Discovering the 3D atomic-resolution structure of molecules such as proteins and viruses is one of the foremost research problems in biology and medicine. Electron Cryomicroscopy (cryo-EM) is a promising vision-based technique for structure estimation which attempts to reconstruct 3D atomic structures from a large set of 2D transmission electron microscope images. This paper presents a new Bayesian framework for cryo-EM structure estimation that builds on modern stochastic optimization techniques to allow one to scale to very large datasets. We also introduce a novel Monte-Carlo technique that reduces the cost of evaluating the objective function during optimization by over five orders of magnitude. The net result is an approach capable of estimating 3D molecular structure from large-scale datasets in about a day on a single CPU workstation.

Discovering the 3D atomic structure of molecules such as proteins and viruses is a fundamental research problem in biology and medicine. Electron Cryomicroscopy (Cryo-EM) is a promising vision-based technique for structure estimation which attempts to reconstruct 3D structures from 2D images. This paper addresses the challenging problem of 3D reconstruction from 2D Cryo-EM images. A new framework for estimation is introduced which relies on modern stochastic optimization techniques to scale to large datasets. We also introduce a novel technique which reduces the cost of evaluating the objective function during optimization by over five orders or magnitude. The net result is an approach capable of estimating 3D molecular structure from large scale datasets in about a day on a single workstation.

Although recent work in non-linear dimensionality reduction investigates multiple choices of divergence measure during optimization \citeyang2013icml,bunte2012neuro, little work discusses the direct effects that divergence measures have on visualization. We study this relationship, theoretically and through an empirical analysis over 10 datasets. Our works shows how the αand βparameters of the generalized alpha-beta divergence can be chosen to discover hidden macro-structures (categories, e.g. birds) or micro-structures (fine-grained classes, e.g. toucans). Our method, which generalizes t-SNE \citetsne, allows us to discover such structure without extensive grid searches over (α, β) due to our theoretical analysis: such structure is apparent with particular choices of (α, β) that generalize across datasets. We also discuss efficient parallel CPU and GPU schemes which are non-trivial due to the tree-structures employed in optimization and the large datasets that do not fully fit into GPU memory. Our method runs 20x faster than the fastest published code \citefmm. We conclude with detailed case studies on the following very large datasets: ILSVRC 2012, a standard computer vision dataset with 1.2M images; SUSY, a particle physics dataset with 5M instances; and HIGGS, another particle physics dataset with 11M instances. This represents the largest published visualization attained by SNE methods. We have open-sourced our visualization code: \texttthttp://rll.berkeley.edu/absne/.

We consider the problem of system identification of helicopter dynamics. Helicopters are complex systems, coupling rigid body dynamics with aerodynamics, engine dynamics, vibration, and other phenomena. Resultantly, they pose a challenging system identification problem, especially when considering non-stationary flight regimes. We pose the dynamics modeling problem as direct high-dimensional regression, and take inspiration from recent results in Deep Learning to represent the helicopter dynamics with a Rectified Linear Unit (ReLU) Network Model, a hierarchical neural network model. We provide a simple method for initializing the parameters of the model, and optimization details for training. We describe three baseline models and show that they are significantly outperformed by the ReLU Network Model in experiments on real data, indicating the power of the model to capture useful structure in system dynamics across a rich array of aerobatic maneuvers. Specifically, the ReLU Network Model improves 58% overall in RMS acceleration prediction over state-of-the-art methods. Predicting acceleration along the helicopter's up-down axis is empirically found to be the most difficult, and the ReLU Network Model improves by 60% over the prior state-of-the-art. We discuss explanations of these performance gains, and also investigate the impact of hyperparameters in the novel model.

There is growing interest in representing image data and feature descriptors using compact binary codes for fast near neighbor search. Although binary codes are motivated by their use as direct indices (addresses) into a hash table, codes longer than 32 bits are not being used as such, as it was thought to be ineffective. We introduce a rigorous way to build multiple hash tables on binary code substrings that enables exact k-nearest neighbor search in Hamming space. The approach is storage efficient and straight-forward to implement. Theoretical analysis shows that the algorithm exhibits sub-linear run-time behavior for uniformly distributed codes. Empirical results show dramatic speedups over a linear scan baseline for datasets of up to one billion codes of 64, 128, or 256 bits.

There has been growing interest in mapping image data onto compact binary codes for fast near neighbor search in vision applications. Although binary codes are motivated by their use as direct indices (addresses) into a hash table, codes longer than 32 bits are not being used in this way, as it was thought to be ineffective. We introduce a rigorous way to build multiple hash tables on binary code substrings that enables exact K-nearest neighbor search in Hamming space. The algorithm is straightforward to implement, storage efficient, and it has sub-linear run-time behavior for uniformly distributed codes. Empirical results show dramatic speed-ups over a linear scan baseline and for datasets with up to one billion items, 64- or 128-bit codes, and search radii up to 25 bits.