We study solution methods for (strongly-)convex-(strongly)-concave Saddle-Point Problems (SPPs) over networks of two type - master/workers (thus centralized) architectures and meshed (thus decentralized) networks. The local functions at each node are assumed to be similar, due to statistical data similarity or otherwise. We establish lower complexity bounds for a fairly general class of algorithms solving the SPP. We show that a given suboptimality $\epsilon>0$ is achieved over master/workers networks in $\Omega\big(\Delta\cdot \delta/\mu\cdot \log (1/\varepsilon)\big)$ rounds of communications, where $\delta>0$ measures the degree of similarity of the local functions, $\mu$ is their strong convexity constant, and $\Delta$ is the diameter of the network. The lower communication complexity bound over meshed networks reads $\Omega\big(1/{\sqrt{\rho}} \cdot {\delta}/{\mu}\cdot\log (1/\varepsilon)\big)$, where $\rho$ is the (normalized) eigengap of the gossip matrix used for the communication between neighbouring nodes. We then propose algorithms matching the lower bounds over either types of networks (up to log-factors). We assess the effectiveness of the proposed algorithms on a robust logistic regression problem.

This paper studies the asymptotic behavior of penalized spline estimates of derivatives. In particular, we show that simply differentiating the penalized spline estimator of the mean regression function itself to estimate the corresponding derivative achieves the optimal L2 rate of convergence.

Marketing campaigns are a set of strategic activities that can promote a business's goal. The effect prediction for marketing campaigns in a real industrial scenario is very complex and challenging due to the fact that prior knowledge is often learned from observation data, without any intervention for the marketing campaign. Furthermore, each subject is always under the interference of several marketing campaigns simultaneously. Therefore, we cannot easily parse and evaluate the effect of a single marketing campaign. To the best of our knowledge, there are currently no effective methodologies to solve such a problem, i.e., modeling an individual-level prediction task based on a hierarchical structure with multiple intertwined events. In this paper, we provide an in-depth analysis of the underlying parse tree-like structure involved in the effect prediction task and we further establish a Hierarchical Capsule Prediction Network (HapNet) for predicting the effects of marketing campaigns. Extensive results based on both the synthetic data and real data demonstrate the superiority of our model over the state-of-the-art methods and show remarkable practicability in real industrial applications.

The advantages and difficulties of application of Pad\'e approximants to two-dimensional regression analysis are discussed. New formulation of residuals is suggested in the method of least squares. It leads to a system of linear equations in case of rational functions. The possibility of using Tikhonov regularization technique to avoid overfitting is demonstrated in this approach. To illustrate the efficiency of the suggested method, several practical cases from physics and reliability theory are considered.

Predicting mechanical properties in metal additive manufacturing (MAM) is vital to ensure the printed parts' performance, reliability, and whether they can fulfill requirements for a specific application. Conducting experiments to estimate mechanical properties in MAM processes, however, is a laborious and expensive task. Also, they can solely be designed for a particular material in a certain MAM process. Nonetheless, Machine learning (ML) methods, which are more flexible and cost-effective solutions, can be utilized to predict mechanical properties based on the processing parameters and material properties. To this end, in this work, a comprehensive framework for benchmarking ML for mechanical properties is introduced. An extensive experimental dataset is collected from more than 90 MAM articles and 140 MAM companies' data sheets containing MAM processing conditions, machines, materials, and resultant mechanical properties, including yield strength, ultimate tensile strength, elastic modulus, elongation, hardness as well as surface roughness. Physics-aware MAM featurization, adjustable ML models, and evaluation metrics are proposed to construct a comprehensive learning framework for mechanical properties prediction. Additionally, the Explainable AI method, i.e., SHAP analysis was studied to explain and interpret the ML models' predicted values for mechanical properties. Moreover, data-driven explicit models have been identified to estimate mechanical properties based on the processing parameters and material properties with more interpretability as compared to the employed ML models.

The high cost of the test can be dramatically reduced, provided that the coverability as an inherent feature of the code under test is predictable. This article offers a machine learning model to predict the extent to which the test could cover a class in terms of a new metric called Coverageability. The prediction model consists of an ensemble of four regression models. The learning samples consist of feature vectors, where features are source code metrics computed for a class. The samples are labeled by the Coverageability values computed for their corresponding classes. We offer a mathematical model to evaluate test effectiveness in terms of size and coverage of the test suite generated automatically for each class. We extend the size of the feature space by introducing a new approach to defining sub-metrics in terms of existing source code metrics. Using feature importance analysis on the learned prediction models, we sort source code metrics in the order of their impact on the test effectiveness. As a result of which, we found the class strict cyclomatic complexity as the most influential source code metric. Our experiments with the prediction models on a large corpus of Java projects containing about 23,000 classes demonstrate the Mean Absolute Error (MAE) of 0.032, Mean Squared Error (MSE) of 0.004, and an R2-score of 0.855. Compared with the state-of-the-art coverage prediction models, our models improve MAE, MSE, and an R2-score by 5.78%, 2.84%, and 20.71%, respectively.

Highlights: Welcome back to our new Machine Learning series. In the previous post, we studied all about Linear Regression, Cost Functions and Gradient Descent. We also built a simple Linear Regression model using Python. In this tutorial post, we will learn how to make our Linear Regression model faster and more powerful. We will start by building a Linear Regression model using multiple features and then, enhance its performance using various techniques. And finally, we'll implement what we learn about Multiple Linear Regression models using a simple code in Python. In our previous post, we studied an example for predicting the price of a house given the size of the house. In that particular example, we worked with the original version of Linear Regression which utilized only a single feature \(x \), the size of the house, in order to predict \(y \), the price of the house.

This study showed that the machine learning-based model has a higher predictive ability than the conventional logistic regression model and may be …

You're looking for a complete Linear Regression and Logistic Regression course that teaches you everything you need to create a Linear or Logistic Regression model in Python, right? You've found the right Linear Regression course! A Verifiable Certificate of Completion is presented to all students who undertake this Machine learning basics course. What is covered in this course? This course teaches you all the steps of creating a Linear Regression model, which is the most popular Machine Learning model, to solve business problems.

In this paper, we consider the meta learning problem for estimating the graphs associated with high-dimensional Ising models, using the method of $\ell_1$-regularized logistic regression for neighborhood selection of each node. Our goal is to use the information learned from the auxiliary tasks in the learning of the novel task to reduce its sufficient sample complexity. To this end, we propose a novel generative model as well as an improper estimation method. In our setting, all the tasks are \emph{similar} in their \emph{random} model parameters and supports. By pooling all the samples from the auxiliary tasks to \emph{improperly} estimate a single parameter vector, we can recover the true support union, assumed small in size, with a high probability with a sufficient sample complexity of $\Omega(1) $ per task, for $K = \Omega(d^3 \log p ) $ tasks of Ising models with $p$ nodes and a maximum neighborhood size $d$. Then, with the support for the novel task restricted to the estimated support union, we prove that consistent neighborhood selection for the novel task can be obtained with a reduced sufficient sample complexity of $\Omega(d^3 \log d)$.