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Quantifying the Empirical Wasserstein Distance to a Set of Measures: Beating the Curse of Dimensionality

Neural Information Processing Systems

We consider the problem of estimating the Wasserstein distance between the empirical measure and a set of probability measures whose expectations over a class of functions (hypothesis class) are constrained. If this class is sufficiently rich to characterize a particular distribution (e.g., all Lipschitz functions), then our formulation recovers the Wasserstein distance to such a distribution. We establish a strong duality result that generalizes the celebrated Kantorovich-Rubinstein duality. We also show that our formulation can be used to beat the curse of dimensionality, which is well known to affect the rates of statistical convergence of the empirical Wasserstein distance. In particular, examples of infinite-dimensional hypothesis classes are presented, informed by a complex correlation structure, for which it is shown that the empirical Wasserstein distance to such classes converges to zero at the standard parametric rate. Our formulation provides insights that help clarify why, despite the curse of dimensionality, the Wasserstein distance enjoys favorable empirical performance across a wide range of statistical applications.


Pretent little ones from becoming iPad kids with these Prime Day deals on Melissa & Doug toys

Popular Science

Amazon Prime Day is live. See the best deals HERE. Melissa & Doug's simple, beautiful toys make fantastic gifts and they're on steep sale during Amazon Prime Day. We may earn revenue from the products available on this page and participate in affiliate programs. Melissa & Doug Fresh Mart Pretend Grocery Store $152.49


AI Can Crack Most Common Passwords in Less Than a Minute -- Here's How to Set a Safe One

#artificialintelligence

In our ever-expanding digital world, passwords are an inevitability: email, apps, subscriptions and loyalty programs -- nearly everything is designed to be secure behind a self-set code that permits entry. According to technology site TechCo, the average person has about 100 passwords, so it's no surprise that when signing up for a new account, individuals can sometimes get lazy with word choice. A new report by Home Security Heroes found that 51% of common passwords can be cracked in less than a minute using an AI password cracker, and 81% can be cracked in less than a month. Home Security Heroes used the AI password cracker PassGAN to run through a list of 15,680,000 passwords. The odds of AI decoding one's password increase when a password has a minimal amount of characters and lacks variety (only using lowercase, only using numbers, etc.).


After It Was Postponed, Neuralink 'Show And Tell' Finally Set For November 30

International Business Times

After its earlier schedule was postponed, Neuralink, Elon Musk's neurotechnology company that creates implantable brain-machine interfaces, is finally set to hold its "Show and Tell" event on November 30. The official Twitter account of Neuralink tweeted on Friday a brief video invitation asking people to join them in its "Show and Tell" event. The tweet also came with the caption, "Nov 30, 6 pm PT," which is presumably the date of the event. In April, Musk shared that Neuralink's first human trials were still set for the end of 2022. In August Musk announced Neuralink's "Show and Tell" event planned for October, but given the tech billionaire's acquisition of Twitter at around that time, the event was pushed to the end of November.


Council Post: 12 Industries And Focuses Set To Be Revolutionized By Quantum Computing

#artificialintelligence

How fast is quantum computing? By some estimates, quantum computers may be 158 million times faster than the fastest current supercomputer. Many of us may think such power is destined to be a tool used solely for complex scientific calculations, but it may soon play a significant role in functions and industries that impact our everyday lives. Further, while quantum technology could play a tremendous role in improving everything from human health to energy exploration, in unscrupulous hands, our increasingly digital work and personal lives could be at added risk. Tech experts are clear: The time to prepare for the impacts of quantum computing (both good and bad) is now.


Set your Chatbot up for Success with the Right Budget

#artificialintelligence

I think it's safe to say that we all love to get a good deal – or at least feel like we are! – and save a little money whenever we can. I think we can also all agree that are certain times when going with the cheapest option or skimping on a line in the budget doesn't pay off in the end. You get what you pay for, right? A conversational AI solution is one of those projects that your organisation should be careful not to underfund. Without the proper level of financial support and ongoing funding, you will never achieve success with a conversational AI project.


The Latest: Trump Says He's 'Set the Stage' for Wall Action

U.S. News

The DEA has reported that land ports of entry are the primary means for getting drugs into the country, not stretches of the border without barriers. The agency says the most common trafficking technique by transnational criminal organizations is to hide drugs in passenger vehicles or tractor-trailers.


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AI Magazine

Automated diagnosis is an important AI problem not only for its potential practical applications but also because it exposes issues common to all automated reasoning efforts and presents real challenges to existing paradigms. Current research in this area addresses many problems, including managing and structuring probabilistic information, modeling physical systems, reasoning with defeasible assumptions, and interleaving deliberation and action. Furthermore, diagnosis programs must face these problems in contexts where scaling up to deal with cases of realistic size results in daunting combinatorics. This article presents these and other issues as discussed at the First International Workshop on Principles of Diagnosis. Diagnosis has historically provided an obliging rock for each succeeding generation of AI researchers to blunt their axes on.


Solving Multiagent Networks Using Distributed Constraint Optimization

AI Magazine

In many cooperative multiagent domains, the effect of local interactions between agents can be compactly represented as a network structure. Given that agents are spread across such a network, agents directly interact only with a small group of neighbors. A distributed constraint optimization problem (DCOP) is a useful framework to reason about such networks of agents. Given agents' inability to communicate and collaborate in large groups in such networks, we focus on an approach called k-optimality for solving DCOPs. In this approach, agents form groups of one or more agents until no group of k or fewer agents can possibly improve the DCOP solution; we define this type of local optimum, and any algorithm guaranteed to reach such a local optimum, as k-optimal.


947

AI Magazine

What Is a Knowledge Representation? Although knowledge representation is one of the central and, in some ways, most familiar concepts in AI, the most fundamental question about it--What is it?--has Numerous papers have lobbied for one or another variety of representation, other papers have argued for various properties a representation should have, and still others have focused on properties that are important to the notion of representation in general. In this article, we go back to basics to address the question directly. We believe that the answer can best be understood in terms of five important and distinctly different roles that a representation plays, each of which places different and, at times, conflicting demands on the properties a representation should have.