The weighted k-nearest neighbors algorithm is one of the most fundamental non-parametric methods in pattern recognition and machine learning. The question of setting the optimal number of neighbors as well as the optimal weights has received much attention throughout the years, nevertheless this problem seems to have remained unsettled. In this paper we offer a simple approach to locally weighted regression/classification, where we make the bias-variance tradeoff explicit. Our formulation enables us to phrase a notion of optimal weights, and to efficiently find these weights as well as the optimal number of neighbors efficiently and adaptively, for each data point whose value we wish to estimate. The applicability of our approach is demonstrated on several datasets, showing superior performance over standard locally weighted methods.

We provide finite-sample analysis of a general framework for using k-nearest neighbor statisticsto estimate functionals of a nonparametric continuous probability density, including entropies and divergences. Rather than plugging a consistent density estimate (which requires k as the sample size n) into the functional of interest, the estimators we consider fix k and perform a bias correction. Thisis more efficient computationally, and, as we show in certain cases, statistically, leading to faster convergence rates. Our framework unifies several previous estimators, for most of which ours are the first finite sample guarantees.

We propose a pool-based non-parametric active learning algorithm for general metric spaces, called MArgin Regularized Metric Active Nearest Neighbor (MARMANN), which outputs a nearest-neighbor classifier. We give prediction error guarantees that depend on the noisy-margin properties of the input sample, and are competitive with those obtained by previously proposed passive learners. We prove that the label complexity of MARMANN is significantly lower than that of any passive learner with similar error guarantees. Our algorithm is based on a generalized sample compression scheme and a new label-efficient active model-selection procedure.

Statistics and Machine Learning Toolbox provides functions and apps to describe, analyze, and model data. You can use descriptive statistics and plots for exploratory data analysis, fit probability distributions to data, generate random numbers for Monte Carlo simulations, and perform hypothesis tests. Regression and classification algorithms let you draw inferences from data and build predictive models. For multidimensional data analysis, Statistics and Machine Learning Toolbox provides feature selection, stepwise regression, principal component analysis (PCA), regularization, and other dimensionality reduction methods that let you identify variables or features that impact your model. The toolbox provides supervised and unsupervised machine learning algorithms, including support vector machines (SVMs), boosted and bagged decision trees, k-nearest neighbor, k-means, k-medoids, hierarchical clustering, Gaussian mixture models, and hidden Markov models.

As Google learned, predicting the spread of influenza, even with mountains of data, is notoriously difficult. Nonetheless, bioinformatician and R user Shirin Glander has created a two-part tutorial about predicting flu deaths with R (part 2 here). The analysis is based on just 136 cases of influenza A H7N9 in China in 2013 (data provided in the outbreaks package) so the intent was not to create a generally predictive model, but by providing all of the R code and graphics Shirin has created a useful example of real-word predictive modeling with R. The tutorial covers loading and cleaning the data (including a nice example of using the mice package to impute missing values) and begins with some exploratory data visualizations. I was particularly impressed by the use of density charts (using the stat_density2d ggplot2 aesthetic) to highlight differences in the scatterplots of flu cases ending in death and recovery. Decision trees (implemented using rpart and visualized using fancyRpartPlot from the rattle package) Random Forests (using caret's "rf" training method) Elastic-Net Regularized Generalized Linear Models (using caret's "glmnet" training method) K-nearest neighbors clustering (using caret's "kknn" training method) Penalized Discriminant Analysis (using caret's "pda" training method) and in Part 2, Extreme gradient boosting using the xgboost package and various preprocessing techniques from the caret package Due to the limited data size, there's not too much difference between the models: in each case, 13-15 of the 23 cases were classified correctly.

Spectral analysis of neighborhood graphs is one of the most widely used techniques for exploratory data analysis, with applications ranging from machine learning to social sciences. In such applications, it is typical to first encode relationships between the data samples using an appropriate similarity function. Popular neighborhood construction techniques such as k-nearest neighbor (k-NN) graphs are known to be very sensitive to the choice of parameters, and more importantly susceptible to noise and varying densities. In this paper, we propose the use of quantile analysis to obtain local scale estimates for neighborhood graph construction. To this end, we build an auto-encoding neural network approach for inferring conditional quantiles of a similarity function, which are subsequently used to obtain robust estimates of the local scales. In addition to being highly resilient to noise or outlying data, the proposed approach does not require extensive parameter tuning unlike several existing methods. Using applications in spectral clustering and single-example label propagation, we show that the proposed neighborhood graphs outperform existing locally scaled graph construction approaches.

In recent years, we've seen a resurgence in AI, or artificial intelligence, and machine learning. Machine learning has led to some amazing results, like being able to analyze medical images and predict diseases on-par with human experts. Google's AlphaGo program was able to beat a world champion in the strategy game go using deep reinforcement learning. Machine learning is even being used to program self driving cars, which is going to change the automotive industry forever. Imagine a world with drastically reduced car accidents, simply by removing the element of human error.

Decision trees are a simple and powerful predictive modeling technique, but they suffer from high-variance. This means that trees can get very different results given different training data. A technique to make decision trees more robust and to achieve better performance is called bootstrap aggregation or bagging for short. In this tutorial, you will discover how to implement the bagging procedure with decision trees from scratch with Python. How to apply bagging to your own predictive modeling problems.

In machine learning, you may often wish to build predictors that allows to classify things into categories based on some set of associated values. For example, it is possible to provide a diagnosis to a patient based on data from previous patients. Many algorithms have been developed for automated classification, and common ones include random forests, support vector machines, Naïve Bayes classifiers, and many types of neural networks. To get a feel for how classification works, we take a simple example of a classification algorithm – k-Nearest Neighbours (kNN) – and build it from scratch in Python 2. You can use a mostly imperative style of coding, rather than a declarative/functional one with lambda functions and list comprehensions to keep things simple if you are starting with Python. Here, we will provide an introduction to the latter approach.

The example used to illustrate the method in the source code is the famous iris data set, consisting of 3 clusters, 150 observations, and 4 variables, first analysed in 1936. How does the methodology perform on large data sets with many variables, or on unstructured data? Why was Python chosen to do this analysis? I think this is great, but I would be interested to know the motivation. The author mentioned other clustering techniques, such as SVM, Naive Bayes (issued from statistical science) or neural networks.