arXiv subjects

Xiaoyi Zhu

Publications and source records attributed to Xiaoyi Zhu.

7 recordsLinked to original sources

arXiv2026

Sublinear Spectral Clustering Oracle with Little Memory

We study the problem of designing \emph{sublinear spectral clustering oracles} for well-clusterable graphs. Such an oracle is an algorithm that, given query access to the adjacency list of a graph $G$, first constructs a compact data structure $\mathcal{D}$ that captures the clustering structure of $G$. Once built, $\mathcal{D}$ enables sublinear time responses to \textsc{WhichCluster}$(G,x)$ queries for any vertex $x$. A major limitation of existing oracles is that constructing $\mathcal{D}$ requires $Ω(\sqrt{n})$ memory, which becomes a bottleneck for massive graphs and memory-limited settings. In this paper, we break this barrier and establish a memory-time trade-off for sublinear spectral clustering oracles. Specifically, for well-clusterable graphs, we present oracles that construct $\mathcal{D}$ using much smaller than $O(\sqrt{n})$ memory (e.g., $O(n^{0.01})$) while still answering membership queries in sublinear time. We also characterize the trade-off frontier between memory usage $S$ and query time $T$, showing, for example, that $S\cdot T=\widetilde{O}(n)$ for clusterable graphs with a logarithmic conductance gap, and we show that this trade-off is nearly optimal (up to logarithmic factors) for a natural class of approaches. Finally, to complement our theory, we validate the performance of our oracles through experiments on synthetic networks.

cs.DS↗

arXiv2026

Few Batches or Little Memory, But Not Both: Simultaneous Space and Adaptivity Constraints in Stochastic Bandits

We study stochastic multi-armed bandits under simultaneous constraints on space and adaptivity: the learner interacts with the environment in $B$ batches and has only $W$ bits of persistent memory. Prior work shows that each constraint alone is surprisingly mild: near-minimax regret $\widetilde{O}(\sqrt{KT})$ is achievable with $O(\log T)$ bits of memory under fully adaptive interaction, and with a $K$-independent $O(\log\log T)$-type number of batches when memory is unrestricted. We show that this picture breaks down in the simultaneously constrained regime. We prove that any algorithm with a $W$-bit memory constraint must use at least $Ω(K/W)$ batches to achieve near-minimax regret $\widetilde{O}(\sqrt{KT})$, even under adaptive grids. In particular, logarithmic memory rules out $O(K^{1-\varepsilon})$ batch complexity. Our proof is based on an information bottleneck. We show that near-minimax regret forces the learner to acquire $Ω(K)$ bits of information about the hidden set of good arms under a suitable hard prior, whereas an algorithm with $B$ batches and $W$ bits of memory allows only $O(BW)$ bits of information. A key ingredient is a localized change-of-measure lemma that yields probability-level arm exploration guarantees, which is of independent interest. We also give an algorithm that, for any bit budget $W$ with $Ω(\log T) \le W \le O(K\log T)$, uses at most $W$ bits of memory and $\widetilde{O}(K/W)$ batches while achieving regret $\widetilde{O}(\sqrt{KT})$, nearly matching our lower bound up to polylogarithmic factors.

cs.LG↗

arXiv2025

Simple and Optimal Algorithms for Heavy Hitters and Frequency Moments in Distributed Models

We consider the problems of distributed heavy hitters and frequency moments in both the coordinator model and the distributed tracking model (also known as the distributed functional monitoring model). We present simple and optimal (up to logarithmic factors) algorithms for $\ell_p$ heavy hitters and $F_p$ estimation ($p \geq 2$) in these distributed models. For $\ell_p$ heavy hitters in the coordinator model, our algorithm requires only one round and uses $\tilde{O}(k^{p-1}/\eps^p)$ bits of communication. For $p > 2$, this is the first near-optimal result. By combining our algorithm with the standard recursive sketching technique, we obtain a near-optimal two-round algorithm for $F_p$ in the coordinator model, matching a significant result from recent work by Esfandiari et al.\ (STOC 2024). Our algorithm and analysis are much simpler and have better costs with respect to logarithmic factors. Furthermore, our technique provides a one-round algorithm for $F_p$, which is a significant improvement over a result of Woodruff and Zhang (STOC 2012). Thanks to the simplicity of our heavy hitter algorithms, we manage to adapt them to the distributed tracking model with only a $\polylog(n)$ increase in communication. For $\ell_p$ heavy hitters, our algorithm has a communication cost of $\tilde{O}(k^{p-1}/\eps^p)$, representing the first near-optimal algorithm for all $p \geq 2$. By applying the recursive sketching technique, we also provide the first near-optimal algorithm for $F_p$ in the distributed tracking model, with a communication cost of $\tilde{O}(k^{p-1}/\eps^2)$ for all $p \geq 2$. Even for $F_2$, our result improves upon the bounds established by Cormode, Muthukrishnan, and Yi (SODA 2008) and Woodruff and Zhang (STOC 2012), nearly matching the existing lower bound for the first time.

