Many of the causal discovery methods rely on the faithfulness assumption to guarantee asymptotic correctness. However, the assumption can be approximately violated in many ways, leading to sub-optimal solutions. Although there is a line of research in Bayesian network structure learning that focuses on weakening the assumption, such as exact search methods with well-defined score functions, they do not scale well to large graphs. In this work, we introduce several strategies to improve the scalability of exact score-based methods in the linear Gaussian setting. In particular, we develop a super-structure estimation method based on the support of inverse covariance matrix which requires assumptions that are strictly weaker than faithfulness, and apply it to restrict the search space of exact search. We also propose a local search strategy that performs exact search on the local clusters formed by each variable and its neighbors within two hops in the super-structure. Numerical experiments validate the efficacy of the proposed procedure, and demonstrate that it scales up to hundreds of nodes with a high accuracy.

When a model's predicted number of events within any time interval is similar to the observed number, it is called well-calibrated. A survival model's calibration can be measured using, for instance, distributional calibration (D-CALIBRATION) [Haider et al., 2020] which computes the squared difference between the observed and predicted number of events within different time intervals. Classically, calibration is addressed in post-training analysis. We develop explicit calibration (X-CAL), which turns D-CALIBRATION into a differentiable objective that can be used in survival modeling alongside maximum likelihood estimation and other objectives. X-CAL allows us to directly optimize calibration and strike a desired trade-off between predictive power and calibration. In our experiments, we fit a variety of shallow and deep models on simulated data, a survival dataset based on MNIST, on length-of-stay prediction using MIMIC-III data, and on brain cancer data from The Cancer Genome Atlas. We show that the models we study can be miscalibrated. We give experimental evidence on these datasets that X-CAL improves D-CALIBRATION without a large decrease in concordance or likelihood.

The vast majority of work in self-supervised learning have focused on assessing recovered features by a chosen set of downstream tasks. While there are several commonly used benchmark datasets, this lens of feature learning requires assumptions on the downstream tasks which are not inherent to the data distribution itself. In this paper, we present an alternative lens, one of parameter identifiability: assuming data comes from a parametric probabilistic model, we train a self-supervised learning predictor with a suitable parametric form, and ask whether the parameters of the optimal predictor can be used to extract the parameters of the ground truth generative model.Specifically, we focus on latent-variable models capturing sequential structures, namely Hidden Markov Models with both discrete and conditionally Gaussian observations. We focus on masked prediction as the self-supervised learning task and study the optimal masked predictor. We show that parameter identifiability is governed by the task difficulty, which is determined by the choice of data model and the amount of tokens to predict. Technique-wise, we uncover close connections with the uniqueness of tensor rank decompositions, a widely used tool in studying identifiability through the lens of the method of moments.

Score matching (SM) provides a compelling approach to learn energy-based models (EBMs) by avoiding the calculation of partition function. However, it remains largely open to learn energy-based latent variable models (EBLVMs), except some special cases. This paper presents a bi-level score matching (BiSM) method to learn EBLVMs with general structures by reformulating SM as a bi-level optimization problem. The higher level introduces a variational posterior of the latent variables and optimizes a modified SM objective, and the lower level optimizes the variational posterior to fit the true posterior. To solve BiSM efficiently, we develop a stochastic optimization algorithm with gradient unrolling. Theoretically, we analyze the consistency of BiSM and the convergence of the stochastic algorithm. Empirically, we show the promise of BiSM in Gaussian restricted Boltzmann machines and highly nonstructural EBLVMs parameterized by deep convolutional neural networks. BiSM is comparable to the widely adopted contrastive divergence and SM methods when they are applicable; and can learn complex EBLVMs with intractable posteriors to generate natural images.

Identifying statistical regularities in solutions to some tasks in multi-task reinforcement learning can accelerate the learning of new tasks.Skill learning offers one way of identifying these regularities by decomposing pre-collected experiences into a sequence of skills.A popular approach to skill learning is maximizing the likelihood of the pre-collected experience with latent variable models,where the latent variables represent the skills. However, there are often many solutions that maximize the likelihood equally well, including degenerate solutions. To address this underspecification, we propose a new objective that combines the maximum likelihood objective with a penalty on the description length of the skills. This penalty incentivizes the skills to maximally extract common structures from the experiences. Empirically, our objective learns skills that solve downstream tasks in fewer samples compared to skills learned from only maximizing likelihood. Further, while most prior works in the offline multi-task setting focus on tasks with low-dimensional observations, our objective can scale to challenging tasks with high-dimensional image observations.

