A Random Graph is a random object which take its values in the space of graphs. We take advantage of the expressibility of graphs in order to model the uncertainty about the existence of causal relationships within a given set of variables. We adopt a Bayesian point of view in order to capture a causal structure via interaction and learning with a causal environment. We test our method over two different scenarios, and the experiments mainly confirm that our technique can learn a causal structure. Furthermore, the experiments and results presented for the first test scenario demonstrate the usefulness of our method to learn a causal structure as well as the optimal action. On the other hand the second experiment, shows that our proposal manages to learn the underlying causal structure of several tasks with different sizes and different causal structures.

Diagnosis of Parkinson's disease (PD) is commonly based on medical observations and assessment of clinical signs, including the characterization of a variety of motor symptoms. However, traditional diagnostic approaches may suffer from subjectivity as they rely on the evaluation of movements that are sometimes subtle to human eyes and therefore difficult to classify, leading to possible misclassification. In the meantime, early non-motor symptoms of PD may be mild and can be caused by many other conditions. Therefore, these symptoms are often overlooked, making diagnosis of PD at an early stage challenging. To address these difficulties and to refine the diagnosis and assessment procedures of PD, machine learning methods have been implemented for the classification of PD and healthy controls or patients with similar clinical presentations (e.g., movement disorders or other Parkinsonian syndromes). To provide a comprehensive overview of data modalities and machine learning methods that have been used in the diagnosis and differential diagnosis of PD, in this study, we conducted a systematic literature review of studies published until February 14, 2020, using the PubMed and IEEE Xplore databases. A total of 209 studies were included, extracted for relevant information and presented in this systematic review, with an investigation of their aims, sources of data, types of data, machine learning methods and associated outcomes. These studies demonstrate a high potential for adaptation of machine learning methods and novel biomarkers in clinical decision making, leading to increasingly systematic, informed diagnosis of PD.

This paper describes the NEMO submission to SIGTYP 2020 shared task which deals with prediction of linguistic typological features for multiple languages using the data derived from World Atlas of Language Structures (WALS). We employ frequentist inference to represent correlations between typological features and use this representation to train simple multi-class estimators that predict individual features. We describe two submitted ridge regression-based configurations which ranked second and third overall in the constrained task. Our best configuration achieved the micro-averaged accuracy score of 0.66 on 149 test languages.

Finite Mixture Regression (FMR) refers to the mixture modeling scheme which learns multiple regression models from the training data set. Each of them is in charge of a subset. FMR is an effective scheme for handling sample heterogeneity, where a single regression model is not enough for capturing the complexities of the conditional distribution of the observed samples given the features. In this paper, we propose an FMR model that 1) finds sample clusters and jointly models multiple incomplete mixed-type targets simultaneously, 2) achieves shared feature selection among tasks and cluster components, and 3) detects anomaly tasks or clustered structure among tasks, and accommodates outlier samples. We provide non-asymptotic oracle performance bounds for our model under a high-dimensional learning framework. The proposed model is evaluated on both synthetic and real-world data sets. The results show that our model can achieve state-of-the-art performance.

The inference of causal relationships using observational data from partially observed multivariate systems with hidden variables is a fundamental question in many scientific domains. Methods extracting causal information from conditional independencies between variables of a system are common tools for this purpose, but are limited in the lack of independencies. To surmount this limitation, we capitalize on the fact that the laws governing the generative mechanisms of a system often result in substructures embodied in the generative functional equation of a variable, which act as sufficient statistics for the influence that other variables have on it. These functional sufficient statistics constitute intermediate hidden variables providing new conditional independencies to be tested. We propose to use the Information Bottleneck method, a technique commonly applied for dimensionality reduction, to find underlying sufficient sets of statistics. Using these statistics we formulate new additional rules of causal orientation that provide causal information not obtainable from standard structure learning algorithms, which exploit only conditional independencies between observable variables. We validate the use of sufficient statistics for structure learning both with simulated systems built to contain specific sufficient statistics and with benchmark data from regulatory rules previously and independently proposed to model biological signal transduction networks.

We consider the parameter estimation problem of a probabilistic generative model prescribed using a natural exponential family of distributions. For this problem, the typical maximum likelihood estimator usually overfits under limited training sample size, is sensitive to noise and may perform poorly on downstream predictive tasks. To mitigate these issues, we propose a distributionally robust maximum likelihood estimator that minimizes the worst-case expected log-loss uniformly over a parametric Kullback-Leibler ball around a parametric nominal distribution. Leveraging the analytical expression of the Kullback-Leibler divergence between two distributions in the same natural exponential family, we show that the min-max estimation problem is tractable in a broad setting, including the robust training of generalized linear models. Our novel robust estimator also enjoys statistical consistency and delivers promising empirical results in both regression and classification tasks.

