Probabilistic graphical models (PGMs) serve as a powerful framework for modeling complex systems with uncertainty and extracting valuable insights from data. However, users face challenges when applying PGMs to their problems in terms of efficiency and usability. This paper presents Fast-PGM, an efficient and open-source library for PGM learning and inference. Fast-PGM supports comprehensive tasks on PGMs, including structure and parameter learning, as well as exact and approximate inference, and enhances efficiency of the tasks through computational and memory optimizations and parallelization techniques.

Despite being successful in board games and reinforcement learning (RL), UCT, a Monte-Carlo Tree Search (MCTS) combined with UCB1 Multi-Armed Bandit (MAB), has had limited success in domain-independent planning until recently. Previous work showed that UCB1, designed for $[0,1]$-bounded rewards, is not appropriate for estimating the distance-to-go which are potentially unbounded in $\mathbb{R}$, such as heuristic functions used in classical planning, then proposed combining MCTS with MABs designed for Gaussian reward distributions and successfully improved the performance. In this paper, we further sharpen our understanding of ideal bandits for planning tasks. Existing work has two issues: First, while Gaussian MABs no longer over-specify the distances as $h\in [0,1]$, they under-specify them as $h\in [-\infty,\infty]$ while they are non-negative and can be further bounded in some cases. Second, there is no theoretical justifications for Full-Bellman backup (Schulte & Keller, 2014) that backpropagates minimum/maximum of samples. We identified \emph{extreme value} statistics as a theoretical framework that resolves both issues at once and propose two bandits, UCB1-Uniform/Power, and apply them to MCTS for classical planning. We formally prove their regret bounds and empirically demonstrate their performance in classical planning.

Intelligent agents must be generalists, capable of quickly adapting to various tasks. In reinforcement learning (RL), model-based RL learns a dynamics model of the world, in principle enabling transfer to arbitrary reward functions through planning. However, autoregressive model rollouts suffer from compounding error, making model-based RL ineffective for long-horizon problems. Successor features offer an alternative by modeling a policy's long-term state occupancy, reducing policy evaluation under new tasks to linear reward regression. Yet, policy improvement with successor features can be challenging. This work proposes a novel class of models, i.e., generalized occupancy models (GOMs), that learn a distribution of successor features from a stationary dataset, along with a policy that acts to realize different successor features. These models can quickly select the optimal action for arbitrary new tasks. By directly modeling long-term outcomes in the dataset, GOMs avoid compounding error while enabling rapid transfer across reward functions. We present a practical instantiation of GOMs using diffusion models and show their efficacy as a new class of transferable models, both theoretically and empirically across various simulated robotics problems.

Sentiment analysis, an increasingly vital field in both academia and industry, plays a pivotal role in machine learning applications, particularly on social media platforms like Reddit. However, the efficacy of sentiment analysis models is hindered by the lack of expansive and fine-grained emotion datasets. To address this gap, our study leverages the GoEmotions dataset, comprising a diverse range of emotions, to evaluate sentiment analysis methods across a substantial corpus of 58,000 comments. Distinguished from prior studies by the Google team, which limited their analysis to only two models, our research expands the scope by evaluating a diverse array of models. We investigate the performance of traditional classifiers such as Naive Bayes and Support Vector Machines (SVM), as well as state-of-the-art transformer-based models including BERT, RoBERTa, and GPT. Furthermore, our evaluation criteria extend beyond accuracy to encompass nuanced assessments, including hierarchical classification based on varying levels of granularity in emotion categorization. Additionally, considerations such as computational efficiency are incorporated to provide a comprehensive evaluation framework. Our findings reveal that the RoBERTa model consistently outperforms the baseline models, demonstrating superior accuracy in fine-grained sentiment classification tasks. This underscores the substantial potential and significance of the RoBERTa model in advancing sentiment analysis capabilities.

Bayesian inversion is central to the quantification of uncertainty within problems arising from numerous applications in science and engineering. To formulate the approach, four ingredients are required: a forward model mapping the unknown parameter to an element of a solution space, often the solution space for a differential equation; an observation operator mapping an element of the solution space to the data space; a noise model describing how noise pollutes the observations; and a prior model describing knowledge about the unknown parameter before the data is acquired. This paper is concerned with learning the prior model from data; in particular, learning the prior from multiple realizations of indirect data obtained through the noisy observation process. The prior is represented, using a generative model, as the pushforward of a Gaussian in a latent space; the pushforward map is learned by minimizing an appropriate loss function. A metric that is well-defined under empirical approximation is used to define the loss function for the pushforward map to make an implementable methodology. Furthermore, an efficient residual-based neural operator approximation of the forward model is proposed and it is shown that this may be learned concurrently with the pushforward map, using a bilevel optimization formulation of the problem; this use of neural operator approximation has the potential to make prior learning from indirect data more computationally efficient, especially when the observation process is expensive, non-smooth or not known. The ideas are illustrated with the Darcy flow inverse problem of finding permeability from piezometric head measurements.

