We propose a novel algorithm for the support estimation of partially known Gaussian graphical models that incorporates prior information about the underlying graph. In contrast to classical approaches that provide a point estimate based on a maximum likelihood or a maximum a posteriori criterion using (simple) priors on the precision matrix, we consider a prior on the graph and rely on annealed Langevin diffusion to generate samples from the posterior distribution. Since the Langevin sampler requires access to the score function of the underlying graph prior, we use graph neural networks to effectively estimate the score from a graph dataset (either available beforehand or generated from a known distribution). Numerical experiments demonstrate the benefits of our approach.

Classification is a fundamental task in many applications on which data-driven methods have shown outstanding performances. However, it is challenging to determine whether such methods have achieved the optimal performance. This is mainly because the best achievable performance is typically unknown and hence, effectively estimating it is of prime importance. In this paper, we consider binary classification problems and we propose an estimator for the false positive rate (FPR) of the Bayes classifier, that is, the optimal classifier with respect to accuracy, from a given dataset. Our method utilizes soft labels, or real-valued labels, which are gaining significant traction thanks to their properties. We thoroughly examine various theoretical properties of our estimator, including its consistency, unbiasedness, rate of convergence, and variance. To enhance the versatility of our estimator beyond soft labels, we also consider noisy labels, which encompass binary labels. For noisy labels, we develop effective FPR estimators by leveraging a denoising technique and the Nadaraya-Watson estimator. Due to the symmetry of the problem, our results can be readily applied to estimate the false negative rate of the Bayes classifier.

Previous theoretical results pertaining to meta-learning on sequences build on contrived assumptions and are somewhat convoluted. We introduce new information-theoretic tools that lead to an elegant and very general decomposition of error into three components: irreducible error, meta-learning error, and intra-task error. These tools unify analyses across many meta-learning challenges. To illustrate, we apply them to establish new results about in-context learning with transformers. Our theoretical results characterizes how error decays in both the number of training sequences and sequence lengths. Our results are very general; for example, they avoid contrived mixing time assumptions made by all prior results that establish decay of error with sequence length.

We seek to model a collection of time series arising from multiple entities interacting over the same time period. Recent work focused on modeling individual time series is inadequate for our intended applications, where collective system-level behavior influences the trajectories of individual entities. To address such problems, we present a new hierarchical switching-state model that can be trained in an unsupervised fashion to simultaneously explain both system-level and individual-level dynamics. We employ a latent system-level discrete state Markov chain that drives latent entity-level chains which in turn govern the dynamics of each observed time series. Feedback from the observations to the chains at both the entity and system levels improves flexibility via context-dependent state transitions. Our hierarchical switching recurrent dynamical models can be learned via closed-form variational coordinate ascent updates to all latent chains that scale linearly in the number of individual time series. This is asymptotically no more costly than fitting separate models for each entity. Experiments on synthetic and real datasets show that our model can produce better forecasts of future entity behavior than existing methods. Moreover, the availability of latent state chains at both the entity and system level enables interpretation of group dynamics.

Disaggregated evaluation is a central task in AI fairness assessment, with the goal to measure an AI system's performance across different subgroups defined by combinations of demographic or other sensitive attributes. The standard approach is to stratify the evaluation data across subgroups and compute performance metrics separately for each group. However, even for moderately-sized evaluation datasets, sample sizes quickly get small once considering intersectional subgroups, which greatly limits the extent to which intersectional groups are considered in many disaggregated evaluations. In this work, we introduce a structured regression approach to disaggregated evaluation that we demonstrate can yield reliable system performance estimates even for very small subgroups. We also provide corresponding inference strategies for constructing confidence intervals and explore how goodness-of-fit testing can yield insight into the structure of fairness-related harms experienced by intersectional groups. We evaluate our approach on two publicly available datasets, and several variants of semi-synthetic data. The results show that our method is considerably more accurate than the standard approach, especially for small subgroups, and goodness-of-fit testing helps identify the key factors that drive differences in performance.

Examples include the number of users who will install a software update, the number of customers who will use a new feature on a website or who will participate in an A/B test. Whether the focus is on estimating the number of individuals initiating an action or predicting the temporal span needed to attain a desired user participation threshold, accurate predictive models play a central role in decision making, resource allocation, and enhancing user experiences. See, e.g., Kohavi et al. (2007) and Bakshy et al. (2014) for further details on online experiments. While participation data can be formally treated as a time series, the problem of forecasting user participation does not lend itself to time series models (see Richardson et al., 2022, and the references therein). Moreover, intricate dynamics that underlie user engagement patterns. Conventional models often assume that initiation times are identically distributed, ignoring the diverse behaviors and preferences exhibited by individuals. In reality, users demonstrate varying propensities to engage, leading to a multitude of initiation timelines. Recognizing this complexity, Richardson et al. (2022) recently proposed a Bayesian model for the users' initiation times, which allows different behaviors to be captured, while simultaneously borrowing strength as is typical in hierarchical Bayesian models.

