Provable Online CP/PARAFAC Decomposition of a Structured Tensor via Dictionary Learning

• URL: http://arxiv.org/abs/2006.16442v1
• Date: Tue, 30 Jun 2020 00:31:06 GMT
• Title: Provable Online CP/PARAFAC Decomposition of a Structured Tensor via Dictionary Learning
• Authors: Sirisha Rambhatla, Xingguo Li, Jarvis Haupt
• Abstract summary: We consider the problem of factorizing a structured 3-mutation tensor into its constituent Polyadic (CP) factors. We develop a provable algorithm for structured tensor factorization.
• Score: 18.464203215845373
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider the problem of factorizing a structured 3-way tensor into its constituent Canonical Polyadic (CP) factors. This decomposition, which can be viewed as a generalization of singular value decomposition (SVD) for tensors, reveals how the tensor dimensions (features) interact with each other. However, since the factors are a priori unknown, the corresponding optimization problems are inherently non-convex. The existing guaranteed algorithms which handle this non-convexity incur an irreducible error (bias), and only apply to cases where all factors have the same structure. To this end, we develop a provable algorithm for online structured tensor factorization, wherein one of the factors obeys some incoherence conditions, and the others are sparse. Specifically we show that, under some relatively mild conditions on initialization, rank, and sparsity, our algorithm recovers the factors exactly (up to scaling and permutation) at a linear rate. Complementary to our theoretical results, our synthetic and real-world data evaluations showcase superior performance compared to related techniques. Moreover, its scalability and ability to learn on-the-fly makes it suitable for real-world tasks.

Related papers

• Nonparametric Partial Disentanglement via Mechanism Sparsity: Sparse Actions, Interventions and Sparse Temporal Dependencies [58.179981892921056]
  This work introduces a novel principle for disentanglement we call mechanism sparsity regularization. We propose a representation learning method that induces disentanglement by simultaneously learning the latent factors. We show that the latent factors can be recovered by regularizing the learned causal graph to be sparse.
  arXiv  Detail & Related papers  (2024-01-10T02:38:21Z)
• Learning Graphical Factor Models with Riemannian Optimization [70.13748170371889]
  This paper proposes a flexible algorithmic framework for graph learning under low-rank structural constraints. The problem is expressed as penalized maximum likelihood estimation of an elliptical distribution. We leverage geometries of positive definite matrices and positive semi-definite matrices of fixed rank that are well suited to elliptical models.
  arXiv  Detail & Related papers  (2022-10-21T13:19:45Z)
• Fast and Provable Tensor Robust Principal Component Analysis via Scaled Gradient Descent [30.299284742925852]
  This paper tackles tensor robust principal component analysis (RPCA) It aims to recover a low-rank tensor from its observations contaminated by sparse corruptions. We show that the proposed algorithm achieves better and more scalable performance than state-of-the-art matrix and tensor RPCA algorithms.
  arXiv  Detail & Related papers  (2022-06-18T04:01:32Z)
• Amortized Inference for Causal Structure Learning [72.84105256353801]
  Learning causal structure poses a search problem that typically involves evaluating structures using a score or independence test. We train a variational inference model to predict the causal structure from observational/interventional data. Our models exhibit robust generalization capabilities under substantial distribution shift.
  arXiv  Detail & Related papers  (2022-05-25T17:37:08Z)
• Nonparametric Sparse Tensor Factorization with Hierarchical Gamma Processes [16.79618682556073]
  We propose a nonparametric factorization approach for sparsely observed tensors. We use hierarchical Gamma processes and Poisson random measures to construct a tensor-valued process. For efficient inference, we use Dirichlet process properties over finite sample partitions, density transformations, and random features.
  arXiv  Detail & Related papers  (2021-10-19T16:17:26Z)
• Fractal Structure and Generalization Properties of Stochastic Optimization Algorithms [71.62575565990502]
  We prove that the generalization error of an optimization algorithm can be bounded on the complexity' of the fractal structure that underlies its generalization measure. We further specialize our results to specific problems (e.g., linear/logistic regression, one hidden/layered neural networks) and algorithms.
  arXiv  Detail & Related papers  (2021-06-09T08:05:36Z)
• Scaling and Scalability: Provable Nonconvex Low-Rank Tensor Estimation from Incomplete Measurements [30.395874385570007]
  A fundamental task is to faithfully recover tensors from highly incomplete measurements. We develop an algorithm to directly recover the tensor factors in the Tucker decomposition. We show that it provably converges at a linear independent rate of the ground truth tensor for two canonical problems.
  arXiv  Detail & Related papers  (2021-04-29T17:44:49Z)
• Causal Expectation-Maximisation [70.45873402967297]
  We show that causal inference is NP-hard even in models characterised by polytree-shaped graphs. We introduce the causal EM algorithm to reconstruct the uncertainty about the latent variables from data about categorical manifest variables. We argue that there appears to be an unnoticed limitation to the trending idea that counterfactual bounds can often be computed without knowledge of the structural equations.
  arXiv  Detail & Related papers  (2020-11-04T10:25:13Z)
• Online nonnegative CP-dictionary learning for Markovian data [8.490619842547739]
  We introduce a novel algorithm that learns a CANDECOMP/PARAFAC basis from a given stream of tensor-valued data under general constraints. We prove that our algorithm converges almost surely to the set of stationary points of the objective function under the hypothesis that the sequence of data tensors is generated by an underlying Markov chain.
  arXiv  Detail & Related papers  (2020-09-16T11:41:01Z)
• Supervised Learning for Non-Sequential Data: A Canonical Polyadic Decomposition Approach [85.12934750565971]
  Efficient modelling of feature interactions underpins supervised learning for non-sequential tasks. To alleviate this issue, it has been proposed to implicitly represent the model parameters as a tensor. For enhanced expressiveness, we generalize the framework to allow feature mapping to arbitrarily high-dimensional feature vectors.
  arXiv  Detail & Related papers  (2020-01-27T22:38:40Z)
• A Unified Framework for Coupled Tensor Completion [42.19293115131073]
  Coupled tensor decomposition reveals the joint data structure by incorporating priori knowledge that come from the latent coupled factors. The TR has powerful expression ability and achieves success in some multi-dimensional data processing applications. The proposed method is validated on numerical experiments on synthetic data, and experimental results on real-world data demonstrate its superiority over the state-of-the-art methods in terms of recovery accuracy.
  arXiv  Detail & Related papers  (2020-01-09T02:15:46Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.