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Low Complexity Gaussian Latent Factor Models and a Blessing of Dimensionality

arXiv.org Machine Learning

Learning the structure of graphical models from data usually incurs a heavy curse of dimensionality that renders this problem intractable in many real-world situations. The rare cases where the curse becomes a blessing provide insight into the limits of the efficiently computable and augment the scarce options for treating very under-sampled, high-dimensional data. We study a special class of Gaussian latent factor models where each (non-iid) observed variable depends on at most one of a set of latent variables. We derive information-theoretic lower bounds on the sample complexity for structure recovery that suggest complexity actually decreases as the dimensionality increases. Contrary to this prediction, we observe that existing structure recovery methods deteriorate with increasing dimension. Therefore, we design a new approach to learning Gaussian latent factor models that benefits from dimensionality. Our approach relies on an unconstrained information-theoretic objective whose global optima correspond to structured latent factor generative models. In addition to improved structure recovery, we also show that we are able to outperform state-of-the-art approaches for covariance estimation on both synthetic and real data in the very under-sampled, high-dimensional regime.


Modeling Relational Data via Latent Factor Blockmodel

arXiv.org Machine Learning

In this paper we address the problem of modeling relational data, which appear in many applications such as social network analysis, recommender systems and bioinformatics. Previous studies either consider latent feature based models but disregarding local structure in the network, or focus exclusively on capturing local structure of objects based on latent blockmodels without coupling with latent characteristics of objects. To combine the benefits of the previous work, we propose a novel model that can simultaneously incorporate the effect of latent features and covariates if any, as well as the effect of latent structure that may exist in the data. To achieve this, we model the relation graph as a function of both latent feature factors and latent cluster memberships of objects to collectively discover globally predictive intrinsic properties of objects and capture latent block structure in the network to improve prediction performance. We also develop an optimization transfer algorithm based on the generalized EM-style strategy to learn the latent factors. We prove the efficacy of our proposed model through the link prediction task and cluster analysis task, and extensive experiments on the synthetic data and several real world datasets suggest that our proposed LFBM model outperforms the other state of the art approaches in the evaluated tasks.


Gaussian process based nonlinear latent structure discovery in multivariate spike train data

Neural Information Processing Systems

A large body of recent work focuses on methods for extracting low-dimensional latent structure from multi-neuron spike train data. Most such methods employ either linear latent dynamics or linear mappings from latent space to log spike rates. Here we propose a doubly nonlinear latent variable model that can identify low-dimensional structure underlying apparently high-dimensional spike train data. We introduce the Poisson Gaussian-Process Latent Variable Model (P-GPLVM), which consists of Poisson spiking observations and two underlying Gaussian processes--one governing a temporal latent variable and another governing a set of nonlinear tuning curves. The use of nonlinear tuning curves enables discovery of low-dimensional latent structure even when spike responses exhibit high linear dimensionality (e.g., as found in hippocampal place cell codes).


Nonparametric Latent Tree Graphical Models: Inference, Estimation, and Structure Learning

arXiv.org Machine Learning

Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for parameter estimation, inference, and structure learning mainly rely on the Gaussian or discrete assumptions, which are restrictive under many applications. In this paper, we propose new nonparametric methods based on reproducing kernel Hilbert space embeddings of distributions that can recover the latent tree structures, estimate the parameters, and perform inference for high dimensional continuous and non-Gaussian variables. The usefulness of the proposed methods are illustrated by thorough numerical results.


Unsupervised Learning with Imbalanced Data via Structure Consolidation Latent Variable Model

arXiv.org Machine Learning

Unsupervised learning on imbalanced data is challenging because, when given imbalanced data, current model is often dominated by the major category and ignores the categories with small amount of data. We develop a latent variable model that can cope with imbalanced data by dividing the latent space into a shared space and a private space. Based on Gaussian Process Latent Variable Models, we propose a new kernel formulation that enables the separation of latent space and derives an efficient variational inference method. The performance of our model is demonstrated with an imbalanced medical image dataset.