arXiv subjects

Haitong Liu

Publications and source records attributed to Haitong Liu.

3 recordsLinked to original sources

arXiv2026

Fast algorithms for learning a Gaussian under halfspace truncation with optimal sample complexity

We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace. Lee, Mehrotra and Zampetakis (FOCS'24) recently obtained the first polynomial time algorithm for this problem, but their resulting sample and time complexity bounds are not optimal. Under non-trivial truncation, for any target accuracy $\varepsilon > 0$ and dimension $d$ we give an efficient algorithm that uses $n = \tilde{O}(d^2/\varepsilon^2)$ samples and learns the underlying Gaussian to error $\varepsilon$ in total variation distance. Our algorithm is also fast: its runtime is dominated by the cost of computing the empirical covariance matrix. Both our sample and time complexity are optimal in terms of $d$ and $\varepsilon$ even without truncation: in this regard, we can learn a Gaussian under halfspace truncation for free. The key ingredient behind our result is a novel reinterpretation of the low-degree moments of the truncated Gaussian in terms of a relative truncation parameter. This relative truncation parameter uniquely determines the parameters of the untruncated Gaussian and enables direct parameter recovery. This reinterpretation allows us to circumvent the time intensive projected stochastic gradient descent procedure that is widely used in learning under truncation.

cs.DS↗

arXiv2025

Protecting Your Video Content: Disrupting Automated Video-based LLM Annotations

Recently, video-based large language models (video-based LLMs) have achieved impressive performance across various video comprehension tasks. However, this rapid advancement raises significant privacy and security concerns, particularly regarding the unauthorized use of personal video data in automated annotation by video-based LLMs. These unauthorized annotated video-text pairs can then be used to improve the performance of downstream tasks, such as text-to-video generation. To safeguard personal videos from unauthorized use, we propose two series of protective video watermarks with imperceptible adversarial perturbations, named Ramblings and Mutes. Concretely, Ramblings aim to mislead video-based LLMs into generating inaccurate captions for the videos, thereby degrading the quality of video annotations through inconsistencies between video content and captions. Mutes, on the other hand, are designed to prompt video-based LLMs to produce exceptionally brief captions, lacking descriptive detail. Extensive experiments demonstrate that our video watermarking methods effectively protect video data by significantly reducing video annotation performance across various video-based LLMs, showcasing both stealthiness and robustness in protecting personal video content. Our code is available at https://github.com/ttthhl/Protecting_Your_Video_Content.

cs.CV↗

arXiv2024

Two-timescale Derivative Free Optimization for Performative Prediction with Markovian Data

This paper studies the performative prediction problem where a learner aims to minimize the expected loss with a decision-dependent data distribution. Such setting is motivated when outcomes can be affected by the prediction model, e.g., in strategic classification. We consider a state-dependent setting where the data distribution evolves according to an underlying controlled Markov chain. We focus on stochastic derivative free optimization (DFO) where the learner is given access to a loss function evaluation oracle with the above Markovian data. We propose a two-timescale DFO($λ$) algorithm that features (i) a sample accumulation mechanism that utilizes every observed sample to estimate the overall gradient of performative risk, and (ii) a two-timescale diminishing step size that balances the rates of DFO updates and bias reduction. Under a general non-convex optimization setting, we show that DFO($λ$) requires ${\cal O}( 1 /ε^3)$ samples (up to a log factor) to attain a near-stationary solution with expected squared gradient norm less than $ε> 0$. Numerical experiments verify our analysis.

math.OC↗