arXiv research

Open problem: Establishing bounds for Cayley-table completion to discover discrete algorithmic axioms.

New kernels allow learning from non-separable data.

Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the celebrated Random Fourier Feature methodology to get an approximation of operator-…

Positive definite operator-valued kernels generalize the well-known notion of reproducing kernels, and are naturally adapted to multi-output learning situations. This paper addresses the problem of learning a finite linear combination of infinite-dimensional operator-valued kernels which are suitable for extending func…

We consider the problem of learning a vector-valued function f in an online learning setting. The function f is assumed to lie in a reproducing Hilbert space of operator-valued kernels. We describe two online algorithms for learning f while taking into account the output structure. A first contribution is an algorithm,…

Although operator-valued kernels have recently received increasing interest in various machine learning and functional data analysis problems such as multi-task learning or functional regression, little attention has been paid to the understanding of their associated feature spaces. In this paper, we explore the potent…

In this note we study the analytical index of pseudo-differential operators by using the notion of (infinite dimensional) operator-valued symbols (in the sense of Ruzhansky and Turunen). Our main tools will be the McKean-Singer index formula together with the operator-valued functional calculus developed here.

This work discovers algebraic structures from data using a differentiable measure.

In this paper we study the Taylor series of an operator-valued function related to the differential of the exponential map. For a smooth manifold $\mathcal{M}$ with a torsion-free affine connection the operator $\mathcal{E}_p(v)$ acting on the space $T_p\mathcal{M}$ is defined to be the composition of the differential …

We introduce Bayesian multi-tensor factorization, a model that is the first Bayesian formulation for joint factorization of multiple matrices and tensors. The research problem generalizes the joint matrix-tensor factorization problem to arbitrary sets of tensors of any depth, including matrices, can be interpreted as u…

A new algorithm for high-dimensional hedging problems.

Random features improve neural operators' generalization properties.

Tensor factorization arises in many machine learning applications, such knowledge base modeling and parameter estimation in latent variable models. However, numerical methods for tensor factorization have not reached the level of maturity of matrix factorization methods. In this paper, we propose a new method for CP te…

Proposes FATTNN for tensor-on-tensor regression with improved prediction and reduced computation.

Deep tensor factorization benefits from implicit regularization with polynomial growth.

Optimal tensor PCA for estimating factors and loadings in high-dimensional panel data.

The paper tackles tensor factorization and completion from noisy data.

Proposes a new tensor factorization model for better link prediction in knowledge graphs.

Streaming tensor factorization is a powerful tool for processing high-volume and multi-way temporal data in Internet networks, recommender systems and image/video data analysis. Existing streaming tensor factorization algorithms rely on least-squares data fitting and they do not possess a mechanism for tensor rank dete…

Efficiently factorizes coupled matrix tensor data for better accuracy and speed.

Most popular word embedding techniques involve implicit or explicit factorization of a word co-occurrence based matrix into low rank factors. In this paper, we aim to generalize this trend by using numerical methods to factor higher-order word co-occurrence based arrays, or \textit{tensors}. We present four word embedd…

New algorithm for online tensor factorization with provable guarantees.

TATD predicts missing entries in time-evolving tensors by exploiting temporal dependency and sparsity.

The popular Alternating Least Squares (ALS) algorithm for tensor decomposition is efficient and easy to implement, but often converges to poor local optima---particularly when the weights of the factors are non-uniform. We propose a modification of the ALS approach that is as efficient as standard ALS, but provably rec…

We study the stability properties of nonlinear multi-task regression in reproducing Hilbert spaces with operator-valued kernels. Such kernels, a.k.a. multi-task kernels, are appropriate for learning prob- lems with nonscalar outputs like multi-task learning and structured out- put prediction. We show that multi-task ke…

Proposes a nonparametric tensor factorization for sparse data.

Matrix factorizations and their extensions to tensor factorizations and decompositions have become prominent techniques for linear and multilinear blind source separation (BSS), especially multiway Independent Component Analysis (ICA), NonnegativeMatrix and Tensor Factorization (NMF/NTF), Smooth Component Analysis (Smo…

Gradient descent in tensor factorization favors low-rank solutions.

SPIDER uses deep neural networks for streaming tensor factorization.

The paper analyzes implicit regularization in tensor factorization using neural networks.

Paper proposes C-STM for multimodal neuroimaging data classification.

Paper introduces ZIPTF and C-ZIPTF for better tensor factorization of zero-inflated count data.

Probabilistic Temporal Tensor Factorization (PTTF) is an effective algorithm to model the temporal tensor data. It leverages a time constraint to capture the evolving properties of tensor data. Nowadays the exploding dataset demands a large scale PTTF analysis, and a parallel solution is critical to accommodate the tre…

Tensor factorizations have become increasingly popular approaches for various learning tasks on structured data. In this work, we extend 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. We study the improvemen…

The paper develops a new probabilistic framework for denoising diffusion models using free entropy and stochastic analysis.

NNEinFact fits any nonnegative tensor factorization quickly and accurately.

Causal deep learning tackles causal inference using tensor factor analysis.

In this paper we consider the problems of supervised classification and regression in the case where attributes and labels are functions: a data is represented by a set of functions, and the label is also a function. We focus on the use of reproducing kernel Hilbert space theory to learn from such functional data. Basi…

CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually specified, however, the determination of tensor rank remains a challenging problem e…

Efficient NTF algorithm for large sparse tensors.

Proposes a method for tensor completion with sparse factors and missing data.

SG-NTF completes HDI tensors with spectral mapping and spatio-temporal gating.

Sparse sampling method for tensor factorization and completion of high rank tensors.

Spatio-temporal data compression method reduces memory usage.

Modeling dynamical systems with ordinary differential equations implies a mechanistic view of the process underlying the dynamics. However in many cases, this knowledge is not available. To overcome this issue, we introduce a general framework for nonparametric ODE models using penalized regression in Reproducing Kerne…

The paper explains implicit regularization in hierarchical tensor factorization and deep CNNs.

Efficiently factorize tensors in streaming data with coreset selection.

We present a Bayesian tensor factorization model for inferring latent group structures from dynamic pairwise interaction patterns. For decades, political scientists have collected and analyzed records of the form "country $i$ took action $a$ toward country $j$ at time $t$"---known as dyadic events---in order to form an…