Disentangled Representation Learning aims to improve the explainability of deep learning methods by training a data encoder that identifies semantically meaningful latent variables in the data generation process. Nevertheless, there is no consensus regarding a universally accepted definition for the objective of disentangled representation learning. In particular, there is a considerable amount of discourse regarding whether should the latent variables be mutually independent or not. In this paper, we first investigate these arguments on the interrelationships between latent variables by establishing a conceptual bridge between Epistemology and Disentangled Representation Learning. Then, inspired by these interdisciplinary concepts, we introduce a two-level latent space framework to provide a general solution to the prior arguments on this issue. Finally, we propose a novel method for disentangled representation learning by employing an integration of mutual information constraint and independence constraint within the Generative Adversarial Network (GAN) framework. Experimental results demonstrate that our proposed method consistently outperforms baseline approaches in both quantitative and qualitative evaluations. The method exhibits strong performance across multiple commonly used metrics and demonstrates a great capability in disentangling various semantic factors, leading to an improved quality of controllable generation, which consequently benefits the explainability of the algorithm.

Ensuring Conditional Independence (CI) constraints is pivotal for the development of fair and trustworthy machine learning models. In this paper, we introduce \sys, a framework that harnesses optimal transport theory for data repair under CI constraints. Optimal transport theory provides a rigorous framework for measuring the discrepancy between probability distributions, thereby ensuring control over data utility. We formulate the data repair problem concerning CIs as a Quadratically Constrained Linear Program (QCLP) and propose an alternating method for its solution. However, this approach faces scalability issues due to the computational cost associated with computing optimal transport distances, such as the Wasserstein distance. To overcome these scalability challenges, we reframe our problem as a regularized optimization problem, enabling us to develop an iterative algorithm inspired by Sinkhorn's matrix scaling algorithm, which efficiently addresses high-dimensional and large-scale data. Through extensive experiments, we demonstrate the efficacy and efficiency of our proposed methods, showcasing their practical utility in real-world data cleaning and preprocessing tasks. Furthermore, we provide comparisons with traditional approaches, highlighting the superiority of our techniques in terms of preserving data utility while ensuring adherence to the desired CI constraints.

Recent empirical studies on domain generalization (DG) have shown that DG algorithms that perform well on some distribution shifts fail on others, and no state-of-the-art DG algorithm performs consistently well on all shifts. Moreover, real-world data often has multiple distribution shifts over different attributes; hence we introduce multi-attribute distribution shift datasets and find that the accuracy of existing DG algorithms falls even further. To explain these results, we provide a formal characterization of generalization under multi-attribute shifts using a canonical causal graph. Based on the relationship between spurious attributes and the classification label, we obtain realizations of the canonical causal graph that characterize common distribution shifts and show that each shift entails different independence constraints over observed variables. As a result, we prove that any algorithm based on a single, fixed constraint cannot work well across all shifts, providing theoretical evidence for mixed empirical results on DG algorithms. Based on this insight, we develop Causally Adaptive Constraint Minimization (CACM), an algorithm that uses knowledge about the data-generating process to adaptively identify and apply the correct independence constraints for regularization. Results on fully synthetic, MNIST, small NORB, and Waterbirds datasets, covering binary and multi-valued attributes and labels, show that adaptive dataset-dependent constraints lead to the highest accuracy on unseen domains whereas incorrect constraints fail to do so. Our results demonstrate the importance of modeling the causal relationships inherent in the data-generating process.

The leading contender is Levi's When the set contains only one function, convex conditionalization and E-admissibility reduce to their strict Bayesian counterparts. Thus, with respect to decision making and representing and updating uncertainty, convex Bay· esianism includes strict Bayesianism as a special case. There are natural constraints on probability judg-- ments that cannot be represented by convex sets of classical probability functions. Working with the convex hull of a nonconvex set of probability func-- tions may result in unnecessary indecisiveness. This is not a convex set. Judgments of irrelevance (conditional irrelevance), that is, probabilistic independence (conditional independence}, are often made, are natural to make, can be made reliably, and provide well-known computational advantages [Pearl, 1988].

In this paper, we derive optimality results for greedy Bayesian-network search algorithms that perform single-edge modifications at each step and use asymptotically consistent scoring criteria. Our results extend those of Meek (1997) and Chickering (2002), who demonstrate that in the limit of large datasets, if the generative distribution is perfect with respect to a DAG defined over the observable variables, such search algorithms will identify this optimal (i.e. We relax their assumption about the generative distribution, and assume only that this distribution satisfies the composition property over the observable variables, which is a more realistic assumption for real domains. Under this assumption, we guarantee that the search algorithms identify an inclusion-optimal model; that is, a model that (1) contains the generative distribution and (2) has no sub-model that contains this distribution. In addition, we show that the composition property is guaranteed to hold whenever the dependence relationships in the generative distribution can be characterized by paths between singleton elements in some generative graphical model (e.g. a DAG, a chain graph, or a Markov network) even when the generative model includes unobserved variables, and even when the observed data is subject to selection bias. Introduction The problem of learning Bayesian networks (a.k.a directed graphical models) from data has received much attention in the UAI community. A simple approach taken by many researchers, particularly those contributing experimental papers, is to apply--in conjunction with a scoring criterion--a greedy single-edge search algorithm to the space of Bayesian-network structures or to the space of equivalence classes of those structures. There are a number of important reasons for the popularity of this approach.

The constraints arising from DAG models with latent variables can be naturally represented by means of acyclic directed mixed graphs (ADMGs). Such graphs contain directed and bidirected arrows, and contain no directed cycles. DAGs with latent variables imply independence constraints in the distribution resulting from a 'fixing' operation, in which a joint distribution is divided by a conditional. This operation generalizes marginalizing and conditioning. Some of these constraints correspond to identifiable 'dormant' independence constraints, with the well known 'Verma constraint' as one example. Recently, models defined by a set of the constraints arising after fixing from a DAG with latents, were characterized via a recursive factorization and a nested Markov property. In addition, a parameterization was given in the discrete case. In this paper we use this parameterization to describe a parameter fitting algorithm, and a search and score structure learning algorithm for these nested Markov models. We apply our algorithms to a variety of datasets.

Directed acyclic graphs (DAGs) are a popular framework to express multivariate probability distributions. Acyclic directed mixed graphs (ADMGs) are generalizations of DAGs that can succinctly capture much richer sets of conditional independencies, and are especially useful in modeling the effects of latent variables implicitly. Unfortunately there are currently no good parameterizations of general ADMGs. In this paper, we apply recent work on cumulative distribution networks and copulas to propose one one general construction for ADMG models. We consider a simple parameter estimation approach, and report some encouraging experimental results.