In this work, we give the first algorithms for tolerant testing of nontrivial classes in the active model: estimating the distance of a target function to a hypothesis class C with respect to some arbitrary distribution D, using only a small number of label queries to a polynomial-sized pool of unlabeled examples drawn from D. Specifically, we show that for the class D of unions of d intervals on the line, we can estimate the error rate of the best hypothesis in the class to an additive error epsilon from only $O(\frac{1}{\epsilon^6}\log \frac{1}{\epsilon})$ label queries to an unlabeled pool of size $O(\frac{d}{\epsilon^2}\log \frac{1}{\epsilon})$. The key point here is the number of labels needed is independent of the VC-dimension of the class. This extends the work of Balcan et al. [2012] who solved the non-tolerant testing problem for this class (distinguishing the zero-error case from the case that the best hypothesis in the class has error greater than epsilon). We also consider the related problem of estimating the performance of a given learning algorithm A in this setting. That is, given a large pool of unlabeled examples drawn from distribution D, can we, from only a few label queries, estimate how well A would perform if the entire dataset were labeled? We focus on k-Nearest Neighbor style algorithms, and also show how our results can be applied to the problem of hyperparameter tuning (selecting the best value of k for the given learning problem).

Meta learning of optimal classifier error rates allows an experimenter to empirically estimate the intrinsic ability of any estimator to discriminate between two populations, circumventing the difficult problem of estimating the optimal Bayes classifier. To this end we propose a weighted nearest neighbor (WNN) graph estimator for a tight bound on the Bayes classification error; the Henze-Penrose (HP) divergence. Similar to recently proposed HP estimators [berisha2016], the proposed estimator is non-parametric and does not require density estimation. However, unlike previous approaches the proposed estimator is rate-optimal, i.e., its mean squared estimation error (MSEE) decays to zero at the fastest possible rate of $O(1/M+1/N)$ where $M,N$ are the sample sizes of the respective populations. We illustrate the proposed WNN meta estimator for several simulated and real data sets.

The conditional mutual information I(X;Y|Z) measures the average information that X and Y contain about each other given Z. This is an important primitive in many learning problems including conditional independence testing, graphical model inference, causal strength estimation and time-series problems. In several applications, it is desirable to have a functional purely of the conditional distribution p_{Y|X,Z} rather than of the joint distribution p_{X,Y,Z}. We define the potential conditional mutual information as the conditional mutual information calculated with a modified joint distribution p_{Y|X,Z} q_{X,Z}, where q_{X,Z} is a potential distribution, fixed airport. We develop K nearest neighbor based estimators for this functional, employing importance sampling, and a coupling trick, and prove the finite k consistency of such an estimator. We demonstrate that the estimator has excellent practical performance and show an application in dynamical system inference.

K-nearest neighbors(KNN for short) is one of the simplest Machine Learning algorithm. KNN is a supervised learning algorithm which can be used for both classification and regression. This is slightly different from the algorithms that we have seen so far. Let me explain this algorithm with an example of classification problem. First step in KNN is to plot training data in a feature space.

We introduce the speculate-correct method to derive error bounds for local classifiers. Using it, we show that k nearest neighbor classifiers, in spite of their famously fractured decision boundaries, have exponential error bounds with O(sqrt((k + ln n) / n)) error bound range for n in-sample examples.

The following problem appeared as an assignment in the coursera course Algorithm-I by Prof.Robert Sedgewick from the Princeton University few years back (and also in the course cos226 offered at Princeton). The problem definition and the description is taken from the course website and lectures. The original assignment was to be done in java, where in this article both the java and a corresponding python implementation will also be described. The idea is to build a BST with points in the nodes, using the x– and y-coordinates of the points as keys in strictly alternating sequence, starting with the x-coordinates, as shown in the next figure. The following figures and animations show how the 2-d-tree is grown with recursive space-partioning for a few sample datasets.

K-Nearest Neighbors (K-NN) is one of the simplest machine learning algorithms. Like other machine learning techniques, it was inspired by human reasoning. For example, when something significant happens in your life, you memorize that experience and use it as a guideline for future decisions. Let me give you a scenario of a person dropping a glass. While the glass is falling, you've made the prediction that the glass will break when it hits the ground.

OpenCV is a library of programming functions mainly aimed at real-time computer vision. This course will show you how machine learning is great choice to solve real-word computer vision problems and how you can use the OpenCV modules to implement the popular machine learning concepts. The video will teach you how to work with the various OpenCV modules for statistical modelling and machine learning. You will start by preparing your data for analysis, learn about supervised and unsupervised learning, and see how to implement them with the help of real-world examples. The course will also show you how you can implement efficient models using the popular machine learning techniques such as classification, regression, decision trees, K-nearest neighbors, boosting, and neural networks with the aid of C and OpenCV.

Machine learning algorithm K Nearest neighbors (k-NN) uses the principle of classifying data by using nearest neighbors. Nearest neighbors classifiers are defined by their characteristic of classifying unlabeled examples by assigning them the class of similar labeled examples. Despite the simplicity of this approach this method is extremely powerful and has been used for computer vision application, predictions and even, identifying patters in genetic data. The k-NN algorithm gets his name from the fact that uses information about the k-Nearest Neighbors to classify unlabeled examples. The letter is a variable term stating how many numbers of nearest neighbors will be used for the classification.

In pattern recognition, the KNN algorithm is a method for classifying objects based on closest training examples in the feature space. KNN is a type of instance-based learning, or lazy learning where the function is only approximated locally and all computation is delayed until classification. The KNN is the fundamental and simplest classification technique when there is little or no prior knowledge about the distribution of the data. The K in KNN refers to number of nearest neighbors that the classifier will use to make its predication. In this video we use Game of Thrones example to explain kNN.