We study the community detection problem on a Gaussian mixture model, in which (1) vertices are divided into $k\geq 2$ distinct communities that are not necessarily equally-sized; (2) the Gaussian perturbations for different entries in the observation matrix are not necessarily independent or identically distributed. We prove necessary and sufficient conditions for the exact recovery of the maximum likelihood estimation (MLE), and discuss the cases when these necessary and sufficient conditions give sharp threshold. Applications include the community detection on a graph where the Gaussian perturbations of observations on each edge is the sum of i.i.d.~Gaussian random variables on its end vertices, in which we explicitly obtain the threshold for the exact recovery of the MLE.

Recently, hyperspectral imaging (HSI) has attracted increasing research attention, especially for the ones based on a coded aperture snapshot spectral imaging (CASSI) system. Existing deep HSI reconstruction models are generally trained on paired data to retrieve original signals upon 2D compressed measurements given by a particular optical hardware mask in CASSI, during which the mask largely impacts the reconstruction performance and could work as a "model hyperparameter" governing on data augmentations. This mask-specific training style will lead to a hardware miscalibration issue, which sets up barriers to deploying deep HSI models among different hardware and noisy environments. To address this challenge, we introduce mask uncertainty for HSI with a complete variational Bayesian learning treatment and explicitly model it through a mask decomposition inspired by real hardware. Specifically, we propose a novel Graph-based Self-Tuning (GST) network to reason uncertainties adapting to varying spatial structures of masks among different hardware. Moreover, we develop a bilevel optimization framework to balance HSI reconstruction and uncertainty estimation, accounting for the hyperparameter property of masks. Extensive experimental results and model discussions validate the effectiveness (over 33/30 dB) of the proposed GST method under two miscalibration scenarios and demonstrate a highly competitive performance compared with the state-of-the-art well-calibrated methods. Our code and pre-trained model are available at https://github.com/Jiamian-Wang/mask_uncertainty_spectral_SCI

Applied mathematics and machine computations have raised a lot of hope since the recent success of supervised learning. Many practitioners in industries have been trying to switch from their old paradigms to machine learning. Interestingly, those data scientists spend more time scrapping, annotating and cleaning data than fine-tuning models. This thesis is motivated by the following question: can we derive a more generic framework than the one of supervised learning in order to learn from clutter data? This question is approached through the lens of weakly supervised learning, assuming that the bottleneck of data collection lies in annotation. We model weak supervision as giving, rather than a unique target, a set of target candidates. We argue that one should look for an ``optimistic'' function that matches most of the observations. This allows us to derive a principle to disambiguate partial labels. We also discuss the advantage to incorporate unsupervised learning techniques into our framework, in particular manifold regularization approached through diffusion techniques, for which we derived a new algorithm that scales better with input dimension then the baseline method. Finally, we switch from passive to active weakly supervised learning, introducing the ``active labeling'' framework, in which a practitioner can query weak information about chosen data. Among others, we leverage the fact that one does not need full information to access stochastic gradients and perform stochastic gradient descent.

One of the most complex tasks of decision making and planning is to gather information. This task becomes even more complex when the state is high-dimensional and its belief cannot be expressed with a parametric distribution. Although the state is high-dimensional, in many problems only a small fraction of it might be involved in transitioning the state and generating observations. We exploit this fact to calculate an information-theoretic expected reward, mutual information (MI), over a much lower-dimensional subset of the state, to improve efficiency and without sacrificing accuracy. A similar approach was used in previous works, yet specifically for Gaussian distributions, and we here extend it for general distributions. Moreover, we apply the dimensionality reduction for cases in which the new states are augmented to the previous, yet again without sacrificing accuracy. We then continue by developing an estimator for the MI which works in a Sequential Monte Carlo (SMC) manner, and avoids the reconstruction of future belief's surfaces. Finally, we show how this work is applied to the informative planning optimization problem. This work is then evaluated in a simulation of an active SLAM problem, where the improvement in both accuracy and timing is demonstrated.

The rapid progress in clinical data management systems and artificial intelligence approaches enable the era of personalized medicine. Intensive care units (ICUs) are the ideal clinical research environment for such development because they collect many clinical data and are highly computerized environments. We designed a retrospective clinical study on a prospective ICU database using clinical natural language to help in the early diagnosis of heart failure in critically ill children. The methodology consisted of empirical experiments of a learning algorithm to learn the hidden interpretation and presentation of the French clinical note data. This study included 1386 patients' clinical notes with 5444 single lines of notes. There were 1941 positive cases (36 % of total) and 3503 negative cases classified by two independent physicians using a standardized approach. The multilayer perceptron neural network outperforms other discriminative and generative classifiers. Consequently, the proposed framework yields an overall classification performance with 89 % accuracy, 88 % recall, and 89 % precision. This study successfully applied learning representation and machine learning algorithms to detect heart failure from clinical natural language in a single French institution. Further work is needed to use the same methodology in other institutions and other languages.

