The covariance structure of multivariate functional data can be highly complex, especially if the multivariate dimension is large, making extension of statistical methods for standard multivariate data to the functional data setting quite challenging. For example, Gaussian graphical models have recently been extended to the setting of multivariate functional data by applying multivariate methods to the coefficients of truncated basis expansions. However, a key difficulty compared to multivariate data is that the covariance operator is compact, and thus not invertible. The methodology in this paper addresses the general problem of covariance modeling for multivariate functional data, and functional Gaussian graphical models in particular. As a first step, a new notion of separability for multivariate functional data is proposed, termed partial separability, leading to a novel Karhunen-Lo\`eve-type expansion for such data. Next, the partial separability structure is shown to be particularly useful in order to provide a well-defined Gaussian graphical model that can be identified with a sequence of finite-dimensional graphical models, each of fixed dimension. This motivates a simple and efficient estimation procedure through application of the joint graphical lasso. Empirical performance of the method for graphical model estimation is assessed through simulation and analysis of functional brain connectivity during a motor task.

This is the fourth in a four-part series on how we approach machine learning at Feature Labs. These articles cover the concepts and a full implementation as applied to predicting customer churn. The project Jupyter Notebooks are all available on GitHub. All of the work documented here was completed with open-source tools and data.) The Machine Learning Modeling ProcessThe outputs of prediction and feature engineering are a set of label times, historical examples of what we want to predict, and features, predictor variables used to train a model to predict the label.

In recent years, the interest in Big Data sources has been steadily growing within the Official Statistic community. The Italian National Institute of Statistics (Istat) is currently carrying out several Big Data pilot studies. One of these studies, the ICT Big Data pilot, aims at exploiting massive amounts of textual data automatically scraped from the websites of Italian enterprises in order to predict a set of target variables (e.g. e-commerce) that are routinely observed by the traditional ICT Survey. In this paper, we show that Deep Learning techniques can successfully address this problem. Essentially, we tackle a text classification task: an algorithm must learn to infer whether an Italian enterprise performs e-commerce from the textual content of its website. To reach this goal, we developed a sophisticated processing pipeline and evaluated its performance through extensive experiments. Our pipeline uses Convolutional Neural Networks and relies on Word Embeddings to encode raw texts into grayscale images (i.e. normalized numeric matrices). Web-scraped texts are huge and have very low signal to noise ratio: to overcome these issues, we adopted a framework known as False Positive Reduction, which has seldom (if ever) been applied before to text classification tasks. Several original contributions enable our processing pipeline to reach good classification results. Empirical evidence shows that our proposal outperforms all the alternative Machine Learning solutions already tested in Istat for the same task.

With the increasing availability of AI-based decision support, there is an increasing need for their certification by both AI manufacturers and notified bodies, as well as the pragmatic (real-world) validation of these systems. Therefore, there is the need for meaningful and informative ways to assess the performance of AI systems in clinical practice. Common metrics (like accuracy scores and areas under the ROC curve) have known problems and they do not take into account important information about the preferences of clinicians and the needs of their specialist practice, like the likelihood and impact of errors and the complexity of cases. In this paper, we present a new accuracy measure, the H-accuracy (Ha), which we claim is more informative in the medical domain (and others of similar needs) for the elements it encompasses. We also provide proof that the H-accuracy is a generalization of the balanced accuracy and establish a relation between the H-accuracy and the Net Benefit. Finally, we illustrate an experimentation in two user studies to show the descriptive power of the Ha score and how complementary and differently informative measures can be derived from its formulation (a Python script to compute Ha is also made available).

The aim of clinical effectiveness research using repositories of electronic health records is to identify what health interventions 'work best' in real-world settings. Since there are several reasons why the net benefit of intervention may differ across patients, current comparative effectiveness literature focuses on investigating heterogeneous treatment effect and predicting whether an individual might benefit from an intervention. The majority of this literature has concentrated on the estimation of the effect of treatment on binary outcomes. However, many medical interventions are evaluated in terms of their effect on future events, which are subject to loss to follow-up. In this study, we describe a framework for the estimation of heterogeneous treatment effect in terms of differences in time-to-event (survival) probabilities. We divide the problem into three phases: (1) estimation of treatment effect conditioned on unique sets of the covariate vector; (2) identification of features important for heterogeneity using an ensemble of non-parametric variable importance methods; and (3) estimation of treatment effect on the reference classes defined by the previously selected features, using one-step Targeted Maximum Likelihood Estimation. We conducted a series of simulation studies and found that this method performs well when either sample size or event rate is high enough and the number of covariates contributing to the effect heterogeneity is moderate. An application of this method to a clinical case study was conducted by estimating the effect of oral anticoagulants on newly diagnosed non-valvular atrial fibrillation patients using data from the UK Clinical Practice Research Datalink.

