This research enhances linear regression models by integrating a Kalman filter and analysing curve areas to minimize loss. The goal is to develop an optimal linear regression equation using stochastic gradient descent (SGD) for weight updating. Our approach involves a stepwise process, starting with user-defined parameters. The linear regression model is trained using SGD, tracking weights and loss separately and zipping them finally. A Kalman filter is then trained based on weight and loss arrays to predict the next consolidated weights. Predictions result from multiplying input averages with weights, evaluated for loss to form a weight-versus-loss curve. The curve's equation is derived using the two-point formula, and area under the curve is calculated via integration. The linear regression equation with minimum area becomes the optimal curve for prediction. Benefits include avoiding constant weight updates via gradient descent and working with partial datasets, unlike methods needing the entire set. However, computational complexity should be considered. The Kalman filter's accuracy might diminish beyond a certain prediction range.

This work presents a generative modeling approach based on successive subspace learning (SSL). Unlike most generative models in the literature, our method does not utilize neural networks to analyze the underlying source distribution and synthesize images. The resulting method, called the progressive attribute-guided extendable robust image generative (PAGER) model, has advantages in mathematical transparency, progressive content generation, lower training time, robust performance with fewer training samples, and extendibility to conditional image generation. PAGER consists of three modules: core generator, resolution enhancer, and quality booster. The core generator learns the distribution of low-resolution images and performs unconditional image generation. The resolution enhancer increases image resolution via conditional generation. Finally, the quality booster adds finer details to generated images. Extensive experiments on MNIST, Fashion-MNIST, and CelebA datasets are conducted to demonstrate generative performance of PAGER.

In the agricultural sector, the COVID-19 threatens to lead to a severe food security crisis in the region, with disruptions in the food supply chain and agricultural production expected to contract between 2.6% and 7%. From the food crop production side, the travel bans and border closures, the late reception and the use of agricultural inputs such as imported seeds, fertilizers, and pesticides could lead to poor food crop production performances. Another layer of disruption introduced by the mobility restriction measures is the scarcity of agricultural workers, mainly seasonal workers. The lockdown measures and border closures limit seasonal workers' availability to get to the farm on time for planting and harvesting activities. Moreover, most of the imported agricultural inputs travel by air, which the pandemic has heavily impacted. Such transportation disruptions can also negatively affect the food crop production system. This chapter assesses food crop production levels in 2020 -- before the harvesting period -- in all African regions and four staples such as maize, cassava, rice, and wheat. The production levels are predicted using the combination of biogeophysical remote sensing data retrieved from satellite images and machine learning artificial neural networks (ANNs) technique. The remote sensing products are used as input variables and the ANNs as the predictive modeling framework. The input remote sensing products are the Normalized Difference Vegetation Index (NDVI), the daytime Land Surface Temperature (LST), rainfall data, and agricultural lands' Evapotranspiration (ET). The output maps and data are made publicly available on a web-based platform, AAgWa (Africa Agriculture Watch, www.aagwa.org), to facilitate access to such information to policymakers, deciders, and other stakeholders.

Topological learning is a wide research area aiming at uncovering the mutual spatial relationships between the elements of a set. Some of the most common and oldest approaches involve the use of unsupervised competitive neural networks. However, these methods are not based on gradient optimization which has been proven to provide striking results in feature extraction also in unsupervised learning. Unfortunately, by focusing mostly on algorithmic efficiency and accuracy, deep clustering techniques are composed of overly complex feature extractors, while using trivial algorithms in their top layer. The aim of this work is to present a novel comprehensive theory aspiring at bridging competitive learning with gradient-based learning, thus allowing the use of extremely powerful deep neural networks for feature extraction and projection combined with the remarkable flexibility and expressiveness of competitive learning. In this paper we fully demonstrate the theoretical equivalence of two novel gradient-based competitive layers. Preliminary experiments show how the dual approach, trained on the transpose of the input matrix i.e. $X^T$, lead to faster convergence rate and higher training accuracy both in low and high-dimensional scenarios.