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A mixture of factor analyzers is a semi-parametric density estimator that generalizes the well-known mixtures of Gaussians model by allowing each Gaussian in the mixture to be represented in a different lower-dimensional manifold. This paper presents a robust and parsimonious model selection algorithm for training a mixture of factor analyzers, carrying out simultaneous clustering and locally linear, globally nonlinear dimensionality reduction. Permitting different number of factors per mixture component, the algorithm adapts the model complexity to the data complexity. We compare the proposed algorithm with related automatic model selection algorithms on a number of benchmarks. The results indicate the effectiveness of this fast and robust approach in clustering, manifold learning and class-conditional modeling.
In this paper, we consider mixtures of two Mallows models for top-$k$ rankings, both with the same location parameter but with different scale parameters, i.e., a mixture of concentric Mallows models. This situation arises when we have a heterogeneou
Mixtures of high dimensional Gaussian distributions have been studied extensively in statistics and learning theory. While the total variation distance appears naturally in the sample complexity of distribution learning, it is analytically difficult
Graph convolutional networks (GCNs) are a widely used method for graph representation learning. To elucidate the capabilities and limitations of GCNs, we investigate their power, as a function of their number of layers, to distinguish between differe
The estimation of an f-divergence between two probability distributions based on samples is a fundamental problem in statistics and machine learning. Most works study this problem under very weak assumptions, in which case it is provably hard. We con
Real-world data typically contain a large number of features that are often heterogeneous in nature, relevance, and also units of measure. When assessing the similarity between data points, one can build various distance measures using subsets of the