Beware: many defence methods can lead to gradient masking, whether intentional or not. Gradient masking does not guarantee adversarial robustness, and has been shown to be circumventable (Tramèr et al., 2017; Athalye et al, 2018). We hope this article provides helpful insights on how to defend against adversarial examples. Please feel free to provide suggestions in the comment section if we're missing something.

Angular measurements are often modeled as circular random variables, where there are natural circular analogues of moments, including correlation. Because a product of circles is a torus, a d-dimensional vector of circular random variables lies on a d-dimensional torus. For such vectors we present here a class of graphical models, which we call torus graphs, based on the full exponential family with pairwise interactions. The topological distinction between a torus and Euclidean space has several important consequences. Our development was motivated by the problem of identifying phase coupling among oscillatory signals recorded from multiple electrodes in the brain: oscillatory phases across electrodes might tend to advance or recede together, indicating coordination across brain areas. The data analyzed here consisted of 24 phase angles measured repeatedly across 840 experimental trials (replications) during a memory task, where the electrodes were in 4 distinct brain regions, all known to be active while memories are being stored or retrieved. In realistic numerical simulations, we found that a standard pairwise assessment, known as phase locking value, is unable to describe multivariate phase interactions, but that torus graphs can accurately identify conditional associations. Torus graphs generalize several more restrictive approaches that have appeared in various scientific literatures, and produced intuitive results in the data we analyzed. Torus graphs thus unify multivariate analysis of circular data and present fertile territory for future research.

Imagine a machine learning algorithm is tasked with identifying the number of bananas within a bowl of fruit. In total, the bowl contains 10 pieces of fruit, 4 of which are bananas, and 6 are apples. The algorithm determines that there are 5 bananas, and 5 apples. The number of bananas that were counted correctly are known as true positives, while the items that were identified incorrectly as bananas are called false positives. In this example, there are 4 true positives, and one false positive, making the algorithms precision 4/5, and its recall is 4/10.

Separating an audio scene such as a cocktail party into constituent, meaningful components is a core task in computer audition. Deep networks are the state-of-the-art approach. They are trained on synthetic mixtures of audio made from isolated sound source recordings so that ground truth for the separation is known. However, the vast majority of available audio is not isolated. The brain uses primitive cues that are independent of the characteristics of any particular sound source to perform an initial segmentation of the audio scene. We present a method for bootstrapping a deep model for music source separation without ground truth by using multiple primitive cues. We apply our method to train a network on a large set of unlabeled music recordings from YouTube to separate vocals from accompaniment without the need for ground truth isolated sources or artificial training mixtures.

The covariance structure of multivariate functional data can be highly complex, especially if the multivariate dimension is large, making extension of statistical methods for standard multivariate data to the functional data setting quite challenging. For example, Gaussian graphical models have recently been extended to the setting of multivariate functional data by applying multivariate methods to the coefficients of truncated basis expansions. However, a key difficulty compared to multivariate data is that the covariance operator is compact, and thus not invertible. The methodology in this paper addresses the general problem of covariance modeling for multivariate functional data, and functional Gaussian graphical models in particular. As a first step, a new notion of separability for multivariate functional data is proposed, termed partial separability, leading to a novel Karhunen-Lo\`eve-type expansion for such data. Next, the partial separability structure is shown to be particularly useful in order to provide a well-defined Gaussian graphical model that can be identified with a sequence of finite-dimensional graphical models, each of fixed dimension. This motivates a simple and efficient estimation procedure through application of the joint graphical lasso. Empirical performance of the method for graphical model estimation is assessed through simulation and analysis of functional brain connectivity during a motor task.

This is the fourth in a four-part series on how we approach machine learning at Feature Labs. These articles cover the concepts and a full implementation as applied to predicting customer churn. The project Jupyter Notebooks are all available on GitHub. All of the work documented here was completed with open-source tools and data.) The Machine Learning Modeling ProcessThe outputs of prediction and feature engineering are a set of label times, historical examples of what we want to predict, and features, predictor variables used to train a model to predict the label.

