Regression is a statistical method used to analyze the relationship between one or more independent variables and a continuous dependent variable. It can be used to predict the value of the dependent variable based on the values of the independent variables. Linear regression is the most common type of regression and is used when the relationship between the variables is linear. Non-linear regression is used when the relationship between the variables is non-linear. Other types of regression include logistic regression, which is used when the dependent variable is binary, and polynomial regression, which is used when the relationship between the variables is non-linear but can be modeled by a polynomial equation.

Recently I have written an article about the risks of using the train_test_split() function provided by the scikit-learn Python package. That article has raised a lot of comments, some positives, and others with some concerns. The main concern in the article was that I used a small dataset to demonstrate my theory, which was: be careful when you use the train_test_split() function, because the different seeds may produce very different models. The main concern was that the train_test_split() function does not behave strangely; the problem is that I used a small dataset to demonstrate my thesis. In this article, I try to discover which is the performance of a Linear Regression model by varying the dataset size.

Logistic regression can be understood as a technique used in both traditional statistics and machine learning.

Actionable Knowledge Discovery (AKD) is a crucial aspect of data mining that is gaining popularity and being applied in a wide range of domains. This is because AKD can extract valuable insights and information, also known as knowledge, from large datasets. The goal of this paper is to examine different research studies that focus on various domains and have different objectives. The paper will review and discuss the methods used in these studies in detail. AKD is a process of identifying and extracting actionable insights from data, which can be used to make informed decisions and improve business outcomes. It is a powerful tool for uncovering patterns and trends in data that can be used for various applications such as customer relationship management, marketing, and fraud detection. The research studies reviewed in this paper will explore different techniques and approaches for AKD in different domains, such as healthcare, finance, and telecommunications. The paper will provide a thorough analysis of the current state of AKD in the field and will review the main methods used by various research studies. Additionally, the paper will evaluate the advantages and disadvantages of each method and will discuss any novel or new solutions presented in the field. Overall, this paper aims to provide a comprehensive overview of the methods and techniques used in AKD and the impact they have on different domains.

In this paper, we propose a kernel principal component analysis model for multi-variate time series forecasting, where the training and prediction schemes are derived from the multi-view formulation of Restricted Kernel Machines. The training problem is simply an eigenvalue decomposition of the summation of two kernel matrices corresponding to the views of the input and output data. When a linear kernel is used for the output view, it is shown that the forecasting equation takes the form of kernel ridge regression. When that kernel is non-linear, a pre-image problem has to be solved to forecast a point in the input space. We evaluate the model on several standard time series datasets, perform ablation studies, benchmark with closely related models and discuss its results.

Online dimension reduction is a common method for high-dimensional streaming data processing. Online principal component analysis, online sliced inverse regression, online kernel principal component analysis and other methods have been studied in depth, but as far as we know, online supervised nonlinear dimension reduction methods have not been fully studied. In this article, an online kernel sliced inverse regression method is proposed. By introducing the approximate linear dependence condition and dictionary variable sets, we address the problem of increasing variable dimensions with the sample size in the online kernel sliced inverse regression method, and propose a reduced-order method for updating variables online. We then transform the problem into an online generalized eigen-decomposition problem, and use the stochastic optimization method to update the centered dimension reduction directions. Simulations and the real data analysis show that our method can achieve close performance to batch processing kernel sliced inverse regression.

This paper improves the state-of-the-art rate of a first-order algorithm for solving entropy regularized optimal transport. The resulting rate for approximating the optimal transport (OT) has been improved from $\widetilde{{O}}({n^{2.5}}/{\epsilon})$ to $\widetilde{{O}}({n^2}/{\epsilon})$, where $n$ is the problem size and $\epsilon$ is the accuracy level. In particular, we propose an accelerated primal-dual stochastic mirror descent algorithm with variance reduction. Such special design helps us improve the rate compared to other accelerated primal-dual algorithms. We further propose a batch version of our stochastic algorithm, which improves the computational performance through parallel computing. To compare, we prove that the computational complexity of the Stochastic Sinkhorn algorithm is $\widetilde{{O}}({n^2}/{\epsilon^2})$, which is slower than our accelerated primal-dual stochastic mirror algorithm. Experiments are done using synthetic and real data, and the results match our theoretical rates. Our algorithm may inspire more research to develop accelerated primal-dual algorithms that have rate $\widetilde{{O}}({n^2}/{\epsilon})$ for solving OT.

The last decade, (2012 - 2022), saw an unprecedented advance in machine learning (ML) techniques, particularly deep learning (DL). As a result of the proven capabilities of DL, a large amount of work has been presented and studied in almost every field. Since 2012, when the convolution neural networks have been reintroduced in the context of \textit{ImagNet} competition, DL continued to achieve superior performance in many challenging tasks and problems. Wireless communications, in general, and medium access control (MAC) techniques, in particular, were among the fields that were heavily affected by this improvement. MAC protocols play a critical role in defining the performance of wireless communication systems. At the same time, the community lacks a comprehensive survey that collects, analyses, and categorizes the recent work in ML-inspired MAC techniques. In this work, we fill this gap by surveying a long line of work in this era. We solidify the impact of machine learning on wireless MAC protocols. We provide a comprehensive background to the widely adopted MAC techniques, their design issues, and their taxonomy, in connection with the famous application domains. Furthermore, we provide an overview of the ML techniques that have been considered in this context. Finally, we augment our work by proposing some promising future research directions and open research questions that are worth further investigation.

Discovering a meaningful symbolic expression that explains experimental data is a fundamental challenge in many scientific fields. We present a novel, open-source computational framework called Scientist-Machine Equation Detector (SciMED), which integrates scientific discipline wisdom in a scientist-in-the-loop approach, with state-of-the-art symbolic regression (SR) methods. SciMED combines a wrapper selection method, that is based on a genetic algorithm, with automatic machine learning and two levels of SR methods. We test SciMED on five configurations of a settling sphere, with and without aerodynamic non-linear drag force, and with excessive noise in the measurements. We show that SciMED is sufficiently robust to discover the correct physically meaningful symbolic expressions from the data, and demonstrate how the integration of domain knowledge enhances its performance. Our results indicate better performance on these tasks than the state-of-the-art SR software packages , even in cases where no knowledge is integrated. Moreover, we demonstrate how SciMED can alert the user about possible missing features, unlike the majority of current SR systems.

We discuss the prediction accuracy of assumed statistical models in terms of prediction errors for the generalized linear model and penalized maximum likelihood methods. We derive the forms of estimators for the prediction errors, such as $C_p$ criterion, information criteria, and leave-one-out cross validation (LOOCV) error, using the generalized approximate message passing (GAMP) algorithm and replica method. These estimators coincide with each other when the number of model parameters is sufficiently small; however, there is a discrepancy between them in particular in the parameter region where the number of model parameters is larger than the data dimension. In this paper, we review the prediction errors and corresponding estimators, and discuss their differences. In the framework of GAMP, we show that the information criteria can be expressed by using the variance of the estimates. Further, we demonstrate how to approach LOOCV error from the information criteria by utilizing the expression provided by GAMP.