# Multi-relational Learning Using Weighted Tensor Decomposition with Modular Loss

@article{London2013MultirelationalLU, title={Multi-relational Learning Using Weighted Tensor Decomposition with Modular Loss}, author={Ben London and Theodoros Rekatsinas and Bert Huang and L. Getoor}, journal={ArXiv}, year={2013}, volume={abs/1303.1733} }

We propose a modular framework for multi-relational learning via tensor decomposition. In our learning setting, the training data contains multiple types of relationships among a set of objects, which we represent by a sparse three-mode tensor. The goal is to predict the values of the missing entries. To do so, we model each relationship as a function of a linear combination of latent factors. We learn this latent representation by computing a low-rank tensor decomposition, using quasi-Newton… Expand

#### Figures, Tables, and Topics from this paper

#### 20 Citations

Tensor factorization for relational learning

- Computer Science, Mathematics
- 2013

It is proposed that tensor factorization can be the basis for scalable solutions for learning from relational data and present novel tensorfactorization algorithms that are particularly suited for this task. Expand

Iterative Splits of Quadratic Bounds for Scalable Binary Tensor Factorization

- Mathematics, Computer Science
- UAI
- 2014

This work shows that an alternative approach is to minimize the quadratic loss (root mean square error) which leads to algorithms with a training time complexity that is reduced from O(n) to O(m), as proposed earlier in the restricted case of alternating least-square algorithms. Expand

Multi-tensor Completion with Common Structures

- Computer Science
- AAAI
- 2015

A novel common structure for multi-data learning is proposed, which assumes that datasets share Common Adjacency Graph (CAG) structure, which is more robust to heterogeneity and unbalance of datasets. Expand

Large-scale factorization of type-constrained multi-relational data

- Mathematics, Computer Science
- 2014 International Conference on Data Science and Advanced Analytics (DSAA)
- 2014

This paper extends the recently proposed state-of-the-art RESCal tensor factorization to consider relational type-constraints and significantly outperforms RESCAL without type- Constraints in both, runtime and prediction quality. Expand

Zero-Truncated Poisson Tensor Factorization for Massive Binary Tensors

- Computer Science, Mathematics
- UAI
- 2015

A scalable Bayesian model for low-rank factorization of massive tensors with binary observations using a zero-truncated Poisson likelihood for binary data, achieving excellent computational scalability, and demonstrating its usefulness in leveraging side-information provided in form of mode-network(s). Expand

Logistic Tensor Factorization for Multi-Relational Data

- Mathematics, Computer Science
- ArXiv
- 2013

This work extends the RESCAL tensor factorization, which has shown state-of-the-art results for multi-relational learning, to account for the binary nature of adjacency tensors and shows that the logistic extension can improve the prediction results significantly. Expand

Multi-Task Metric Learning on Network Data

- Mathematics, Computer Science
- PAKDD
- 2015

A multi-task version of SPML, abbreviated as MT-SPML, which is able to learn across multiple related tasks on multiple networks via shared intermediate parametrization, and works on general networks, thus is suitable for a wide variety of problems. Expand

Using Joint Tensor Decomposition on RDF Graphs

- Computer Science
- DC@ISWC
- 2016

The goal of this thesis is to develop and evaluate models for joint tensor factorization on RDF graphs that arise from parameter estimation in statistic models or algebraic approaches and yield promising results inspite of being derived from an ad-hoc approach. Expand

Complex-Valued Embedding Models for Knowledge Graphs

- Computer Science
- 2017

An experimentals survey of state-of-the-art factorization models, not towards a purely comparative end, but as a means to get insight about their inductive abilities, and proposes new researchdirections to improve on existing models, including ComplEx. Expand

Probabilistic Latent-Factor Database Models

- Mathematics, Computer Science
- LD4KD
- 2014

We describe a general framework for modelling probabilistic databases using factorization approaches. The framework includes tensor-based approaches which have been very successful in modelling… Expand

#### References

SHOWING 1-10 OF 25 REFERENCES

A Three-Way Model for Collective Learning on Multi-Relational Data

- Computer Science
- ICML
- 2011

This work presents a novel approach to relational learning based on the factorization of a three-way tensor that is able to perform collective learning via the latent components of the model and provide an efficient algorithm to compute the factorizations. Expand

Link Pattern Prediction with tensor decomposition in multi-relational networks

- Computer Science
- 2011 IEEE Symposium on Computational Intelligence and Data Mining (CIDM)
- 2011

A tensor decomposition model is proposed to solve the LPP problem, which allows to capture the correlations among different relation types and reveal the impact of various relations on prediction performance. Expand

Scalable Tensor Factorizations with Missing Data

- Computer Science
- SDM
- 2010

An algorithm called CP-WOPT (CP Weighted OPTimization) is developed using a first-order optimization approach to solve the weighted least squares problem of CANDECOMP/PARAFAC, and is shown to successfully factor tensors with noise and up to 70% missing data. Expand

Modelling Relational Data using Bayesian Clustered Tensor Factorization

- Computer Science, Mathematics
- NIPS
- 2009

The Bayesian Clustered Tensor Factorization (BCTF) model is introduced, which embeds a factorized representation of relations in a nonparametric Bayesian clustering framework that is fully Bayesian but scales well to large data sets. Expand

Temporal Collaborative Filtering with Bayesian Probabilistic Tensor Factorization

- Computer Science
- SDM
- 2010

This work proposes a factor-based algorithm that is able to take time into account, and provides a fully Bayesian treatment to avoid tuning parameters and achieve automatic model complexity control. Expand

Temporal Link Prediction Using Matrix and Tensor Factorizations

- Mathematics, Computer Science
- TKDD
- 2011

This article considers bipartite graphs that evolve over time and considers matrix- and tensor-based methods for predicting future links and shows that Tensor- based techniques are particularly effective for temporal data with varying periodic patterns. Expand

Link Propagation: A Fast Semi-supervised Learning Algorithm for Link Prediction

- Computer Science
- SDM
- 2009

We propose Link Propagation as a new semi-supervised learning method for link prediction problems, where the task is to predict unknown parts of the network structure by using auxiliary information… Expand

Fast maximum margin matrix factorization for collaborative prediction

- Computer Science, Mathematics
- ICML
- 2005

This work investigates a direct gradient-based optimization method for MMMF and finds that MMMf substantially outperforms all nine methods he tested and demonstrates it on large collaborative prediction problems. Expand

Multilinear algebra for analyzing data with multiple linkages

- Computer Science
- 2006

It is shown that multilinear algebra provides a tool for multilink analysis and is shown how the PARAFAC decomposition can be used to understand the structure of the document space and define paper-paper similarities based on multiple linkages. Expand

Collaborative Filtering on a Budget

- Computer Science
- AISTATS
- 2010

This paper proposes a new model for representing and compressing matrix factors via hashing that allows for essentially unbounded storage (at a graceful storage / performance trade-off) for users and items to be represented in a pre-defined memory footprint. Expand