Finding a fixed point to a nonexpansive operator, i.e., $x^*=Tx^*$, abstracts many problems in numerical linear algebra, optimization, and other areas of scientific computing. To solve fixed-point problems, we propose ARock, an algorithmic framework in which multiple agents (machines, processors, or cores) update $x$ in an asynchronous parallel fashion. Asynchrony is crucial to parallel computing since it reduces synchronization wait, relaxes communication bottleneck, and thus speeds up computing significantly. At each step of ARock, an agent updates a randomly selected coordinate $x_i$ based on possibly out-of-date information on $x$. The agents share $x$ through either global memory or communication. If writing $x_i$ is atomic, the agents can read and write $x$ without memory locks. Theoretically, we show that if the nonexpansive operator $T$ has a fixed point, then with probability one, ARock generates a sequence that converges to a fixed points of $T$. Our conditions on $T$ and step sizes are weaker than comparable work. Linear convergence is also obtained. We propose special cases of ARock for linear systems, convex optimization, machine learning, as well as distributed and decentralized consensus problems. Numerical experiments of solving sparse logistic regression problems are presented.

Sparse matrix factorization is a popular tool to obtain interpretable data decompositions, which are also effective to perform data completion or denoising. Its applicability to large datasets has been addressed with online and randomized methods, that reduce the complexity in one of the matrix dimension, but not in both of them. In this paper, we tackle very large matrices in both dimensions. We propose a new factorization method that scales gracefully to terabyte-scale datasets. Those could not be processed by previous algorithms in a reasonable amount of time. We demonstrate the efficiency of our approach on massive functional Magnetic Resonance Imaging (fMRI) data, and on matrix completion problems for recommender systems, where we obtain significant speedups compared to state-of-the art coordinate descent methods. Matrix factorization is a flexible tool for uncovering latent factors in low-rank or sparse models. For instance, building on low-rank structure, it has proven very powerful for matrix completion, e.g. in recommender systems (Srebro et al., 2004; Candès & Recht, 2009). In signal processing and computer vision, matrix factorization with a sparse regularization is often called dictionary learning and has proven very effective for denoising and visual feature encoding (see Mairal, 2014, for a review).

The title for this monthly talk from WWCode-SV Data Science Group is "Scalable Machine Learning in R and Python with H2O" . The focus of this talk is scalable machine learning using the H2O R and Python packages. H2O is an open source, distributed machine learning platform designed for big data, with the added benefit that it's easy to use on a laptop (in addition to a multi-node Hadoop or Spark cluster). The core machine learning algorithms of H2O are implemented in high-performance Java, however, fully-featured APIs are available in R, Python, Scala, REST/JSON, and also through a web interface. Since H2O's algorithm implementations are distributed, this allows the software to scale to very large datasets that may not fit into RAM on a single machine.

There are many posts on KDnuggets covering the explanation of key terms and concepts in the areas of Data Science, Machine Learning, Deep Learning, Big Data, etc. (see here, here, and here). In fact, it's one of the tasks that KDnuggets takes quite seriously: introducing and clarifying concepts in the minds of new and seasoned practitioners alike. In many of these posts, concepts and terminology are often expounded upon and fit into The Big Picture, sometimes miring down the key concept in exchange for defining some greater notion. This is the first in a series of such posts on KDnuggets which will offer concise explanations of a related set of terms (machine learning, in this case), specifically taking a no-frills approach for those looking to isolate and define. Not enough information provided in these definitions for you?

XGBoost algorithm has become the ultimate weapon of many data scientist. It's a highly sophisticated algorithm, powerful enough to deal with all sorts of irregularities of data. Building a model using XGBoost is easy. But, improving the model using XGBoost is difficult (at least I struggled a lot). This algorithm uses multiple parameters.

The simplest answer is it classifies things by drawing a line between two groups of data points. From the linked wiki "More formally, a support vector machine constructs a hyperplane or set of hyperplanes in a high- or infinite-dimensional space, which can be used for classification, regression, or other tasks." The hyperplanes being the "lines" and a high dimensional space meaning you track a bunch of types of data about the things you want to classify. Say you want to know how likely it is to rain tomorrow based on what you know today. You could record the temperature, wind speed, humidity, time of the year, number of days since it last rained, etc.

Posted by Kaz Sato, Staff Developer Advocate, Google and Ray Sakai, Product Manager, Reactive Inc. At GCP NEXT 2016, the biggest Google Cloud Platform event held this year in San Francisco, Jeff Dean, Google Senior Fellow, presented the Cloud Vision API with Cloud Vision Explorer. This amazing demo is now available for anyone and we warmly invite you to give it a try. To recap, Cloud Vision API is an image analysis service that's part of Cloud Platform. It enables you to understand the content of images by encapsulating powerful machine learning models in an easy-to-use REST API.

The computational and storage complexity of kernel machines presents the primary barrier to their scaling to large, modern, datasets. A common way to tackle the scalability issue is to use the conjugate gradient algorithm, which relieves the constraints on both storage (the kernel matrix need not be stored) and computation (both stochastic gradients and parallelization can be used). Even so, conjugate gradient is not without its own issues: the conditioning of kernel matrices is often such that conjugate gradients will have poor convergence in practice. Preconditioning is a common approach to alleviating this issue. Here we propose preconditioned conjugate gradients for kernel machines, and develop a broad range of preconditioners particularly useful for kernel matrices. We describe a scalable approach to both solving kernel machines and learning their hyperparameters. We show this approach is exact in the limit of iterations and outperforms state-of-the-art approximations for a given computational budget.

Dictionary learning is a cutting-edge area in imaging processing, that has recently led to state-of-the-art results in many signal processing tasks. The idea is to conduct a linear decomposition of a signal using a few atoms of a learned and usually over-completed dictionary instead of a pre-defined basis. Determining a proper size of the to-be-learned dictionary is crucial for both precision and efficiency of the process, while most of the existing dictionary learning algorithms choose the size quite arbitrarily. In this paper, a novel regularization method called the Grouped Smoothly Clipped Absolute Deviation (GSCAD) is employed for learning the dictionary. The proposed method can simultaneously learn a sparse dictionary and select the appropriate dictionary size. Efficient algorithm is designed based on the alternative direction method of multipliers (ADMM) which decomposes the joint non-convex problem with the non-convex penalty into two convex optimization problems. Several examples are presented for image denoising and the experimental results are compared with other state-of-the-art approaches.

Partition functions of probability distributions are important quantities for model evaluation and comparisons. We present a new method to compute partition functions of complex and multimodal distributions. Such distributions are often sampled using simulated tempering, which augments the target space with an auxiliary inverse temperature variable. Our method exploits the multinomial probability law of the inverse temperatures, and provides estimates of the partition function in terms of a simple quotient of Rao-Blackwellized marginal inverse temperature probability estimates, which are updated while sampling. We show that the method has interesting connections with several alternative popular methods, and offers some significant advantages. In particular, we empirically find that the new method provides more accurate estimates than Annealed Importance Sampling when calculating partition functions of large Restricted Boltzmann Machines (RBM); moreover, the method is sufficiently accurate to track training and validation log-likelihoods during learning of RBMs, at minimal computational cost.