In this paper, we consider data acquired by multimodal sensors capturing complementary aspects and features of a measured phenomenon. We focus on a scenario in which the measurements share mutual sources of variability but might also be contaminated by other measurement-specific sources such as interferences or noise. Our approach combines manifold learning, which is a class of nonlinear data-driven dimension reduction methods, with the well-known Riemannian geometry of symmetric and positive-definite (SPD) matrices. Manifold learning typically includes the spectral analysis of a kernel built from the measurements. Here, we take a different approach, utilizing the Riemannian geometry of the kernels. In particular, we study the way the spectrum of the kernels changes along geodesic paths on the manifold of SPD matrices. We show that this change enables us, in a purely unsupervised manner, to derive a compact, yet informative, description of the relations between the measurements, in terms of their underlying components. Based on this result, we present new algorithms for extracting the common latent components and for identifying common and measurement-specific components.

In todays world the request for very complex models for huge data sets is rising steadily. The problem with these models is that by raising the complexity of the models, it gets much harder to interpret them. The growing field of \emph{interpretable machine learning} tries to make up for the lack of interpretability in these complex (or even blackbox-)models by using specific techniques that can help to understand those models better. In this article a new kind of interpretable machine learning method is presented, which can help to understand the partitioning of the feature space into predicted classes in a classification model using quantile shifts. To illustrate in which situations this quantile shift method (QSM) could become beneficial, it is applied to a theoretical medical example and a real data example. Basically, real data points (or specific points of interest) are used and the changes of the prediction after slightly raising or decreasing specific features are observed. By comparing the predictions before and after the manipulations, under certain conditions the observed changes in the predictions can be interpreted as neighborhoods of the classes with regard to the manipulated features. Chordgraphs are used to visualize the observed changes.

Recent work has shown potential in using Mixed Integer Programming (MIP) solvers to optimize certain aspects of neural networks (NN). However little research has gone into training NNs with solvers. State of the art methods to train NNs are typically gradient-based and require significant data, computation on GPUs and extensive hyper-parameter tuning. In contrast, training with MIP solvers should not require GPUs or hyper-parameter tuning but can likely not handle large amounts of data. This work builds on recent advances that train binarized NNs using MIP solvers. We go beyond current work by formulating new MIP models to increase the amount of data that can be used and to train non-binary integer-valued networks. Our results show that comparable results to using gradient descent can be achieved when minimal data is available.

One of the central goals in precision health is the understanding and interpretation of high-dimensional biological data to identify genes and markers associated with disease initiation, development, and outcomes. Though significant effort has been committed to harness gene expression data for multiple analyses while accounting for time-to-event modeling by including survival times, many traditional analyses have focused separately on non-negative matrix factorization (NMF) of the gene expression data matrix and survival regression with Cox proportional hazards model. In this work, Cox proportional hazards regression is integrated with NMF by imposing survival constraints. This is accomplished by jointly optimizing the Frobenius norm and partial log likelihood for events such as death or relapse. Simulation results on synthetic data demonstrated the superiority of the proposed method, when compared to other algorithms, in finding survival associated gene clusters. In addition, using human cancer gene expression data, the proposed technique can unravel critical clusters of cancer genes. The discovered gene clusters reflect rich biological implications and can help identify survival-related biomarkers. Towards the goal of precision health and cancer treatments, the proposed algorithm can help understand and interpret high-dimensional heterogeneous genomics data with accurate identification of survival-associated gene clusters.

In machine learning (ML), ensemble methods such as bagging, boosting, and stacking are widely-established approaches that regularly achieve top-notch predictive performance. Stacking (also called "stacked generalization") is an ensemble method that combines heterogeneous base models, arranged in at least one layer, and then employs another metamodel to summarize the predictions of those models. Although it may be a highly-effective approach for increasing the predictive performance of ML, generating a stack of models from scratch can be a cumbersome trial-and-error process. This challenge stems from the enormous space of available solutions, with different sets of data instances and features that could be used for training, several algorithms to choose from, and instantiations of these algorithms using diverse parameters (i.e., models) that perform differently according to various metrics. In this work, we present a knowledge generation model, which supports ensemble learning with the use of visualization, and a visual analytics system for stacked generalization. Our system, StackGenVis, assists users in dynamically adapting performance metrics, managing data instances, selecting the most important features for a given data set, choosing a set of top-performant and diverse algorithms, and measuring the predictive performance. In consequence, our proposed tool helps users to decide between distinct models and to reduce the complexity of the resulting stack by removing overpromising and underperforming models. The applicability and effectiveness of StackGenVis are demonstrated with two use cases: a real-world healthcare data set and a collection of data related to sentiment/stance detection in texts. Finally, the tool has been evaluated through interviews with three ML experts.