cs.DS↗

arXiv2025

Space Complexity of Euclidean Clustering

The $(k, z)$-Clustering problem in Euclidean space $\mathbb{R}^d$ has been extensively studied. Given the scale of data involved, compression methods for the Euclidean $(k, z)$-Clustering problem, such as data compression and dimension reduction, have received significant attention in the literature. However, the space complexity of the clustering problem, specifically, the number of bits required to compress the cost function within a multiplicative error $\varepsilon$, remains unclear in existing literature. This paper initiates the study of space complexity for Euclidean $(k, z)$-Clustering and offers both upper and lower bounds. Our space bounds are nearly tight when $k$ is constant, indicating that storing a coreset, a well-known data compression approach, serves as the optimal compression scheme. Furthermore, our lower bound result for $(k, z)$-Clustering establishes a tight space bound of $Θ( n d )$ for terminal embedding, where $n$ represents the dataset size. Our technical approach leverages new geometric insights for principal angles and discrepancy methods, which may hold independent interest.

cs.CG↗

arXiv2023

Adversarially Robust Distributed Count Tracking via Partial Differential Privacy

We study the distributed tracking model, also known as distributed functional monitoring. This model involves $k$ sites each receiving a stream of items and communicating with the central server. The server's task is to track a function of all items received thus far continuously, with minimum communication cost. For count tracking, it is known that there is a $\sqrt{k}$ gap in communication between deterministic and randomized algorithms. However, existing randomized algorithms assume an "oblivious adversary" who constructs the entire input streams before the algorithm starts. Here we consider adaptive adversaries who can choose new items based on previous answers from the algorithm. Deterministic algorithms are trivially robust to adaptive adversaries, while randomized ones may not. Therefore, we investigate whether the $\sqrt{k}$ advantage of randomized algorithms is from randomness itself or the oblivious adversary assumption. We provide an affirmative answer to this question by giving a robust algorithm with optimal communication. Existing robustification techniques do not yield optimal bounds due to the inherent challenges of the distributed nature of the problem. To address this, we extend the differential privacy framework by introducing "partial differential privacy" and proving a new generalization theorem. This theorem may have broader applications beyond robust count tracking, making it of independent interest.

cs.DS↗

arXiv2022

A Deep Learning and Geospatial Data-Based Channel Estimation Technique for Hybrid Massive MIMO Systems

This paper presents a novel channel estimation technique for the multi-user massive multiple-input multiple-output (MU-mMIMO) systems using angular-based hybrid precoding (AB-HP). The proposed channel estimation technique generates group-wise channel state information (CSI) of user terminal (UT) zones in the service area by deep neural networks (DNN) and fuzzy c-Means (FCM) clustering. The slow time-varying CSI between the base station (BS) and feasible UT locations in the service area is calculated from the geospatial data by offline ray tracing and a DNN-based path estimation model associated with the 1-dimensional convolutional neural network (1D-CNN) and regression tree ensembles. Then, the UT-level CSI of all feasible locations is grouped into clusters by a proposed FCM clustering. Finally, the service area is divided into a number of non-overlapping UT zones. Each UT zone is characterized by a corresponding set of clusters named as UT-group CSI, which is utilized in the analog RF beamformer design of AB-HP to reduce the required large online CSI overhead in the MU-mMIMO systems. Then, the reduced-size online CSI is employed in the baseband (BB) precoder of AB-HP. Simulations are conducted in the indoor scenario at 28 GHz and tested in an AB-HP MU-mMIMO system with a uniform rectangular array (URA) having 16x16=256 antennas and 22 RF chains. Illustrative results indicate that 91.4% online CSI can be reduced by using the proposed offline channel estimation technique as compared to the conventional online channel sounding. The proposed DNN-based path estimation technique produces same amount of UT-level CSI with runtime reduced by 65.8% as compared to the computationally expensive ray tracing.

cs.IT↗

arXiv2021

Deep image prior for undersampling high-speed photoacoustic microscopy

Photoacoustic microscopy (PAM) is an emerging imaging method combining light and sound. However, limited by the laser's repetition rate, state-of-the-art high-speed PAM technology often sacrifices spatial sampling density (i.e., undersampling) for increased imaging speed over a large field-of-view. Deep learning (DL) methods have recently been used to improve sparsely sampled PAM images; however, these methods often require time-consuming pre-training and large training dataset with ground truth. Here, we propose the use of deep image prior (DIP) to improve the image quality of undersampled PAM images. Unlike other DL approaches, DIP requires neither pre-training nor fully-sampled ground truth, enabling its flexible and fast implementation on various imaging targets. Our results have demonstrated substantial improvement in PAM images with as few as 1.4$\%$ of the fully sampled pixels on high-speed PAM. Our approach outperforms interpolation, is competitive with pre-trained supervised DL method, and is readily translated to other high-speed, undersampling imaging modalities.

eess.IV↗