Non-local methods exploiting the self-similarity of natural signals have been well studied, for example in image analysis and restoration. Existing approaches, however, rely on k-nearest neighbors (KNN) matching in a fixed feature space. The main hurdle in optimizing this feature space w.r.t. application performance is the non-differentiability of the KNN selection rule. To overcome this, we propose a continuous deterministic relaxation of KNN selection that maintains differentiability w.r.t. pairwise distances, but retains the original KNN as the limit of a temperature parameter approaching zero. To exploit our relaxation, we propose the neural nearest neighbors block (N3 block), a novel non-local processing layer that leverages the principle of self-similarity and can be used as building block in modern neural network architectures. We show its effectiveness for the set reasoning task of correspondence classification as well as for image restoration, including image denoising and single image super-resolution, where we outperform strong convolutional neural network (CNN) baselines and recent non-local models that rely on KNN selection in hand-chosen features spaces.

K-nearest neighbor (kNN) search refers to the problem of finding K points closest toa given data point on a distance metric of interest. It is an important task in a wide range of applications, including similarity search in data mining [15,19], fast kernel methods in machine learning [17, 30, 38], nonparametric density estimation [5, 29, 31] and intrinsic dimension estimation [6, 26] in statistics, aswell as anomaly detection algorithms [2, 10, 37]. Numerous algorithms have been proposed for kNN search; the readers are referred to [35, 46] and references therein. Our interest is kNN search in emerging applications. Two 1 salient features of such applications are the expected scalability of the algorithms andtheir ability to handle data of high dimensionality. Additionally, such applications often desire more accurate kNN search. For example, robotic route planning [23] and face-based surveillance systems [34] require a high accuracy forthe robust execution of tasks. However, most existing work on kNN search [1, 4, 12, 15] have focused mainly on the fast computation and accuracy isofalessconcern.

Approximate nearest neighbor algorithms are used to speed up nearest neighbor search in a wide array of applications. However, current indexing methods feature several hyperparameters that need to be tuned to reach an acceptable accuracy--speed trade-off. A grid search in the parameter space is often impractically slow due to a time-consuming index-building procedure. Therefore, we propose an algorithm for automatically tuning the hyperparameters of indexing methods based on randomized space-partitioning trees. In particular, we present results using randomized k-d trees, random projection trees and randomized PCA trees. The tuning algorithm adds minimal overhead to the index-building process but is able to find the optimal hyperparameters accurately. We demonstrate that the algorithm is significantly faster than existing approaches, and that the indexing methods used are competitive with the state-of-the-art methods in query time while being faster to build.

In the era of deep learning, understanding over-fitting phenomenon becomes increasingly important. It is observed that carefully designed deep neural networks achieve small testing error even when the training error is close to zero. One possible explanation is that for many modern machine learning algorithms, over-fitting can greatly reduce the estimation bias, while not increasing the estimation variance too much. To illustrate the above idea, we prove that the proposed interpolated nearest neighbor algorithm achieves the minimax optimal rate in both regression and classification regimes, and observe that they are empirically better than the traditional $k$ nearest neighbor method in some cases.

The project is about predicting coronary heart disease by using three different ML algorithms. And to know which is the best approach. There are roughly two controls per case of CHD. Many of the CHD positive men have undergone blood pressure reduction treatment and other programs to reduce their risk factors after their occurrence of CHD. In some cases the measurements were made after these treatments.

Disclosure of financial support: This work was supported by the Di Giovanni Foundation, the Montreal English School Board, the B-Strong Foundation, the Colannini Foundation, the Montreal Neurological Institute and Hospital and the McGill Department of Orthopedics. Samaneh Siyar is a Visiting Scholar in the Neurosurgical Simulation Research and Training Centre. Dr. H. Azarnoush previously held the Postdoctoral Neuro-Oncology Fellowship from the Montreal Neurological Institute and Hospital and is a Visiting Professor in the Neurosurgical Simulation Research and Training Centre. Dr. Winkler-Schwartz holds a Robert Maudsley Fellowship from the Royal College of Physicians and Surgeons of Canada and Nirros Ponnudurai is supported by a Heffez Family Bursary. Dr. Del Maestro is the William Feindel Emeritus Professor in Neuro-Oncology at McGill University. 2 Acknowledgments We thank all the medical students, residents, and neurosurgeons from the Montreal Neurological Institute and Hospital and at other institutions who participated in this study. We would also like to thank Robert DiRaddo, Group Leader, Simulation, Life Sciences Division, National Research Council Canada at Boucherville and his team, including Denis Laroche, Valérie Pazos, Nusrat Choudhury and Linda Pecora for their support in the development of the scenarios used in these studies and all the members of the Simulation, Life Sciences Division, National Research Council Canada.

