Soft Multivariate Truncated Normal Distribution (soft tMVN)
We propose a new distribution, called the soft tMVN distribution, which provides a smooth approximation to the truncated multivariate normal (tMVN) distribution with linear constraints. An efficient blocked Gibbs sampler is developed to sample from the soft tMVN distribution in high dimensions. We provide theoretical support to the approximation capability of the soft tMVN and provide further empirical evidence thereof. The soft tMVN distribution can be used to approximate simulations from a multivariate truncated normal distribution with linear constraints, or itself as a prior in shape-constrained problems. …

Batch Virtual Adversarial Training (BVAT)
We present batch virtual adversarial training (BVAT), a novel regularization method for graph convolutional networks (GCNs). BVAT addresses the shortcoming of GCNs that do not consider the smoothness of the model’s output distribution against local perturbations around the input. We propose two algorithms, sample-based BVAT and optimization-based BVAT, which are suitable to promote the smoothness of the model for graph-structured data by either finding virtual adversarial perturbations for a subset of nodes far from each other or generating virtual adversarial perturbations for all nodes with an optimization process. Extensive experiments on three citation network datasets Cora, Citeseer and Pubmed and a knowledge graph dataset Nell validate the effectiveness of the proposed method, which establishes state-of-the-art results in the semi-supervised node classification tasks. …

Markov Random Field (MRF)
In the domain of physics and probability, a Markov random field (often abbreviated as MRF), Markov network or undirected graphical model is a set of random variables having a Markov property described by an undirected graph. A Markov random field is similar to a Bayesian network in its representation of dependencies; the differences being that Bayesian networks are directed and acyclic, whereas Markov networks are undirected and may be cyclic. Thus, a Markov network can represent certain dependencies that a Bayesian network cannot (such as cyclic dependencies); on the other hand, it can’t represent certain dependencies that a Bayesian network can (such as induced dependencies). …

Bumping
Bumping is a simple algorithm that can help your classifier escape from a local minimum. The idea behind bumping is that we can break the symmetry of the problem (or escape the local minimum) by training a decision tree on random subsample. This is similar to bagging. The hope is that in the subsample there will be a preferred split so the tree can pick it. We fit several trees on different bootstrap) samples (sampling with replacement) and choose the one with the best performance on the full training set as the winner. The more rounds of bumping we do, the more likely we are to escape. It costs more CPU time as well though. …