We derive closed-form expressions for the Bayes optimal decision boundaries in binary classification of high dimensional overlapping Gaussian mixture model (GMM) data, and show how they depend on the eigenstructure of the class covariances, for particularly interesting structured data. We empirically demonstrate, through experiments on synthetic GMMs inspired by real-world data, that deep neural networks trained for classification, learn predictors which approximate the derived optimal classifiers. We further extend our study to networks trained on authentic data, observing that decision thresholds correlate with the covariance eigenvectors rather than the eigenvalues, mirroring our GMM analysis. This provides theoretical insights regarding neural networks' ability to perform probabilistic inference and distill statistical patterns from intricate distributions.

Forward stagewise regression is a simple algorithm that can be used to estimate regularized models. The updating rule adds a small constant to a regression coefficient in each iteration, such that the underlying optimization problem is solved slowly with small improvements. This is similar to gradient boosting, with the essential difference that the step size is determined by the product of the gradient and a step length parameter in the latter algorithm. One often overlooked challenge in gradient boosting for distributional regression is the issue of a vanishing small gradient, which practically halts the algorithm's progress. We show that gradient boosting in this case oftentimes results in suboptimal models, especially for complex problems certain distributional parameters are never updated due to the vanishing gradient. Therefore, we propose a stagewise boosting-type algorithm for distributional regression, combining stagewise regression ideas with gradient boosting. Additionally, we extend it with a novel regularization method, correlation filtering, to provide additional stability when the problem involves a large number of covariates. Furthermore, the algorithm includes best-subset selection for parameters and can be applied to big data problems by leveraging stochastic approximations of the updating steps. Besides the advantage of processing large datasets, the stochastic nature of the approximations can lead to better results, especially for complex distributions, by reducing the risk of being trapped in a local optimum. The performance of our proposed stagewise boosting distributional regression approach is investigated in an extensive simulation study and by estimating a full probabilistic model for lightning counts with data of more than 9.1 million observations and 672 covariates.

Supervised classification is one of the most ubiquitous tasks in machine learning. Generative classifiers based on Bayesian networks are often used because of their interpretability and competitive accuracy. The widely used naive and TAN classifiers are specific instances of Bayesian network classifiers with a constrained underlying graph. This paper introduces novel classes of generative classifiers extending TAN and other famous types of Bayesian network classifiers. Our approach is based on staged tree models, which extend Bayesian networks by allowing for complex, context-specific patterns of dependence. We formally study the relationship between our novel classes of classifiers and Bayesian networks. We introduce and implement data-driven learning routines for our models and investigate their accuracy in an extensive computational study. The study demonstrates that models embedding asymmetric information can enhance classification accuracy.

Staged trees are probabilistic graphical models capable of representing any class of non-symmetric independence via a coloring of its vertices. Several structural learning routines have been defined and implemented to learn staged trees from data, under the frequentist or Bayesian paradigm. They assume a data set has been observed fully and, in practice, observations with missing entries are either dropped or imputed before learning the model. Here, we introduce the first algorithms for staged trees that handle missingness within the learning of the model. To this end, we characterize the likelihood of staged tree models in the presence of missing data and discuss pseudo-likelihoods that approximate it. A structural expectation-maximization algorithm estimating the model directly from the full likelihood is also implemented and evaluated. A computational experiment showcases the performance of the novel learning algorithms, demonstrating that it is feasible to account for different missingness patterns when learning staged trees.

Conformal prediction methodologies have significantly advanced the quantification of uncertainties in predictive models. Yet, the construction of confidence regions for model parameters presents a notable challenge, often necessitating stringent assumptions regarding data distribution or merely providing asymptotic guarantees. We introduce a novel approach termed CCR, which employs a combination of conformal prediction intervals for the model outputs to establish confidence regions for model parameters. We present coverage guarantees under minimal assumptions on noise and that is valid in finite sample regime. Our approach is applicable to both split conformal predictions and black-box methodologies including full or cross-conformal approaches. In the specific case of linear models, the derived confidence region manifests as the feasible set of a Mixed-Integer Linear Program (MILP), facilitating the deduction of confidence intervals for individual parameters and enabling robust optimization. We empirically compare CCR to recent advancements in challenging settings such as with heteroskedastic and non-Gaussian noise.