Assume that $X_{1}, \ldots, X_{N}$ is an $\varepsilon$-contaminated sample of $N$ independent Gaussian vectors in $\mathbb{R}^d$ with mean $\mu$ and covariance $\Sigma$. In the strong $\varepsilon$-contamination model we assume that the adversary replaced an $\varepsilon$ fraction of vectors in the original Gaussian sample by any other vectors. We show that there is an estimator $\widehat \mu$ of the mean satisfying, with probability at least $1 - \delta$, a bound of the form \[ \|\widehat{\mu} - \mu\|_2 \le c\left(\sqrt{\frac{\operatorname{Tr}(\Sigma)}{N}} + \sqrt{\frac{\|\Sigma\|\log(1/\delta)}{N}} + \varepsilon\sqrt{\|\Sigma\|}\right), \] where $c > 0$ is an absolute constant and $\|\Sigma\|$ denotes the operator norm of $\Sigma$. In the same contaminated Gaussian setup, we construct an estimator $\widehat \Sigma$ of the covariance matrix $\Sigma$ that satisfies, with probability at least $1 - \delta$, \[ \left\|\widehat{\Sigma} - \Sigma\right\| \le c\left(\sqrt{\frac{\|\Sigma\|\operatorname{Tr}(\Sigma)}{N}} + \|\Sigma\|\sqrt{\frac{\log(1/\delta)}{N}} + \varepsilon\|\Sigma\|\right). \] Both results are optimal up to multiplicative constant factors. Despite the recent significant interest in robust statistics, achieving both dimension-free bounds in the canonical Gaussian case remained open. In fact, several previously known results were either dimension-dependent and required $\Sigma$ to be close to identity, or had a sub-optimal dependence on the contamination level $\varepsilon$. As a part of the analysis, we derive sharp concentration inequalities for central order statistics of Gaussian, folded normal, and chi-squared distributions.

The advancement of social media contributes to the growing amount of content they share frequently. This framework provides a sophisticated place for people to report various real-life events. Detecting these events with the help of natural language processing has received researchers' attention, and various algorithms have been developed for this goal. In this paper, we propose a Semantic Modular Model (SMM) consisting of 5 different modules, namely Distributional Denoising Autoencoder, Incremental Clustering, Semantic Denoising, Defragmentation, and Ranking and Processing. The proposed model aims to (1) cluster various documents and ignore the documents that might not contribute to the identification of events, (2) identify more important and descriptive keywords. Compared to the state-of-the-art methods, the results show that the proposed model has a higher performance in identifying events with lower ranks and extracting keywords for more important events in three English Twitter datasets: FACup, SuperTuesday, and USElection. The proposed method outperformed the best reported results in the mean keyword-precision metric by 7.9\%.

Traditional models of active learning assume a learner can directly manipulate or query a covariate $X$ in order to study its relationship with a response $Y$. However, if $X$ is a feature of a complex system, it may be possible only to indirectly influence $X$ by manipulating a control variable $Z$, a scenario we refer to as Indirect Active Learning. Under a nonparametric model of Indirect Active Learning with a fixed budget, we study minimax convergence rates for estimating the relationship between $X$ and $Y$ locally at a point, obtaining different rates depending on the complexities and noise levels of the relationships between $Z$ and $X$ and between $X$ and $Y$. We also identify minimax rates for passive learning under comparable assumptions. In many cases, our results show that, while there is an asymptotic benefit to active learning, this benefit is fully realized by a simple two-stage learner that runs two passive experiments in sequence.

In this paper, we propose a method for measuring the similarity low sample tabular data with synthetically generated data with a larger number of samples than original. This process is also known as data augmentation. But significance levels obtained from non-parametric tests are suspect when sample size is small. Our method uses a combination of geometry, topology and robust statistics for hypothesis testing in order to compare the "validity" of generated data. We also compare the results with common global metric methods available in the literature for large sample size data.

