Comp 1000 powerpoint chapter 2 simulation exam video 2
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Furthermore, we suggested an algorithm to find such a hyperplane. In the text we showed that to find a hyperplane (parameterised by w and b ) that linearly separates this data we need, for each Hence we have N datapoints in an N -ĭimensional space. The angle between two vectors, explain why ρ x,z ≥ ρ x,y is geometrically obvious.Ĭonsider a ‘Boltzman machine’ distribution on binary variables x i ∈, and x is an N -dimensional vector. With reference to the correlation coefficient as
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Show that the entropy of this distribution isĪnd that therefore as the number of states N increases to infinity, the entropy diverges to infinity.įor variables x, y, and z = x + y, show that the correlation coefficients are related by ρ x,z ≥ ρ x,y. Ĭonsider a uniform distribution p i = 1 /N defined on states i = 1. Show that for the whitened data matrix, given in Equation (8.4.30), ZZ T = N I. ( y − ( y ) ) ( y − ( y ) ) T = ( Mx + η − M μĪnd the independence of x and η, derive the formula for the covariance of p ( y ). We can do this by the lengthy process of completing the square. We now need to find the mean and covariance of this Gaussian. This establishes that p ( y ) is Gaussian. This exercise concerns the derivation of Equation (8.4.15). For the Gauss-gamma posterior p ( μ, λ | μ 0, α, β, X ) given in Equation (8.8.28) compute the marginal posterior p ( μ | μ 0, α, β, X ).