Neural Information Processing Systems http://nips.cc/

First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper proposes a novel model selection criterion for binary latent feature models. It is like variational Bayes, except that rather than assuming a factorized posterior over latent variables and parameters, it approximately integrates out the parameters using the BIC. They demonstrate improved held-out likelihood scores compared to several existing IBP implementations. The proposed approach seems like a reasonable thing to do, and is motivated by a plausible asymptotic argument.

This paper extends factorized asymptotic Bayesian (FAB) inference for latent feature models~(LFMs). FAB inference has not been applicable to models, including LFMs, without a specific condition on the Hesqsian matrix of a complete log-likelihood, which is required to derive a factorized information criterion''~(FIC). Our asymptotic analysis of the Hessian matrix of LFMs shows that FIC of LFMs has the same form as those of mixture models. FAB/LFMs have several desirable properties (e.g., automatic hidden states selection and parameter identifiability) and empirically perform better than state-of-the-art Indian Buffet processes in terms of model selection, prediction, and computational efficiency.

Many data-science applications involve detecting a shared signal between two high-dimensional variables. Using random matrix theory methods, we determine when such signal can be detected and reconstructed from sample correlations, despite the background of sampling noise induced correlations. We consider three different covariance matrices constructed from two high-dimensional variables: their individual self covariance, their cross covariance, and the self covariance of the concatenated (joint) variable, which incorporates the self and the cross correlation blocks. We observe the expected Baik, Ben Arous, and Péché detectability phase transition in all these covariance matrices, and we show that joint and cross covariance matrices always reconstruct the shared signal earlier than the self covariances. Whether the joint or the cross approach is better depends on the mismatch of dimensionalities between the variables. We discuss what these observations mean for choosing the right method for detecting linear correlations in data and how these findings may generalize to nonlinear statistical dependencies.

Biased labelers are a systemic problem in crowdsourcing, and a comprehensive toolbox for handling their responses is still being developed. A typical crowdsourcing application can be divided into three steps: data collection, data curation, and learning. At present these steps are often treated separately. We present Bayesian Bias Mitigation for Crowdsourcing (BBMC), a Bayesian model to unify all three. Most data curation methods account for the effects of labeler bias by modeling all labels as coming from a single latent truth.

This paper extends factorized asymptotic Bayesian (FAB) inference for latent feature models (LFMs). FAB inference has not been applicable to models, including LFMs, without a specific condition on the Hessian matrix of a complete loglikelihood, which is required to derive a "factorized information criterion" (FIC). Our asymptotic analysis of the Hessian matrix of LFMs shows that FIC of LFMs has the same form as those of mixture models. FAB/LFMs have several desirable properties (e.g., automatic hidden states selection and parameter identifiability) and empirically perform better than state-of-the-art Indian Buffet processes in terms of model selection, prediction, and computational efficiency.

We define a probability distribution over equivalence classes of binary matrices with a finite number of rows and an unbounded number of columns. This distribution is suitable for use as a prior in probabilistic models that represent objects using a potentially infinite array of features. We identify a simple generative process that results in the same distribution over equivalence classes, which we call the Indian buffet process. We illustrate the use of this distribution as a prior in an infinite latent feature model, deriving a Markov chain Monte Carlo algorithm for inference in this model and applying the algorithm to an image dataset.

Over recent years Dirichlet processes and the associated Chinese restaurant process (CRP) have found many applications in clustering while the Indian buffet process (IBP) is increasingly used to describe latent feature models. In the clustering case, we associate to each data point a latent allocation variable. These latent variables can share the same value and this induces a partition of the data set. The CRP is a prior distribution on such partitions. In latent feature models, we associate to each data point a potentially infinite number of binary latent variables indicating the possession of some features and the IBP is a prior distribution on the associated infinite binary matrix.

Ubiquitous linear Gaussian exploratory tools such as principle component analysis (PCA) and factor analysis (FA) remain widely used as tools for: exploratory analysis, pre-processing, data visualization and related tasks. However, due to their rigid assumptions including crowding of high dimensional data, they have been replaced in many settings by more flexible and still interpretable latent feature models. The Feature allocation is usually modelled using discrete latent variables assumed to follow either parametric Beta-Bernoulli distribution or Bayesian nonparametric prior. In this work we propose a simple and tractable parametric feature allocation model which can address key limitations of current latent feature decomposition techniques. The new framework allows for explicit control over the number of features used to express each point and enables a more flexible set of allocation distributions including feature allocations with different sparsity levels. This approach is used to derive a novel adaptive Factor analysis (aFA), as well as, an adaptive probabilistic principle component analysis (aPPCA) capable of flexible structure discovery and dimensionality reduction in a wide case of scenarios. We derive both standard Gibbs sampler, as well as, an expectation-maximization inference algorithms that converge orders of magnitude faster to a reasonable point estimate solution. The utility of the proposed aPPCA model is demonstrated for standard PCA tasks such as feature learning, data visualization and data whitening. We show that aPPCA and aFA can infer interpretable high level features both when applied on raw MNIST and when applied for interpreting autoencoder features. We also demonstrate an application of the aPPCA to more robust blind source separation for functional magnetic resonance imaging (fMRI).

Over recent years Dirichlet processes and the associated Chinese restaurant process (CRP) have found many applications in clustering while the Indian buffet process (IBP) is increasingly used to describe latent feature models. In the clustering case, we associate to each data point a latent allocation variable. These latent variables can share the same value and this induces a partition of the data set. The CRP is a prior distribution on such partitions. In latent feature models, we associate to each data point a potentially infinite number of binary latent variables indicating the possession of some features and the IBP is a prior distribution on the associated infinite binary matrix.