We describe a necessary and sufficient condition for the convergence to minimum Bayes risk when training two-layer ReLU-networks by gradient descent in the mean field regime with omni-directional initial parameter distribution. This article extends recent results of Chizat and Bach to ReLU-activated networks and to the situation in which there are no parameters which exactly achieve MBR. The condition does not depend on the initalization of parameters and concerns only the weak convergence of the realization of the neural network, not its parameter distribution.

The vulnerability of deep networks to adversarial attacks is a central problem for deep learning from the perspective of both cognition and security. The current most successful defense method is to train a classifier using adversarial images created during learning. Another defense approach involves transformation or purification of the original input to remove adversarial signals before the image is classified. We focus on defending naturally-trained classifiers using Markov Chain Monte Carlo (MCMC) sampling with an Energy-Based Model (EBM) for adversarial purification. In contrast to adversarial training, our approach is intended to secure pre-existing and highly vulnerable classifiers. The memoryless behavior of long-run MCMC sampling will eventually remove adversarial signals, while metastable behavior preserves consistent appearance of MCMC samples after many steps to allow accurate long-run prediction. Balancing these factors can lead to effective purification and robust classification. We evaluate adversarial defense with an EBM using the strongest known attacks against purification. Our contributions are 1) an improved method for training EBM's with realistic long-run MCMC samples, 2) an Expectation-Over-Transformation (EOT) defense that resolves theoretical ambiguities for stochastic defenses and from which the EOT attack naturally follows, and 3) state-of-the-art adversarial defense for naturally-trained classifiers and competitive defense compared to adversarially-trained classifiers on Cifar-10, SVHN, and Cifar-100. Code and pre-trained models are available at https://github.com/point0bar1/ebm-defense.

Kernel methods have proven to be powerful techniques for pattern analysis and machine learning (ML) in a variety of domains. However, many of their original or advanced implementations remain in Matlab. With the incredible rise and adoption of Python in the ML and data science world, there is a clear need for a well-defined library that enables not only the use of popular kernels, but also allows easy definition of customized kernels to fine-tune them for diverse applications. The kernelmethods library fills that important void in the python ML ecosystem in a domain-agnostic fashion, allowing the sample data type to be anything from numerical, categorical, graphs or a combination of them. In addition, this library provides a number of well-defined classes to make various kernel-based operations efficient (for large scale datasets), modular (for ease of domain adaptation), and inter-operable (across different ecosystems). The library is available at https://github.com/raamana/kernelmethods.

The reliable estimation of forecast uncertainties is crucial for risk-sensitive optimal decision making. In this paper, we propose implicit generative ensemble post-processing, a novel framework for multivariate probabilistic electricity price forecasting. We use a likelihood-free implicit generative model based on an ensemble of point forecasting models to generate multivariate electricity price scenarios with a coherent dependency structure as a representation of the joint predictive distribution. Our ensemble post-processing method outperforms well-established model combination benchmarks. This is demonstrated on a data set from the German day-ahead market. As our method works on top of an ensemble of domain-specific expert models, it can readily be deployed to other forecasting tasks.

In this paper, we report our recent practice at Tencent for user modeling based on mobile app usage. User behaviors on mobile app usage, including retention, installation, and uninstallation, can be a good indicator for both long-term and short-term interests of users. For example, if a user installs Snapseed recently, she might have a growing interest in photographing. Such information is valuable for numerous downstream applications, including advertising, recommendations, etc. Traditionally, user modeling from mobile app usage heavily relies on handcrafted feature engineering, which requires onerous human work for different downstream applications, and could be sub-optimal without domain experts. However, automatic user modeling based on mobile app usage faces unique challenges, including (1) retention, installation, and uninstallation are heterogeneous but need to be modeled collectively, (2) user behaviors are distributed unevenly over time, and (3) many long-tailed apps suffer from serious sparsity. In this paper, we present a tailored AutoEncoder-coupled Transformer Network (AETN), by which we overcome these challenges and achieve the goals of reducing manual efforts and boosting performance. We have deployed the model at Tencent, and both online/offline experiments from multiple domains of downstream applications have demonstrated the effectiveness of the output user embeddings.