--We present a way to use T opological Data Analysis (TDA) for machine learning tasks on grayscale images. We apply persistent homology to generate a wide range of topological features using a point cloud obtained from an image, its natural grayscale filtration, and different filtrations defined on the binarized image. We show that this topological machine learning pipeline can be used as a highly relevant dimensionality reduction by applying it to the MNIST digits dataset. We conduct a feature selection and study their correlations while providing an intuitive interpretation of their importance, which is relevant in both machine learning and TDA. Finally, we show that we can classify digit images while reducing the size of the feature set by a factor 5 compared to the grayscale pixel value features and maintain similar accuracy. I NTRODUCTION Topological Data Analysis (TDA) [1] applies techniques from algebraic topology to study and extract topological and geometric information on the shape of data. In this paper, we use persistent homology [2], a tool from TDA that extracts features representing the numbers of connected components, cycles, and voids and their birth and death during an iterative process called a filtration. Each of those features is summarized as a point in a persistence diagram .

If you have been in machine learning for quite some time then you must be developing models to attain high accuracy, as accuracy is the prime metric to compare models, but what if I tell you that model evaluation does not always consider accuracy only. When we have to evaluate a model we do consider accuracy but what we majorly focus on is how much robust our model is, how will it perform on a different dataset and how much flexibility it has to offer. Accuracy, no doubt, is an important metric to consider but it does not always give the full picture. What we mean when we say that the model is robust is that it has realized and learned about the data in a correct and desirable manner, hence the predictions made by it are close to the actual values. Due to the enormous mathematical techniques involved and uncertain nature of data, it may happen that the model results in better accuracy but fails to realize the data properly and hence performs poorly when the data is varied.

CLTV is a customer relationship management (CRM) issue with an enterprise approach to understanding and influencing customer behavior through meaningful communication to improve customer acquisition, customer retention, customer loyalty, and customer profitability. The whole idea is that, business wants to predict the average amount of $$ customers will spend on the business over the entire life of relationship. Although statistical methods can be very powerful, but these methods make several stringent assumptions on the types of data and their distribution, and typically can only handle a limited number of variables. Regression-based methods are usually based on a fixed-form equation, and assume a single best solution, which means that we can compare only a few alternative solutions manually. Further, when the models are applied to real data, the key assumptions of the methods are often violated.

In the majority of molecular optimization tasks, predictive machine learning (ML) models are limited due to the unavailability and cost of generating big experimental datasets on the specific task. To circumvent this limitation, ML models are trained on big theoretical datasets or experimental indicators of molecular suitability that are either publicly available or inexpensive to acquire. These approaches produce a set of candidate molecules which have to be ranked using limited experimental data or expert knowledge. Under the assumption that structure is related to functionality, here we use a molecular fragment-based graphical autoencoder to generate unique structural fingerprints to efficiently search through the candidate set. We demonstrate that fragment-based graphical autoencoding reduces the error in predicting physical characteristics such as the solubility and partition coefficient in the small data regime compared to other extended circular fingerprints and string based approaches. We further demonstrate that this approach is capable of providing insight into real world molecular optimization problems, such as searching for stabilization additives in organic semiconductors by accurately predicting 92% of test molecules given 69 training examples. This task is a model example of black box molecular optimization as there is minimal theoretical and experimental knowledge to accurately predict the suitability of the additives.

Emotion recognition based on EEG has become an active research area. As one of the machine learning models, CNN has been utilized to solve diverse problems including issues in this domain. In this work, a study of CNN and its spatiotemporal feature extraction has been conducted in order to explore capabilities of the model in varied window sizes and electrode orders. Our investigation was conducted in subject-independent fashion. Results have shown that temporal information in distinct window sizes significantly affects recognition performance in both 10-fold and leave-one-subject-out cross validation. Spatial information from varying electrode order has modicum effect on classification. SVM classifier depending on spatiotemporal knowledge on the same dataset was previously employed and compared to these empirical results. Even though CNN and SVM have a homologous trend in window size effect, CNN outperformed SVM using leave-one-subject-out cross validation. This could be caused by different extracted features in the elicitation process.