In this paper, we explore salient questions about user interests, conversations and friendships in the Facebook social network, using a novel latent space model that integrates several data types. A key challenge of studying Facebook's data is the wide range of data modalities such as text, network links, and categorical labels. Our latent space model seamlessly combines all three data modalities over millions of users, allowing us to study the interplay between user friendships, interests, and higher-order network-wide social trends on Facebook. The recovered insights not only answer our initial questions, but also reveal surprising facts about user interests in the context of Facebook's ecosystem. We also confirm that our results are significant with respect to evidential information from the study subjects.

Sparse coding is an unsupervised learning algorithm that learns a succinct high-level representation of the inputs given only unlabeled data; it represents each input as a sparse linear combination of a set of basis functions. Originally applied to modeling the human visual cortex, sparse coding has also been shown to be useful for self-taught learning, in which the goal is to solve a supervised classification task given access to additional unlabeled data drawn from different classes than that in the supervised learning problem. Shift-invariant sparse coding (SISC) is an extension of sparse coding which reconstructs a (usually time-series) input using all of the basis functions in all possible shifts. In this paper, we present an efficient algorithm for learning SISC bases. Our method is based on iteratively solving two large convex optimization problems: The first, which computes the linear coefficients, is an L1-regularized linear least squares problem with potentially hundreds of thousands of variables. Existing methods typically use a heuristic to select a small subset of the variables to optimize, but we present a way to efficiently compute the exact solution. The second, which solves for bases, is a constrained linear least squares problem. By optimizing over complex-valued variables in the Fourier domain, we reduce the coupling between the different variables, allowing the problem to be solved efficiently. We show that SISC's learned high-level representations of speech and music provide useful features for classification tasks within those domains. When applied to classification, under certain conditions the learned features outperform state of the art spectral and cepstral features.

Sparse coding provides a class of algorithms for finding succinct representations of stimuli; given only unlabeled input data, it discovers basis functions that capture higher-level features in the data. However, finding sparse codes remains a very difficult computational problem.

Sparse coding provides a class of algorithms for finding succinct representations of stimuli; given only unlabeled input data, it discovers basis functions that capture higher-levelfeatures in the data. However, finding sparse codes remains a very difficult computational problem.

Although discriminatively trained classifiers are usually more accurate when labeled training data is abundant, previous work has shown that when training data is limited, generative classifiers can outperform them. This paper describes a hybrid model in which a high-dimensional subset of the parameters are trained to maximize generative likelihood, and another, small, subset of parameters are discriminatively trained to maximize conditional likelihood. We give a sample complexity bound showing that in order to fit the discriminative parameters well, the number of training examples required depends only on the logarithm of the number of feature occurrences and feature set size. Experimental results show that hybrid models can provide lower test error and can produce better accuracy/coverage curves than either their purely generative or purely discriminative counterparts. We also discuss several advantages of hybrid models, and advocate further work in this area.

Classifiers often achieve higher test set accuracy than generative Classifiers (e.g., [6, 4, 14]).