5,358 research outputs found
GC-Flow: A Graph-Based Flow Network for Effective Clustering
Graph convolutional networks (GCNs) are \emph{discriminative models} that
directly model the class posterior for semi-supervised
classification of graph data. While being effective, as a representation
learning approach, the node representations extracted from a GCN often miss
useful information for effective clustering, because the objectives are
different. In this work, we design normalizing flows that replace GCN layers,
leading to a \emph{generative model} that models both the class conditional
likelihood and the class prior . The resulting neural
network, GC-Flow, retains the graph convolution operations while being equipped
with a Gaussian mixture representation space. It enjoys two benefits: it not
only maintains the predictive power of GCN, but also produces well-separated
clusters, due to the structuring of the representation space. We demonstrate
these benefits on a variety of benchmark data sets. Moreover, we show that
additional parameterization, such as that on the adjacency matrix used for
graph convolutions, yields additional improvement in clustering.Comment: ICML 2023. Code is available at https://github.com/xztcwang/GCFlo
From patterned response dependency to structured covariate dependency: categorical-pattern-matching
Data generated from a system of interest typically consists of measurements
from an ensemble of subjects across multiple response and covariate features,
and is naturally represented by one response-matrix against one
covariate-matrix. Likely each of these two matrices simultaneously embraces
heterogeneous data types: continuous, discrete and categorical. Here a matrix
is used as a practical platform to ideally keep hidden dependency among/between
subjects and features intact on its lattice. Response and covariate dependency
is individually computed and expressed through mutliscale blocks via a newly
developed computing paradigm named Data Mechanics. We propose a categorical
pattern matching approach to establish causal linkages in a form of information
flows from patterned response dependency to structured covariate dependency.
The strength of an information flow is evaluated by applying the combinatorial
information theory. This unified platform for system knowledge discovery is
illustrated through five data sets. In each illustrative case, an information
flow is demonstrated as an organization of discovered knowledge loci via
emergent visible and readable heterogeneity. This unified approach
fundamentally resolves many long standing issues, including statistical
modeling, multiple response, renormalization and feature selections, in data
analysis, but without involving man-made structures and distribution
assumptions. The results reported here enhance the idea that linking patterns
of response dependency to structures of covariate dependency is the true
philosophical foundation underlying data-driven computing and learning in
sciences.Comment: 32 pages, 10 figures, 3 box picture
Semi-Supervised Generation with Cluster-aware Generative Models
Deep generative models trained with large amounts of unlabelled data have
proven to be powerful within the domain of unsupervised learning. Many real
life data sets contain a small amount of labelled data points, that are
typically disregarded when training generative models. We propose the
Cluster-aware Generative Model, that uses unlabelled information to infer a
latent representation that models the natural clustering of the data, and
additional labelled data points to refine this clustering. The generative
performances of the model significantly improve when labelled information is
exploited, obtaining a log-likelihood of -79.38 nats on permutation invariant
MNIST, while also achieving competitive semi-supervised classification
accuracies. The model can also be trained fully unsupervised, and still improve
the log-likelihood performance with respect to related methods
Auxiliary Deep Generative Models
Deep generative models parameterized by neural networks have recently
achieved state-of-the-art performance in unsupervised and semi-supervised
learning. We extend deep generative models with auxiliary variables which
improves the variational approximation. The auxiliary variables leave the
generative model unchanged but make the variational distribution more
expressive. Inspired by the structure of the auxiliary variable we also propose
a model with two stochastic layers and skip connections. Our findings suggest
that more expressive and properly specified deep generative models converge
faster with better results. We show state-of-the-art performance within
semi-supervised learning on MNIST, SVHN and NORB datasets.Comment: Proceedings of the 33rd International Conference on Machine Learning,
New York, NY, USA, 2016, JMLR: Workshop and Conference Proceedings volume 48,
Proceedings of the 33rd International Conference on Machine Learning, New
York, NY, USA, 201
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Improved streamflow forecasting using self-organizing radial basis function artificial neural networks
Streamflow forecasting has always been a challenging task for water resources engineers and managers and a major component of water resources system control. In this study, we explore the applicability of a Self Organizing Radial Basis (SORB) function to one-step ahead forecasting of daily streamflow. SORB uses a Gaussian Radial Basis Function architecture in conjunction with the Self-Organizing Feature Map (SOFM) used in data classification. SORB outperforms the two other ANN algorithms, the well known Multi-layer Feedforward Network (MFN) and Self-Organizing Linear Output map (SOLO) neural network for simulation of daily streamflow in the semi-arid Salt River basin. The applicability of the linear regression model was also investigated and concluded that the regression model is not reliable for this study. To generalize the model and derive a robust parameter set, cross-validation is applied and its outcome is compared with the split sample test. Cross-validation justifies the validity of the nonlinear relationship set up between input and output data. © 2004 Elsevier B.V. All rights reserved
Diffeomorphic Transformations for Time Series Analysis: An Efficient Approach to Nonlinear Warping
The proliferation and ubiquity of temporal data across many disciplines has
sparked interest for similarity, classification and clustering methods
specifically designed to handle time series data. A core issue when dealing
with time series is determining their pairwise similarity, i.e., the degree to
which a given time series resembles another. Traditional distance measures such
as the Euclidean are not well-suited due to the time-dependent nature of the
data. Elastic metrics such as dynamic time warping (DTW) offer a promising
approach, but are limited by their computational complexity,
non-differentiability and sensitivity to noise and outliers. This thesis
proposes novel elastic alignment methods that use parametric \& diffeomorphic
warping transformations as a means of overcoming the shortcomings of DTW-based
metrics. The proposed method is differentiable \& invertible, well-suited for
deep learning architectures, robust to noise and outliers, computationally
efficient, and is expressive and flexible enough to capture complex patterns.
Furthermore, a closed-form solution was developed for the gradient of these
diffeomorphic transformations, which allows an efficient search in the
parameter space, leading to better solutions at convergence. Leveraging the
benefits of these closed-form diffeomorphic transformations, this thesis
proposes a suite of advancements that include: (a) an enhanced temporal
transformer network for time series alignment and averaging, (b) a
deep-learning based time series classification model to simultaneously align
and classify signals with high accuracy, (c) an incremental time series
clustering algorithm that is warping-invariant, scalable and can operate under
limited computational and time resources, and finally, (d) a normalizing flow
model that enhances the flexibility of affine transformations in coupling and
autoregressive layers.Comment: PhD Thesis, defended at the University of Navarra on July 17, 2023.
277 pages, 8 chapters, 1 appendi
Hybrid Models with Deep and Invertible Features
We propose a neural hybrid model consisting of a linear model defined on a
set of features computed by a deep, invertible transformation (i.e. a
normalizing flow). An attractive property of our model is that both
p(features), the density of the features, and p(targets | features), the
predictive distribution, can be computed exactly in a single feed-forward pass.
We show that our hybrid model, despite the invertibility constraints, achieves
similar accuracy to purely predictive models. Moreover the generative component
remains a good model of the input features despite the hybrid optimization
objective. This offers additional capabilities such as detection of
out-of-distribution inputs and enabling semi-supervised learning. The
availability of the exact joint density p(targets, features) also allows us to
compute many quantities readily, making our hybrid model a useful building
block for downstream applications of probabilistic deep learning.Comment: ICML 201
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