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}

TD learning is the most widely studied algorithm for evaluating the performance of a given policy from data in Markov Decision Processes[1]. The convergence of TD learning with decaying stepsizes was proved in [2]. Over the last few years, there has been a resurgent interest in understanding the non-asymptotic convergence behavior of TD learning and further using it to study other other reinforcement algorithms which use TD learning within their framework. The first result of this type was obtained in [3] who used a projection step in their version of the TD learning algorithm. The first finite-time bounds for unprojected TD learning were obtained in [4], who studied both fixed step-sizes and decaying step-sizes.

Sampling from a multimodal distribution is a fundamental and challenging problem in computational science and statistics. Among various approaches proposed for this task, one popular method is Annealed Importance Sampling (AIS). In this paper, we propose an ensemble-based version of AIS by combining it with population-based Monte Carlo methods to improve its efficiency. By keeping track of an ensemble instead of a single particle along some continuation path between the starting distribution and the target distribution, we take advantage of the interaction within the ensemble to encourage the exploration of undiscovered modes. Specifically, our main idea is to utilize either the snooker algorithm or the genetic algorithm used in Evolutionary Monte Carlo. We discuss how the proposed algorithm can be implemented and derive a partial differential equation governing the evolution of the ensemble under the continuous time and mean-field limit. We also test the efficiency of the proposed algorithm on various continuous and discrete distributions.

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.

An intelligent driving system should be capable of dynamically formulating appropriate driving strategies based on the current environment and vehicle status, while ensuring the security and reliability of the system. However, existing methods based on reinforcement learning and imitation learning suffer from low safety, poor generalization, and inefficient sampling. Additionally, they cannot accurately predict future driving trajectories, and the accurate prediction of future driving trajectories is a precondition for making optimal decisions. To solve these problems, in this paper, we introduce a Safe and Generalized end-to-end Autonomous Driving System (SGADS) for complex and various scenarios. Our SGADS incorporates variational inference with normalizing flows, enabling the intelligent vehicle to accurately predict future driving trajectories. Moreover, we propose the formulation of robust safety constraints. Furthermore, we combine reinforcement learning with demonstrations to augment search process of the agent. The experimental results demonstrate that our SGADS can significantly improve safety performance, exhibit strong generalization, and enhance the training efficiency of intelligent vehicles in complex urban scenarios compared to existing methods.

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.

Effective decision-making in autonomous driving relies on accurate inference of other traffic agents' future behaviors. To achieve this, we propose an online learning-based behavior prediction model and an efficient planner for Partially Observable Markov Decision Processes (POMDPs). We develop a learning-based prediction model, enhanced with a recurrent neural memory network, to dynamically update latent belief states and infer the intentions of other agents. The model can also integrate the ego vehicle's intentions to reflect closed-loop interactions among agents, and it learns from both offline data and online interactions. For planning, we employ an option-based Monte-Carlo Tree Search (MCTS) planner, which reduces computational complexity by searching over action sequences. Inside the MCTS planner, we use predicted long-term multi-modal trajectories to approximate future updates, which eliminates iterative belief updating and improves the running efficiency. Our approach also incorporates deep Q-learning (DQN) as a search prior, which significantly improves the performance of the MCTS planner. Experimental results from simulated environments validate the effectiveness of our proposed method. The online belief update model can significantly enhance the accuracy and temporal consistency of predictions, leading to improved decision-making performance. Employing DQN as a search prior in the MCTS planner considerably boosts its performance and outperforms an imitation learning-based prior. Additionally, we show that the option-based MCTS substantially outperforms the vanilla method in terms of performance and efficiency.