A detailed explanation of one of the most used machine learning algorithms, k-Nearest Neighbors, and its implementation from scratch in Python.

In this end-to-end Python machine learning tutorial, you'll learn how to use Scikit-Learn to build and tune a supervised learning model! We'll be training and tuning a random forest for wine quality (as judged by wine snobs experts) based on traits like acidity, residual sugar, and alcohol concentration. Before we start, we should state that this guide is meant for beginners who are interested in applied machine learning. Our goal is introduce you to one of the most flexible and useful libraries for machine learning in Python. We'll skip the theory and math in this tutorial, but we'll still recommend great resources for learning those. To move quickly, we'll assume you have this background.

Everyday, we depend on many systems and machines. We use a car to travel, a lift go up and down, and a plane to fly. Electricity comes through turbines and in a hospital machine keeps us alive. Some failures are an just an inconvenience, while others could mean life or death. When stakes are high, we perform regular maintenance on our systems. For example, cars are serviced once every few months and aircrafts are serviced daily.

We consider large scale empirical risk minimization (ERM) problems, where both the problem dimension and variable size is large. In these cases, most second order methods are infeasible due to the high cost in both computing the Hessian over all samples and computing its inverse in high dimensions. In this paper, we propose a novel adaptive sample size second-order method, which reduces the cost of computing the Hessian by solving a sequence of ERM problems corresponding to a subset of samples and lowers the cost of computing the Hessian inverse using a truncated eigenvalue decomposition. We show that while we geometrically increase the size of the training set at each stage, a single iteration of the truncated Newton method is sufficient to solve the new ERM within its statistical accuracy. Moreover, for a large number of samples we are allowed to double the size of the training set at each stage, and the proposed method subsequently reaches the statistical accuracy of the full training set approximately after two effective passes. In addition to this theoretical result, we show empirically on a number of well known data sets that the proposed truncated adaptive sample size algorithm outperforms stochastic alternatives for solving ERM problems.

We study the stochastic online problem of learning to influence in a social network with semi-bandit feedback, where we observe how users influence each other. The problem combines challenges of limited feedback, because the learning agent only observes the influenced portion of the network, and combinatorial number of actions, because the cardinality of the feasible set is exponential in the maximum number of influencers. We propose a computationally efficient UCB-like algorithm, IMLinUCB, and analyze it. Our regret bounds are polynomial in all quantities of interest; reflect the structure of the network and the probabilities of influence. Moreover, they do not depend on inherently large quantities, such as the cardinality of the action set. To the best of our knowledge, these are the first such results. IMLinUCB permits linear generalization and therefore is suitable for large-scale problems. Our experiments show that the regret of IMLinUCB scales as suggested by our upper bounds in several representative graph topologies; and based on linear generalization, IMLinUCB can significantly reduce regret of real-world influence maximization semi-bandits.

We employ random geometric digraphs to construct semi-parametric classifiers. These data-random digraphs are from parametrized random digraph families called proximity catch digraphs (PCDs). A related geometric digraph family, class cover catch digraph (CCCD), has been used to solve the class cover problem by using its approximate minimum dominating set. CCCDs showed relatively good performance in the classification of imbalanced data sets, and although CCCDs have a convenient construction in $\mathbb{R}^d$, finding minimum dominating sets is NP-hard and its probabilistic behaviour is not mathematically tractable except for $d=1$. On the other hand, a particular family of PCDs, called \emph{proportional-edge} PCDs (PE-PCDs), has mathematical tractable minimum dominating sets in $\mathbb{R}^d$; however their construction in higher dimensions may be computationally demanding. More specifically, we show that the classifiers based on PE-PCDs are prototype-based classifiers such that the exact minimum number of prototypes (equivalent to minimum dominating sets) are found in polynomial time on the number of observations. We construct two types of classifiers based on PE-PCDs. One is a family of hybrid classifiers depend on the location of the points of the training data set, and another type is a family of classifiers solely based on class covers. We assess the classification performance of our PE-PCD based classifiers by extensive Monte Carlo simulations, and compare them with that of other commonly used classifiers. We also show that, similar to CCCD classifiers, our classifiers are relatively better in classification in the presence of class imbalance.

Stochastic gradient descent (SGD) is a well known method for regression and classification tasks. However, it is an inherently sequential algorithm at each step, the processing of the current example depends on the parameters learned from the previous examples. Prior approaches to parallelizing linear learners using SGD, such as HOGWILD! and ALLREDUCE, do not honor these dependencies across threads and thus can potentially suffer poor convergence rates and/or poor scalability. This paper proposes SYMSGD, a parallel SGD algorithm that, to a first-order approximation, retains the sequential semantics of SGD. Each thread learns a local model in addition to a model combiner, which allows local models to be combined to produce the same result as what a sequential SGD would have produced. This paper evaluates SYMSGD's accuracy and performance on 6 datasets on a shared-memory machine shows upto 11x speedup over our heavily optimized sequential baseline on 16 cores and 2.2x, on average, faster than HOGWILD!.

In many distributed learning problems, the heterogeneous loading of computing machines may harm the overall performance of synchronous strategies. In this paper, we propose an effective asynchronous distributed framework for the minimization of a sum of smooth functions, where each machine performs iterations in parallel on its local function and updates a shared parameter asynchronously. In this way, all machines can continuously work even though they do not have the latest version of the shared parameter. We prove the convergence of the consistency of this general distributed asynchronous method for gradient iterations then show its efficiency on the matrix factorization problem for recommender systems and on binary classification.

A principled approach to understand network structures is to formulate generative models. Given a collection of models, however, an outstanding key task is to determine which one provides a more accurate description of the network at hand, discounting statistical fluctuations. This problem can be approached using two principled criteria that at first may seem equivalent: selecting the most plausible model in terms of its posterior probability; or selecting the model with the highest predictive performance in terms of identifying missing links. Here we show that while these two approaches yield consistent results in most of cases, there are also notable instances where they do not, that is, where the most plausible model is not the most predictive. We show that in the latter case the improvement of predictive performance can in fact lead to overfitting both in artificial and empirical settings. Furthermore, we show that, in general, the predictive performance is higher when we average over collections of models that are individually less plausible, than when we consider only the single most plausible model.

In this work we develop a theory of hierarchical clustering for graphs. Our modeling assumption is that graphs are sampled from a graphon, which is a powerful and general model for generating graphs and analyzing large networks. Graphons are a far richer class of graph models than stochastic blockmodels, the primary setting for recent progress in the statistical theory of graph clustering. We define what it means for an algorithm to produce the "correct" clustering, give sufficient conditions in which a method is statistically consistent, and provide an explicit algorithm satisfying these properties.