Time-dependent systems, especially in the parametrized setting, describe a huge number of problems and are therefore a pervasive topic of extended scientific interest and industrial value. Indeed, parametric dynamical systems modeling and control play a fundamental role in many research fields, as in the case of fluid dynamics, chemical reactions, biological problems and more. In the majority of scenarios, the most suitable way to study such dynamics passes through numerical simulation. Especially for what concerns problems modelled by differential and partial differential equations, numerical approximation represent the standard to compute the system's response. However, a problem of dimensionality of the system's numerical discretization often appears significant, as performing multiple simulations in large-scale settings typically reveals demands of computational resources difficult to handle. This gives rise to the need of finding alternatives to classical numerical methods (Finite Element Method, Finite Volume Method, Finite Difference Method) in order to approximate the parametric response of a given system at a reduced computational cost. Reduced order models (ROMs) demonstrated to be a powerful tools in this regard and nowadays it is possible to find a large variety of applications in a number of different fields as heat transfer, fluid dynamics, shape optimization, uncertainty quantification. The main idea of ROMs is to approximate a high dimensional model, usually referred as full order model (FOM), with a low dimensional one still preserving the solution's key features. There mainly exist two different techniques to obtain a ROM: intrusive and non-intrusive approaches.

Mixtures of probabilistic principal component analysis (MPPCA) is a well-known mixture model extension of principal component analysis (PCA). Similar to PCA, MPPCA assumes the data samples in each mixture contain homoscedastic noise. However, datasets with heterogeneous noise across samples are becoming increasingly common, as larger datasets are generated by collecting samples from several sources with varying noise profiles. The performance of MPPCA is suboptimal for data with heteroscedastic noise across samples. This paper proposes a heteroscedastic mixtures of probabilistic PCA technique (HeMPPCAT) that uses a generalized expectation-maximization (GEM) algorithm to jointly estimate the unknown underlying factors, means, and noise variances under a heteroscedastic noise setting. Simulation results illustrate the improved factor estimates and clustering accuracies of HeMPPCAT compared to MPPCA.

Motivation: Gene-disease associations are fundamental for understanding disease etiology and developing effective interventions and treatments. Identifying genes not yet associated with a disease due to a lack of studies is a challenging task in which prioritization based on prior knowledge is an important element. The computational search for new candidate disease genes may be eased by positive-unlabeled learning, the machine learning setting in which only a subset of instances are labeled as positive while the rest of the data set is unlabeled. In this work, we propose a set of effective network-based features to be used in a novel Markov diffusion-based multi-class labeling strategy for putative disease gene discovery. Results: The performances of the new labeling algorithm and the effectiveness of the proposed features have been tested on ten different disease data sets using three machine learning algorithms. The new features have been compared against classical topological and functional/ontological features and a set of network-and biological-derived features already used in gene discovery tasks. The predictive power of the integrated methodology in searching for new disease genes has been found to be competitive against state-of-the-art algorithms. Availability and implementation: The source code of NIAPU can be accessed at https://github.

We study the sample complexity of reducing reinforcement learning to a sequence of empirical risk minimization problems over the policy space. Such reductions-based algorithms exhibit local convergence in the function space, as opposed to the parameter space for policy gradient algorithms, and thus are unaffected by the possibly non-linear or discontinuous parameterization of the policy class. We propose a variance-reduced variant of Conservative Policy Iteration that improves the sample complexity of producing a $\varepsilon$-functional local optimum from $O(\varepsilon^{-4})$ to $O(\varepsilon^{-3})$. Under state-coverage and policy-completeness assumptions, the algorithm enjoys $\varepsilon$-global optimality after sampling $O(\varepsilon^{-2})$ times, improving upon the previously established $O(\varepsilon^{-3})$ sample requirement.

The Expectation Maximization (EM) algorithm is widely used as an iterative modification to maximum likelihood estimation when the data is incomplete. We focus on a semi-supervised case to learn the model from labeled and unlabeled samples. Existing work in the semi-supervised case has focused mainly on performance rather than convergence guarantee, however we focus on the contribution of the labeled samples to the convergence rate. The analysis clearly demonstrates how the labeled samples improve the convergence rate for the exponential family mixture model. In this case, we assume that the population EM (EM with unlimited data) is initialized within the neighborhood of global convergence for the population EM that consists solely of samples that have not been labeled. The analysis for the labeled samples provides a comprehensive description of the convergence rate for the Gaussian mixture model. In addition, we extend the findings for labeled samples and offer an alternative proof for the population EM's convergence rate with unlabeled samples for the symmetric mixture of two Gaussians.