This work proposes an iterative sparse-regularized regression method to recover governing equations of nonlinear dynamical systems from noisy state measurements. The method is inspired by the Sparse Identification of Nonlinear Dynamics (SINDy) approach of {\it [Brunton et al., PNAS, 113 (15) (2016) 3932-3937]}, which relies on two main assumptions: the state variables are known {\it a priori} and the governing equations lend themselves to sparse, linear expansions in a (nonlinear) basis of the state variables. The aim of this work is to improve the accuracy and robustness of SINDy in the presence of state measurement noise. To this end, a reweighted $\ell_1$-regularized least squares solver is developed, wherein the regularization parameter is selected from the corner point of a Pareto curve. The idea behind using weighted $\ell_1$-norm for regularization -- instead of the standard $\ell_1$-norm -- is to better promote sparsity in the recovery of the governing equations and, in turn, mitigate the effect of noise in the state variables. We also present a method to recover single physical constraints from state measurements. Through several examples of well-known nonlinear dynamical systems, we demonstrate empirically the accuracy and robustness of the reweighted $\ell_1$-regularized least squares strategy with respect to state measurement noise, thus illustrating its viability for a wide range of potential applications.

Over the past years, the industrial sector has seen many innovations brought about by automation. Inherent in this automation is the installation of sensor networks for status monitoring and data collection. One of the major challenges in these data-rich environments is how to extract and exploit information from these large volume of data to detect anomalies, discover patterns to reduce downtimes and manufacturing errors, reduce energy usage, predict faults/failures, effective maintenance schedules, etc. To address these issues, we developed TSML. Its technology is based on using the pipeline of lightweight filters as building blocks to process huge amount of industrial time series data in parallel.

Ensuring safety and explainability of machine learning (ML) is a topic of increasing relevance as data-driven applications venture into safety-critical application domains, traditionally committed to high safety standards that are not satisfied with an exclusive testing approach of otherwise inaccessible black-box systems. Especially the interaction between safety and security is a central challenge, as security violations can lead to compromised safety. The contribution of this paper to addressing both safety and security within a single concept of protection applicable during the operation of ML systems is active monitoring of the behaviour and the operational context of the data-driven system based on distance measures of the Empirical Cumulative Distribution Function (ECDF). We investigate abstract datasets (XOR, Spiral, Circle) and current security-specific datasets for intrusion detection (CICIDS2017) of simulated network traffic, using distributional shift detection measures including the Kolmogorov-Smirnov, Kuiper, Anderson-Darling, Wasserstein and mixed Wasserstein-Anderson-Darling measures. Our preliminary findings indicate that the approach can provide a basis for detecting whether the application context of an ML component is valid in the safety-security. Our preliminary code and results are available at https://github.com/ISorokos/SafeML.

Safety is a top priority for civil aviation. Data mining in digital Flight Data Recorder (FDR) or Quick Access Recorder (QAR) data, commonly referred as black box data on aircraft, has gained interest from researchers, airlines, and aviation regulation agencies for safety management. New anomaly detection methods based on supervised or unsupervised learning have been developed to monitor pilot operations and detect any risks from onboard digital flight data recorder data. However, all existing anomaly detection methods are offline learning - the models are trained once using historical data and used for all future predictions. In practice, new QAR data are generated by every flight and collected by airlines whenever a datalink is available. Offline methods cannot respond to new data in time. Though these offline models can be updated by being re-trained after adding new data to the original training set, it is time-consuming and computational costly to train a new model every time new data come in. To address this problem, we propose a novel incremental anomaly detection method to identify common patterns and detect outliers in flight operations from FDR data. The proposed method is based on Gaussian Mixture Model (GMM). An initial GMM cluster model is trained on historical offline data. Then, it continuously adapts to new incoming data points via an expectation-maximization (EM) algorithm. To track changes in flight operation patterns, only model parameters need to be saved, not the raw flight data. The proposed method was tested on two sets of simulation data. Comparable results were found from the proposed online method and a classic offline model. A real-world application of the proposed method is demonstrated using FDR data from daily operations of an airline. Results are presented and future challenges of using online learning scheme for flight data analytics are discussed.

What are the meanings or different terms associated with machine learning? You will see some examples so that you understand what machine learning actually is. It also contains steps involved in building a machine learning model, not just linear models, any machine learning model.