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Additional resources for 4-Manifolds which embed in R5 R6, and Seifert manifolds for fibered knots
Using Bayes’ theorem this joint probability can be decomposed either as p(y)p(x|y) or as p(x)p(y|x). This gives rise to two different approaches to classification problems. The first, which we call the generative approach, models the class-conditional distributions p(x|y) for y = C1 , . . , CC and also the prior probabilities of each class, and then computes the posterior probability for each class using p(y|x) = discriminative approach generative model example p(y)p(x|y) C c=1 p(Cc )p(x|Cc ) .
Why learning? An inverse dynamics model can be used in the following manner: a planning module decides on a trajectory that takes the robot from its start to goal states, and this specifies the desired positions, velocities and accelerations at each time. The inverse dynamics model is used to compute the torques needed to achieve this trajectory and errors are corrected using a feedback controller. The dataset consists of 48,933 input-output pairs, of which 44,484 were used as a training set and the remaining 4,449 were used as a test set.
1/2 Then defining ψ(x) = Σp φ(x) we obtain a simple dot product representation k(x, x ) = ψ(x) · ψ(x ). If an algorithm is defined solely in terms of inner products in input space then it can be lifted into feature space by replacing occurrences of those inner products by k(x, x ); this is sometimes called the kernel trick. This technique is particularly valuable in situations where it is more convenient to compute the kernel than the feature vectors themselves. As we will see in the coming sections, this often leads to considering the kernel as the object of primary interest, and its corresponding feature space as having secondary practical importance.