Nearest Neighbors Algorithm is a Lazy Learning Algorithm, in which the algorithm tries to approximate the predictions with the help of similar existing vectors in the training dataset. The predictions made by the K-Nearest Neighbors algorithm is based on averaging the target values of the spatial neighbors. The selection process for neighbors in the Hermitian space is done with the help of distance metrics such as Euclidean distance, Minkowski distance, Mahalanobis distance etc. A majority of the metrics such as Euclidean distance are scale variant, meaning that the results could vary for different range of values used for the features. Standard techniques used for the normalization of scaling factors are feature scaling method such as Z-score normalization technique, Min-Max scaling etc. Scaling methods uniformly assign equal weights to all the features, which might result in a non-ideal situation. This paper proposes a novel method to assign weights to individual feature with the help of out of bag errors obtained from constructing multiple decision tree models.

Hello World of Machine Learning is a video series to acquaint, enable and empower you to understand What, How and When of Machine Learning This is chapter - 2 of the series and in this chapter, we'll be exploring our first Machine Learning Algorithm called KNN (K Nearest Neighbor). This chapter will explain 1. What is KNN and how it works? Hope it helps you in learning something new.. enjoy! Please take a moment to Like! Subscribe!

Knowing when a classifier's prediction can be trusted is useful in many applications and critical for safely using AI. While the bulk of the effort in machine learning research has been towards improving classifier performance, understanding when a classifier's predictions should and should not be trusted has received far less attention. The standard approach is to use the classifier's discriminant or confidence score; however, we show there exists an alternative that is more effective in many situations. We propose a new score, called the trust score, which measures the agreement between the classifier and a modified nearest-neighbor classifier on the testing example. We show empirically that high (low) trust scores produce surprisingly high precision at identifying correctly (incorrectly) classified examples, consistently outperforming the classifier's confidence score as well as many other baselines. Further, under some mild distributional assumptions, we show that if the trust score for an example is high (low), the classifier will likely agree (disagree) with the Bayes-optimal classifier. Our guarantees consist of non-asymptotic rates of statistical consistency under various nonparametric settings and build on recent developments in topological data analysis.

In the $k$-nearest neighborhood model ($k$-NN), we are given a set of points $P$, and we shall answer queries $q$ by returning the $k$ nearest neighbors of $q$ in $P$ according to some metric. This concept is crucial in many areas of data analysis and data processing, e.g., computer vision, document retrieval and machine learning. Many $k$-NN algorithms have been published and implemented, but often the relation between parameters and accuracy of the computed $k$-NN is not explicit. We study property testing of $k$-NN graphs in theory and evaluate it empirically: given a point set $P \subset \mathbb{R}^\delta$ and a directed graph $G=(P,E)$, is $G$ a $k$-NN graph, i.e., every point $p \in P$ has outgoing edges to its $k$ nearest neighbors, or is it $\epsilon$-far from being a $k$-NN graph? Here, $\epsilon$-far means that one has to change more than an $\epsilon$-fraction of the edges in order to make $G$ a $k$-NN graph. We develop a randomized algorithm with one-sided error that decides this question, i.e., a property tester for the $k$-NN property, with complexity $O(\sqrt{n} k^2 / \epsilon^2)$ measured in terms of the number of vertices and edges it inspects, and we prove a lower bound of $\Omega(\sqrt{n / \epsilon k})$. We evaluate our tester empirically on the $k$-NN models computed by various algorithms and show that it can be used to detect $k$-NN models with bad accuracy in significantly less time than the building time of the $k$-NN model.