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Zerui Tao

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4 papers

2 author rows

AAAI Conference 2024 Conference Paper

Efficient Nonparametric Tensor Decomposition for Binary and Count Data

Zerui Tao
Toshihisa Tanaka
Qibin Zhao

In numerous applications, binary reactions or event counts are observed and stored within high-order tensors. Tensor decompositions (TDs) serve as a powerful tool to handle such high-dimensional and sparse data. However, many traditional TDs are explicitly or implicitly designed based on the Gaussian distribution, which is unsuitable for discrete data. Moreover, most TDs rely on predefined multi-linear structures, such as CP and Tucker formats. Therefore, they may not be effective enough to handle complex real-world datasets. To address these issues, we propose ENTED, an Efficient Nonparametric TEnsor Decomposition for binary and count tensors. Specifically, we first employ a nonparametric Gaussian process (GP) to replace traditional multi-linear structures. Next, we utilize the Pólya-Gamma augmentation which provides a unified framework to establish conjugate models for binary and count distributions. Finally, to address the computational issue of GPs, we enhance the model by incorporating sparse orthogonal variational inference of inducing points, which offers a more effective covariance approximation within GPs and stochastic natural gradient updates for nonparametric models. We evaluate our model on several real-world tensor completion tasks, considering binary and count datasets. The results manifest both better performance and computational advantages of the proposed model.

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ICML Conference 2024 Conference Paper

Generalization Analysis of Stochastic Weight Averaging with General Sampling

Peng Wang
Li Shen 0008
Zerui Tao
Shuaida He
Dacheng Tao

Stochastic weight averaging (SWA) method has empirically proven its advantages compared to stochastic gradient descent (SGD). Despite it is widespread used, theoretical investigations have been limited, particularly in scenarios beyond the ideal setting of convex and sampling with replacement. However, non-convex cases and sampling without replacement are very practical in real-world applications. The main challenges under the above settings are two-folds: (i) All the historical gradient information introduced by SWA is considered, while the analysis of SGD using the tool of uniform stability requires only to bound the current gradient. (ii) The $(1+\alpha\beta)$-expansion property causes the boundary of each gradient step dependent on the previous step, making the boundary of each historical gradient in SWA nested and the theoretical analysis even harder. To address the theoretical challenges, we adopt mathematical induction to find a recursive representation that bounds the gradient at each step. Based on this, we establish stability bounds supporting sampling with and without replacement in the non-convex setting. Furthermore, the derived generalization bounds of SWA are sharper than SGD. At last, experimental results on several benchmarks verify our theoretical results.

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NeurIPS Conference 2023 Conference Paper

Undirected Probabilistic Model for Tensor Decomposition

Zerui Tao
Toshihisa Tanaka
Qibin Zhao

Tensor decompositions (TDs) serve as a powerful tool for analyzing multiway data. Traditional TDs incorporate prior knowledge about the data into the model, such as a directed generative process from latent factors to observations. In practice, selecting proper structural or distributional assumptions beforehand is crucial for obtaining a promising TD representation. However, since such prior knowledge is typically unavailable in real-world applications, choosing an appropriate TD model can be challenging. This paper aims to address this issue by introducing a flexible TD framework that discards the structural and distributional assumptions, in order to learn as much information from the data. Specifically, we construct a TD model that captures the joint probability of the data and latent tensor factors through a deep energy-based model (EBM). Neural networks are then employed to parameterize the joint energy function of tensor factors and tensor entries. The flexibility of EBM and neural networks enables the learning of underlying structures and distributions. In addition, by designing the energy function, our model unifies the learning process of different types of tensors, such as static tensors and dynamic tensors with time stamps. The resulting model presents a doubly intractable nature due to the presence of latent tensor factors and the unnormalized probability function. To efficiently train the model, we derive a variational upper bound of the conditional noise-contrastive estimation objective that learns the unnormalized joint probability by distinguishing data from conditional noises. We show advantages of our model on both synthetic and several real-world datasets.

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ICML Conference 2022 Conference Paper

Permutation Search of Tensor Network Structures via Local Sampling

Chao Li 0013
Junhua Zeng
Zerui Tao
Qibin Zhao

Recent works put much effort into tensor network structure search (TN-SS), aiming to select suitable tensor network (TN) structures, involving the TN-ranks, formats, and so on, for the decomposition or learning tasks. In this paper, we consider a practical variant of TN-SS, dubbed TN permutation search (TN-PS), in which we search for good mappings from tensor modes onto TN vertices (core tensors) for compact TN representations. We conduct a theoretical investigation of TN-PS and propose a practically-efficient algorithm to resolve the problem. Theoretically, we prove the counting and metric properties of search spaces of TN-PS, analyzing for the first time the impact of TN structures on these unique properties. Numerically, we propose a novel meta-heuristic algorithm, in which the searching is done by randomly sampling in a neighborhood established in our theory, and then recurrently updating the neighborhood until convergence. Numerical results demonstrate that the new algorithm can reduce the required model size of TNs in extensive benchmarks, implying the improvement in the expressive power of TNs. Furthermore, the computational cost for the new algorithm is significantly less than that in (Li and Sun, 2020).

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