Unsupervised learning is the most challenging problem in machine learning and especially in deep learning. Among many scenarios, we study an unsupervised learning problem of high economic value --- learning to predict without costly pairing of input data and corresponding labels. Part of the difficulty in this problem is a lack of solid evaluation measures. In this paper, we take a practical approach to grounding unsupervised learning by using the same success criterion as for supervised learning in prediction tasks but we do not require the presence of paired input-output training data. In particular, we propose an objective function that aims to make the predicted outputs fit well the structure of the output while preserving the correlation between the input and the predicted output. We experiment with a synthetic structural prediction problem and show that even with simple linear classifiers, the objective function is already highly non-convex. We further demonstrate the nature of this non-convex optimization problem as well as potential solutions. In particular, we show that with regularization via a generative model, learning with the proposed unsupervised objective function converges to an optimal solution.
This paper presents a tutorial introduction to the use of variational methods for inference and learning in graphical models (Bayesian networks and Markov random fields). We present a number of examples of graphical models, including the QMR-DT database, the sigmoid belief network, the Boltzmann machine, and several variants of hidden Markov models, in which it is infeasible to run exact inference algorithms. We then introduce variational methods, which exploit laws of large numbers to transform the original graphical model into a simplified graphical model in which inference is efficient. Inference in the simpified model provides bounds on probabilities of interest in the original model. We describe a general framework for generating variational transformations based on convex duality. Finally we return to the examples and demonstrate how variational algorithms can be formulated in each case. We present a model that generates natural language descriptions of images and their regions. Our approach leverages datasets of images and their sentence descriptions to learn about the inter-modal correspondences between language and visual data. Our alignment model is based on a novel combination of Convolutional Neural Networks over image regions, bidirectional Recurrent Neural Networks over sentences, and a structured objective that aligns the two modalities through a multimodal embedding. We then describe a Multimodal Recurrent Neural Network architecture that uses the inferred alignments to learn to generate novel descriptions of image regions. We demonstrate that our alignment model produces state of the art results in retrieval experiments on Flickr8K, Flickr30K and MSCOCO datasets. We then show that the generated descriptions significantly outperform retrieval baselines on both full images and on a new dataset of region-level annotations. SUMMARY A generalization of the sampling method introduced by (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed. For numerical problems in a large number of dimensions, Monte Carlo methods are often more efficient than conventional numerical methods. However, implementation of the Monte Carlo methods requires sampling from high dimensional probability distributions and this may be very difficult and expensive in analysis and computer time. General methods for sampling from, or estimating expectations with respect to, such distributions are as follows. (i) If possible, factorize the distribution into the product of one-dimensional conditional distributions from which samples may be obtained. (ii) Use importance sampling, which may also be used for variance reduction. That is, in order to evaluate the integral J = X) p(x)dx = Ev(f), where p(x) is a probability density function, instead of obtaining independent samples XI, ..., Xv from p(x) and using the estimate J, = Zf(xi) N, we instead obtain the sample from a distribution with density q(x) and use the estimate J2 = Y f(xj)p(x1) q(xj)N . This may be advantageous if it is easier to sample from q(x) thanp(x), but it is a difficult method to use in a large number of dimensions, since the values of the weights w(xi) = p(x1) q(xj) for reasonable values of N may all be extremely small, or a few may be extremely large. In estimating the probability of an event A, however, these difficulties may not be as serious since the only values of w(x) which are important are those for which x -A. Since the methods proposed by Trotter & Tukey (1956) for the estimation of conditional expectations require the use of importance sampling, the same difficulties may be encountered in their use. (iii) Use a simulation technique; that is, if it is difficult to sample directly from p(x) or if p(x) is unknown, sample from some distribution q(y) and obtain the sample x values as some function of the corresponding y values. If we want samples from the conditional dis  We describe latent Dirichlet allocation (LDA), a generative probabilistic model for collections of discrete data such as text corpora. LDA is a three-level hierarchical Bayesian model, in which each item of a collection is modeled as a finite mixture over an underlying set of topics. Each topic is, in turn, modeled as an infinite mixture over an underlying set of topic probabilities. In the context of text modeling, the topic probabilities provide an explicit representation of a document. We present efficient approximate inference techniques based on variational methods and an EM algorithm for empirical Bayes parameter estimation. We report results in document modeling, text classification, and collaborative filtering, comparing to a mixture of unigrams model and the probabilistic LSI model. 