Due to lack of data, overfitting ubiquitously exists in real-world applications of deep neural networks (DNNs). In this paper, we propose advanced dropout, a model-free methodology, to mitigate overfitting and improve the performance of DNNs. The advanced dropout technique applies a model-free and easily implemented distribution with a parametric prior, and adaptively adjusts dropout rate. Specifically, the distribution parameters are optimized by stochastic gradient variational Bayes (SGVB) inference in order to carry out an end-to-end training of DNNs. We evaluate the effectiveness of the advanced dropout against nine dropout techniques on five widely used datasets in computer vision. The advanced dropout outperforms all the referred techniques by 0.83% on average for all the datasets. An ablation study is conducted to analyze the effectiveness of each component. Meanwhile, convergence of dropout rate and ability to prevent overfitting are discussed in terms of classification performance. Moreover, we extend the application of the advanced dropout to uncertainty inference and network pruning, and we find that the advanced dropout is superior to the corresponding referred methods. The advanced dropout improves classification accuracies by 4% in uncertainty inference and by 0.2% and 0.5% when pruning more than 90% of nodes and 99.8% of parameters, respectively.

Federated learning is typically approached as an optimization problem, where the goal is to minimize a global loss function by distributing computation across client devices that possess local data and specify different parts of the global objective. We present an alternative perspective and formulate federated learning as a posterior inference problem, where the goal is to infer a global posterior distribution by having client devices each infer the posterior of their local data. While exact inference is often intractable, this perspective provides a principled way to search for global optima in federated settings. Further, starting with the analysis of federated quadratic objectives, we develop a computation- and communication-efficient approximate posterior inference algorithm -- federated posterior averaging (FedPA). Our algorithm uses MCMC for approximate inference of local posteriors on the clients and efficiently communicates their statistics to the server, where the latter uses them to refine a global estimate of the posterior mode. Finally, we show that FedPA generalizes federated averaging (FedAvg), can similarly benefit from adaptive optimizers, and yields state-of-the-art results on four realistic and challenging benchmarks, converging faster, to better optima.

Prediction is critical for decision-making under uncertainty and lends validity to statistical inference. With targeted prediction, the goal is to optimize predictions for specific decision tasks of interest, which we represent via functionals. Although classical decision analysis extracts predictions from a Bayesian model, these predictions are often difficult to interpret and slow to compute. Instead, we design a class of parametrized actions for Bayesian decision analysis that produce optimal, scalable, and simple targeted predictions. For a wide variety of action parametrizations and loss functions--including linear actions with sparsity constraints for targeted variable selection--we derive a convenient representation of the optimal targeted prediction that yields efficient and interpretable solutions. Customized out-of-sample predictive metrics are developed to evaluate and compare among targeted predictors. Through careful use of the posterior predictive distribution, we introduce a procedure that identifies a set of near-optimal, or acceptable targeted predictors, which provide unique insights into the features and level of complexity needed for accurate targeted prediction. Simulations demonstrate excellent prediction, estimation, and variable selection capabilities. Targeted predictions are constructed for physical activity data from the National Health and Nutrition Examination Survey (NHANES) to better predict and understand the characteristics of intraday physical activity.

One of the main approaches for causal structure learning is constraint-based methods. These methods are particularly valued as they are guaranteed to asymptotically find a structure which is statistically equivalent to the ground truth. However, they may require exponentially large number of conditional independence (CI) tests in the number of variables of the system. In this paper, we propose a novel recursive constraint-based method for causal structure learning. The key idea of the proposed approach is to recursively use Markov blanket information in order to identify a variable that can be removed from the set of variables without changing the statistical relations among the remaining variables. Once such a variable is found, its neighbors are identified, the removable variable is removed, and the Markov blanket information of the remaining variables is updated. Our proposed approach reduces the required number of conditional independence tests for structure learning compared to the state of the art. We also provide a lower bound on the number of CI tests required by any constraint-based method. Comparing this lower bound to our achievable bound demonstrates the efficiency of our approach. We evaluate and compare the performance of the proposed method on both synthetic and real world structures against the state of the art.