Since the MPLE objective function for LDFA-H given in Eq. (9) is not guaranteed convex, an EM-algorithm may find a local minimum according to a choice of the initial value. Hence a good initialization is crucial to a successful estimation. According to the equivalence between CCA and probablistic CCA shown by A. Anonymous, it gives (r 1) (r 1) (r 1) (r 1) Lasso problem is solved by the P-GLASSO algorithm by Mazumder et al. (2010). We simulated realistic data with known cross-region connectivity as follows. Notice that the amplitudes of the top four factors dominate the others.

We perform a random search [43] for hyperparameter optimization over the search ranges in Table 6.

Models are trained on a single Titan Xp GPU on an internal cluster. Training time is typically 6-8 hours on 4 CPUs and 32GB of RAM. We train with batch size B = 128 . Like ShapeWorld, RNN encoders and decoders are single layer GRUs with hidden size 1024 and embedding size 500. For additional example games from both datasets, see Figure S1.

GANs trained by a two time-scale update rule converge to a local Nash equilibrium.

Third, the probabilistic bounds we obtain for SGD (i.e., on quantiles) provide novel insights over the previously known in-expectation