Fortunately numbers are the dimensions of the k-th persistent homology there are many such suitable options, one option is the parameterized by the threshold r. p-Wasserstein distance with p > 0 being a parameter. Especially when p =, we call the -Wasserstein distance More than just counting topological structures with the bottleneck distance. We skip the exact definition of persistent Betti numbers, we can detect at which threshold p-Wasserstein distance here since it is too technical, the values a topological structure is born and dead.

The increasing digitalization in industry and society leads to a growing abundance of data available to be processed and exploited. However, the high volume of data requires considerable computational resources for applying machine learning approaches. Prototype selection techniques have been applied to reduce the requirements of computational resources that are needed by these techniques. In this paper, we propose an approach for speeding up existing prototype selection techniques. It builds an abstract representation of the dataset, using the notion of spatial partition. The second step uses this abstract representation to prune the search space efficiently and select a set of candidate prototypes. After, some conventional prototype selection algorithms can be applied to the candidates selected by our approach. Our approach was integrated with five conventional prototype selection algorithms and tested on 14 widely recognized datasets used in classification tasks. The performance of the modified algorithms was compared to that of their original versions in terms of accuracy and reduction rate. The experimental results demonstrate that, overall, our proposed approach maintains accuracy while enhancing the reduction rate of the original prototype selection algorithms and simultaneously reducing their execution times.

This paper measures the skew in how well two families of LLMs represent diverse geographic populations. A spatial probing task is used with geo-referenced corpora to measure the degree to which pre-trained language models from the opt and bloom series represent diverse populations around the world. Results show that these models perform much better for some populations than others. In particular, populations across the US and the UK are represented quite well while those in South and Southeast Asia are poorly represented. Analysis shows that both families of models largely share the same skew across populations. At the same time, this skew cannot be fully explained by sociolinguistic factors, economic factors, or geographic factors. The basic conclusion from this analysis is that pre-trained models do not equally represent the world's population: there is a strong skew towards specific geographic populations. This finding challenges the idea that a single model can be used for all populations.

In recent years, the gripping use of unmanned aerial vehicles (UAVs) has emerged as a new trending research direction [1, 2]. However, the grabbing scenes in the open world are very complex, which leads to the development of robotic grasping systems with advanced cognitive and adaptable grasping capabilities. To achieve high-level cognitive abilities, reinforcement learning embodiment is studied[3, 4]. In [3], Scalable Deep Reinforcement Learning is used to handle large amounts of off-policy image data for complex tasks like grasping. However, RL-based embodiment has posed challenges in terms of generalization capability, sample-effectiveness capability, and profound reasoning capability, especially in dynamic and uncertain real environments. Recently, Large multimodal models (LMMs), such as MiniGPT-4 [5] and LLaVA [6], have exhibited impressive performance in the domains of natural instruction-following and visual cognition. Therefore, LMMs are integrated with the physical world in the embodied agent. Apart from RL algorithms for specific tasks, LMMs-based agents have generalization capabilities [7, 8] though fine-tune methods, such as human demonstrations [9], vision-language cross-modal connector[10], ever-growing skill library [11] and so on. On-policy (RL) algorithms face challenges in terms of sample efficiency.

The proliferation of digital images and the advancements in deep learning have paved the way for innovative solutions in various domains, especially in the field of image classification. Our project presents an in-depth study and implementation of an image classification system specifically tailored to identify and classify images of Indian cities. Drawing from an extensive dataset, our model classifies images into five major Indian cities: Ahmedabad, Delhi, Kerala, Kolkata, and Mumbai to recognize the distinct features and characteristics of each city/state. To achieve high precision and recall rates, we adopted two approaches. The first, a vanilla Convolutional Neural Network (CNN) and then we explored the power of transfer learning by leveraging the VGG16 model. The vanilla CNN achieved commendable accuracy and the VGG16 model achieved a test accuracy of 63.6%. Evaluations highlighted the strengths and potential areas of improvement, positioning our model as not only competitive but also scalable for broader applications. With an emphasis on open-source ethos, our work aims to contribute to the community, encouraging further development and diverse applications. Our findings demonstrate the potential applications in tourism, urban planning, and even real-time location identification systems, among others.

Estimating 3D pose from monocular images is a highly ambiguous problem. Physical constraints can be exploited to restrict the space of feasible configurations. In this paper we propose an approach to constraining the prediction of a discriminative predictor. We first show that the mean prediction of a Gaussian process implicitly satisfies linear constraints if those constraints are satisfied by the training examples. We then show how, by performing a change of variables, a GP can be forced to satisfy quadratic constraints. As evidenced by the experiments, our method outperforms state-of-the-art approaches on the tasks of rigid and non-rigid pose estimation.

As increasing amounts of sensitive personal information finds its way into data repositories, it is important to develop analysis mechanisms that can derive aggregate information from these repositories without revealing information about individual data instances. Though the differential privacy model provides a framework to analyze such mechanisms for databases belonging to a single party, this framework has not yet been considered in a multi-party setting. In this paper, we propose a privacy-preserving protocol for composing a differentially private aggregate classifier using classifiers trained locally by separate mutually untrusting parties. The protocol allows these parties to interact with an untrusted curator to construct additive shares of a perturbed aggregate classifier. We also present a detailed theoretical analysis containing a proof of differential privacy of the perturbed aggregate classifier and a bound on the excess risk introduced by the perturbation. We verify the bound with an experimental evaluation on a real dataset.

In this paper, we point out that there exist scaling and initialization problems in most existing multiple kernel learning (MKL) approaches, which employ the large margin principle to jointly learn both a kernel and an SVM classifier. The reason is that the margin itself can not well describe how good a kernel is due to the negligence of the scaling. We use the ratio between the margin and the radius of the minimum enclosing ball to measure the goodness of a kernel, and present a new minimization formulation for kernel learning. This formulation is invariant to scalings of learned kernels, and when learning linear combination of basis kernels it is also invariant to scalings of basis kernels and to the types (e.g., L

We consider multi-task learning in the setting of multiple linear regression, and where some relevant features could be shared across the tasks.

In Tanzania, farmers are using an AI-assisted app that works in their native language of Swahili to detect a devastating cassava disease before it spreads. In South Africa, computer scientists have built machine learning models to analyze the impact of racial segregation in housing. And in Nairobi, Kenya, AI classifies images from thousands of surveillance cameras perched on lampposts in the bustling city's center. The projected benefit of AI adoption on Africa's economy is tantalizing. Estimates suggest that four African countries alone--Nigeria, Ghana, Kenya, and South Africa--could rake in up to 136 billion worth of economic benefits by 2030 if businesses there begin using more AI tools.