In today's data-driven world, the proliferation of publicly available information intensifies the challenge of information leakage (IL), raising security concerns. IL involves unintentionally exposing secret (sensitive) information to unauthorized parties via systems' observable information. Conventional statistical approaches, which estimate mutual information (MI) between observable and secret information for detecting IL, face challenges such as the curse of dimensionality, convergence, computational complexity, and MI misestimation. Furthermore, emerging supervised machine learning (ML) methods, though effective, are limited to binary system-sensitive information and lack a comprehensive theoretical framework. To address these limitations, we establish a theoretical framework using statistical learning theory and information theory to accurately quantify and detect IL. We demonstrate that MI can be accurately estimated by approximating the log-loss and accuracy of the Bayes predictor. As the Bayes predictor is typically unknown in practice, we propose to approximate it with the help of automated machine learning (AutoML). First, we compare our MI estimation approaches against current baselines, using synthetic data sets generated using the multivariate normal (MVN) distribution with known MI. Second, we introduce a cut-off technique using one-sided statistical tests to detect IL, employing the Holm-Bonferroni correction to increase confidence in detection decisions. Our study evaluates IL detection performance on real-world data sets, highlighting the effectiveness of the Bayes predictor's log-loss estimation, and finds our proposed method to effectively estimate MI on synthetic data sets and thus detect ILs accurately.

We study the complexity-theoretic boundaries of tractability for three classical problems in the context of Hierarchical Task Network Planning: the validation of a provided plan, whether an executable plan exists, and whether a given state can be reached by some plan. We show that all three problems can be solved in polynomial time on primitive task networks of constant partial order width (and a generalization thereof), whereas for the latter two problems this holds only under a provably necessary restriction to the state space. Next, we obtain an algorithmic meta-theorem along with corresponding lower bounds to identify tight conditions under which general polynomial-time solvability results can be lifted from primitive to general task networks. Finally, we enrich our investigation by analyzing the parameterized complexity of the three considered problems, and show that (1) fixed-parameter tractability for all three problems can be achieved by replacing the partial order width with the vertex cover number of the network as the parameter, and (2) other classical graph-theoretic parameters of the network (including treewidth, treedepth, and the aforementioned partial order width) do not yield fixed-parameter tractability for any of the three problems.

Existing methods, such as concept bottleneck models (CBMs), have been successful in providing concept-based interpretations for black-box deep learning models. They typically work by predicting concepts given the input and then predicting the final class label given the predicted concepts. However, (1) they often fail to capture the high-order, nonlinear interaction between concepts, e.g., correcting a predicted concept (e.g., "yellow breast") does not help correct highly correlated concepts (e.g., "yellow belly"), leading to suboptimal final accuracy; (2) they cannot naturally quantify the complex conditional dependencies between different concepts and class labels (e.g., for an image with the class label "Kentucky Warbler" and a concept "black bill", what is the probability that the model correctly predicts another concept "black crown"), therefore failing to provide deeper insight into how a black-box model works. In response to these limitations, we propose Energy-based Concept Bottleneck Models (ECBMs). Our ECBMs use a set of neural networks to define the joint energy of candidate (input, concept, class) tuples. With such a unified interface, prediction, concept correction, and conditional dependency quantification are then represented as conditional probabilities, which are generated by composing different energy functions. Our ECBMs address both limitations of existing CBMs, providing higher accuracy and richer concept interpretations. Empirical results show that our approach outperforms the state-of-the-art on real-world datasets.

Widespread adoption of AI for medical decision making is still hindered due to ethical and safety-related concerns. For AI-based decision support systems in healthcare settings it is paramount to be reliable and trustworthy. Common deep learning approaches, however, have the tendency towards overconfidence under data shift. Such inappropriate extrapolation beyond evidence-based scenarios may have dire consequences. This highlights the importance of reliable estimation of local uncertainty and its communication to the end user. While stochastic neural networks have been heralded as a potential solution to these issues, this study investigates their actual reliability in clinical applications. We centered our analysis on the exemplary use case of mortality prediction for ICU hospitalizations using EHR from MIMIC3 study. For predictions on the EHR time series, Encoder-Only Transformer models were employed. Stochasticity of model functions was achieved by incorporating common methods such as Bayesian neural network layers and model ensembles. Our models achieve state of the art performance in terms of discrimination performance (AUC ROC: 0.868+-0.011, AUC PR: 0.554+-0.034) and calibration on the mortality prediction benchmark. However, epistemic uncertainty is critically underestimated by the selected stochastic deep learning methods. A heuristic proof for the responsible collapse of the posterior distribution is provided. Our findings reveal the inadequacy of commonly used stochastic deep learning approaches to reliably recognize OoD samples. In both methods, unsubstantiated model confidence is not prevented due to strongly biased functional posteriors, rendering them inappropriate for reliable clinical decision support. This highlights the need for approaches with more strictly enforced or inherent distance-awareness to known data points, e.g., using kernel-based techniques.