Intuition and Simulation Sample Clauses

Intuition and Simulation. ‌ To gain some intuitional insight into MRD, we will show a simulation to explain the model. We now want to simulate three different subsets of observed data {Yi ∶ 1 ≤ i ≤ 3}, by mixing different latent functions linearly. This means, we take only some of the input functions to simulate a dataset Yi. After mixing, we push the datasets to higher dimensions for each dataset set Yi to have different dimen- sionality from each other. We perform the increase in dimensionality by multiply- ing with a matrix Ai ∈ Rqi×Di of high dimensional noise Ai = N (0, α ). Each output data set Yi has its own noise variance, input dimensionality qi and output dimensionality Di assigned to it. This means, with this simulation, we will show several aspects of the strengths of MRD: • Ability to handle differing signal to noise ratios for each dataset Yi by differ- ing noise variances in Ai. • Learn differing mappings fi for each dataset Yi by allowing different kernel structures Ki. ⋅ • Identify independency (and dependency) structures from different input di- mensions q of the input X q to the observed datasets by ARD parameteriza- tion of the covariance functions Ki.