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.

Traditional methods for unsupervised learning of finite mixture models require to evaluate the likelihood of all components of the mixture. This becomes computationally prohibitive when the number of components is large, as it is, for example, in the sum-product (transform) networks. Therefore, we propose to apply a combination of the expectation maximization and the Metropolis-Hastings algorithm to evaluate only a small number of, stochastically sampled, components, thus substantially reducing the computational cost. The Markov chain of component assignments is sequentially generated across the algorithm's iterations, having a non-stationary target distribution whose parameters vary via a gradient-descent scheme. We put emphasis on generality of our method, equipping it with the ability to train both shallow and deep mixture models which involve complex, and possibly nonlinear, transformations. The performance of our method is illustrated in a variety of synthetic and real-data contexts, considering deep models, such as mixtures of normalizing flows and sum-product (transform) networks.

Data collected by multiple methods or from multiple sources is called multi-view data. To make full use of the multi-view data, multi-view learning plays an increasingly important role. Traditional multi-view learning methods rely on a large number of labeled and completed multi-view data. However, it is expensive and time-consuming to obtain a large number of labeled multi-view data in real-world applications. Moreover, multi-view data is often incomplete because of data collection failures, self-deficiency, or other reasons. Therefore, we may have to face the problem of fewer labeled and incomplete multi-view data in real application scenarios. In this paper, a transductive semi-supervised incomplete multi-view TSK fuzzy system modeling method (SSIMV_TSK) is proposed to address these challenges. First, in order to alleviate the dependency on labeled data and keep the model interpretable, the proposed method integrates missing view imputation, pseudo label learning of unlabeled data, and fuzzy system modeling into a single process to yield a model with interpretable fuzzy rules. Then, two new mechanisms, i.e. the bidirectional structural preservation of instance and label, as well as the adaptive multiple alignment collaborative learning, are proposed to improve the robustness of the model. The proposed method has the following distinctive characteristics: 1) it can deal with the incomplete and few labeled multi-view data simultaneously; 2) it integrates the missing view imputation and model learning as a single process, which is more efficient than the traditional two-step strategy; 3) attributed to the interpretable fuzzy inference rules, this method is more interpretable. Experimental results on real datasets show that the proposed method significantly outperforms the state-of-the-art methods.

Recently, deep reinforcement learning (RL) has achieved remarkable empirical success by integrating deep neural networks into RL frameworks. However, these algorithms often require a large number of training samples and admit little theoretical understanding. To mitigate these issues, we propose a theoretically principled nearest neighbor (NN) function approximator that can improve the value networks in deep RL methods. Inspired by human similarity judgments, the NN approximator estimates the action values using rollouts on past observations and can provably obtain a small regret bound that depends only on the intrinsic complexity of the environment. We present (1) Nearest Neighbor Actor-Critic (NNAC), an online policy gradient algorithm that demonstrates the practicality of combining function approximation with deep RL, and (2) a plug-and-play NN update module that aids the training of existing deep RL methods. Experiments on classical control and MuJoCo locomotion tasks show that the NN-accelerated agents achieve higher sample efficiency and stability than the baseline agents. Based on its theoretical benefits, we believe that the NN approximator can be further applied to other complex domains to speed-up learning.

Recent research on fair regression focused on developing new fairness notions and approximation methods as target variables and even the sensitive attribute are continuous in the regression setting. However, all previous fair regression research assumed the training data and testing data are drawn from the same distributions. This assumption is often violated in real world due to the sample selection bias between the training and testing data. In this paper, we develop a framework for fair regression under sample selection bias when dependent variable values of a set of samples from the training data are missing as a result of another hidden process. Our framework adopts the classic Heckman model for bias correction and the Lagrange duality to achieve fairness in regression based on a variety of fairness notions. Heckman model describes the sample selection process and uses a derived variable called the Inverse Mills Ratio (IMR) to correct sample selection bias. We use fairness inequality and equality constraints to describe a variety of fairness notions and apply the Lagrange duality theory to transform the primal problem into the dual convex optimization. For the two popular fairness notions, mean difference and mean squared error difference, we derive explicit formulas without iterative optimization, and for Pearson correlation, we derive its conditions of achieving strong duality. We conduct experiments on three real-world datasets and the experimental results demonstrate the approach's effectiveness in terms of both utility and fairness metrics.

