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We develop a general method for estimating a finite mixture of non-normalized models. Here, a non-normalized model is defined to be a parametric distribution with an intractable normalization constant. Existing methods for estimating non-normalized models without computing the normalization constant are not applicable to mixture models because they contain more than one intractable normalization constant. The proposed method is derived by extending noise contrastive estimation (NCE), which estimates non-normalized models by discriminating between the observed data and some artificially generated noise. We also propose an extension of NCE with multiple noise distributions. Then, based on the observation that conventional classification learning with neural networks is implicitly assuming an exponential family as a generative model, we introduce a method for clustering unlabeled data by estimating a finite mixture of distributions in an exponential family. Estimation of this mixture model is attained by the proposed extensions of NCE where the training data of neural networks are used as noise. Thus, the proposed method provides a probabilistically principled clustering method that is able to utilize a deep representation. Application to image clustering using a deep neural network gives promising results.
We consider the semi-supervised clustering problem where crowdsourcing provides noisy information about the pairwise comparisons on a small subset of data, i.e., whether a sample pair is in the same cluster. We propose a new approach that includes a
We consider the problem of clustering datasets in the presence of arbitrary outliers. Traditional clustering algorithms such as k-means and spectral clustering are known to perform poorly for datasets contaminated with even a small number of outliers
Learning generative models that span multiple data modalities, such as vision and language, is often motivated by the desire to learn more useful, generalisable representations that faithfully capture common underlying factors between the modalities.
The problem of multimodal clustering arises whenever the data are gathered with several physically different sensors. Observations from different modalities are not necessarily aligned in the sense there there is no obvious way to associate or to com
We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are assumed to