scholarly journals Interpretable Variational Graph Autoencoder with Noninformative Prior

2021 ◽  
Vol 13 (2) ◽  
pp. 51
Author(s):  
Lili Sun ◽  
Xueyan Liu ◽  
Min Zhao ◽  
Bo Yang
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Expert Knowledge ◽  
Structural Information ◽  
Standard Normal Distribution ◽  
Noninformative Prior ◽  
Latent Space ◽  
Distribution Parameters ◽  
Standard Normal ◽  
Low Dimensional

Variational graph autoencoder, which can encode structural information and attribute information in the graph into low-dimensional representations, has become a powerful method for studying graph-structured data. However, most existing methods based on variational (graph) autoencoder assume that the prior of latent variables obeys the standard normal distribution which encourages all nodes to gather around 0. That leads to the inability to fully utilize the latent space. Therefore, it becomes a challenge on how to choose a suitable prior without incorporating additional expert knowledge. Given this, we propose a novel noninformative prior-based interpretable variational graph autoencoder (NPIVGAE). Specifically, we exploit the noninformative prior as the prior distribution of latent variables. This prior enables the posterior distribution parameters to be almost learned from the sample data. Furthermore, we regard each dimension of a latent variable as the probability that the node belongs to each block, thereby improving the interpretability of the model. The correlation within and between blocks is described by a block–block correlation matrix. We compare our model with state-of-the-art methods on three real datasets, verifying its effectiveness and superiority.

scholarly journals Predictive learning as a network mechanism for extracting low-dimensional latent space representations

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Stefano Recanatesi ◽  
Matthew Farrell ◽  
Guillaume Lajoie ◽  
Sophie Deneve ◽  
Mattia Rigotti ◽  
...  
Keyword(s):  
Latent Variables ◽  
Latent Structure ◽  
Network Activity ◽  
Semantic Organization ◽  
Sequential Processing ◽  
Predictive Learning ◽  
Neural Representations ◽  
Latent Space ◽  
Low Dimensional ◽  
Sensory Prediction

AbstractArtificial neural networks have recently achieved many successes in solving sequential processing and planning tasks. Their success is often ascribed to the emergence of the task’s low-dimensional latent structure in the network activity – i.e., in the learned neural representations. Here, we investigate the hypothesis that a means for generating representations with easily accessed low-dimensional latent structure, possibly reflecting an underlying semantic organization, is through learning to predict observations about the world. Specifically, we ask whether and when network mechanisms for sensory prediction coincide with those for extracting the underlying latent variables. Using a recurrent neural network model trained to predict a sequence of observations we show that network dynamics exhibit low-dimensional but nonlinearly transformed representations of sensory inputs that map the latent structure of the sensory environment. We quantify these results using nonlinear measures of intrinsic dimensionality and linear decodability of latent variables, and provide mathematical arguments for why such useful predictive representations emerge. We focus throughout on how our results can aid the analysis and interpretation of experimental data.

scholarly journals Collective dynamics of repeated inference in variational autoencoder rapidly find cluster structure

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Yoshihiro Nagano ◽  
Ryo Karakida ◽  
Masato Okada
Keyword(s):  
Activity Pattern ◽  
Latent Variables ◽  
Cluster Structure ◽  
Generative Models ◽  
Cluster Center ◽  
Specific Data ◽  
Global Cluster ◽  
Latent Space ◽  
Variational Autoencoder ◽  
Low Dimensional

Abstract Deep neural networks are good at extracting low-dimensional subspaces (latent spaces) that represent the essential features inside a high-dimensional dataset. Deep generative models represented by variational autoencoders (VAEs) can generate and infer high-quality datasets, such as images. In particular, VAEs can eliminate the noise contained in an image by repeating the mapping between latent and data space. To clarify the mechanism of such denoising, we numerically analyzed how the activity pattern of trained networks changes in the latent space during inference. We considered the time development of the activity pattern for specific data as one trajectory in the latent space and investigated the collective behavior of these inference trajectories for many data. Our study revealed that when a cluster structure exists in the dataset, the trajectory rapidly approaches the center of the cluster. This behavior was qualitatively consistent with the concept retrieval reported in associative memory models. Additionally, the larger the noise contained in the data, the closer the trajectory was to a more global cluster. It was demonstrated that by increasing the number of the latent variables, the trend of the approach a cluster center can be enhanced, and the generalization ability of the VAE can be improved.