We propose a clustering method that involves chaining four known techniques into a pipeline yielding an algorithm with stronger recovery guarantees than any of the four components separately. Given $n$ points in $\mathbb R^d$, the first component of our pipeline, which we call leapfrog distances, is reminiscent of density-based clustering, yielding an $n\times n$ distance matrix. The leapfrog distances are then translated to new embeddings using multidimensional scaling and spectral methods, two other known techniques, yielding new embeddings of the $n$ points in $\mathbb R^{d'}$, where $d'$ satisfies $d'\ll d$ in general. Finally, sum-of-norms (SON) clustering is applied to the re-embedded points. Although the fourth step (SON clustering) can in principle be replaced by any other clustering method, our focus is on provable guarantees of recovery of underlying structure. Therefore, we establish that the re-embedding improves recovery SON clustering, since SON clustering is a well-studied method that already has provable guarantees.

Mental disorders such as depression and suicidal ideation are hazardous, affecting more than 300 million people over the world. However, on social media, mental disorder symptoms can be observed, and automated approaches are increasingly capable of detecting them. The considerable number of social media users and the tremendous quantity of user-generated data on social platforms provide a unique opportunity for researchers to distinguish patterns that correlate with mental status. This research offers a roadmap for analysis, where mental state detection can be based on machine learning techniques. We describe the common approaches for predicting and identifying the disorder using user-generated content. This research is organized according to the data collection, feature extraction, and prediction algorithms. Furthermore, we review several recent studies conducted to explore different features of candidate profiles and their analytical methods. Following, we debate various aspects of the development of experimental auto-detection frameworks for identifying users who suffer from disorders, and we conclude with a discussion of future trends. The introduced methods can help complement screening procedures, identify at-risk people through social media monitoring on a large scale, and make disorders easier to treat in the future.

Machine Learning (ML) is being used in multiple disciplines due to its powerful capability to infer relationships within data. In particular, Software Engineering (SE) is one of those disciplines in which ML has been used for multiple tasks, like software categorization, bugs prediction, and testing. In addition to the multiple ML applications, some studies have been conducted to detect and understand possible pitfalls and issues when using ML. However, to the best of our knowledge, only a few studies have focused on presenting ML best practices or guidelines for the application of ML in different domains. In addition, the practices and literature presented in previous literature (i) are domain-specific (e.g., concrete practices in biomechanics), (ii) describe few practices, or (iii) the practices lack rigorous validation and are presented in gray literature. In this paper, we present a study listing 127 ML best practices systematically mining 242 posts of 14 different Stack Exchange (STE) websites and validated by four independent ML experts. The list of practices is presented in a set of categories related to different stages of the implementation process of an ML-enabled system; for each practice, we include explanations and examples. In all the practices, the provided examples focus on SE tasks. We expect this list of practices could help practitioners to understand better the practices and use ML in a more informed way, in particular newcomers to this new area that sits at the intersection of software engineering and machine learning.

STEALTH is a method for using some AI-generated model, without suffering from malicious attacks (i.e. lying) or associated unfairness issues. After recursively bi-clustering the data, STEALTH system asks the AI model a limited number of queries about class labels. STEALTH asks so few queries (1 per data cluster) that malicious algorithms (a) cannot detect its operation, nor (b) know when to lie.

Disease heterogeneity has been a critical challenge for precision diagnosis and treatment, especially in neurologic and neuropsychiatric diseases. Many diseases can display multiple distinct brain phenotypes across individuals, potentially reflecting disease subtypes that can be captured using MRI and machine learning methods. However, biological interpretability and treatment relevance are limited if the derived subtypes are not associated with genetic drivers or susceptibility factors. Herein, we describe Gene-SGAN - a multi-view, weakly-supervised deep clustering method - which dissects disease heterogeneity by jointly considering phenotypic and genetic data, thereby conferring genetic correlations to the disease subtypes and associated endophenotypic signatures. We first validate the generalizability, interpretability, and robustness of Gene-SGAN in semi-synthetic experiments. We then demonstrate its application to real multi-site datasets from 28,858 individuals, deriving subtypes of Alzheimer's disease and brain endophenotypes associated with hypertension, from MRI and SNP data. Derived brain phenotypes displayed significant differences in neuroanatomical patterns, genetic determinants, biological and clinical biomarkers, indicating potentially distinct underlying neuropathologic processes, genetic drivers, and susceptibility factors. Overall, Gene-SGAN is broadly applicable to disease subtyping and endophenotype discovery, and is herein tested on disease-related, genetically-driven neuroimaging phenotypes.