We analyze the $\ell_1$ and $\ell_\infty$ convergence rates of k nearest neighbor density estimation method. Our analysis includes two different cases depending on whether the support set is bounded or not. In the first case, the probability density function has a bounded support and is bounded away from zero. We show that kNN density estimation is minimax optimal under both $\ell_1$ and $\ell_\infty$ criteria, if the support set is known. If the support set is unknown, then the convergence rate of $\ell_1$ error is not affected, while $\ell_\infty$ error does not converge. In the second case, the probability density function can approach zero and is smooth everywhere. Moreover, the Hessian is assumed to decay with the density values. For this case, our result shows that the $\ell_\infty$ error of kNN density estimation is nearly minimax optimal. The $\ell_1$ error does not reach the minimax lower bound, but is better than kernel density estimation.

Classification is a major tool of statistics and machine learning. A classification method first processes a training set of objects with given classes (labels), with the goal of afterward assigning new objects to one of these classes. When running the resulting prediction method on the training data or on test data, it can happen that an object is predicted to lie in a class that differs from its given label. This is sometimes called label bias, and raises the question whether the object was mislabeled. Our goal is to visualize aspects of the data classification to obtain insight. The proposed display reflects to what extent each object's label is (dis)similar to its prediction, how far each object lies from the other objects in its class, and whether some objects lie far from all classes. The display is constructed for discriminant analysis, the k-nearest neighbor classifier, support vector machines, logistic regression, and majority voting. It is illustrated on several benchmark datasets containing images and texts.

This course material is aimed at people who are already familiar with ... What you'll learn This course is about the fundamental concepts of machine learning, facusing on neural networks. This topic is getting very hot nowadays because these learning algorithms can be used in several fields from software engineering to investment banking. Learning algorithms can recognize patterns which can help detect cancer for example. We may construct algorithms that can have a very good guess about stock prices movement in the market.

This work introduces Conditional Image Retrieval (CIR) systems: IR methods that can efficiently specialize to specific subsets of images on the fly. These systems broaden the class of queries IR systems support, and eliminate the need for expensive re-fitting to specific subsets of data. Specifically, we adapt tree-based K-Nearest Neighbor (KNN) data-structures to the conditional setting by introducing additional inverted-index data-structures. This speeds conditional queries and does not slow queries without conditioning. We present two new datasets for evaluating the performance of CIR systems and evaluate a variety of design choices. As a motivating application, we present an algorithm that can explore shared semantic content between works of art of vastly different media and cultural origin. Finally, we demonstrate that CIR data-structures can identify Generative Adversarial Network (GAN) "blind spots": areas where GANs fail to properly model the true data distribution.

Deep neural networks require large training sets but suffer from high computational cost and long training times. Training on much smaller training sets while maintaining nearly the same accuracy would be very beneficial. In the few-shot learning setting, a model must learn a new class given only a small number of samples from that class. One-shot learning is an extreme form of few-shot learning where the model must learn a new class from a single example. We propose the `less than one'-shot learning task where models must learn $N$ new classes given only $M

The Wasserstein distance provides a notion of dissimilarities between probability measures, which has recent applications in learning of structured data with varying size such as images and text documents. In this work, we analyze the $k$-nearest neighbor classifier ($k$-NN) under the Wasserstein distance and establish the universal consistency on families of distributions. Using previous known results on the consistency of the $k$-NN classifier on infinite dimensional metric spaces, it suffices to show that the families is a countable union of finite dimensional components. As a result, we are able to prove universal consistency of $k$-NN on spaces of finitely supported measures, the space of finite wavelet series and the spaces of Gaussian measures with commuting covariance matrices.

The objective of this study is to develop a good risk model for classifying business delinquency by simultaneously exploring several machine learning based methods including regularization, hyper-parameter optimization, and model ensembling algorithms. The rationale under the analyses is firstly to obtain good base binary classifiers (include Logistic Regression ($LR$), K-Nearest Neighbors ($KNN$), Decision Tree ($DT$), and Artificial Neural Networks ($ANN$)) via regularization and appropriate settings of hyper-parameters. Then two model ensembling algorithms including bagging and boosting are performed on the good base classifiers for further model improvement. The models are evaluated using accuracy, Area Under the Receiver Operating Characteristic Curve (AUC of ROC), recall, and F1 score via repeating 10-fold cross-validation 10 times. The results show the optimal base classifiers along with the hyper-parameter settings are $LR$ without regularization, $KNN$ by using 9 nearest neighbors, $DT$ by setting the maximum level of the tree to be 7, and $ANN$ with three hidden layers. Bagging on $KNN$ with $K$ valued 9 is the optimal model we can get for risk classification as it reaches the average accuracy, AUC, recall, and F1 score valued 0.90, 0.93, 0.82, and 0.89, respectively.

Accurate prediction of travel time is an essential feature to support Intelligent Transportation Systems (ITS). The non-linearity of traffic states, however, makes this prediction a challenging task. Here we propose to use dynamic linear models (DLMs) to approximate the non-linear traffic states. Unlike a static linear regression model, the DLMs assume that their parameters are changing across time. We design a DLM with model parameters defined at each time unit to describe the spatio-temporal characteristics of time-series traffic data. Based on our DLM and its model parameters analytically trained using historical data, we suggest an optimal linear predictor in the minimum mean square error (MMSE) sense. We compare our prediction accuracy of travel time for freeways in California (I210-E and I5-S) under highly congested traffic conditions with those of other methods: the instantaneous travel time, k-nearest neighbor, support vector regression, and artificial neural network. We show significant improvements in the accuracy, especially for short-term prediction.

Get Udemy Coupon Code New What you'll learn Mathematics and Statistics behind Machine Learning Mathematics and Statistics behind Deep Learning Mathematics and Statistics behind Artificial Intelligence Python Programming Language from Scratch Python with it's Libraries Learn Numpy, Pandas, Matplotlib, Scikit-Learn Learn Natural Language Processing Learn Tokenization in Natural Language Processing Learn Implementation of R Packages and Libraries on Different Data Sets Learn Implementation of Python Libraries on Different Data Sets Algorithms and Models of Machine Learning Algorithms and Models of Deep Learning k-Nearest Neighbors, Naive Bayes etc Supervised and Unsupervised Learning Description DATA SCIENCE Data science continues to evolve as one of the most promising and in-demand career paths for skilled professionals. Today, successful data professionals understand that they must advance past the traditional skills of analyzing large amounts of data, data mining, and programming skills. What Does a Data Scientist Do? In the past decade, data scientists have become necessary assets and are present in almost all organizations. These professionals are well-rounded, data-driven individuals with high-level technical skills who are capable of building complex quantitative algorithms to organize and synthesize large amounts of information used to answer questions and drive strategy in their organization.

In the era of big data, a large number of text data generated by the Internet has given birth to a variety of text representation methods. In natural language processing (NLP), text representation transforms text into vectors that can be processed by computer without losing the original semantic information. However, these methods are difficult to effectively extract the semantic features among words and distinguish polysemy in language. Therefore, a text feature representation model based on convolutional neural network (CNN) and variational autoencoder (VAE) is proposed to extract the text features and apply the obtained text feature representation on the text classification tasks. CNN is used to extract the features of text vector to get the semantics among words and VAE is introduced to make the text feature space more consistent with Gaussian distribution. In addition, the output of the improved word2vec model is employed as the input of the proposed model to distinguish different meanings of the same word in different contexts. The experimental results show that the proposed model outperforms in k-nearest neighbor (KNN), random forest (RF) and support vector machine (SVM) classification algorithms.