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.

Earthquake prediction has been a challenging research area for many decades, where the future occurrence of this highly uncertain calamity is predicted. In this paper, several parametric and non-parametric features were calculated, where the non-parametric features were calculated using the parametric features. $8$ seismic features were calculated using Gutenberg-Richter law, the total recurrence, and the seismic energy release. Additionally, criterions such as Maximum Relevance and Maximum Redundancy were applied to choose the pertinent features. These features along with others were used as input for an Extreme Learning Machine (ELM) Regression Model. Magnitude and time data of $5$ decades from the Assam-Guwahati region were used to create this model for magnitude prediction. The Testing Accuracy and Testing Speed were computed taking the Root Mean Squared Error (RMSE) as the parameter for evaluating the mode. As confirmed by the results, ELM shows better scalability with much faster training and testing speed (up to a thousand times faster) than traditional Support Vector Machines. The testing RMSE came out to be around $0.097$. To further test the model's robustness -- magnitude-time data from California was used to calculate the seismic indicators which were then fed into an ELM and then tested on the Assam-Guwahati region. The model proves to be robust and can be implemented in early warning systems as it continues to be a major part of Disaster Response and management.

Federated learning is a distributed machine learning paradigm that collaboratively trains a model with data on many clients. Unlike traditional distributed machine learning methods, which partition data into different clients to improve the efficiency of the learning algorithm, the goal of federated learning is to solve the learning problem without requiring the clients to reveal too much local information. With the increasing demand for data security and privacy protection, federated learning has received significant attention in both industry and academia. For example, banks want to collaboratively train a credit card scoring model without disclosing information about their customers, or hospitals want to carry out researches on a rare disease with each other due to the small number of sample cases, but they can't expose their patients' identity. For more on the progress of federated learning, see [1, 2]. The term federated learning was introduced by McMahan et al. [3], they also proposed the Federated Averaging(FedAvg) algorithm. FedAvg composes multiple rounds of local stochastic gradient descent updates and server-side averaging aggregation to train a centralized model.

Structural health monitoring is important to make sure bridges do not fail. Since direct monitoring can be complicated and expensive, indirect methods have been a focus on research. Indirect monitoring can be much cheaper and easier to conduct, however there are challenges with getting accurate results. This work focuses on damage quantification by using accelerometers. Tests were conducted on a model bridge and car with four accelerometers attached to to the vehicle. Different weights were placed on the bridge to simulate different levels of damage, and 31 tests were run for 20 different damage levels. The acceleration data collected was normalized and a Fast-Fourier Transform (FFT) was performed on that data. Both the normalized acceleration data and the normalized FFT data were inputted into a Non-Linear Principal Component Analysis (separately) and three principal components were extracted for each data set. Support Vector Regression (SVR) and Gaussian Process Regression (GPR) were used as the supervised machine learning methods to develop models. Multiple models were created so that the best one could be selected, and the models were compared by looking at their Mean Squared Errors (MSE). This methodology should be applied in the field to measure how effective it can be in real world applications.

The Victoria Amazonica plant, often known as the Giant Water Lily, has the largest floating spherical leaf in the world, with a maximum leaf diameter of 3 meters. It spreads its leaves by the force of its spines and creates a large shadow underneath, killing any plants that require sunlight. These water tyrants use their formidable spines to compel each other to the surface and increase their strength to grab more space from the surface. As they spread throughout the pond or basin, with the earliest-growing leaves having more room to grow, each leaf gains a unique size. Its flowers are transsexual and when they bloom, Cyclocephala beetles are responsible for the pollination process, being attracted to the scent of the female flower. After entering the flower, the beetle becomes covered with pollen and transfers it to another flower for fertilization. After the beetle leaves, the flower turns into a male and changes color from white to pink. The male flower dies and sinks into the water, releasing its seed to help create a new generation. In this paper, the mathematical life cycle of this magnificent plant is introduced, and each leaf and blossom are treated as a single entity. The proposed bio-inspired algorithm is tested with 24 benchmark optimization test functions, such as Ackley, and compared to ten other famous algorithms, including the Genetic Algorithm. The proposed algorithm is tested on 10 optimization problems: Minimum Spanning Tree, Hub Location Allocation, Quadratic Assignment, Clustering, Feature Selection, Regression, Economic Dispatching, Parallel Machine Scheduling, Color Quantization, and Image Segmentation and compared to traditional and bio-inspired algorithms. Overall, the performance of the algorithm in all tasks is satisfactory.