Related papers: Provable learning of Noisy-or Networks
Progress in the application of machine learning techniques to the prediction of solid-state and molecular materials properties has been greatly facilitated by the development state-of-the-art feature representations and novel deep learning…
Robust tensor CP decomposition involves decomposing a tensor into low rank and sparse components. We propose a novel non-convex iterative algorithm with guaranteed recovery. It alternates between low-rank CP decomposition through gradient…
This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…
Large-scale deep neural networks consume expensive training costs, but the training results in less-interpretable weight matrices constructing the networks. Here, we propose a mode decomposition learning that can interpret the weight…
Beyond their origin in modeling many-body quantum systems, tensor networks have emerged as a promising class of models for solving machine learning problems, notably in unsupervised generative learning. While possessing many desirable…
This work addresses the problem of learning sparse representations of tensor data using structured dictionary learning. It proposes learning a mixture of separable dictionaries to better capture the structure of tensor data by generalizing…
Discovering and parameterising latent confounders represent important and challenging problems in causal structure learning and density estimation respectively. In this paper, we focus on both discovering and learning the distribution of…
We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random…
Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…
Bayesian network models with latent variables are widely used in statistics and machine learning. In this paper we provide a complete algebraic characterization of Bayesian network models with latent variables when the observed variables…
Empirical networks are often globally sparse, with a small average number of connections per node, when compared to the total size of the network. However, this sparsity tends not to be homogeneous, and networks can also be locally dense,…
Although deep learning has shown its powerful performance in many applications, the mathematical principles behind neural networks are still mysterious. In this paper, we consider the problem of learning a one-hidden-layer neural network…
In recent years we see a rapidly growing line of research which shows learnability of various models via common neural network algorithms. Yet, besides a very few outliers, these results show learnability of models that can be learned using…
Graphical models are powerful tools for modeling high-dimensional data, but learning graphical models in the presence of latent variables is well-known to be difficult. In this work we give new results for learning Restricted Boltzmann…
Tensors in the form of multilinear arrays are ubiquitous in data science applications. Captured real-world data, including video, hyperspectral images, and discretized physical systems, naturally occur as tensors and often come with…
We propose a new Bayesian Markov switching regression model for multidimensional arrays (tensors) of binary time series. We assume a zero-inflated logit regression with time-varying parameters and apply it to multilayer temporal networks.…
Multivariate polynomials arise in many different disciplines. Representing such a polynomial as a vector of univariate polynomials can offer useful insight, as well as more intuitive understanding. For this, techniques based on tensor…
We show how fitting sparse linear models over learned deep feature representations can lead to more debuggable neural networks. These networks remain highly accurate while also being more amenable to human interpretation, as we demonstrate…
Large-scale recurrent networks have drawn increasing attention recently because of their capabilities in modeling a large variety of real-world phenomena and physical mechanisms. This paper studies how to identify all authentic connections…
Low-rank approximation models of data matrices have become important machine learning and data mining tools in many fields including computer vision, text mining, bioinformatics and many others. They allow for embedding high-dimensional…