Existing Graph Neural Network (GNN) methods that learn graph representations focus on learning node and edge representations by predicting observed edges in the graph. Although such approaches have shown advances in downstream node classification tasks, they are ineffective in jointly representing larger k-node sets, k{>}2. We propose MHM-GNN, an inductive unsupervised graph representation approach that combines joint k-node representations with energy-based models (hypergraph Markov networks) and GNNs. To address the intractability of the loss that arises from this combination, we endow our optimization with a loss upper bound using a finite-sample unbiased Markov Chain Monte Carlo estimator. Our experiments show that the unsupervised joint k-node representations of MHM-GNN produce better unsupervised representations than existing approaches from the literature.

Fine-grained zero-shot learning task requires some form of side-information to transfer discriminative information from seen to unseen classes. As manually annotated visual attributes are extremely costly and often impractical to obtain for a large number of classes, in this study we use DNA as a side information for the first time for fine-grained zero-shot classification of species. Mitochondrial DNA plays an important role as a genetic marker in evolutionary biology and has been used to achieve near perfect accuracy in species classification of living organisms. We implement a simple hierarchical Bayesian model that uses DNA information to establish the hierarchy in the image space and employs local priors to define surrogate classes for unseen ones. On the benchmark CUB dataset we show that DNA can be equally promising, yet in general a more accessible alternative than word vectors as a side information. This is especially important as obtaining robust word representations for fine-grained species names is not a practicable goal when information about these species in free-form text is limited. On a newly compiled fine-grained insect dataset that uses DNA information from over a thousand species we show that the Bayesian approach outperforms state-of-the-art by a wide margin.

The Bayes-Adaptive Markov Decision Process (BAMDP) formalism pursues the Bayes-optimal solution to the exploration-exploitation trade-off in reinforcement learning. As the computation of exact solutions to Bayesian reinforcement-learning problems is intractable, much of the literature has focused on developing suitable approximation algorithms. In this work, before diving into algorithm design, we first define, under mild structural assumptions, a complexity measure for BAMDP planning. As efficient exploration in BAMDPs hinges upon the judicious acquisition of information, our complexity measure highlights the worst-case difficulty of gathering information and exhausting epistemic uncertainty. To illustrate its significance, we establish a computationally-intractable, exact planning algorithm that takes advantage of this measure to show more efficient planning. We then conclude by introducing a specific form of state abstraction with the potential to reduce BAMDP complexity and gives rise to a computationally-tractable, approximate planning algorithm.

Score matching estimators for point processes have gained widespread attention in recent years because they do not require the calculation of intensity integrals, thereby effectively addressing the computational challenges in maximum likelihood estimation (MLE). Some existing works have proposed score matching estimators for point processes. However, this work demonstrates that the incompleteness of the estimators proposed in those works renders them applicable only to specific problems, and they fail for more general point processes. To address this issue, this work introduces the weighted score matching estimator to point processes. Theoretically, we prove the consistency of the estimator we propose. Experimental results indicate that our estimator accurately estimates model parameters on synthetic data and yields results consistent with MLE on real data. In contrast, existing score matching estimators fail to perform effectively.

Greedy algorithms have long been a workhorse for learning graphical models, and more broadly for learning statistical models with sparse structure. In the context of learning directed acyclic graphs, greedy algorithms are popular despite their worst-case exponential runtime. In practice, however, they are very efficient. We provide new insight into this phenomenon by studying a general greedy score-based algorithm for learning DAGs. Unlike edge-greedy algorithms such as the popular GES and hill-climbing algorithms, our approach is vertex-greedy and requires at most a polynomial number of score evaluations. We then show how recent polynomial-time algorithms for learning DAG models are a special case of this algorithm, thereby illustrating how these order-based algorithms can be rigourously interpreted as score-based algorithms. This observation suggests new score functions and optimality conditions based on the duality between Bregman divergences and exponential families, which we explore in detail. Explicit sample and computational complexity bounds are derived. Finally, we provide extensive experiments suggesting that this algorithm indeed optimizes the score in a variety of settings.