scholarly journals Extracting Low-Dimensional Latent Structure from Time Series in the Presence of Delays

2015 ◽  
Vol 27 (9) ◽  
pp. 1825-1856 ◽  
Author(s):  
Karthik C. Lakshmanan ◽  
Patrick T. Sadtler ◽  
Elizabeth C. Tyler-Kabara ◽  
Aaron P. Batista ◽  
Byron M. Yu
Keyword(s):  
Time Series ◽  
Time Delay ◽  
Motor Cortex ◽  
Dimensionality Reduction ◽  
Gaussian Process ◽  
Latent Variables ◽  
Time Delays ◽  
High Dimensional ◽  
Latent Space ◽  
Low Dimensional

Noisy, high-dimensional time series observations can often be described by a set of low-dimensional latent variables. Commonly used methods to extract these latent variables typically assume instantaneous relationships between the latent and observed variables. In many physical systems, changes in the latent variables manifest as changes in the observed variables after time delays. Techniques that do not account for these delays can recover a larger number of latent variables than are present in the system, thereby making the latent representation more difficult to interpret. In this work, we introduce a novel probabilistic technique, time-delay gaussian-process factor analysis (TD-GPFA), that performs dimensionality reduction in the presence of a different time delay between each pair of latent and observed variables. We demonstrate how using a gaussian process to model the evolution of each latent variable allows us to tractably learn these delays over a continuous domain. Additionally, we show how TD-GPFA combines temporal smoothing and dimensionality reduction into a common probabilistic framework. We present an expectation/conditional maximization either (ECME) algorithm to learn the model parameters. Our simulations demonstrate that when time delays are present, TD-GPFA is able to correctly identify these delays and recover the latent space. We then applied TD-GPFA to the activity of tens of neurons recorded simultaneously in the macaque motor cortex during a reaching task. TD-GPFA is able to better describe the neural activity using a more parsimonious latent space than GPFA, a method that has been used to interpret motor cortex data but does not account for time delays. More broadly, TD-GPFA can help to unravel the mechanisms underlying high-dimensional time series data by taking into account physical delays in the system.

scholarly journals A Flow-Based Deep Latent Variable Model for Speech Spectrogram Modeling and Enhancement

2020 ◽  
Author(s):  
Aditya Arie Nugraha ◽  
Kouhei Sekiguchi ◽  
Kazuyoshi Yoshii
Keyword(s):  
Speech Enhancement ◽  
Latent Variables ◽  
Latent Variable ◽  
Generative Models ◽  
Latent Variable Model ◽  
Variable Model ◽  
Variational Autoencoder ◽  
Latent Representations ◽  
Low Dimensional ◽  
Better Than

This paper describes a deep latent variable model of speech power spectrograms and its application to semi-supervised speech enhancement with a deep speech prior. By integrating two major deep generative models, a variational autoencoder (VAE) and a normalizing flow (NF), in a mutually-beneficial manner, we formulate a flexible latent variable model called the NF-VAE that can extract low-dimensional latent representations from high-dimensional observations, akin to the VAE, and does not need to explicitly represent the distribution of the observations, akin to the NF. In this paper, we consider a variant of NF called the generative flow (GF a.k.a. Glow) and formulate a latent variable model called the GF-VAE. We experimentally show that the proposed GF-VAE is better than the standard VAE at capturing fine-structured harmonics of speech spectrograms, especially in the high-frequency range. A similar finding is also obtained when the GF-VAE and the VAE are used to generate speech spectrograms from latent variables randomly sampled from the standard Gaussian distribution. Lastly, when these models are used as speech priors for statistical multichannel speech enhancement, the GF-VAE outperforms the VAE and the GF.

scholarly journals A generative modeling approach for interpreting population-level variability in brain structure

2020 ◽  
Author(s):  
Ran Liu ◽  
Cem Subakan ◽  
Aishwarya H. Balwani ◽  
Jennifer Whitesell ◽  
Julie Harris ◽  
...  
Keyword(s):  
Brain Structure ◽  
Latent Variables ◽  
Population Level ◽  
Individual Variability ◽  
Neural Structure ◽  
Modeling Approach ◽  
Structured Perturbations ◽  
Generative Modeling ◽  
Latent Space ◽  
Low Dimensional

