This article belongs to the series "Probabilistic Deep Learning". This weekly series covers probabilistic approaches to deep learning. The main goal is to extend deep learning models to quantify uncertainty, i.e., know what they do not know. In this article, we will introduce the concept of probabilistic logistic regression, a powerful technique that allows for the inclusion of uncertainty in the prediction process. We will explore how this approach can lead to more robust and accurate predictions, especially in cases where the data is noisy, or the model is overfitting.

Machine learning and deep learning play vital roles in predicting diseases in the medical field. Machine learning algorithms are widely classified as supervised, unsupervised, and reinforcement learning. This paper contains a detailed description of our experimental research work in that we used a supervised machine-learning algorithm to build our model for outbreaks of the novel Coronavirus that has spread over the whole world and caused many deaths, which is one of the most disastrous Pandemics in the history of the world. The people suffered physically and economically to survive in this lockdown. This work aims to understand better how machine learning, ensemble, and deep learning models work and are implemented in the real dataset. In our work, we are going to analyze the current trend or pattern of the coronavirus and then predict the further future of the covid-19 confirmed cases or new cases by training the past Covid-19 dataset by using the machine learning algorithm such as Linear Regression, Polynomial Regression, K-nearest neighbor, Decision Tree, Support Vector Machine and Random forest algorithm are used to train the model. The decision tree and the Random Forest algorithm perform better than SVR in this work. The performance of SVR and lasso regression are low in all prediction areas Because the SVR is challenging to separate the data using the hyperplane for this type of problem. So SVR mostly gives a lower performance in this problem. Ensemble (Voting, Bagging, and Stacking) and deep learning models(ANN) also predict well. After the prediction, we evaluated the model using MAE, MSE, RMSE, and MAPE. This work aims to find the trend/pattern of the covid-19.

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.

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.

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.

Coral reefs play a vital role in maintaining the ecological balance of the marine ecosystem. Various marine organisms depend on coral reefs for their existence and their natural processes. Coral reefs provide the necessary habitat for reproduction and growth for various exotic species of the marine ecosystem. In this article, we discuss the most important parameters which influence the lifecycle of coral and coral reefs such as ocean acidification, deoxygenation and other physical parameters such as flow rate and surface area. Ocean acidification depends on the amount of dissolved Carbon dioxide (CO2). This is due to the release of H+ ions upon the reaction of the dissolved CO2 gases with the calcium carbonate compounds in the ocean. Deoxygenation is another problem that leads to hypoxia which is characterized by a lesser amount of dissolved oxygen in water than the required amount for the existence of marine organisms. In this article, we highlight the importance of physical parameters such as flow rate which influence gas exchange, heat dissipation, bleaching sensitivity, nutrient supply, feeding, waste and sediment removal, growth and reproduction. In this paper, we also bring out these important parameters and propose an ensemble machine learning-based model for analyzing these parameters and provide better rates that can help us to understand and suitably improve the ocean composition which in turn can eminently improve the sustainability of the marine ecosystem, mainly the coral reefs

This work demonstrates how mixed effects random forests enable accurate predictions of depression severity using multimodal physiological and digital activity data collected from an 8-week study involving 31 patients with major depressive disorder. We show that mixed effects random forests outperform standard random forests and personal average baselines when predicting clinical Hamilton Depression Rating Scale scores (HDRS_17). Compared to the latter baseline, accuracy is significantly improved for each patient by an average of 0.199-0.276 in terms of mean absolute error (p<0.05). This is noteworthy as these simple baselines frequently outperform machine learning methods in mental health prediction tasks. We suggest that this improved performance results from the ability of the mixed effects random forest to personalise model parameters to individuals in the dataset. However, we find that these improvements pertain exclusively to scenarios where labelled patient data are available to the model at training time. Investigating methods that improve accuracy when generalising to new patients is left as important future work.

This paper introduces FlexCodeTS, a new conditional density estimator for time series. FlexCodeTS is a flexible nonparametric conditional density estimator, which can be based on an arbitrary regression method. It is shown that FlexCodeTS inherits the rate of convergence of the chosen regression method. Hence, FlexCodeTS can adapt its convergence by employing the regression method that best fits the structure of data. From an empirical perspective, FlexCodeTS is compared to NNKCDE and GARCH in both simulated and real data. FlexCodeTS is shown to generally obtain the best performance among the selected methods according to either the CDE loss or the pinball loss.