In this paper, we analyze the impact of data freshness on real-time supervised learning, where a neural network is trained to infer a time-varying target (e.g., the position of the vehicle in front) based on features (e.g., video frames) observed at a sensing node (e.g., camera or lidar). One might expect that the performance of real-time supervised learning degrades monotonically as the feature becomes stale. Using an information-theoretic analysis, we show that this is true if the feature and target data sequence can be closely approximated as a Markov chain; it is not true if the data sequence is far from Markovian. Hence, the prediction error of real-time supervised learning is a function of the Age of Information (AoI), where the function could be non-monotonic. Several experiments are conducted to illustrate the monotonic and non-monotonic behaviors of the prediction error. To minimize the inference error in real-time, we propose a new "selection-from-buffer" model for sending the features, which is more general than the "generate-at-will" model used in earlier studies. By using Gittins and Whittle indices, low-complexity scheduling strategies are developed to minimize the inference error, where a new connection between the Gittins index theory and Age of Information (AoI) minimization is discovered. These scheduling results hold (i) for minimizing general AoI functions (monotonic or non-monotonic) and (ii) for general feature transmission time distributions. Data-driven evaluations are presented to illustrate the benefits of the proposed scheduling algorithms.

We consider a discounted cost constrained Markov decision process (CMDP) policy optimization problem, in which an agent seeks to maximize a discounted cumulative reward subject to a number of constraints on discounted cumulative utilities. To solve this constrained optimization program, we study an online actor-critic variant of a classic primal-dual method where the gradients of both the primal and dual functions are estimated using samples from a single trajectory generated by the underlying time-varying Markov processes. This online primal-dual natural actor-critic algorithm maintains and iteratively updates three variables: a dual variable (or Lagrangian multiplier), a primal variable (or actor), and a critic variable used to estimate the gradients of both primal and dual variables. These variables are updated simultaneously but on different time scales (using different step sizes) and they are all intertwined with each other. Our main contribution is to derive a finite-time analysis for the convergence of this algorithm to the global optimum of a CMDP problem. Specifically, we show that with a proper choice of step sizes the optimality gap and constraint violation converge to zero in expectation at a rate $\mathcal{O}(1/K^{1/6})$, where K is the number of iterations. To our knowledge, this paper is the first to study the finite-time complexity of an online primal-dual actor-critic method for solving a CMDP problem. We also validate the effectiveness of this algorithm through numerical simulations.

Restricted Boltzmann Machines (RBMs) offer a versatile architecture for unsupervised machine learning that can in principle approximate any target probability distribution with arbitrary accuracy. However, the RBM model is usually not directly accessible due to its computational complexity, and Markov-chain sampling is invoked to analyze the learned probability distribution. For training and eventual applications, it is thus desirable to have a sampler that is both accurate and efficient. We highlight that these two goals generally compete with each other and cannot be achieved simultaneously. More specifically, we identify and quantitatively characterize three regimes of RBM learning: independent learning, where the accuracy improves without losing efficiency; correlation learning, where higher accuracy entails lower efficiency; and degradation, where both accuracy and efficiency no longer improve or even deteriorate. These findings are based on numerical experiments and heuristic arguments.

In recent years Landmark Complexes have been successfully employed for localization-free and metric-free autonomous exploration using a group of sensing-limited and communication-limited robots in a GPS-denied environment. To ensure rapid and complete exploration, existing works make assumptions on the density and distribution of landmarks in the environment. These assumptions may be overly restrictive, especially in hazardous environments where landmarks may be destroyed or completely missing. In this paper, we first propose a deep reinforcement learning framework for multi-agent cooperative exploration in environments with sparse landmarks while reducing client-server communication. By leveraging recent development on partial observability and credit assignment, our framework can train the exploration policy efficiently for multi-robot systems. The policy receives individual rewards from actions based on a proximity sensor with limited range and resolution, which is combined with group rewards to encourage collaborative exploration and construction of the Landmark Complex through observation of 0-, 1- and 2-dimensional simplices. In addition, we employ a three-stage curriculum learning strategy to mitigate the reward sparsity by gradually adding random obstacles and destroying random landmarks. Experiments in simulation demonstrate that our method outperforms the state-of-the-art landmark complex exploration method in efficiency among different environments with sparse landmarks.

Enabling the capability of assessing risk and making risk-aware decisions is essential to applying reinforcement learning to safety-critical robots like drones. In this paper, we investigate a specific case where a nano quadcopter robot learns to navigate an apriori-unknown cluttered environment under partial observability. We present a distributional reinforcement learning framework to generate adaptive risk-tendency policies. Specifically, we propose to use lower tail conditional variance of the learnt return distribution as intrinsic uncertainty estimation, and use exponentially weighted average forecasting (EWAF) to adapt the risk-tendency in accordance with the estimated uncertainty. In simulation and real-world empirical results, we show that (1) the most effective risk-tendency vary across states, (2) the agent with adaptive risk-tendency achieves superior performance compared to risk-neutral policy or risk-averse policy baselines.