AbstractUnderstanding how neural structure varies across individuals is critical for characterizing the effects of disease, learning, and aging on the brain. However, disentangling the different factors that give rise to individual variability is still an outstanding challenge. In this paper, we introduce a deep generative modeling approach to find different modes of variation across many individuals. To do this, we start by training a variational autoencoder on a collection of auto-fluorescence images from a little over 1,700 mouse brains at 25 micron resolution. To then tap into the learned factors and validate the model’s expressiveness, we developed a novel bi-directional technique to interpret the latent space–by making structured perturbations to both, the high-dimensional inputs of the network, as well as the low-dimensional latent variables in its bottleneck. Our results demonstrate that through coupling generative modeling frameworks with structured perturbations, it is possible to probe the latent space to provide insights into the representations of brain structure formed in deep neural networks.

scholarly journals A tractable latent variable model for nonlinear dimensionality reduction

2020 ◽  
Vol 117 (27) ◽  
pp. 15403-15408
Author(s):  
Lawrence K. Saul
Keyword(s):  
Latent Variables ◽  
Latent Variable ◽  
Linear Equations ◽  
Three Dimensional ◽  
Coarse Graining ◽  
Graph Laplacian ◽  
Latent Variable Model ◽  
Nonlinear Dimensionality Reduction ◽  
Variable Model ◽  
Low Dimensional

We propose a latent variable model to discover faithful low-dimensional representations of high-dimensional data. The model computes a low-dimensional embedding that aims to preserve neighborhood relationships encoded by a sparse graph. The model both leverages and extends current leading approaches to this problem. Like t-distributed Stochastic Neighborhood Embedding, the model can produce two- and three-dimensional embeddings for visualization, but it can also learn higher-dimensional embeddings for other uses. Like LargeVis and Uniform Manifold Approximation and Projection, the model produces embeddings by balancing two goals—pulling nearby examples closer together and pushing distant examples further apart. Unlike these approaches, however, the latent variables in our model provide additional structure that can be exploited for learning. We derive an Expectation–Maximization procedure with closed-form updates that monotonically improve the model’s likelihood: In this procedure, embeddings are iteratively adapted by solving sparse, diagonally dominant systems of linear equations that arise from a discrete graph Laplacian. For large problems, we also develop an approximate coarse-graining procedure that avoids the need for negative sampling of nonadjacent nodes in the graph. We demonstrate the model’s effectiveness on datasets of images and text.

scholarly journals A Flow-Based Deep Latent Variable Model for Speech Spectrogram Modeling and Enhancement

2020 ◽  
Author(s):  
Aditya Arie Nugraha ◽  
Kouhei Sekiguchi ◽  
Kazuyoshi Yoshii
Keyword(s):  
Speech Enhancement ◽  
Latent Variables ◽  
Latent Variable ◽  
Generative Models ◽  
Latent Variable Model ◽  
Variable Model ◽  
Variational Autoencoder ◽  
Latent Representations ◽  
Low Dimensional ◽  
Better Than

This paper describes a deep latent variable model of speech power spectrograms and its application to semi-supervised speech enhancement with a deep speech prior. By integrating two major deep generative models, a variational autoencoder (VAE) and a normalizing flow (NF), in a mutually-beneficial manner, we formulate a flexible latent variable model called the NF-VAE that can extract low-dimensional latent representations from high-dimensional observations, akin to the VAE, and does not need to explicitly represent the distribution of the observations, akin to the NF. In this paper, we consider a variant of NF called the generative flow (GF a.k.a. Glow) and formulate a latent variable model called the GF-VAE. We experimentally show that the proposed GF-VAE is better than the standard VAE at capturing fine-structured harmonics of speech spectrograms, especially in the high-frequency range. A similar finding is also obtained when the GF-VAE and the VAE are used to generate speech spectrograms from latent variables randomly sampled from the standard Gaussian distribution. Lastly, when these models are used as speech priors for statistical multichannel speech enhancement, the GF-VAE outperforms the VAE and the GF.

scholarly journals Predictive learning as a network mechanism for extracting low-dimensional latent space representations