Perception, localization, planning, and control, high-level functions often organized in a so-called pipeline, are amongst the core building blocks of modern autonomous (ground, air, and underwater) vehicle architectures. These functions are increasingly being implemented using learning-enabled components (LECs), i.e., (software) components leveraging knowledge acquisition and learning processes such as deep learning. Providing quantified component-level assurance as part of a wider (dynamic) assurance case can be useful in supporting both pre-operational approval of LECs (e.g., by regulators), and runtime hazard mitigation, e.g., using assurance-based failover configurations. This paper develops a notion of assurance for LECs based on i) identifying the relevant dependability attributes, and ii) quantifying those attributes and the associated uncertainty, using probabilistic techniques. We give a practical grounding for our work using an example from the aviation domain: an autonomous taxiing capability for an unmanned aircraft system (UAS), focusing on the application of LECs as sensors in the perception function. We identify the applicable quantitative measures of assurance, and characterize the associated uncertainty using a non-parametric Bayesian approach, namely Gaussian process regression. We additionally discuss the relevance and contribution of LEC assurance to system-level assurance, the generalizability of our approach, and the associated challenges.

Check out all the on-demand sessions from the Intelligent Security Summit here. Classical machine learning (ML) algorithms have proven to be powerful tools for a wide range of tasks, including image and speech recognition, natural language processing (NLP) and predictive modeling. However, classical algorithms are limited by the constraints of classical computing and can struggle to process large and complex datasets or to achieve high levels of accuracy and precision. Enter quantum machine learning (QML). QML combines the power of quantum computing with the predictive capabilities of ML to overcome the limitations of classical algorithms and offer improvements in performance.

Many algorithms are capable of underpinning decision systems. They vary in efficacy regarding properties such as accuracy, speed, and interpretability. In order to fulfill business requirements and objectives, companies are often torn about which algorithms to use. One of the most common yet thorniest issues is the tradeoff between accuracy and interpretability, especially when business goals require the algorithm to be both, but available methods outperform in one area while underperforming in the other. Logistic regression models, for one, are highly interpretable, but not necessarily accurate.

Are you looking for the Best Online Courses on Machine Learning?. But confused because of so many courses available online. Your search will end after reading this article. In this article, you will find the 20 Best Online Courses on Machine Learning. So, give your few minutes to this article and find out the Best Online Courses on Machine Learning for you. Machine Learning is very powerful and popular. Many people are shifting their careers into the ML field. The reason behind the popularity of Machine Learning is its power to make useless data into more meaningful data. Machine Learning models allow us to predict of various outcomes from the data.

You've just stumbled upon the most complete, in-depth Visualization/Dimensionality Reduction course online. This course is designed to give you the Visualization/Dimensionality Reduction skills you need to become an expert data scientist. By the end of the course, you will understand Visualization/Dimensionality Reduction extremely well and be able to use the techniques on your own projects and be productive as a computer scientist and data analyst. What makes this course a bestseller? Like you, thousands of others were frustrated and fed up with fragmented Youtube tutorials or incomplete or outdated courses which assume you already know a bunch of stuff, as well as thick, college-like textbooks able to send even the most caffeine-fuelled coder to sleep.

Developing Hybrid Machine Learning Models to Assign Health Score to Railcar Fleets for Optimal Decision Making Mahyar Ejlali, Ebrahim Arian, Sajjad Taghiyeh, Kristina Chambers, Amir Hossein Sadeghi, Demet Cakdi, Robert B Handfield An expert hybrid predictive fault method is proposed based on fast-DBSCAN and PCA. Inspection data from 1986-2020 of North American Railcar Owner (NARO) is used. The model is able to predict future faults in the railcar fleet accurately. Abstract A large amount of data is generated during the operation of a railcar fleet, which can easily lead to dimensional disaster and reduce the resiliency of the railcar network. To solve these issues and offer predictive maintenance, this research introduces a hybrid fault diagnosis expert system method that combines density-based spatial clustering of applications with noise (DBSCAN) and principal component analysis (PCA). Firstly, the DBSCAN method is used to cluster categorical data that are similar to one another within the same group. Secondly, PCA algorithm is applied to reduce the dimensionality of the data and eliminate redundancy in order to improve the accuracy of fault diagnosis. Finally, we explain the engineered features and evaluate the selected models by using the Gain Chart and Area Under Curve (AUC) metrics. We use the hybrid expert system model to enhance maintenance planning decisions by assigning a health score to the railcar system of the North American Railcar Owner (NARO). According to the experimental results, our expert model can detect 96.4% of failures within 50% of the sample. This suggests that our method is effective at diagnosing failures in railcars fleet. Keywords: Expert system, Predictive maintenance, Railcar maintenance, Machine learning, Maintenance health score 1. Introduction Maintenance consists of activities that ensure the railcar assets continue to operate safely and reliably. These activities include inspection, repair, testing, and replacement of parts.