Our analysis demonstrates that only a vanishingly small fraction of the function space is reachable after a polynomial number of gradient descent iterations.

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

We study how the word usage of U.S. Congressional speeches varies across states and party affiliation, how words are used differently across sections of the ArXiv, and how the co-purchase patterns of groceries can vary across seasons.

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

Drawing on variational perturbation theory of statistical physics, we use these insights to construct a family of new variational bounds.

The key insight of the approach is that quantization methods, in particular product quantization, perform poorly when there is large variance in the norms of the data points.

Discovering statistical structure from links is a fundamental problem in the analysis of social networks. Choosing a misspecified model, or equivalently, an incorrect inference algorithm will result in an invalid analysis or even falsely uncover patterns that are in fact artifacts of the model. This work focuses on unifying two of the most widely used link-formation models: the stochastic blockmodel (SBM) and the small world (or latent space) model (SWM). Integrating techniques from kernel learning, spectral graph theory, and nonlinear dimensionality reduction, we develop the first statistically sound polynomial-time algorithm to discover latent patterns in sparse graphs for both models. When the network comes from an SBM, the algorithm outputs a block structure. When it is from an SWM, the algorithm outputs estimates of each node's latent position.

In many real-world applications, however, several objective functions have to be considered simultaneously.

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

Matching is an effective strategy to tackle this problem.