One of the most important factors driving Python's popularity as a statistical modeling language is its widespread use as the language of choice in data science and machine learning. Today, there's a huge demand for data science expertise as more and more businesses apply it within their operations. Python offers the right mix of power, versatility, and support from its community to lead the way. It's worth noting, however, that sound statistical modeling occupies a central role in a data science stack, but some statistical modeling fundamentals often get overlooked, leading to poor analysis and bad decisions. This article covers some of the essential statistical modeling frameworks and methods for Python, which can help us do statistical modeling and probabilistic computation.

Overall, we obtain really good accuracy values for every model. We can observe that the Gradient Boosting, Logistic Regression and Random Forest models seem to overfit since they have an extremely high training set accuracy but a lower test set accuracy, so we'll discard them. We will choose the SVM classifier above the remaining models because it has the highest test set accuracy, which is really near to the training set accuracy.

Leveraging on the underlying low-dimensional structure of data, low-rank and sparse modeling approaches have achieved great success in a wide range of applications. However, in many applications the data can display structures beyond simply being low-rank or sparse. Fully extracting and exploiting hidden structure information in the data is always desirable and favorable. To reveal more underlying effective manifold structure, in this paper, we explicitly model the data relation. Specifically, we propose a structure learning framework that retains the pairwise similarities between the data points. Rather than just trying to reconstruct the original data based on self-expression, we also manage to reconstruct the kernel matrix, which functions as similarity preserving. Consequently, this technique is particularly suitable for the class of learning problems that are sensitive to sample similarity, e.g., clustering and semisupervised classification. To take advantage of representation power of deep neural network, a deep auto-encoder architecture is further designed to implement our model. Extensive experiments on benchmark data sets demonstrate that our proposed framework can consistently and significantly improve performance on both evaluation tasks. We conclude that the quality of structure learning can be enhanced if similarity information is incorporated. Introduction With the advancements in information technology, high-dimensional data become very common for representing the data. However, it is difficult to deal Preprint submitted to Elsevier December 4, 2019 arXiv:1912.01197v1 Fortunately, in practice data are not unstructured.

We developed an explainable artificial intelligence (AI) early warning score (xAI-EWS) system for early detection of acute critical illness. While maintaining a high predictive performance, our system explains to the clinician on which relevant electronic health records (EHRs) data the prediction is grounded. Acute critical illness is often preceded by deterioration of routinely measured clinical parameters, e.g., blood pressure and heart rate. Early clinical prediction is typically based on manually calculated screening metrics that simply weigh these parameters, such as Early Warning Scores (EWS). The predictive performance of EWSs yields a tradeoff between sensitivity and specificity that can lead to negative outcomes for the patient. Previous work on EHR-trained AI systems offers promising results with high levels of predictive performance in relation to the early, real-time prediction of acute critical illness. However, without insight into the complex decisions by such system, clinical translation is hindered. In this letter, we present our xAI-EWS system, which potentiates clinical translation by accompanying a prediction with information on the EHR data explaining it.

We consider a sparse multi-task regression framework for fitting a collection of related sparse models. Representing models as nodes in a graph with edges between related models, a framework that fuses lasso regressions with the total variation penalty is investigated. Under a form of restricted eigenvalue assumption, bounds on prediction and squared error are given that depend upon the sparsity of each model and the differences between related models. This assumption relates to the smallest eigenvalue restricted to the intersection of two cone sets of the covariance matrix constructed from each of the agents' covariances. We show that this assumption can be satisfied if the constructed covariance matrix satisfies a restricted isometry property. In the case of a grid topology high-probability bounds are given that match, up to log factors, the no-communication setting of fitting a lasso on each model, divided by the number of agents. A decentralised dual method that exploits a convex-concave formulation of the penalised problem is proposed to fit the models and its effectiveness demonstrated on simulations against the group lasso and variants.

