We give the first polynomial-time algorithm for robust regression in the listdecodable setting where an adversary can corrupt a greater than1/2 fraction ofexamples.

On the positive side, we give anα = 1.01-approximate proper learner that uses O(1/( 2γ2)) samples (which is optimal) and runs in timepoly(d/) 2 O(1/γ

In the first model, we are givenn i.i.d.

In the first model, we are givenn i.i.d.

Insuch situations, weallowthealgorithm toreturn asmall listofcandidates such that one of the candidates is close to the true parameter.

Inthisbasicsetting, linear regression is well-understood.

Robust learning is a critical field that seeks to develop efficient algorithms that can recover an underlying model despite possibly malicious corruptions in the data. In recent decades, being able to deal with corrupted measurements has become of crucial importance.

In this paper, we propose a new numerical method for the underdamped Langevin diffusion (ULD) and present a non-asymptotic analysis of its sampling error in the 2-Wasserstein distance when the $d$-dimensional target distribution $p(x)\propto e^{-f(x)}$ is strongly log-concave and has varying degrees of smoothness. Precisely, under the assumptions that the gradient and Hessian of $f$ are Lipschitz continuous, our algorithm achieves a 2-Wasserstein error of $\varepsilon$ in $\mathcal{O}(\sqrt{d}/\varepsilon)$ and $\mathcal{O}(\sqrt{d}/\sqrt{\varepsilon})$ steps respectively. Therefore, our algorithm has a similar complexity as other popular Langevin MCMC algorithms under matching assumptions. However, if we additionally assume that the third derivative of $f$ is Lipschitz continuous, then our algorithm achieves a 2-Wasserstein error of $\varepsilon$ in $\mathcal{O}(\sqrt{d}/\varepsilon^{\frac{1}{3}})$ steps. To the best of our knowledge, this is the first gradient-only method for ULD with third order convergence. To support our theory, we perform Bayesian logistic regression across a range of real-world datasets, where our algorithm achieves competitive performance compared to an existing underdamped Langevin MCMC algorithm and the popular No U-Turn Sampler (NUTS).

Fox News Flash top sports headlines are here. Check out what's clicking on Foxnews.com. Alex Kane has been on a roll in the second half of the year with Major League Wrestling. The Georgia native became the MLW World Heavyweight Champion in July with a win over Alex Hammerstone at "Never Say Never" and has successfully defended the title three times since the victory with his faction – the Bomaye Fight Club – behind him. Thursday night will be one of Kane's toughest matches yet as he steps into the ring against the "Indy God" Matt Cardona at "One Shot" in New York City.

Former litigator Jacqueline Schafer, the CEO and founder of Clearbrief, said AI is frequently used in courtrooms, and she created Clearbrief to fact-check citations and court docs created by generative AI. Some researchers are increasingly convinced they will not be able to remove hallucinations from artificial intelligence (AI) models, which remain a considerable hurdle for large-scale public acceptance. "We currently do not understand a lot of the black box nature of how machine learning comes to its conclusions," Kevin Kane, CEO of quantum encryption company American Binary, told Fox News Digital. "Under the current approach to walking this path of AI, it's not clear how we would do that. We'd have to change how they work a lot."