We survey in this article the connections between Machine Learning and Control Theory. Control Theory provide useful concepts and tools for Machine Learning. Conversely Machine Learning can be used to solve large control problems. In the first part of the paper, we develop the connections between reinforcement learning and Markov Decision Processes, which are discrete time control problems. In the second part, we review the concept of supervised learning and the relation with static optimization. Deep learning which extends supervised learning, can be viewed as a control problem. In the third part, we present the links between stochastic gradient descent and mean-field theory. Conversely, in the fourth and fifth parts, we review machine learning approaches to stochastic control problems, and focus on the deterministic case, to explain, more easily, the numerical algorithms.

In order to help physicists to expand their knowledge of the climate in the Lesser Antilles, we aim to identify the spatio-temporal configurations using clustering analysis on wind speed and cumulative rainfall datasets. But we show that using the L2 norm in conventional clustering methods as K-Means (KMS) and Hierarchical Agglomerative Clustering (HAC) can induce undesirable effects. So, we propose to replace Euclidean distance (L2) by a dissimilarity measure named Expert Deviation (ED). Based on the symmetrized Kullback-Leibler divergence, the ED integrates the properties of the observed physical parameters and climate knowledge. This measure helps comparing histograms of four patches, corresponding to geographical zones, that are influenced by atmospheric structures. The combined evaluation of the internal homogeneity and the separation of the clusters obtained using ED and L2 was performed. The results, which are compared using the silhouette index, show five clusters with high indexes. For the two available datasets one can see that, unlike KMS-L2, KMS-ED discriminates the daily situations favorably, giving more physical meaning to the clusters discovered by the algorithm. The effect of patches is observed in the spatial analysis of representative elements for KMS-ED. The ED is able to produce different configurations which makes the usual atmospheric structures clearly identifiable. Atmospheric physicists can interpret the locations of the impact of each cluster on a specific zone according to atmospheric structures. KMS-L2 does not lead to such an interpretability, because the situations represented are spatially quite smooth. This climatological study illustrates the advantage of using ED as a new approach.

We consider the task of learning Ising models when the signs of different random variables are flipped independently with possibly unequal, unknown probabilities. In this paper, we focus on the problem of robust estimation of tree-structured Ising models. Without any additional assumption of side information, this is an open problem. We first prove that this problem is unidentifiable, however, this unidentifiability is limited to a small equivalence class of trees formed by leaf nodes exchanging positions with their neighbors. Next, we propose an algorithm to solve the above problem with logarithmic sample complexity in the number of nodes and polynomial run-time complexity. Lastly, we empirically demonstrate that, as expected, existing algorithms are not inherently robust in the proposed setting whereas our algorithm correctly recovers the underlying equivalence class.

Discovering causal structure among a set of variables is a fundamental problem in many domains. However, state-of-the-art methods seldom consider the possibility that the observational data has missing values (incomplete data), which is ubiquitous in many real-world situations. The missing value will significantly impair the performance and even make the causal discovery algorithms fail. In this paper, we propose an approach to discover causal structures from incomplete data by using a novel encoder and reinforcement learning (RL). The encoder is designed for missing data imputation as well as feature extraction. In particular, it learns to encode the currently available information (with missing values) into a robust feature representation which is then used to determine where to search the best graph. The encoder is integrated into a RL framework that can be optimized using the actor-critic algorithm. Our method takes the incomplete observational data as input and generates a causal structure graph. Experimental results on synthetic and real data demonstrate that our method can robustly generate causal structures from incomplete data. Compared with the direct combination of data imputation and causal discovery methods, our method performs generally better and can even obtain a performance gain as much as 43.2%.

Early recognition of clinical deterioration is one of the main steps for reducing inpatient morbidity and mortality. The challenging task of clinical deterioration identification in hospitals lies in the intense daily routines of healthcare practitioners, in the unconnected patient data stored in the Electronic Health Records (EHRs) and in the usage of low accuracy scores. Since hospital wards are given less attention compared to the Intensive Care Unit, ICU, we hypothesized that when a platform is connected to a stream of EHR, there would be a drastic improvement in dangerous situations awareness and could thus assist the healthcare team. With the application of machine learning, the system is capable to consider all patient's history and through the use of high-performing predictive models, an intelligent early warning system is enabled. In this work we used 121,089 medical encounters from six different hospitals and 7,540,389 data points, and we compared popular ward protocols with six different scalable machine learning methods (three are classic machine learning models, logistic and probabilistic-based models, and three gradient boosted models). The results showed an advantage in AUC (Area Under the Receiver Operating Characteristic Curve) of 25 percentage points in the best Machine Learning model result compared to the current state-of-the-art protocols. This is shown by the generalization of the algorithm with leave-one-group-out (AUC of 0.949) and the robustness through cross-validation (AUC of 0.961). We also perform experiments to compare several window sizes to justify the use of five patient timestamps. A sample dataset, experiments, and code are available for replicability purposes.