Predictive analytics, sometimes referred to as big data analytics, relies on aspects of data mining as well as algorithms to develop predictive models. These predictive models can be used by enterprise marketers to more effectively develop predictions of future user behaviors based on the sourced historical data. These statistical models are growing as a result of the wide swaths of available current data as well as the advent of capable artificial intelligence and machine learning. The applications of predictive analytics are extensive and often require four key components to maintain effectiveness. Fundamental to any aspect of data science, it's difficult to develop accurate predictions or craft a decision tree if you're garnering insights from inadequate data sources.

Digital phenotyping approaches that collect and analyze Smartphone-user data on locations, activities, and even feelings - combined with machine learning to recognize patterns and make predictions from the data - have emerged as promising tools for monitoring patients with psychosis spectrum illnesses, according to a report in the September/October issue of Harvard Review of Psychiatry. The journal is published in the Lippincott portfolio by Wolters Kluwer.John Tourous, MD, MBI, of Harvard Medical School and colleagues reviewed available evidence on digital phenotyping and machine learning to improve care for people living with schizophrenia, bipolar disorder, and related illnesses. Digital phenotyping provides a much-needed bridge between patients' symptomatology and the behaviors that can be used to assess and monitor psychiatric disorders." "Digital phenotyping is the use of data from smartphones and wearables collected in situ for capturing a digital expression of human behaviors," according to the authors. Psychiatry researchers think that collecting and analyzing this kind of behavioral information might be useful in understanding how patients with severe mental illness are functioning in everyday life outside of the clinic or lab - in particular, to assess symptoms and predict clinical relapses.

We propose a new binary classification model called Phase Separation Binary Classifier (PSBC). It consists of a discretization of a nonlinear reaction-diffusion equation coupled with an ODE, and is inspired by fluid behavior, namely, on how binary fluids phase separate. Hence, parameters and hyperparameters have physical meaning, whose effects are carefully studied in several different scenarios. PSBC's coefficients are trainable weights, chosen according to a minimization problem using Gradient Descent; optimization relies on a classical Backpropagation with weight sharing. The model can be seen under the framework of feedforward networks, and is endowed with a nonlinear activation function that is linear in trainable weights but polynomial in other variables, yielding a cost function that is also polynomial. In view of the model's connection with ODEs and parabolic PDEs, forward propagation amounts to an initial value problem. Thus, stability conditions are established using the concept of Invariant regions. Interesting model compression properties are thoroughly discussed. We illustrate the classifier's qualities by applying it to the subset of numbers "0" and "1" of the classical MNIST database, where we are able to discern individuals with more than 94\% accuracy, sometimes using less only about 10\% of variables.

Accurately determining a change in protein binding affinity upon mutations is important for the discovery and design of novel therapeutics and to assist mutagenesis studies. Determination of change in binding affinity upon mutations requires sophisticated, expensive, and time-consuming wet-lab experiments that can be aided with computational methods. Most of the computational prediction techniques require protein structures that limit their applicability to protein complexes with known structures. In this work, we explore the sequence-based prediction of change in protein binding affinity upon mutation. We have used protein sequence information instead of protein structures along with machine learning techniques to accurately predict the change in protein binding affinity upon mutation. Our proposed sequence-based novel change in protein binding affinity predictor called PANDA gives better accuracy than existing methods over the same validation set as well as on an external independent test dataset. On an external test dataset, our proposed method gives a maximum Pearson correlation coefficient of 0.52 in comparison to the state-of-the-art existing protein structure-based method called MutaBind which gives a maximum Pearson correlation coefficient of 0.59. Our proposed protein sequence-based method, to predict a change in binding affinity upon mutations, has wide applicability and comparable performance in comparison to existing protein structure-based methods.

For supervised learning models, the analysis of generalization ability (generalizability) is vital because the generalizability expresses how well a model will perform on unseen data. Traditional generalization methods, such as the VC dimension, do not apply to deep neural network (DNN) models. Thus, new theories to explain the generalizability of DNNs are required. In this study, we hypothesize that the DNN with a simpler decision boundary has better generalizability by the law of parsimony (Occam's Razor). We create the decision boundary complexity (DBC) score to define and measure the complexity of decision boundary of DNNs. The idea of the DBC score is to generate data points (called adversarial examples) on or near the decision boundary. Our new approach then measures the complexity of the boundary using the entropy of eigenvalues of these data. The method works equally well for high-dimensional data. We use training data and the trained model to compute the DBC score. And, the ground truth for model's generalizability is its test accuracy. Experiments based on the DBC score have verified our hypothesis. The DBC is shown to provide an effective method to measure the complexity of a decision boundary and gives a quantitative measure of the generalizability of DNNs.