Related papers: Weighted Tensor Decomposition for Learning Latent …
Tensor data are increasingly available in many application domains. We develop several tensor decomposition methods for binary tensor data. Different from classical tensor decompositions for continuous-valued data with squared error loss,…
The power of multivariate functions is their ability to model a wide variety of phenomena, but have the disadvantages that they lack an intuitive or interpretable representation, and often require a (very) large number of parameters. We…
We study the problem of learning mixtures of linear dynamical systems (MLDS) from input-output data. The mixture setting allows us to leverage observations from related dynamical systems to improve the estimation of individual models.…
We present an alternating least squares type numerical optimization scheme to estimate conditionally-independent mixture models in $\mathbb{R}^n$, without parameterizing the distributions. Following the method of moments, we tackle an…
Tensor time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to…
Data used for analytics and machine learning often take the form of tables with categorical entries. We introduce a family of lossless compression algorithms for such data that proceed in four steps: $(i)$ Estimate latent variables…
This work considers the problem of estimating the parameters of negative mixture models, i.e. mixture models that possibly involve negative weights. The contributions of this paper are as follows. (i) We show that every rational probability…
Compressed sensing techniques enable efficient acquisition and recovery of sparse, high-dimensional data signals via low-dimensional projections. In this work, we propose Uncertainty Autoencoders, a learning framework for unsupervised…
Learning generative probabilistic models is a core problem in machine learning, which presents significant challenges due to the curse of dimensionality. This paper proposes a joint dimensionality reduction and non-parametric density…
Scientific computations or measurements may result in huge volumes of data. Often these can be thought of representing a real-valued function on a high-dimensional domain, and can be conceptually arranged in the format of a tensor of high…
High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…
Probabilistic models help us encode latent structures that both model the data and are ideally also useful for specific downstream tasks. Among these, mixture models and their time-series counterparts, hidden Markov models, identify…
Tensor decomposition methods are popular tools for analysis of multi-way datasets from social media, healthcare, spatio-temporal domains, and others. Widely adopted models such as Tucker and canonical polyadic decomposition (CPD) follow a…
Many problems in computational neuroscience, neuroinformatics, pattern/image recognition, signal processing and machine learning generate massive amounts of multidimensional data with multiple aspects and high dimensionality. Tensors (i.e.,…
The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…
In recent years, image recognition method has been a research hotspot in various fields such as video surveillance, biometric identification, unmanned vehicles, human-computer interaction, and medical image recognition. Existing recognition…
Dynamic mode decomposition (DMD) is a recently developed tool for the analysis of the behavior of complex dynamical systems. In this paper, we will propose an extension of DMD that exploits low-rank tensor decompositions of potentially…
Higher-order tensor datasets arise commonly in recommendation systems, neuroimaging, and social networks. Here we develop probable methods for estimating a possibly high rank signal tensor from noisy observations. We consider a generative…
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…
In numerous settings, it is increasingly common to deal with longitudinal data organized as high-dimensional multi-dimensional arrays, also known as tensors. Within this framework, the time-continuous property of longitudinal data often…