In recent years, the interest in Big Data sources has been steadily growing within the Official Statistic community. The Italian National Institute of Statistics (Istat) is currently carrying out several Big Data pilot studies. One of these studies, the ICT Big Data pilot, aims at exploiting massive amounts of textual data automatically scraped from the websites of Italian enterprises in order to predict a set of target variables (e.g. e-commerce) that are routinely observed by the traditional ICT Survey. In this paper, we show that Deep Learning techniques can successfully address this problem. Essentially, we tackle a text classification task: an algorithm must learn to infer whether an Italian enterprise performs e-commerce from the textual content of its website. To reach this goal, we developed a sophisticated processing pipeline and evaluated its performance through extensive experiments. Our pipeline uses Convolutional Neural Networks and relies on Word Embeddings to encode raw texts into grayscale images (i.e. normalized numeric matrices). Web-scraped texts are huge and have very low signal to noise ratio: to overcome these issues, we adopted a framework known as False Positive Reduction, which has seldom (if ever) been applied before to text classification tasks. Several original contributions enable our processing pipeline to reach good classification results. Empirical evidence shows that our proposal outperforms all the alternative Machine Learning solutions already tested in Istat for the same task.

With the increasing availability of AI-based decision support, there is an increasing need for their certification by both AI manufacturers and notified bodies, as well as the pragmatic (real-world) validation of these systems. Therefore, there is the need for meaningful and informative ways to assess the performance of AI systems in clinical practice. Common metrics (like accuracy scores and areas under the ROC curve) have known problems and they do not take into account important information about the preferences of clinicians and the needs of their specialist practice, like the likelihood and impact of errors and the complexity of cases. In this paper, we present a new accuracy measure, the H-accuracy (Ha), which we claim is more informative in the medical domain (and others of similar needs) for the elements it encompasses. We also provide proof that the H-accuracy is a generalization of the balanced accuracy and establish a relation between the H-accuracy and the Net Benefit. Finally, we illustrate an experimentation in two user studies to show the descriptive power of the Ha score and how complementary and differently informative measures can be derived from its formulation (a Python script to compute Ha is also made available).

The aim of clinical effectiveness research using repositories of electronic health records is to identify what health interventions 'work best' in real-world settings. Since there are several reasons why the net benefit of intervention may differ across patients, current comparative effectiveness literature focuses on investigating heterogeneous treatment effect and predicting whether an individual might benefit from an intervention. The majority of this literature has concentrated on the estimation of the effect of treatment on binary outcomes. However, many medical interventions are evaluated in terms of their effect on future events, which are subject to loss to follow-up. In this study, we describe a framework for the estimation of heterogeneous treatment effect in terms of differences in time-to-event (survival) probabilities. We divide the problem into three phases: (1) estimation of treatment effect conditioned on unique sets of the covariate vector; (2) identification of features important for heterogeneity using an ensemble of non-parametric variable importance methods; and (3) estimation of treatment effect on the reference classes defined by the previously selected features, using one-step Targeted Maximum Likelihood Estimation. We conducted a series of simulation studies and found that this method performs well when either sample size or event rate is high enough and the number of covariates contributing to the effect heterogeneity is moderate. An application of this method to a clinical case study was conducted by estimating the effect of oral anticoagulants on newly diagnosed non-valvular atrial fibrillation patients using data from the UK Clinical Practice Research Datalink.

--We present a way to use T opological Data Analysis (TDA) for machine learning tasks on grayscale images. We apply persistent homology to generate a wide range of topological features using a point cloud obtained from an image, its natural grayscale filtration, and different filtrations defined on the binarized image. We show that this topological machine learning pipeline can be used as a highly relevant dimensionality reduction by applying it to the MNIST digits dataset. We conduct a feature selection and study their correlations while providing an intuitive interpretation of their importance, which is relevant in both machine learning and TDA. Finally, we show that we can classify digit images while reducing the size of the feature set by a factor 5 compared to the grayscale pixel value features and maintain similar accuracy. I NTRODUCTION Topological Data Analysis (TDA) [1] applies techniques from algebraic topology to study and extract topological and geometric information on the shape of data. In this paper, we use persistent homology [2], a tool from TDA that extracts features representing the numbers of connected components, cycles, and voids and their birth and death during an iterative process called a filtration. Each of those features is summarized as a point in a persistence diagram .