Learning theory mostly addresses the standard learning paradigm, assuming the availability of complete and correct supervision signals for large amounts of data. However, in practice, machine learning researchers and practitioners acquire and make use of a range of {\em incidental supervision} signals that only have statistical associations with the gold supervision. This paper addresses the question: {\em Can one quantify models' performance when learning with such supervision signals, without going through an exhaustive experimentation process with various supervision signals and learning protocols?} To quantify the benefits of various incidental supervision signals, we propose a unified PAC-Bayesian Informativeness measure (PABI), characterizing the reduction in uncertainty that incidental supervision signals provide. We then demonstrate PABI's use in quantifying various types of incidental signals such as partial labels, noisy labels, constraints, cross-domain signals, and some combinations of these. Experiments on named entity recognition and question answering show that PABI correlates well with learning performance, providing a promising way to determine, ahead of learning, which supervision signals would be beneficial.

As learning solutions reach critical applications in social, industrial, and medical domains, the need to curtail their behavior becomes paramount. There is now ample evidence that without explicit tailoring, learning can lead to biased, unsafe, and prejudiced solutions. To tackle these problems, we develop a generalization theory of constrained learning based on the probably approximately correct (PAC) learning framework. In particular, we show that imposing requirements does not make a learning problem harder in the sense that any PAC learnable class is also PAC constrained learnable using a constrained counterpart of the empirical risk minimization (ERM) rule. For typical parametrized models, however, this learner involves solving a non-convex optimization program for which even obtaining a feasible solution may be hard. To overcome this issue, we prove that under mild conditions the empirical dual problem of constrained learning is also a PAC constrained learner that now leads to a practical constrained learning algorithm. We analyze the generalization properties of this solution and use it to illustrate how constrained learning can address problems in fair and robust classification.

Abstract Machine learning models, trained on data from ab initio quantum simulations, are yielding molecular dynamics potentials with unprecedented accuracy. One limiting factor is the quantity of available training data, which can be expensive to obtain. A quantum simulation often provides all atomic forces, in addition to the total energy of the system. These forces provide much more information than the energy alone. It may appear that training a model to this large quantity of force data would introduce significant computational costs. Actually, training to all available force data should only be a few times more expensive than training to energies alone. Here, we present a new algorithm for efficient force training, and benchmark its accuracy by training to forces from real-world datasets for organic chemistry and bulk aluminum.

This paper proposes Variational Auto-Regressive Gaussian Process (VAR-GP), a principled Bayesian updating mechanism to incorporate new data for sequential tasks in the context of continual learning. It relies on a novel auto-regressive characterization of the variational distribution and inference is made scalable using sparse inducing point approximations. Experiments on standard continual learning benchmarks demonstrate the ability of VAR-GPs to perform well at new tasks without compromising performance on old ones, yielding competitive results to state-of-the-art methods. In addition, we qualitatively show how VAR-GP improves the predictive entropy estimates as we train on new tasks. Further, we conduct a thorough ablation study to verify the effectiveness of inferential choices.

We propose a hierarchical learning strategy aimed at generating sparse representations and associated models for large noisy datasets. The hierarchy follows from approximation spaces identified at successively finer scales. For promoting model generalization at each scale, we also introduce a novel, projection based penalty operator across multiple dimension, using permutation operators for incorporating proximity and ordering information. The paper presents a detailed analysis of approximation properties in the reconstruction Reproducing Kernel Hilbert Spaces (RKHS) with emphasis on optimality and consistency of predictions and behavior of error functionals associated with the produced sparse representations. Results show the performance of the approach as a data reduction and modeling strategy on both synthetic (univariate and multivariate) and real datasets (time series). The sparse model for the test datasets, generated by the presented approach, is also shown to efficiently reconstruct the underlying process and preserve generalizability.