We explore the sequential decision making problem where the goal is to estimate uniformly well a number of linear models, given a shared budget of random contexts independently sampled from a known distribution. The decision maker must query one of the linear models for each incoming context, and receives an observation corrupted by noise levels that are unknown, and depend on the model instance. We present Trace-UCB, an adaptive allocation algorithm that learns the noise levels while balancing contexts accordingly across the different linear functions, and derive guarantees for simple regret in both expectation and high-probability. Finally, we extend the algorithm and its guarantees to high dimensional settings, where the number of linear models times the dimension of the contextual space is higher than the total budget of samples. Simulations with real data suggest that Trace-UCB is remarkably robust, outperforming a number of baselines even when its assumptions are violated.

Very few K-nearest-neighbor (KNN) ensembles exist, despite the efficacy of this approach in regression, classification, and outlier detection. Those that do exist focus on bagging features, rather than varying k or bagging observations; it is unknown whether varying k or bagging observations can improve prediction. Given recent studies from topological data analysis, varying k may function like multiscale topological methods, providing stability and better prediction, as well as increased ensemble diversity. This paper explores 7 KNN ensemble algorithms combining bagged features, bagged observations, and varied k to understand how each of these contribute to model fit. Specifically, these algorithms are tested on Tweedie regression problems through simulations and 6 real datasets; results are compared to state-of-the-art machine learning models including extreme learning machines, random forest, boosted regression, and Morse-Smale regression. Results on simulations suggest gains from varying k above and beyond bagging features or samples, as well as the robustness of KNN ensembles to the curse of dimensionality. KNN regression ensembles perform favorably against state-of-the-art algorithms and dramatically improve performance over KNN regression. Further, real dataset results suggest varying k is a good strategy in general (particularly for difficult Tweedie regression problems) and that KNN regression ensembles often outperform state-of-the-art methods. These results for k-varying ensembles echo recent theoretical results in topological data analysis, where multidimensional filter functions and multiscale coverings provide stability and performance gains over single-dimensional filters and single-scale covering. This opens up the possibility of leveraging multiscale neighborhoods and multiple measures of local geometry in ensemble methods.

Machine learning is a method of data analysis that automates analytical model building. It is inherently different rather than pushing the commands by programmer regarding how to solve; it explains how to proceed towards learning to solve the problem on its own. Resurging interest in machine learning is due to the fact that it works by learning to identify patterns in data and then make predictions from those patterns. These technologies are widely used in projects including Spelling correction in web search engines, Analysis of information from IOT devices, Real-time language translation and much more. Machine learning algorithms are replacing a large amount of the jobs across the world, in the upcoming years.

No one doubts that software engineering shapes every last facet of our 21st century existence. Given his vested interest in companies whose fortunes were built on software engineering, it was no surprise when Marc Andreessen declared that "software is eating the world." But what does that actually mean, and, just as important, does it still apply, if it ever did? These questions came to me recently when I reread Andreessen's op-ed piece and noticed that he equated "software" with "programming." Just as significant, he equated "eating" with industry takeovers by "Silicon Valley-style entrepreneurial technology companies" and then rattled through the usual honor roll of Amazon, Netflix, Apple, Google, and the like.

At events, in meetings and in general conversation with people, it's struck me that many seem to use data science, machine learning and artificial intelligence interchangeably. And while in passing that's okay, there are distinctions between each that make them very different. Here, we look at how to define each of those three categories and why they're different. Data science is the craft of turning data into action. Data is being generated and, perhaps more importantly, digitally captured at outstanding new levels.

My latest machine learning book has been published and will be available during the last week of July. In this book you will learn all the important Machine Learning algorithms that are commonly used in the field of data science. These algorithms can be used for supervised as well as unsupervised learning, reinforcement learning, and semi-supervised learning. A few famous algorithms that are covered in this book are Linear regression, Logistic Regression, SVM, Naïve Bayes, K-Means, Random Forest, and Feature engineering. In this book you will also learn how these algorithms work and their practical implementation to resolve your problems.

Those eager to learn something, anything new about computer programming, allows programming skill development (it doesn't matter for what purpose – ex: building a platform in Hadoop or working with SQL, Shogun, C#, Scikit, etc. Building some experience in Matlab, Octave, Scilab, etc is another sure way to become better exposed as something as complex as building code for ICA (Independent Component Analysis) can be handled in only a very few lines of code. I have met many very successful ML professionals who have developed their skills by self-learning, studying hard and applying their innate scientific skills to apply ML algorithms. Also, Matlab can get things done very quickly. ICA (ICA is a technique to separate linearly mixed sources) can be accomplished very quickly in spite of the significant work that would go into coding such analysis initially. One person I know who has a strong background in Math and Physics is a team leader at Goldman Sachs, having locked himself away for close to six months only to come out a darn good applied data scientist.

We consider the problem of training generative models with deep neural networks as generators, i.e. to map latent codes to data points. Whereas the dominant paradigm combines simple priors over codes with complex deterministic models, we propose instead to use more flexible code distributions. These distributions are estimated non-parametrically by reversing the generator map during training. The benefits include: more powerful generative models, better modeling of latent structure and explicit control of the degree of generalization.

We consider the problem of undirected graphical model inference. In many applications, instead of perfectly recovering the unknown graph structure, a more realistic goal is to infer some graph invariants (e.g., the maximum degree, the number of connected subgraphs, the number of isolated nodes). In this paper, we propose a new inferential framework for testing nested multiple hypotheses and constructing confidence intervals of the unknown graph invariants under undirected graphical models. Compared to perfect graph recovery, our methods require significantly weaker conditions. This paper makes two major contributions: (i) Methodologically, for testing nested multiple hypotheses, we propose a skip-down algorithm on the whole family of monotone graph invariants (The invariants which are non-decreasing under addition of edges). We further show that the same skip-down algorithm also provides valid confidence intervals for the targeted graph invariants. (ii) Theoretically, we prove that the length of the obtained confidence intervals are optimal and adaptive to the unknown signal strength. We also prove generic lower bounds for the confidence interval length for various invariants. Numerical results on both synthetic simulations and a brain imaging dataset are provided to illustrate the usefulness of the proposed method.

We propose and analyze a regularization approach for structured prediction problems. We characterize a large class of loss functions that allows to naturally embed structured outputs in a linear space. We exploit this fact to design learning algorithms using a surrogate loss approach and regularization techniques. We prove universal consistency and finite sample bounds characterizing the generalization properties of the proposed methods. Experimental results are provided to demonstrate the practical usefulness of the proposed approach.