相关论文: Supervised multiway factorization

Training deep neural networks with spatio-temporal (i.e., 3D) or multidimensional convolutions of higher-order is computationally challenging due to millions of unknown parameters across dozens of layers. To alleviate this, one approach is…

Mapper is an algorithm that summarizes the topological information contained in a dataset and provides an insightful visualization. It takes as input a point cloud which is possibly high-dimensional, a filter function on it and an open…

The problem of decomposing a given covariance matrix as the sum of a positive semi-definite matrix of given rank and a positive semi-definite diagonal matrix, is considered. We present a projection-type algorithm to address this problem.…

We consider to model matrix time series based on a tensor CP-decomposition. Instead of using an iterative algorithm which is the standard practice for estimating CP-decompositions, we propose a new and one-pass estimation procedure based on…

When modeling multivariate data, one might have an extra parameter of contextual information that could be used to treat some observations as more similar to others. For example, images of faces can vary by age, and one would expect the…

We present a matrix factorization algorithm that scales to input matrices that are large in both dimensions (i.e., that contains morethan 1TB of data). The algorithm streams the matrix columns while subsampling them, resulting in low…

Tensor factorization has received increasing interest due to its intrinsic ability to capture latent factors in multi-dimensional data with many applications such as recommender systems and Electronic Health Records (EHR) mining. PARAFAC2…

Centroid-based methods including k-means and fuzzy c-means are known as effective and easy-to-implement approaches to clustering purposes in many applications. However, these algorithms cannot be directly applied to supervised tasks. This…

Conformal Prediction (CP) is a popular method for uncertainty quantification that converts a pretrained model's point prediction into a prediction set, with the set size reflecting the model's confidence. Although existing CP methods are…

We introduce Neural Conditional Probability (NCP), an operator-theoretic approach to learning conditional distributions with a focus on statistical inference tasks. NCP can be used to build conditional confidence regions and extract key…

Factor analysis provides a canonical framework for imposing lower-dimensional structure such as sparse covariance in high-dimensional data. High-dimensional data on the same set of variables are often collected under different conditions,…

Many complex systems can be reduced to their key components through spectrally decomposing matrices that capture their dynamics. These matrices can in turn be constructed from data, often by least-squares fitting: examples of algorithms to…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

Nonnegative CANDECOMP/PARAFAC (NCP) decomposition is an important tool to process nonnegative tensor. Sometimes, additional sparse regularization is needed to extract meaningful nonnegative and sparse components. Thus, an optimization…

Factored stochastic constraint programming (FSCP) is a formalism to represent multi-stage decision making problems under uncertainty. FSCP models support factorized probabilistic models and involve constraints over decision and random…

In this work, we present a new approach for the distributed computation of the PARAFAC decomposition of a third-order tensor across a network of collaborating nodes. We are interested in the case where the overall data gathered across the…

Motivation: How do we integratively analyze large-scale multi-platform genomic data that are high dimensional and sparse? Furthermore, how can we incorporate prior knowledge, such as the association between genes, in the analysis…

Real-world relations among entities can often be observed and determined by different perspectives/views. For example, the decision made by a user on whether to adopt an item relies on multiple aspects such as the contextual information of…

In this paper, we consider the optimization problem Submodular Cover (SCP), which is to find a minimum cardinality subset of a finite universe $U$ such that the value of a submodular function $f$ is above an input threshold $\tau$. In…

There is growing interest to extend low-rank matrix decompositions to multi-way arrays, or tensors. One fundamental low-rank tensor decomposition is the canonical polyadic decomposition (CPD). The challenge of fitting a low-rank,…