2018 ◽  
Author(s):  
Stefano Recanatesi ◽  
Matthew Farrell ◽  
Guillaume Lajoie ◽  
Sophie Deneve ◽  
Mattia Rigotti ◽  
...  
Keyword(s):  
Latent Variables ◽  
Latent Structure ◽  
Network Activity ◽  
Semantic Organization ◽  
Sequential Processing ◽  
Predictive Learning ◽  
Neural Representations ◽  
Latent Space ◽  
Low Dimensional ◽  
Sensory Prediction

Artificial neural networks have recently achieved many successes in solving sequential processing and planning tasks. Their success is often ascribed to the emergence of the task’s low-dimensional latent structure in the network activity – i.e., in the learned neural representations. Here, we investigate the hypothesis that a means for generating representations with easily accessed low-dimensional latent structure, possibly reflecting an underlying semantic organization, is through learning to predict observations about the world. Specifically, we ask whether and when network mechanisms for sensory prediction coincide with those for extracting the underlying latent variables. Using a recurrent neural network model trained to predict a sequence of observations we show that network dynamics exhibit low-dimensional but nonlinearly transformed representations of sensory inputs that map the latent structure of the sensory environment. We quantify these results using nonlinear measures of intrinsic dimensionality and linear decodability of latent variables, and provide mathematical arguments for why such useful predictive representations emerge. We focus throughout on how our results can aid the analysis and interpretation of experimental data.

scholarly journals Dirichlet Process Prior for Student’s t Graph Variational Autoencoders

2021 ◽  
Vol 13 (3) ◽  
pp. 75
Author(s):  
Yuexuan Zhao ◽  
Jing Huang
Keyword(s):  
Latent Variables ◽  
Dirichlet Process ◽  
Prior Distribution ◽  
Standard Normal Distribution ◽  
Dirichlet Process Prior ◽  
External Relations ◽  
Latent Features ◽  
Standard Normal ◽  
Heavy Tailed ◽  
Student’S T

Graph variational auto-encoder (GVAE) is a model that combines neural networks and Bayes methods, capable of deeper exploring the influential latent features of graph reconstruction. However, several pieces of research based on GVAE employ a plain prior distribution for latent variables, for instance, standard normal distribution (N(0,1)). Although this kind of simple distribution has the advantage of convenient calculation, it will also make latent variables contain relatively little helpful information. The lack of adequate expression of nodes will inevitably affect the process of generating graphs, which will eventually lead to the discovery of only external relations and the neglect of some complex internal correlations. In this paper, we present a novel prior distribution for GVAE, called Dirichlet process (DP) construction for Student’s t (St) distribution. The DP allows the latent variables to adapt their complexity during learning and then cooperates with heavy-tailed St distribution to approach sufficient node representation. Experimental results show that this method can achieve a relatively better performance against the baselines.

Probability-Based and Measurement-Related Hypotheses With Full Restriction for Investigations by Means of Confirmatory Factor Analysis

Methodology ◽  
2011 ◽  
Vol 7 (4) ◽  
pp. 157-164
Author(s):  
Karl Schweizer
Keyword(s):  
Factor Analysis ◽  
Confirmatory Factor Analysis ◽  
Cognitive Processing ◽  
Latent Variables ◽  
Repeated Measures ◽  
Latent Variable ◽  
Model Fit ◽  
Repeated Measures Data ◽  
Confirmatory Factor ◽  
And Performance

Probability-based and measurement-related hypotheses for confirmatory factor analysis of repeated-measures data are investigated. Such hypotheses comprise precise assumptions concerning the relationships among the true components associated with the levels of the design or the items of the measure. Measurement-related hypotheses concentrate on the assumed processes, as, for example, transformation and memory processes, and represent treatment-dependent differences in processing. In contrast, probability-based hypotheses provide the opportunity to consider probabilities as outcome predictions that summarize the effects of various influences. The prediction of performance guided by inexact cues serves as an example. In the empirical part of this paper probability-based and measurement-related hypotheses are applied to working-memory data. Latent variables according to both hypotheses contribute to a good model fit. The best model fit is achieved for the model including latent variables that represented serial cognitive processing and performance according to inexact cues in combination with a latent variable for subsidiary processes.

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