Today, treatment effect estimation at the individual level is a vital problem in many areas of science and business. For example, in marketing, estimates of the treatment effect are used to select the most efficient promo-mechanics; in medicine, individual treatment effects are used to determine the optimal dose of medication for each patient and so on. At the same time, the question on choosing the best method, i.e., the method that ensures the smallest predictive error (for instance, RMSE) or the highest total (average) value of the effect, remains open. Accordingly, in this paper we compare the effectiveness of machine learning methods for estimation of individual treatment effects. The comparison is performed on the Criteo Uplift Modeling Dataset. In this paper we show that the combination of the Logistic Regression method and the Difference Score method as well as Uplift Random Forest method provide the best correctness of Individual Treatment Effect prediction on the top 30\% observations of the test dataset.

Deep neural networks (DNNs) are poorly-calibrated when trained in conventional ways. To improve confidence calibration of DNNs, we propose a novel training method, distance-based learning from errors (DBLE). DBLE bases its confidence estimation on distances in the representation space. We first adapt prototypical learning for training of a classification model for DBLE. It yields a representation space where the distance from a test sample to its ground-truth class center can calibrate the model performance. At inference, however, these distances are not available due to the lack of ground-truth labels. To circumvent this by approximately inferring the distance for every test sample, we propose to train a confidence model jointly with the classification model by merely learning from mis-classified training samples, which we show to be highly beneficial for effective learning. On multiple datasets and DNN architectures, we demonstrate that DBLE outperforms alternative single-modal confidence calibration approaches. DBLE also achieves comparable performance with computationally-expensive ensemble approaches with lower computational cost and lower number of parameters.

Machine learning has seen tremendous advances in the past few years which has lead to deep learning models being deployed in varied applications of day-to-day life. Attacks on such models using perturbations, particularly in real-life scenarios, pose a serious challenge to their applicability, pushing research into the direction which aims to enhance the robustness of these models. After the introduction of these perturbations by Szegedy et al., significant amount of research has focused on the reliability of such models, primarily in two aspects - white-box, where the adversary has access to the targeted model and related parameters; and the black-box, which resembles a real-life scenario with the adversary having almost no knowledge of the model to be attacked. We propose to attract attention on the latter scenario and thus, present a comprehensive comparative study among the different adversarial black-box attack approaches proposed till date. The second half of this literature survey focuses on the defense techniques. This is the first study, to the best of our knowledge, that specifically focuses on the black-box setting to motivate future work on the same.

We present two new remarkably simple stochastic second-order methods for minimizing the average of a very large number of sufficiently smooth and strongly convex functions. The first is a stochastic variant of Newton's method (SN), and the second is a stochastic variant of cubically regularized Newton's method (SCN). We establish local linear-quadratic convergence results. Unlike existing stochastic variants of second order methods, which require the evaluation of a large number of gradients and/or Hessians in each iteration to guarantee convergence, our methods do not have this shortcoming. For instance, the simplest variants of our methods in each iteration need to compute the gradient and Hessian of a {\em single} randomly selected function only. In contrast to most existing stochastic Newton and quasi-Newton methods, our approach guarantees local convergence faster than with first-order oracle and adapts to the problem's curvature. Interestingly, our method is not unbiased, so our theory provides new intuition for designing new stochastic methods.

ABSTRACT Regularization of the classical Laplacian matrices was empirically shown to improve spectral clustering in sparse networks. It was observed that small regularizations are preferable, but this point was left as a heuristic argument. In this paper we formally determine a proper regularization which is intimately related to alternative state-of-the-art spectral techniques for sparse graphs. Index T erms-- Regularized Laplacian, Bethe-Hessian, spectral clustering, sparse networks, community detection 1. INTRODUCTION Community detection [1] is one of the central unsupervised learning tasks on graphs. The community detection problem has vast applications in different fields of science [2] and can be seen as the simplest form of clustering, i.e. the problem of dividing objects into similarity classes.