In large-scale machine learning, the number of data examples is usually very large. To search for the optimal solution, one often uses stochastic gradient methods which only require one (or a small batch of) random example(s) per iteration in order to form an estimator of the full gradient. While full-gradient based methods can enjoy an accelerated (and optimal) convergence rate if Nesterov's momentum trick is used [35-37], theory for stochastic gradient methods are generally lagging behind and less is known for their acceleration. At a high level, momentum is dangerous if stochastic gradients are present. If some gradient estimator is very inaccurate, then adding it to the momentum and moving further in this direction (for every future iteration) may hurt the convergence performance. In other words, when naively equipped with momentum, stochastic gradient methods are "very prune to error accumulation" [25] and do not yield accelerated convergence rates in general.

This article develops a framework for testing general hypothesis in high-dimensional models where the number of variables may far exceed the number of observations. Existing literature has considered less than a handful of hypotheses, such as testing individual coordinates of the model parameter. However, the problem of testing general and complex hypotheses remains widely open. We propose a new inference method developed around the hypothesis adaptive projection pursuit framework, which solves the testing problems in the most general case. The proposed inference is centered around a new class of estimators defined as $l_1$ projection of the initial guess of the unknown onto the space defined by the null. This projection automatically takes into account the structure of the null hypothesis and allows us to study formal inference for a number of long-standing problems. For example, we can directly conduct inference on the sparsity level of the model parameters and the minimum signal strength. This is especially significant given the fact that the former is a fundamental condition underlying most of the theoretical development in high-dimensional statistics, while the latter is a key condition used to establish variable selection properties. Moreover, the proposed method is asymptotically exact and has satisfactory power properties for testing very general functionals of the high-dimensional parameters. The simulation studies lend further support to our theoretical claims and additionally show excellent finite-sample size and power properties of the proposed test.

I would probably spend the time on simple (yet useful) algorithms that are representative of these fields (and maybe save reinforcement learning for later).

Introduce yourself to the basics of data science and leave armed with practical experience extracting value from big data. This course teaches the basic techniques of data science, including both SQL and NoSQL solutions for massive data management (e.g., MapReduce and contemporaries), algorithms for data mining (e.g., clustering and association rule mining), and basic statistical modelling (e.g., linear and non-linear regression).

Machine Learning is getting a lot more air time these days but are we actually sure what it is? It gives computers the ability to learn without being explicitly programmed" (Arthur Samuel, 1959). This is an old quote but it has held the test of time. But,how can computers "learn" – have we really reached the age of artificial intelligence where they will take over the world and make humans redundant? Let's explore the core of the definition: the ability to learn What this really means is there are a set of algorithms that, rather than simply following a static set of program instructions, they can make data driven predictions, or decisions through building a model. Supervised learning – The computer is presented with example inputs (training data) and their desired outputs, given by a "teacher", and the goal is to learn a general rule that maps inputs to outputs. The "easiest" example of supervised learning is a decision tree – this uses a tree-like graph or model of decisions and ...

When I first started out learning about machine learning algorithms, it turned out to be quite a task to gain an intuition of what the algorithms are doing. Not just because it was difficult to understand all the mathematical theory and notations, but it was also plain boring. When I turned to online tutorials for answers, I could again only see equations or high level explanations without going through the detail in a majority of the cases. It was then that one of my data science colleagues introduced me to the concept of working out an algorithm in an excel sheet. And that worked wonders for me.

By using Python to glean value from your raw data, you can simplify the often complex journey from data to value. In this practical, hands-on course, learn how to use Python for data preparation, data munging, data visualization, and predictive analytics. She helps to provide you with a working understanding of machine learning, as well as outlier analysis, cluster analysis, and network analysis. Plus, Lillian explains how to create web-based data visualizations with Plot.ly, and how to use Python to scrape the web and capture your own data sets.

Convex sparsity-promoting regularizations are ubiquitous in modern statistical learning. By construction, they yield solutions with few non-zero coefficients, which correspond to saturated constraints in the dual optimization formulation. Working set (WS) strategies are generic optimization techniques that consist in solving simpler problems that only consider a subset of constraints, whose indices form the WS. Working set methods therefore involve two nested iterations: the outer loop corresponds to the definition of the WS and the inner loop calls a solver for the subproblems. For the Lasso estimator a WS is a set of features, while for a Group Lasso it refers to a set of groups. In practice, WS are generally small in this context so the associated feature Gram matrix can fit in memory. Here we show that the Gauss-Southwell rule (a greedy strategy for block coordinate descent techniques) leads to fast solvers in this case. Combined with a working set strategy based on an aggressive use of so-called Gap Safe screening rules, we propose a solver achieving state-of-the-art performance on sparse learning problems. Results are presented on Lasso and multi-task Lasso estimators.

We consider the nonlinear Kalman filtering problem using Kullback-Leibler (KL) and $\alpha$-divergence measures as optimization criteria. Unlike linear Kalman filters, nonlinear Kalman filters do not have closed form Gaussian posteriors because of a lack of conjugacy due to the nonlinearity in the likelihood. In this paper we propose novel algorithms to optimize the forward and reverse forms of the KL divergence, as well as the alpha-divergence which contains these two as limiting cases. Unlike previous approaches, our algorithms do not make approximations to the divergences being optimized, but use Monte Carlo integration techniques to derive unbiased algorithms for direct optimization. We assess performance on radar and sensor tracking, and options pricing problems, showing general improvement over the UKF and EKF, as well as competitive performance with particle filtering.

Spark's popularity means the field is expanding in terms of both use and capability. Faster than Hadoop and MapReduce, but compatible with Java, Scala, Python, and R, this open source clustering framework is becoming a must-have skill. Spark: Big Data Cluster Computing in Production goes beyond the basics to show you how to bring Spark to real-world production environments. With expert instruction, real-life use cases, and frank discussion, this guide helps you move past the challenges and bring proof-of-concept Spark applications live.