Crowdsourcing has become a popular paradigm for labeling large datasets. However, ithas given rise to the computational task of aggregating the crowdsourced labels provided by a collection of unreliable annotators. We approach this problem bytransforming it into a standard inference problem in graphical models, and applying approximate variational methods, including belief propagation (BP) and mean field (MF). We show that our BP algorithm generalizes both majority votingand a recent algorithm by Karger et al. [1], while our MF method is closely related to a commonly used EM algorithm. In both cases, we find that the performance of the algorithms critically depends on the choice of a prior distribution onthe workers' reliability; by choosing the prior properly, both BP and MF (and EM) perform surprisingly well on both simulated and real-world datasets, competitive with state-of-the-art algorithms based on more complicated modeling assumptions.

The partition function plays a key role in probabilistic modeling including conditional random fields, graphical models, and maximum likelihood estimation. To optimize partition functions, this article introduces a quadratic variational upper bound. This inequality facilitates majorization methods: optimization of complicated functions through the iterative solution of simpler sub-problems. Such bounds remain efficient to compute even when the partition function involves a graphical model (with small tree-width) or in latent likelihood settings. For large-scale problems, low-rank versions of the bound are provided and outperform LBFGS as well as first-order methods. Several learning applications are shown and reduce to fast and convergent update rules. Experimental results show advantages over state-of-the-art optimization methods.

We introduce a large-volume box classification for binary prediction, which maintains a subset of weight vectors, and specifically axis-aligned boxes. Our learning algorithm seeks for a box of large volume that contains ``simple'' weight vectors which most of are accurate on the training set. Two versions of the learning process are cast as convex optimization problems, and it is shown how to solve them efficiently. The formulation yields a natural PAC-Bayesian performance bound and it is shown to minimize a quantity directly aligned with it. The algorithm outperforms SVM and the recently proposed AROW algorithm on a majority of $30$ NLP datasets and binarized USPS optical character recognition datasets.

Statistical features of neuronal spike trains are known to be non-Poisson. Here, we investigate the extent to which the non-Poissonian feature affects the efficiency of transmitting information on fluctuating firing rates. For this purpose, we introduce the Kullbuck-Leibler (KL) divergence as a measure of the efficiency of information encoding, and assume that spike trains are generated by time-rescaled renewal processes. We show that the KL divergence determines the lower bound of the degree of rate fluctuations below which the temporal variation of the firing rates is undetectable from sparse data. We also show that the KL divergence, as well as the lower bound, depends not only on the variability of spikes in terms of the coefficient of variation, but also significantly on the higher-order moments of interspike interval (ISI) distributions. We examine three specific models that are commonly used for describing the stochastic nature of spikes (the gamma, inverse Gaussian (IG) and lognormal ISI distributions), and find that the time-rescaled renewal process with the IG distribution achieves the largest KL divergence, followed by the lognormal and gamma distributions.

We present a truncation-free online variational inference algorithm for Bayesian nonparametric models. Unlike traditional (online) variational inference algorithms that require truncations for the model or the variational distribution, our method adapts model complexity on the fly. Our experiments for Dirichlet process mixture models and hierarchical Dirichlet process topic models on two large-scale data sets show better performance than previous online variational inference algorithms.

The usability of Brain Computer Interfaces (BCI) based on the P300 speller is severely hindered by the need for long training times and many repetitions of the same stimulus. In this contribution we introduce a set of unsupervised hierarchical probabilistic models that tackle both problems simultaneously by incorporating prior knowledge from two sources: information from other training subjects (through transfer learning) and information about the words being spelled (through language models). We show, that due to this prior knowledge, the performance of the unsupervised models parallels and in some cases even surpasses that of supervised models, while eliminating the tedious training session.

We introduce a new learning algorithm, named smooth-projected neighborhood pursuit, for estimating high dimensional undirected graphs. In particularly, we focus on the nonparanormal graphical model and provide theoretical guarantees for graph estimation consistency. In addition to new computational and theoretical analysis, we also provide an alternative view to analyze the tradeoff between computational efficiencyand statistical error under a smoothing optimization framework. Numerical results on both synthetic and real datasets are provided to support our theory.

We study the problem of maximum marginal prediction (MMP) in probabilistic graphical models, a task that occurs, for example, as the Bayes optimal decision rule under a Hamming loss. MMP is typically performed as a two-stage procedure: oneestimates each variable's marginal probability and then forms a prediction from the states of maximal probability. In this work we propose a simple yet effective technique for accelerating MMP when inference is sampling-based: instead of the above two-stage procedure we directly estimate the posterior probability of each decision variable. This allows us to identify the point of time when we are sufficiently certain about any individual decision. Whenever this is the case, we dynamically prune the variables we are confident about from the underlying factor graph. Consequently, at any time only samples of variables whose decision is still uncertain need to be created. Experiments in two prototypical scenarios, multi-label classification and image inpainting, show that adaptive sampling can drastically accelerate MMP without sacrificing prediction accuracy.

We present a probabilistic formulation of max-margin matrix factorization and build accordingly a nonparametric Bayesian model which automatically resolves the unknown number of latent factors. Our work demonstrates a successful example thatintegrates Bayesian nonparametrics and max-margin learning, which are conventionally two separate paradigms and enjoy complementary advantages. We develop an efficient variational algorithm for posterior inference, and our extensive empiricalstudies on large-scale MovieLens and EachMovie data sets appear to justify the aforementioned dual advantages.

The empirical success of the belief propagation approximate inference algorithm has inspired numerous theoretical and algorithmic advances. Yet, for continuous non-Gaussian domains performing belief propagation remains a challenging task: recent innovations such as nonparametric or kernel belief propagation, while useful, come with a substantial computational cost and offer little theoretical guarantees, even for tree structured models. In this work we present Nonparanormal BP for performing efficient inference on distributions parameterized by a Gaussian copulas network and any univariate marginals. For tree structured networks, our approach is guaranteed to be exact for this powerful class of non-Gaussian models. Importantly, the method is as efficient as standard Gaussian BP, and its convergence properties do not depend on the complexity of the univariate marginals, even when a nonparametric representation is used.