Steven, that means you have to transmit the accusation of witchcraft, followed by a computer program, followed by the coded data. Why not just transmit the computer program followed by the coded data? I don’t expect my own environment to be random noise, but that has nothing to do with witchcraft...
Alan, I agree that VC dimension is an important conceptually different way of thinking about “complexity”. One of its primary selling points is that, for example, it doesn’t attach infinite complexity to a model class that contains one real-valued parameter, if that model class isn’t very flexible (i.e., it says only “the data points are greater than R”). But VC complexity doesn’t plug into standard probability theory as easily as Solomonoff induction.
Steven, that means you have to transmit the accusation of witchcraft, followed by a computer program, followed by the coded data. Why not just transmit the computer program followed by the coded data? I don’t expect my own environment to be random noise, but that has nothing to do with witchcraft...
Alan, I agree that VC dimension is an important conceptually different way of thinking about “complexity”. One of its primary selling points is that, for example, it doesn’t attach infinite complexity to a model class that contains one real-valued parameter, if that model class isn’t very flexible (i.e., it says only “the data points are greater than R”). But VC complexity doesn’t plug into standard probability theory as easily as Solomonoff induction.