We investigate the problem of learning a topic model - the well-known Latent Dirichlet Allocation - in a distributed manner, using a cluster of C processors and dividing the corpus to be learned equally among them. We propose a simple approximated method that can be tuned, trading speed for accuracy according to the task at hand. Our approach is asynchronous, and therefore suitable for clusters of heterogenous machines.
@cite_7 broke eq:z_sampling in three components and took leverage on the resulting sparsity in @math of some of them -- that, combined with an efficient storage scheme led to a speed up of the order of 20x.
@cite_7
2110591510
We establish @math and @math error bounds for functions of many variables that are approximated by linear combinations of ReLU (rectified linear unit) and squared ReLU ridge functions with @math and @math controls on their inner and outer parameters. With the squared ReLU ridge function, we show that the @math approximation error is inversely proportional to the inner layer @math sparsity and it need only be sublinear in the outer layer @math sparsity. Our constructions are obtained using a variant of the Jones-Barron probabilistic method, which can be interpreted as either stratified sampling with proportionate allocation or two-stage cluster sampling. We also provide companion error lower bounds that reveal near optimality of our constructions. Despite the sparsity assumptions, we showcase the richness and flexibility of these ridge combinations by defining a large family of functions, in terms of certain spectral conditions, that are particularly well approximated by them. We propose a new approach for semantic segmentation of 3D city models. Starting from an SfM reconstruction of a street-side scene, we perform classification and facade splitting purely in 3D, obviating the need for slow image-based semantic segmentation methods. We show that a properly trained pure-3D approach produces high quality labelings, with significant speed benefits (20x faster) allowing us to analyze entire streets in a matter of minutes. Additionally, if speed is not of the essence, the 3D labeling can be combined with the results of a state-of-the-art 2D classifier, further boosting the performance. Further, we propose a novel facade separation based on semantic nuances between facades. Finally, inspired by the use of architectural principles for 2D facade labeling, we propose new 3D-specific principles and an efficient optimization scheme based on an integer quadratic programming formulation. Phenomenally successful in practical inference problems, convolutional neural networks (CNN) are widely deployed in mobile devices, data centers, and even supercomputers. The number of parameters needed in CNNs, however, are often large and undesirable. Consequently, various methods have been developed to prune a CNN once it is trained. Nevertheless, the resulting CNNs offer limited benefits. While pruning the fully connected layers reduces a CNN's size considerably, it does not improve inference speed noticeably as the compute heavy parts lie in convolutions. Pruning CNNs in a way that increase inference speed often imposes specific sparsity structures, thus limiting the achievable sparsity levels. We present a method to realize simultaneously size economy and speed improvement while pruning CNNs. Paramount to our success is an efficient general sparse-with-dense matrix multiplication implementation that is applicable to convolution of feature maps with kernels of arbitrary sparsity patterns. Complementing this, we developed a performance model that predicts sweet spots of sparsity levels for different layers and on different computer architectures. Together, these two allow us to demonstrate 3.1--7.3 @math convolution speedups over dense convolution in AlexNet, on Intel Atom, Xeon, and Xeon Phi processors, spanning the spectrum from mobile devices to supercomputers. We also open source our project at this https URL. The increased availability of data in recent years has led several authors to ask whether it is possible to use data as a computational resource. That is, if more data is available, beyond the sample complexity limit, is it possible to use the extra examples to speed up the computation time required to perform the learning task? We give the first positive answer to this question for a natural supervised learning problem --- we consider agnostic PAC learning of halfspaces over @math -sparse vectors in @math . This class is inefficiently learnable using @math examples. Our main contribution is a novel, non-cryptographic, methodology for establishing computational-statistical gaps, which allows us to show that, under a widely believed assumption that refuting random @math formulas is hard, it is impossible to efficiently learn this class using only @math examples. We further show that under stronger hardness assumptions, even @math examples do not suffice. On the other hand, we show a new algorithm that learns this class efficiently using @math examples. This formally establishes the tradeoff between sample and computational complexity for a natural supervised learning problem.