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Explore a comprehensive lecture on testing assumptions in learning algorithms presented by Arsen Vasilyan from MIT at the Simons Institute's Sublinear Algorithms Boot Camp. Delve into the critical examination of two fundamental assumptions in supervised learning theory: distributional assumptions and the absence of distribution shift. Understand how these assumptions, while often necessary for theoretical guarantees, can lead to catastrophic failures when not satisfied in real-world applications. Learn about the innovative use of property testing to mitigate dependence on these assumptions and alert users to potential violations. Discover how insights from property testing can be applied to construct testers for various function classes, addressing both distributional assumptions and distribution shift. Gain valuable knowledge on enhancing the reliability and robustness of algorithms used in critical decision-making processes across society.