We study the problem of computing the minimum adversarial perturbation of the Nearest Neighbor (NN) classifiers. Previous attempts either conduct attacks on continuous approximations of NN models or search for the perturbation by some heuristic methods. In this paper, we propose the first algorithm that is able to compute the minimum adversarial perturbation. The main idea is to formulate the problem as a list of convex quadratic programming (QP) problems that can be efficiently solved by the proposed algorithms for 1-NN models. Furthermore, we show that dual solutions for these QP problems could give us a valid lower bound of the adversarial perturbation that can be used for formal robustness verification, giving us a nice view of attack/verification for NN models. For $K$-NN models with larger $K$, we show that the same formulation can help us efficiently compute the upper and lower bounds of the minimum adversarial perturbation, which can be used for attack and verification.

Conditional Mutual Information (CMI) is a measure of conditional dependence between random variables X and Y, given another random variable Z. It can be used to quantify conditional dependence among variables in many data-driven inference problems such as graphical models, causal learning, feature selection and time-series analysis. While k-nearest neighbor (kNN) based estimators as well as kernel-based methods have been widely used for CMI estimation, they suffer severely from the curse of dimensionality. In this paper, we leverage advances in classifiers and generative models to design methods for CMI estimation. Specifically, we introduce an estimator for KL-Divergence based on the likelihood ratio by training a classifier to distinguish the observed joint distribution from the product distribution. We then show how to construct several CMI estimators using this basic divergence estimator by drawing ideas from conditional generative models. We demonstrate that the estimates from our proposed approaches do not degrade in performance with increasing dimension and obtain significant improvement over the widely used KSG estimator. Finally, as an application of accurate CMI estimation, we use our best estimator for conditional independence testing and achieve superior performance than the state-of-the-art tester on both simulated and real data-sets.

You see that the model makes reasonably accurate predictions, with the exception of one wrong classification in row 29, where "Versicolor" was predicted while the test label is "Virginica". This is already some indication of your model's performance, but you might want to go even deeper into your analysis.

A variety of machine learning applications expect to achieve rapid learning from a limited number of labeled data. However, the success of most current models is the result of heavy training on big data. Meta-learning addresses this problem by extracting common knowledge across different tasks that can be quickly adapted to new tasks. However, they do not fully explore weakly-supervised information, which is usually free or cheap to collect. In this paper, we show that weakly-labeled data can significantly improve the performance of meta-learning on few-shot classification. We propose prototype propagation network (PPN) trained on few-shot tasks together with data annotated by coarse-label. Given a category graph of the targeted fine-classes and some weakly-labeled coarse-classes, PPN learns an attention mechanism which propagates the prototype of one class to another on the graph, so that the K-nearest neighbor (KNN) classifier defined on the propagated prototypes results in high accuracy across different few-shot tasks. The training tasks are generated by subgraph sampling, and the training objective is obtained by accumulating the level-wise classification loss on the subgraph. The resulting graph of prototypes can be continually re-used and updated for new tasks and classes. We also introduce two practical test/inference settings which differ according to whether the test task can leverage any weakly-supervised information as in training. On two benchmarks, PPN significantly outperforms most recent few-shot learning methods in different settings, even when they are also allowed to train on weakly-labeled data.

We introduce a variant of the $k$-nearest neighbor classifier in which $k$ is chosen adaptively for each query, rather than supplied as a parameter. The choice of $k$ depends on properties of each neighborhood, and therefore may significantly vary between different points. (For example, the algorithm will use larger $k$ for predicting the labels of points in noisy regions.) We provide theory and experiments that demonstrate that the algorithm performs comparably to, and sometimes better than, $k$-NN with an optimal choice of $k$. In particular, we derive bounds on the convergence rates of our classifier that depend on a local quantity we call the `advantage' which is significantly weaker than the Lipschitz conditions used in previous convergence rate proofs. These generalization bounds hinge on a variant of the seminal Uniform Convergence Theorem due to Vapnik and Chervonenkis; this variant concerns conditional probabilities and may be of independent interest.

A common need when you are analyzing real-world data-sets is determining which data point stand out as being different to all others data points. Such data points are known as anomalies. This article was originally published on Medium by Davis David. In this article, you will learn a couple of Machine Learning-Based Approaches for Anomaly Detection and then show how to apply one of these approaches to solve a specific use case for anomaly detection (Credit Fraud detection) in part two. A common need when you analyzing real-world data-sets is determining which data point stand out as being different to all others data points.

The scikit-learnthe library has functions that enable us to build these pipelines by concatenating various modules together. We just need to specify the modules along with the corresponding parameters. It will then build a pipeline using these modules that processes the data and trains the system. The pipeline can include modules that perform various functions like feature selection, preprocessing, random forests, clustering, and so on. In this section, we will see how to build a pipeline to select the top K features from an input data point and then classify them using an Extremely Random Forest classifier.

Operating with ignorance is an important concern of the Machine Learning research, especially when the objective is to discover knowledge from the imperfect data. Data mining (driven by appropriate knowledge discovery tools) is about processing available (observed, known and understood) samples of data aiming to build a model (e.g., a classifier) to handle data samples, which are not yet observed, known or understood. These tools traditionally take samples of the available data (known facts) as an input for learning. We want to challenge the indispensability of this approach and we suggest considering the things the other way around. What if the task would be as follows: how to learn a model based on our ignorance, i.e. by processing the shape of 'voids' within the available data space? Can we improve traditional classification by modeling also the ignorance? In this paper, we provide some algorithms for the discovery and visualizing of the ignorance zones in two-dimensional data spaces and design two ignorance-aware smart prototype selection techniques (incremental and adversarial) to improve the performance of the nearest neighbor classifiers. We present experiments with artificial and real datasets to test the concept of the usefulness of ignorance discovery in machine learning.

In this paper, we aim to predict students’ learning perfor-mance by combining two-modality sensing variables, namely eye tracking that monitors learners’ eye movements and elec-troencephalography (EEG) that measures learners’ cerebral activity. Our long-term goal is to use both data to provide ap-propriate adaptive assistance for students to enhance their learning experience and optimize their performance. An ex-perimental study was conducted in order to collet gaze data and brainwave signals of fifteen students during an interac-tion with a virtual learning environment. Different classifica-tion algorithms were used to discriminate between two groups of learners: students who successfully resolve the problem-solving tasks and students who do not. Experimental results demonstrated that the K-Nearest Neighbor classifier achieved good accuracy when combining both eye movement and EEG features compared to using solely eye movement or EEG.

Classic k-Nearest Neighbor (kNN) algorithms approximate a regression or classification function at a query point based on the k-nearest training observations. In real-world datasets, however, the set of k neighbors is frequently not uniformly distributed around a given query point. This can result in a locally biased estimate and thus in degraded regression or classification results. This paper presents two new kNN algorithms that adjust the weight of the k-nearest neighbors to achieve a more balanced distribution. Experiments on real-world datasets and a range of synthetic training distributions and noise levels identify conditions under which the algorithms can improve accuracy with minimal increase in computation time.