhance data acquisition speed, the system employs five parallel AD5933 units, with multiple techniques implemented to ensure high synchronization during simultaneous measurements. Performance testing shows that the system achieves a signal-to-noise ratio greater than 50 dB, a relative standard deviation below 0.3%, and a reciprocity error under 0.8%. Imaging experiments using a water tank phantom, human lungs during breathing, and a resting human calf further demonstrate that this portable EIT system can accurately measure biological tissues with high precision and low cost.

physics.med-ph↗

arXiv2024

Auditing and Enforcing Conditional Fairness via Optimal Transport

Conditional demographic parity (CDP) is a measure of the demographic parity of a predictive model or decision process when conditioning on an additional feature or set of features. Many algorithmic fairness techniques exist to target demographic parity, but CDP is much harder to achieve, particularly when the conditioning variable has many levels and/or when the model outputs are continuous. The problem of auditing and enforcing CDP is understudied in the literature. In light of this, we propose novel measures of {conditional demographic disparity (CDD)} which rely on statistical distances borrowed from the optimal transport literature. We further design and evaluate regularization-based approaches based on these CDD measures. Our methods, \fairbit{} and \fairlp{}, allow us to target CDP even when the conditioning variable has many levels. When model outputs are continuous, our methods target full equality of the conditional distributions, unlike other methods that only consider first moments or related proxy quantities. We validate the efficacy of our approaches on real-world datasets.

cs.LG↗

arXiv2024

Laser: Parameter-Efficient LLM Bi-Tuning for Sequential Recommendation with Collaborative Information

Sequential recommender systems are essential for discerning user preferences from historical interactions and facilitating targeted recommendations. Recent innovations employing Large Language Models (LLMs) have advanced the field by encoding item semantics, yet they often necessitate substantial parameter tuning and are resource-demanding. Moreover, these works fails to consider the diverse characteristics of different types of users and thus diminishes the recommendation accuracy. In this paper, we propose a parameter-efficient Large Language Model Bi-Tuning framework for sequential recommendation with collaborative information (Laser). Specifically, Bi-Tuning works by inserting trainable virtual tokens at both the prefix and suffix of the input sequence and freezing the LLM parameters, thus optimizing the LLM for the sequential recommendation. In our Laser, the prefix is utilized to incorporate user-item collaborative information and adapt the LLM to the recommendation task, while the suffix converts the output embeddings of the LLM from the language space to the recommendation space for the follow-up item recommendation. Furthermore, to capture the characteristics of different types of users when integrating the collaborative information via the prefix, we introduce M-Former, a lightweight MoE-based querying transformer that uses a set of query experts to integrate diverse user-specific collaborative information encoded by frozen ID-based sequential recommender systems, significantly improving the accuracy of recommendations. Extensive experiments on real-world datasets demonstrate that Laser can parameter-efficiently adapt LLMs to effective recommender systems, significantly outperforming state-of-the-art methods.

cs.IR↗

arXiv2023

Decision Making under Costly Sequential Information Acquisition: the Paradigm of Reversible and Irreversible Decisions

Decision making in modern stochastic systems, including e-commerce platforms, financial markets and healthcare systems, has evolved into a multifaceted process that combines information acquisition and adaptive information sources. This paper initiates a study on such integrated settings, where these elements are not only fundamental but, also, interact in a complex and stochastically intertwined manner. We introduce a relatively simple model, which, however, captures the involved novel elements. A decision maker (DM) may choose between an established product $A$ of known value and a new product $B$ whose value is unknown. In parallel, the DM observes signals about the unknown value of product $B$ and can, also, opt to exchange it for product $A$ if $B$ is initially chosen. Mathematically, the model gives rise to sequential optimal stopping problems with distinct informational regimes (before and after buying product $B$), differentiated by the initial, coarser signal and the subsequent, more accurate one. We analyze in detail the underlying problems using predominantly viscosity solution techniques, departing from the existing literature on information acquisition which is based on traditional optimal stopping arguments. More broadly, the modeling approach introduced herein offers a novel framework for developing more complex interactions among decisions, information sources and information costs in stochastic environments, through a sequence of nested obstacle problems.

math.OC↗

arXiv2022

A Short and General Duality Proof for Wasserstein Distributionally Robust Optimization

We present a general duality result for Wasserstein distributionally robust optimization that holds for any Kantorovich transport cost, measurable loss function, and nominal probability distribution. Assuming an interchangeability principle inherent in existing duality results, our proof only uses one-dimensional convex analysis. Furthermore, we demonstrate that the interchangeability principle holds if and only if certain measurable projection and weak measurable selection conditions are satisfied. To illustrate the broader applicability of our approach, we provide a rigorous treatment of duality results in distributionally robust Markov decision processes and distributionally robust multistage stochastic programming. Additionally, we extend our analysis to other problems such as infinity-Wasserstein distributionally robust optimization, risk-averse optimization, and globalized distributionally robust counterpart.

math.OC↗