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.

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.

Knowledge Graphs (KGs) are a major asset for companies thanks to their great flexibility in data representation and their numerous applications, e.g., vocabulary sharing, Q/A or recommendation systems. To build a KG it is a common practice to rely on automatic methods for extracting knowledge from various heterogeneous sources. But in a noisy and uncertain world, knowledge may not be reliable and conflicts between data sources may occur. Integrating unreliable data would directly impact the use of the KG, therefore such conflicts must be resolved. This could be done manually by selecting the best data to integrate. This first approach is highly accurate, but costly and time-consuming. That is why recent efforts focus on automatic approaches, which represents a challenging task since it requires handling the uncertainty of extracted knowledge throughout its integration into the KG. We survey state-of-the-art approaches in this direction and present constructions of both open and enterprise KGs and how their quality is maintained. We then describe different knowledge extraction methods, introducing additional uncertainty. We also discuss downstream tasks after knowledge acquisition, including KG completion using embedding models, knowledge alignment, and knowledge fusion in order to address the problem of knowledge uncertainty in KG construction. We conclude with a discussion on the remaining challenges and perspectives when constructing a KG taking into account uncertainty.

Representing the nodes of continuous-time temporal graphs in a low-dimensional latent space has wide-ranging applications, from prediction to visualization. Yet, analyzing continuous-time relational data with timestamped interactions introduces unique challenges due to its sparsity. Merely embedding nodes as trajectories in the latent space overlooks this sparsity, emphasizing the need to quantify uncertainty around the latent positions. In this paper, we propose TGNE (\textbf{T}emporal \textbf{G}aussian \textbf{N}etwork \textbf{E}mbedding), an innovative method that bridges two distinct strands of literature: the statistical analysis of networks via Latent Space Models (LSM)\cite{Hoff2002} and temporal graph machine learning. TGNE embeds nodes as piece-wise linear trajectories of Gaussian distributions in the latent space, capturing both structural information and uncertainty around the trajectories. We evaluate TGNE's effectiveness in reconstructing the original graph and modelling uncertainty. The results demonstrate that TGNE generates competitive time-varying embedding locations compared to common baselines for reconstructing unobserved edge interactions based on observed edges. Furthermore, the uncertainty estimates align with the time-varying degree distribution in the network, providing valuable insights into the temporal dynamics of the graph. To facilitate reproducibility, we provide an open-source implementation of TGNE at \url{https://github.com/aida-ugent/tgne}.

Probabilistic verification of neural networks is concerned with formally analysing the output distribution of a neural network under a probability distribution of the inputs. Examples of probabilistic verification include verifying the demographic parity fairness notion or quantifying the safety of a neural network. We present a new algorithm for the probabilistic verification of neural networks based on an algorithm for computing and iteratively refining lower and upper bounds on probabilities over the outputs of a neural network. By applying state-of-the-art bound propagation and branch and bound techniques from non-probabilistic neural network verification, our algorithm significantly outpaces existing probabilistic verification algorithms, reducing solving times for various benchmarks from the literature from tens of minutes to tens of seconds. Furthermore, our algorithm compares favourably even to dedicated algorithms for restricted subsets of probabilistic verification. We complement our empirical evaluation with a theoretical analysis, proving that our algorithm is sound and, under mildly restrictive conditions, also complete when using a suitable set of heuristics.

The Neural Network Field Theory correspondence (NNFT) is a mapping from neural network (NN) architectures into the space of statistical field theories (SFTs). The Bayesian renormalization group (BRG) is an information-theoretic coarse graining scheme that generalizes the principles of the Exact Renormalization Group (ERG) to arbitrarily parameterized probability distributions, including those of NNs. In BRG, coarse graining is performed in parameter space with respect to an information-theoretic distinguishability scale set by the Fisher information metric. In this paper, we unify NNFT and BRG to form a powerful new framework for exploring the space of NNs and SFTs, which we coin BRG-NNFT. With BRG-NNFT, NN training dynamics can be interpreted as inducing a flow in the space of SFTs from the information-theoretic `IR' $\rightarrow$ `UV'. Conversely, applying an information-shell coarse graining to the trained network's parameters induces a flow in the space of SFTs from the information-theoretic `UV' $\rightarrow$ `IR'. When the information-theoretic cutoff scale coincides with a standard momentum scale, BRG is equivalent to ERG. We demonstrate the BRG-NNFT correspondence on two analytically tractable examples. First, we construct BRG flows for trained, infinite-width NNs, of arbitrary depth, with generic activation functions. As a special case, we then restrict to architectures with a single infinitely-wide layer, scalar outputs, and generalized cos-net activations. In this case, we show that BRG coarse-graining corresponds exactly to the momentum-shell ERG flow of a free scalar SFT. Our analytic results are corroborated by a numerical experiment in which an ensemble of asymptotically wide NNs are trained and subsequently renormalized using an information-shell BRG scheme.