Is it possible to crowdsource categorization? Amongst the challenges: (a) each worker has only a partial view of the data, (b) different workers may have different clustering criteria and may produce different numbers of categories, (c) the underlying category structure may be hierarchical. We propose a Bayesian model of how workers may approach clustering and show how one may infer clusters / categories, as well as worker parameters, using this model. Our experiments, carried out on large collections of images, suggest that Bayesian crowdclustering works well and may be superior to single-expert annotations.

For many real-world applications, we often need to select correlated variables-- such as genetic variations and imaging features associated with Alzheimer's disease--in a high dimensional space. The correlation between variables presents a challenge to classical variable selection methods. To address this challenge, the elastic net has been developed and successfully applied to many applications. Despite its great success, the elastic net does not exploit the correlation information embedded in the data to select correlated variables. To overcome this limitation, we present a novel hybrid model, EigenNet, that uses the eigenstructures of data to guide variable selection.

A number of recent scientific and engineering problems require signals to be decomposed into a product of a slowly varying positive envelope and a quickly varying carrier whose instantaneous frequency also varies slowly over time. Although signal processing provides algorithms for so-called amplitude-and frequencydemodulation (AFD), there are well known problems with all of the existing methods. Motivated by the fact that AFD is ill-posed, we approach the problem using probabilistic inference. The new approach, called probabilistic amplitude and frequency demodulation (PAFD), models instantaneous frequency using an auto-regressive generalization of the von Mises distribution, and the envelopes using Gaussian auto-regressive dynamics with a positivity constraint. A novel form of expectation propagation is used for inference. We demonstrate that although PAFD is computationally demanding, it outperforms previous approaches on synthetic and real signals in clean, noisy and missing data settings.

Inferring key unobservable features of individuals is an important task in the applied sciences. In particular, an important source of data in fields such as marketing, social sciences and medicine is questionnaires: answers in such questionnaires are noisy measures of target unobserved features. While comprehensive surveys help to better estimate the latent variables of interest, aiming at a high number of questions comes at a price: refusal to participate in surveys can go up, as well as the rate of missing data; quality of answers can decline; costs associated with applying such questionnaires can also increase. In this paper, we cast the problem of refining existing models for questionnaire data as follows: solve a constrained optimization problem of preserving the maximum amount of information found in a latent variable model using only a subset of existing questions. The goal is to find an optimal subset of a given size. For that, we first define an information theoretical measure for quantifying the quality of a reduced questionnaire. Three different approximate inference methods are introduced to solve this problem. Comparisons against a simple but powerful heuristic are presented.

We examine: Temporal dynamics Necker cube & binocular rivalry Spatial attention Bonus: explicit depth modelling Full story & details: T018!

It has been argued that perceptual multistability reflects probabilistic inference performed by the brain when sensory input is ambiguous. Alternatively, more traditional explanations of multistability refer to low-level mechanisms such as neuronal adaptation. We employ a Deep Boltzmann Machine (DBM) model of cortical processing to demonstrate that these two different approaches can be combined in the same framework. Based on recent developments in machine learning, we show how neuronal adaptation can be understood as a mechanism that improves probabilistic, sampling-based inference. Using the ambiguous Necker cube image, we analyze the perceptual switching exhibited by the model. We also examine the influence of spatial attention, and explore how binocular rivalry can be modeled with the same approach. Our work joins earlier studies in demonstrating how the principles underlying DBMs relate to cortical processing, and offers novel perspectives on the neural implementation of approximate probabilistic inference in the brain.

We introduce a variational Bayesian inference algorithm which can be widely applied to sparse linear models. The algorithm is based on the spike and slab prior which, from a Bayesian perspective, is the golden standard for sparse inference. We apply the method to a general multi-task and multiple kernel learning model in which a common set of Gaussian process functions is linearly combined with task-specific sparse weights, thus inducing relation between tasks. This model unifies several sparse linear models, such as generalized linear models, sparse factor analysis and matrix factorization with missing values, so that the variational algorithm can be applied to all these cases. We demonstrate our approach in multioutput Gaussian process regression, multi-class classification, image processing applications and collaborative filtering.

In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex forms and better properties than traditional Cauchy and double exponential priors. We first propose a new class of normal scale mixtures through a novel generalized beta distribution that encompasses many interesting priors as special cases. This encompassing framework should prove useful in comparing competing priors, considering properties and revealing close connections. We then develop a class of variational Bayes approximations through the new hierarchy presented that will scale more efficiently to the types of truly massive data sets that are now encountered routinely.

In standard Gaussian Process regression input locations are assumed to be noise free. We present a simple yet effective GP model for training on input points corrupted by i.i.d.

Components estimated by independent component analysis and related methods are typically not independent in real data. A very common form of nonlinear dependency between the components is correlations in their variances or energies. Here, we propose a principled probabilistic model to model the energycorrelations between the latent variables. Our two-stage model includes a linear mixing of latent signals into the observed ones like in ICA. The main new feature is a model of the energy-correlations based on the structural equation model (SEM), in particular, a Linear Non-Gaussian SEM. The SEM is closely related to divisive normalization which effectively reduces energy correlation. Our new twostage model enables estimation of both the linear mixing and the interactions related to energy-correlations, without resorting to approximations of the likelihood function or other non-principled approaches. We demonstrate the applicability of our method with synthetic dataset, natural images and brain signals.