Many machine learning applications require operating on a spatially distributed dataset. Despite technological advances, privacy considerations and communication constraints may prevent gathering the entire dataset in a central unit. In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers, which is commonly used in the optimization literature due to its fast convergence. In contrast to distributed optimization, distributed sampling allows for uncertainty quantification in Bayesian inference tasks. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. For our theoretical results, we use convex optimization tools to establish a fundamental inequality on the generated local sample iterates. This inequality enables us to show convergence of the distribution associated with these iterates to the underlying target distribution in Wasserstein distance. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.

The Deep Learning revolution has enabled groundbreaking achievements in recent years. From breast cancer detection to protein folding, deep learning algorithms have been at the core of very important advancements. However, these modern advancements are becoming more and more data-hungry, especially on labeled data whose availability is scarce: this is even more prevalent in the medical context. In this work, we show how active learning could be very effective in data scarcity situations, where obtaining labeled data (or annotation budget is very limited). We compare several selection criteria (BALD, MeanSTD, and MaxEntropy) on the ISIC 2016 dataset. We also explored the effect of acquired pool size on the model's performance. Our results suggest that uncertainty is useful to the Melanoma detection task, and confirms the hypotheses of the author of the paper of interest, that \textit{bald} performs on average better than other acquisition functions. Our extended analyses however revealed that all acquisition functions perform badly on the positive (cancerous) samples, suggesting exploitation of class unbalance, which could be crucial in real-world settings. We finish by suggesting future work directions that would be useful to improve this current work. The code of our implementation is open-sourced at \url{https://github.com/bonaventuredossou/ece526_course_project}

The HERMES (High Energy Rapid Modular Ensemble of Satellites) Pathfinder mission serves as an in-orbit demonstration of a constellation of nanosatellites whose primary scientific purpose is to discover intense high-energy transients, such as gamma-ray bursts, across a broad energy range (few keV to few MeV) with unparalleled temporal precision and exact localisation. By 2024, the first constellation of six nanosatellites is expected to be launched. To fully exploit satellite data and allow faint astronomical events to emerge, a precise estimation of satellite background count rates is required to determine whether the event is statistically valid or not. The dynamics of the background are related to the satellite's orbital information, which varies in the order of minutes, potentially hiding long transient events. This work introduces two main contributions I have brought ahead; first a novel background estimator is presented that could potentially be fitted to any type of X/Gamma-ray satellite space telescope, capable of capturing long-term dynamics and accurate enough to detect faint transients. This estimator is built using a Neural Network and tested on data from the Fermi Gamma-ray Space Telescope's Gamma Burst Monitor (GBM). As a second objective, it is employed a trigger algorithm, called FOCuS (Functional Online CUSUM), to extract events from the background using the background estimator. The resulting framework, DeepGRB, can identify astronomical events that are both present and absent from the Fermi-GBM catalog. The analysis of the discovered events reveals the strengths and weaknesses of the framework.

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.