Learning new skills by observing humans' behaviors is an essential capability of AI. In this work, we leverage instructional videos to study humans' decision-making processes, focusing on learning a model to plan goal-directed actions in real-life videos. In contrast to conventional action recognition, goal-directed actions are based on expectations of their outcomes requiring causal knowledge of potential consequences of actions. Thus, integrating the environment structure with goals is critical for solving this task. Previous works learn a single world model will fail to distinguish various tasks, resulting in an ambiguous latent space; planning through it will gradually neglect the desired outcomes since the global information of the future goal degrades quickly as the procedure evolves. We address these limitations with a new formulation of procedure planning and propose novel algorithms to model human behaviors through Bayesian Inference and model-based Imitation Learning. Experiments conducted on real-world instructional videos show that our method can achieve state-of-the-art performance in reaching the indicated goals. Furthermore, the learned contextual information presents interesting features for planning in a latent space.

MC Dropout is a mainstream "free lunch" method in medical imaging for approximate Bayesian computations (ABC). Its appeal is to solve out-of-the-box the daunting task of ABC and uncertainty quantification in Neural Networks (NNs); to fall within the variational inference (VI) framework; and to propose a highly multimodal, faithful predictive posterior. We question the properties of MC Dropout for approximate inference, as in fact MC Dropout changes the Bayesian model; its predictive posterior assigns $0$ probability to the true model on closed-form benchmarks; the multimodality of its predictive posterior is not a property of the true predictive posterior but a design artefact. To address the need for VI on arbitrary models, we share a generic VI engine within the pytorch framework. The code includes a carefully designed implementation of structured (diagonal plus low-rank) multivariate normal variational families, and mixtures thereof. It is intended as a go-to no-free-lunch approach, addressing shortcomings of mean-field VI with an adjustable trade-off between expressivity and computational complexity.

Topic models provide a useful text-mining tool for learning, extracting and discovering latent structures in large text corpora. Although a plethora of methods have been proposed for topic modeling, a formal theoretical investigation on the statistical identifiability and accuracy of latent topic estimation is lacking in the literature. In this paper, we propose a maximum likelihood estimator (MLE) of latent topics based on a specific integrated likelihood, which is naturally connected to the concept of volume minimization in computational geometry. Theoretically, we introduce a new set of geometric conditions for topic model identifiability, which are weaker than conventional separability conditions relying on the existence of anchor words or pure topic documents. We conduct finite-sample error analysis for the proposed estimator and discuss the connection of our results with existing ones. We conclude with empirical studies on both simulated and real datasets.

We give a new interpretation of basic belief assignment transformation into probability distribution, and use directed acyclic network called belief evolution network to describe the causality between the focal elements of a BBA. On this basis, a new probability transformations method called full causality probability transformation is proposed, and this method is superior to all previous method after verification from the process and the result. In addition, using this method combined with disjunctive combination rule, we propose a new probabilistic combination rule called disjunctive transformation combination rule. It has an excellent ability to merge conflicts and an interesting pseudo-Matthew effect, which offer a new idea to information fusion besides the combination rule of Dempster.

We introduce SMProbLog, a generalization of the probabilistic logic programming language ProbLog. A ProbLog program defines a distribution over logic programs by specifying for each clause the probability that it belongs to a randomly sampled program, and these probabilities are mutually independent. The semantics of ProbLog is given by the success probability of a query, which corresponds to the probability that the query succeeds in a randomly sampled program. It is well-defined when each random sample uniquely determines the truth values of all logical atoms. Argumentation problems, however, represent an interesting practical application where this is not always the case. SMProbLog generalizes the semantics of ProbLog to the setting where multiple truth assignments are possible for a randomly sampled program, and implements the corresponding algorithms for both inference and learning tasks. We then show how this novel framework can be used to reason about probabilistic argumentation problems. Therefore, the key contribution of this paper are: a more general semantics for ProbLog programs, its implementation into a probabilistic programming framework for both inference and parameter learning, and a novel approach to probabilistic argumentation problems based on such framework.