Several algorithms for solving constraint satisfaction problems are based on survey propagation, a variational inference scheme used to obtain approximate marginal probability estimates for variable assignments. These marginals correspond to how frequently each variable is set to true among satisfying assignments, and are used to inform branching decisions during search; however, marginal estimates obtained via survey propagation are approximate and can be self-contradictory. We introduce a more general branching strategy based on streamlining constraints, which sidestep hard assignments to variables. We show that streamlined solvers consistently outperform decimation-based solvers on random k-SAT instances for several problem sizes, shrinking the gap between empirical performance and theoretical limits of satisfiability by 16.3% on average for k = 3, 4, 5, 6.

Information projections are the key building block of variational inference algorithms and are used to approximate a target probabilistic model by projecting it onto a family of tractable distributions. In general, there is no guarantee on the quality of the approximation obtained. To overcome this issue, we introduce a new class of random projections to reduce the dimensionality and hence the complexity of the original model. In the spirit of random projections, the projection preserves (with high probability) key properties of the target distribution. We show that information projections can be combined with random projections to obtain provable guarantees on the quality of the approximation obtained, regardless of the complexity of the original model. We demonstrate empirically that augmenting mean field with a random projection step dramatically improves partition function and marginal probability estimates, both on synthetic and real world data.

Random projections have played an important role in scaling up machine learning and data mining algorithms. Recently they have also been applied to probabilistic inference to estimate properties of high-dimensional distributions; however, they all rely on the same class of projections based on universal hashing. We provide a general framework to analyze random projections which relates their statistical properties to their Fourier spectrum, which is a well-studied area of theoretical computer science. Using this framework we introduce two new classes of hash functions for probabilistic inference and model counting that show promising performance on synthetic and real-world benchmarks.

The state of the art in computer vision has rapidly advanced over the past decade largely aided by shared image datasets. However, most of these datasets tend to consist of assorted collections of images from the web that do not include 3D information or pose information. Furthermore, they target the problem of object category recognition - whereas solving the problem of object instance recognition might be sufficient for many robotic tasks. To address these issues, we present a high-quality, large-scale dataset of 3D object instances, with accurate calibration information for every image. We anticipate that “solving” this dataset will effectively remove many perception-related problems for mobile, sensing-based robots. The contributions of this work consist of: (1) BigBIRD, a dataset of 100 objects (and growing), composed of, for each object, 600 3D point clouds and 600 high-resolution (12 MP) images spanning all views, (2) a method for jointly calibrating a multi-camera system, (3) details of our data collection system, which collects all required data for a single object in under 6 minutes with minimal human effort, and (4) multiple software components (made available in open source), used to automate multi-sensor calibration and the data collection process. All code and data are available at http://rll.eecs.berkeley.edu/bigbird.