We present a variety of projection-based linear regression algorithms with a focus on modern machine-learning models and their algorithmic performance. We study the role of the relaxation parameter in generalized Kaczmarz algorithms and establish a priori regret bounds with explicit $λ$-dependence to quantify how much an algorithm's performance deviates from its optimal performance. A detailed analysis of relaxation parameter is also provided. Applications include: explicit regret bounds for the framework of Kaczmarz algorithm models, non-orthogonal Fourier expansions, and the use of regret estimates in modern machine learning models, including for noisy data, i.e., regret bounds for the noisy Kaczmarz algorithms. Motivated by machine-learning practice, our wider framework treats bounded operators (on infinite-dimensional Hilbert spaces), with updates realized as (block) Kaczmarz algorithms, leading to new and versatile results.

This study presents the application of generative deep learning techniques to evaluate marine fog visibility nowcasting using the FATIMA (Fog and turbulence interactions in the marine atmosphere) campaign observations collected during July 2022 in the North Atlantic in the Grand Banks area and vicinity of Sable Island (SI), northeast of Canada. The measurements were collected using the Vaisala Forward Scatter Sensor model FD70 and Weather Transmitter model WXT50, and Gill R3A ultrasonic anemometer mounted on the Research Vessel Atlantic Condor. To perform nowcasting, the time series of fog visibility (Vis), wind speed, dew point depression, and relative humidity with respect to water were preprocessed to have lagged time step features. Generative nowcasting of Vis time series for lead times of 30 and 60 minutes were performed using conditional generative adversarial networks (cGAN) regression at visibility thresholds of Vis < 1 km and < 10 km. Extreme gradient boosting (XGBoost) was used as a baseline method for comparison against cGAN. At the 30 min lead time, Vis was best predicted with cGAN at Vis < 1 km (RMSE = 0.151 km) and with XGBoost at Vis < 10 km (RMSE = 2.821 km). At the 60 min lead time, Vis was best predicted with XGBoost at Vis < 1 km (RMSE = 0.167 km) and Vis < 10 km (RMSE = 3.508 km), but the cGAN RMSE was similar to XGBoost. Despite nowcasting Vis at 30 min being quite difficult, the ability of the cGAN model to track the variation in Vis at 1 km suggests that there is potential for generative analysis of marine fog visibility using observational meteorological parameters.

Since the launch of applications such as DALL-E, Midjourney, and Stable Diffusion, generative artificial intelligence has been controversial as a tool for creating artwork. While some have presented longtermist worries about these technologies as harbingers of fully automated futures to come, more pressing is the impact of generative AI on creative labour in the present. Already, business leaders have begun replacing human artistic labour with AI-generated images. In response, the artistic community has launched a protest movement, which argues that AI image generation is a kind of theft. This paper analyzes, substantiates, and critiques these arguments, concluding that AI image generators involve an unethical kind of labour theft. If correct, many other AI applications also rely upon theft.

Motivated by applications, we consider here new operator theoretic approaches to Conditional mean embeddings (CME). Our present results combine a spectral analysis-based optimization scheme with the use of kernels, stochastic processes, and constructive learning algorithms. For initially given non-linear data, we consider optimization-based feature selections. This entails the use of convex sets of positive definite (p.d.) kernels in a construction of optimal feature selection via regression algorithms from learning models. Thus, with initial inputs of training data (for a suitable learning algorithm,) each choice of p.d. kernel $K$ in turn yields a variety of Hilbert spaces and realizations of features. A novel idea here is that we shall allow an optimization over selected sets of kernels $K$ from a convex set $C$ of positive definite kernels $K$. Hence our \textquotedblleft optimal\textquotedblright{} choices of feature representations will depend on a secondary optimization over p.d. kernels $K$ within a specified convex set $C$.

In this paper we show how specific families of positive definite kernels serve as powerful tools in analyses of iteration algorithms for multiple layer feedforward Neural Network models. Our focus is on particular kernels that adapt well to learning algorithms for data-sets/features which display intrinsic self-similarities at feedforward iterations of scaling.

For several years till date, the major issues in terms of solving for classification problems are the issues of Imbalanced data. Because majority of the machine learning algorithms by default assumes all data are balanced, the algorithms do not take into consideration the distribution of the data sample class. The results tend to be unsatisfactory and skewed towards the majority sample class distribution. This implies that the consequences as a result of using a model built using an Imbalanced data without handling for the Imbalance in the data could be misleading both in practice and theory. Most researchers have focused on the application of Synthetic Minority Oversampling Technique (SMOTE) and Adaptive Synthetic (ADASYN) Sampling Approach in handling data Imbalance independently in their works and have failed to better explain the algorithms behind these techniques with computed examples. This paper focuses on both synthetic oversampling techniques and manually computes synthetic data points to enhance easy comprehension of the algorithms. We analyze the application of these synthetic oversampling techniques on binary classification problems with different Imbalanced ratios and sample sizes.

The universal approximation theorem established the density of specific families of neural networks in the space of continuous functions and in certain Bochner spaces, defined between any two Euclidean spaces. We extend and refine this result by proving that there exist dense neural network architectures on a larger class of function spaces and that these architectures may be written down using only a small number of functions. We prove that upon appropriately randomly selecting the neural networks architecture's activation function we may still obtain a dense set of neural networks, with positive probability. This result is used to overcome the difficulty of appropriately selecting an activation function in more exotic architectures. Conversely, we show that given any neural network architecture on a set of continuous functions between two T0 topological spaces, there exists a unique finest topology on that set of functions which makes the neural network architecture into a universal approximator. Several examples are considered throughout the paper.

Waste management is one of the significant problems throughout the world. Contemporaneous methods find it difficult to manage the volume of solid waste generated by the growing urban population. In this paper, we propose a system which is very hygienic and cheap that uses Artificial Intelligence algorithms for detection of the garbage. Once the garbage is detected the system calculates the position of the garbage by the use of the camera only. The proposed system is capable of distinguishing between valuables and garbage with more than 95% confidence in real time. Finally, a robotic arm controlled by the microcontroller is used to pick up the garbage and places it in the bin. Concluding, the paper explains a system that is capable of working as a human in terms of inspecting and collecting the garbage. The system is able to achieve 3-4 frames per second on the Raspberry Pi, capable of detecting the garbage in real time with 90%+ confidence.

A multi-robot system, like a robot formation, contains information that is distributed throughout the system. As the collective increases in numbers or explores distant or difficult areas, obtaining collective situational awareness becomes critical. We propose a method for extracting system and environmental information distributed over a collective of robots.

The field of multi-robot coordination, specifically robot formation control, is rapidly expanding, with many applications proposed. In our previous work, we considered the problem of establishing and maintaining a formation of robots given an already connected network. We now propose a distributed auction-based method to autonomously initialize and reorganize the network structure of a formation of robots.