Given ancestral constraints, some pruning of the search tree is possible. Lemma 3 (supplementary material) is the key result here. I believe it to be true, but I don't understand the proof. The phrase "By the EC tree edge generation rules, G_k also contains edge Z - W" needs more explanation. In addition there are implied constraints ( "implied constraints" is the standard terminology, here they are called "projected constraints").

This paper provides theoretical bounds that are tighter than existing variational bounds for the problem of learning latent variable models. The authors extend applied existing theory of hash-based learning and amortized inference to design a black-box learning algorithm. They later applied it to learning a Sigmoid Belief Network. The main advantage to this approach seems to be the partitioning of the search space for posterior distributions into buckets/subsets that are faster to search than with a typical sampling method. The proposed inference scheme then leverages mean-field inference (used heavily in the context of variational inference) within each subset. One of the main technical contributions is the tighter bound on the likelihood using two aggregate estimators which was an extension of an existing work (specific to undirected graphical models) to the directed models setting.

Gaussian graphical models with sparsity in the inverse covariance matrix are of significant interest in many modern applications. For the problem of recovering the graphical structure, information criteria provide useful optimization objectives for algorithms searching through sets of graphs or for selection of tuning parameters of other methods such as the graphical lasso, which is a likelihood penalization technique. In this paper we establish the asymptotic consistency of an extended Bayesian information criterion for Gaussian graphical models in a scenario where both the number of variables p and the sample size n grow. Compared to earlier work on the regression case, our treatment allows for growth in the number of non-zero parameters in the true model, which is necessary in order to cover connected graphs. We demonstrate the performance of this criterion on simulated data when used in conjuction with the graphical lasso, and verify that the criterion indeed performs better than either cross-validation or the ordinary Bayesian information criterion when p and the number of non-zero parameters q both scale with n.

We develop a novel Bayesian nonparametric model for random bipartite graphs. The model is based on the theory of completely random measures and is able to handle a potentially infinite number of nodes. We show that the model has appealing properties and in particular it may exhibit a power-law behavior. We derive a posterior characterization, an Indian Buffet-like generative process for network growth, and a simple and efficient Gibbs sampler for posterior simulation. Our model is shown to be well fitted to several real-world social networks.

Dependent Dirichlet processes (DPs) are dependent sets of random measures, each being marginally Dirichlet process distributed. They are used in Bayesian nonparametric models when the usual exchangebility assumption does not hold. We propose a simple and general framework to construct dependent DPs by marginalizing and normalizing a single gamma process over an extended space. The result is a set of DPs, each located at a point in a space such that neighboring DPs are more dependent. We describe Markov chain Monte Carlo inference, involving the typical Gibbs sampling and three different Metropolis-Hastings proposals to speed up convergence.

Autonomous agents operating in real-world scenarios frequently encounter uncertainty and make decisions based on incomplete information. Planning under uncertainty can be mathematically formalized using partially observable Markov decision processes (POMDPs). However, finding an optimal plan for POMDPs can be computationally expensive and is feasible only for small tasks. In recent years, approximate algorithms, such as tree search and sample-based methodologies, have emerged as state-of-the-art POMDP solvers for larger problems. Despite their effectiveness, these algorithms offer only probabilistic and often asymptotic guarantees toward the optimal solution due to their dependence on sampling.

Gaussian processes are the model of choice in Bayesian optimization and active learning. Yet, they are highly dependent on cleverly chosen hyperparameters to reach their full potential, and little effort is devoted to finding good hyperparameters in the literature. We demonstrate the impact of selecting good hyperparameters for GPs and present two acquisition functions that explicitly prioritize hyperparameter learning. Statistical distance-based Active Learning (SAL) considers the average disagreement between samples from the posterior, as measured by a statistical distance. SAL outperforms the state-of-the-art in Bayesian active learning on several test functions.

Image captioning aims to describe visual content in natural language. As'a picture is worth a thousand words', there could be various correct descriptions for an image. However, with maximum likelihood estimation as the training objective, the captioning model is penalized whenever its prediction mismatches with the label. For instance, when the model predicts a word expressing richer semantics than the label, it will be penalized and optimized to prefer more concise expressions, referred to as conciseness optimization. In contrast, predictions that are more concise than labels lead to richness optimization. Such conflicting optimization directions could eventually result in the model generating general descriptions.

Some of the most successful knowledge graph embedding (KGE) models for link prediction – CP, RESCAL, TuckER, ComplEx – can be interpreted as energy-based models. Under this perspective they are not amenable for exact maximum-likelihood estimation (MLE), sampling and struggle to integrate logical constraints. This work re-interprets the score functions of these KGEs as circuits – constrained computational graphs allowing efficient marginalisation. Then, we design two recipes to obtain efficient generative circuit models by either restricting their activations to be non-negative or squaring their outputs. Our interpretation comes with little or no loss of performance for link prediction, while the circuits framework unlocks exact learning by MLE, efficient sampling of new triples, and guarantee that logical constraints are satisfied by design.

Policy Mirror Descent (PMD) is a general family of algorithms that covers a wide range of novel and fundamental methods in reinforcement learning. With exact policy evaluation, PI is known to converge linearly with a rate given by the discount factor \gamma of a Markov Decision Process. In this work, we bridge the gap between PI and PMD with exact policy evaluation and show that the dimension-free \gamma -rate of PI can be achieved by the general family of unregularised PMD algorithms under an adaptive step-size. We show that both the rate and step-size are unimprovable for PMD: we provide matching lower bounds that demonstrate that the \gamma -rate is optimal for PMD methods as well as PI and that the adaptive step-size is necessary to achieve it. Our work is the first to relate PMD to rate-optimality and step-size necessity.