Adversarial examples are a widely studied phenomenon in machine learning models. While most of the attention has been focused on neural networks, other practical models also suffer from this issue. In this work, we propose an algorithm for evaluating the adversarial robustness of k-nearest neighbor classification, i.e., finding a minimum-norm adversarial example. Diverging from previous proposals, we take a geometric approach by performing a search that expands outwards from a given input point. On a high level, the search radius expands to the nearby Voronoi cells until we find a cell that classifies differently from the input point.

This is a tutorial and survey paper for Locally Linear Embedding (LLE) and its variants. The idea of LLE is fitting the local structure of manifold in the embedding space. In this paper, we first cover LLE, kernel LLE, inverse LLE, and feature fusion with LLE. Then, we cover out-of-sample embedding using linear reconstruction, eigenfunctions, and kernel mapping. Incremental LLE is explained for embedding streaming data. Landmark LLE methods using the Nystrom approximation and locally linear landmarks are explained for big data embedding. We introduce the methods for parameter selection of number of neighbors using residual variance, Procrustes statistics, preservation neighborhood error, and local neighborhood selection. Afterwards, Supervised LLE (SLLE), enhanced SLLE, SLLE projection, probabilistic SLLE, supervised guided LLE (using Hilbert-Schmidt independence criterion), and semi-supervised LLE are explained for supervised and semi-supervised embedding. Robust LLE methods using least squares problem and penalty functions are also introduced for embedding in the presence of outliers and noise. Then, we introduce fusion of LLE with other manifold learning methods including Isomap (i.e., ISOLLE), principal component analysis, Fisher discriminant analysis, discriminant LLE, and Isotop. Finally, we explain weighted LLE in which the distances, reconstruction weights, or the embeddings are adjusted for better embedding; we cover weighted LLE for deformed distributed data, weighted LLE using probability of occurrence, SLLE by adjusting weights, modified LLE, and iterative LLE.

We study a version of adversarial classification where an adversary is empowered to corrupt data inputs up to some distance $\varepsilon$, using tools from variational analysis. In particular, we describe necessary conditions associated with the optimal classifier subject to such an adversary. Using the necessary conditions, we derive a geometric evolution equation which can be used to track the change in classification boundaries as $\varepsilon$ varies. This evolution equation may be described as an uncoupled system of differential equations in one dimension, or as a mean curvature type equation in higher dimension. In one dimension we rigorously prove that one can use the initial value problem starting from $\varepsilon=0$, which is simply the Bayes classifier, in order to solve for the global minimizer of the adversarial problem. Numerical examples illustrating these ideas are also presented.

In Python scikit-learn library, there are various univariate feature selection methods such as Regression F-score, ANOVA and Chi-squared. Perhaps due to the ease of applying these methods (sometimes with just a single line of code), it might be tempting to just use these methods without taking into consideration the type of features you have. I have seen some machine learning practitioners took this for granted and made this mistake (including myself). While the scikit-learn documentation is clear on which feature selection method should be used for regression and classification, it does not specify whether these methods are suitable to apply to both continuous and categorical features. Let's say you have a classification task and after reading the documentation, you know you should use either Chi-squared test or ANOVA.

"AB-Joins" are like SQL Joins but for two time series data sets. In this new post, we use STUMPY to analyze and compare Queen/Bowie's song "Under Pressure" with Vanilla Ice's "Ice Ice Baby" and discover remarkable similarities in the bass line:

MKclass v0.3: Implements performance measures and scores for statistical classification including accuracy, sensitivity, specificity, recall, similarity coefficients, AUC, GINI index, Brier score and more. It calculates optimal cut-offs and decisions stumps according to (Iba and Langley (1991) follows Lemeshow and Hosmer and Hosmer et al. (1997) for goodness of fit tests and Porta (2014) for epidemiological risk measures. See the vignette to get started.

Multi-view clustering has been applied in many real-world applications where original data often contain noises. Some graph-based multi-view clustering methods have been proposed to try to reduce the negative influence of noises. However, previous graph-based multi-view clustering methods treat all features equally even if there are redundant features or noises, which is obviously unreasonable. In this paper, we propose a novel multi-view clustering framework Double Self-weighted Multi-view Clustering (DSMC) to overcome the aforementioned deficiency. DSMC performs double self-weighted operations to remove redundant features and noises from each graph, thereby obtaining robust graphs. For the first self-weighted operation, it assigns different weights to different features by introducing an adaptive weight matrix, which can reinforce the role of the important features in the joint representation and make each graph robust. For the second self-weighting operation, it weights different graphs by imposing an adaptive weight factor, which can assign larger weights to more robust graphs. Furthermore, by designing an adaptive multiple graphs fusion, we can fuse the features in the different graphs to integrate these graphs for clustering. Experiments on six real-world datasets demonstrate its advantages over other state-of-the-art multi-view clustering methods.

Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of probability theory. Programs may use both higher-order functions and continuous distributions, or even define a probability distribution on functions. But standard probability theory does not handle higher-order functions well: the category of measurable spaces is not cartesian closed. Here we introduce quasi-Borel spaces. We show that these spaces: form a new formalization of probability theory replacing measurable spaces; form a cartesian closed category and so support higher-order functions; form a well-pointed category and so support good proof principles for equational reasoning; and support continuous probability distributions. We demonstrate the use of quasi-Borel spaces for higher-order functions and probability by: showing that a well-known construction of probability theory involving random functions gains a cleaner expression; and generalizing de Finetti's theorem, that is a crucial theorem in probability theory, to quasi-Borel spaces.

Probabilistic time-series models become popular in the forecasting field as they help to make optimal decisions under uncertainty. Despite the growing interest, a lack of thorough analysis hinders choosing what is worth applying for the desired task. In this paper, we analyze the performance of three prominent probabilistic time-series models for sales forecasting. To remove the role of random chance in architecture's performance, we make two experimental principles; 1) Large-scale dataset with various cross-validation sets. 2) A standardized training and hyperparameter selection. The experimental results show that a simple Multi-layer Perceptron and Linear Regression outperform the probabilistic models on RMSE without any feature engineering. Overall, the probabilistic models fail to achieve better performance on point estimation, such as RMSE and MAPE, than comparably simple baselines. We analyze and discuss the performances of probabilistic time-series models.

Researchers have proposed a wide variety of model explanation approaches, but it remains unclear how most methods are related or when one method is preferable to another. We establish a new class of methods, removal-based explanations, that are based on the principle of simulating feature removal to quantify each feature's influence. These methods vary in several respects, so we develop a framework that characterizes each method along three dimensions: 1) how the method removes features, 2) what model behavior the method explains, and 3) how the method summarizes each feature's influence. Our framework unifies 25 existing methods, including several of the most widely used approaches (SHAP, LIME, Meaningful Perturbations, permutation tests). This new class of explanation methods has rich connections that we examine using tools that have been largely overlooked by the explainability literature. To anchor removal-based explanations in cognitive psychology, we show that feature removal is a simple application of subtractive counterfactual reasoning. Ideas from cooperative game theory shed light on the relationships and trade-offs among different methods, and we derive conditions under which all removal-based explanations have information-theoretic interpretations. Through this analysis, we develop a unified framework that helps practitioners better understand model explanation tools, and that offers a strong theoretical foundation upon which future explainability research can build.