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Review Day Slides
Review Day Slides

The Learnability of Quantum States
The Learnability of Quantum States

... “If the possible hypotheses have sufficiently fewer bits than the data you’ve collected, and if one of those hypotheses succeeds in explaining your data, then that hypothesis will probably also explain most of the data you haven’t collected” In particular: If you want to output a hypothesis from set ...
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... yourself from this game. It is also called a stopping time. You can decide whether to exit the game at the moment n only basing on the past: using the values of X1 , . . . , Xn , which you already know by this moment. Speaking formally, the event {τ = n} depends only on X1 , . . . , Xn . So we consi ...
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... Law of Large Numbers states that as an experiment is repeated many times the empirical probability will approach the theoretical probability. Properties of probability 1. The probability of an event that can never occur is 0. 2. The probability of an event that will always occur is 1. 3. The probabi ...
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... dry air meeting warm, wet air then we can predict when and where it will rain, by tracking air currents, temperature, and moisture. ...
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... Thus the chance that Y deviates from its mean by more than k standard deviations is less than 1/k 2 for any random variable Y . For k = 1 this is non-informative, since k 2 = 1. For k = 2 this is 0.25 – in other words, the chance is less than a quarter that Y deviates by more than 2 standard deviati ...
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Indeterminism

Indeterminism is the concept that events (certain events, or events of certain types) are not caused, or not caused deterministically (cf. causality) by prior events. It is the opposite of determinism and related to chance. It is highly relevant to the philosophical problem of free will, particularly in the form of metaphysical libertarianism.In science, most specifically quantum theory in physics, indeterminism is the belief that no event is certain and the entire outcome of anything is a probability. The Heisenberg uncertainty relations and the “Born rule”, proposed by Max Born, are often starting points in support of the indeterministic nature of the universe. Indeterminism is also asserted by Sir Arthur Eddington, and Murray Gell-Mann. Indeterminism has been promoted by the French biologist Jacques Monod's essay ""Chance and Necessity"". The physicist-chemist Ilya Prigogine argued for indeterminism in complex systems.
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