Collecting data is a significant challenge in machine learning, and more generally in statistics. The amount of data necessary to get a sharp estimation of a function can get unreasonably high, especially when the task involves highdimensional objects. In various applications, extracting and gathering enough unlabeled data is not a big challenge. However, labeling them can be a very costly and time-consuming process. In fields such as statistical physics, we would often need to run complex simulations or call an expert to label data manually. Hence we want to be able to get a satisfying estimation with a more compact set of labeled data. Among the proposed solutions, we can mention fewshot learning (Li et al., 2006) and transfer learning (Ben-David et al., 2010). Those solutions leverage from another model previously trained on a similar task to simplify our model's training. To dodge the issue, we can also resort to generative adversarial models (Goodfellow et al., 2014) or diffusion models (Trabucco et al., 2023): the idea is to augment a dataset using generated data,

Mobile Internet user credit assessment is an important way for communication operators to establish decisions and formulate measures, and it is also a guarantee for operators to obtain expected benefits. However, credit evaluation methods have long been monopolized by financial industries such as banks and credit. As supporters and providers of platform network technology and network resources, communication operators are also builders and maintainers of communication networks. Internet data improves the user's credit evaluation strategy. This paper uses the massive data provided by communication operators to carry out research on the operator's user credit evaluation model based on the fusion LightGBM algorithm. First, for the massive data related to user evaluation provided by operators, key features are extracted by data preprocessing and feature engineering methods, and a multi-dimensional feature set with statistical significance is constructed; then, linear regression, decision tree, LightGBM, and other machine learning algorithms build multiple basic models to find the best basic model; finally, integrates Averaging, Voting, Blending, Stacking and other integrated algorithms to refine multiple fusion models, and finally establish the most suitable fusion model for operator user evaluation.

In this work, we study the problem of common and unique feature extraction from noisy data. When we have N observation matrices from N different and associated sources corrupted by sparse and potentially gross noise, can we recover the common and unique components from these noisy observations? This is a challenging task as the number of parameters to estimate is approximately thrice the number of observations. Despite the difficulty, we propose an intuitive alternating minimization algorithm called triple component matrix factorization (TCMF) to recover the three components exactly. TCMF is distinguished from existing works in literature thanks to two salient features. First, TCMF is a principled method to separate the three components given noisy observations provably. Second, the bulk of the computation in TCMF can be distributed. On the technical side, we formulate the problem as a constrained nonconvex nonsmooth optimization problem. Despite the intricate nature of the problem, we provide a Taylor series characterization of its solution by solving the corresponding Karush-Kuhn-Tucker conditions. Using this characterization, we can show that the alternating minimization algorithm makes significant progress at each iteration and converges into the ground truth at a linear rate. Numerical experiments in video segmentation and anomaly detection highlight the superior feature extraction abilities of TCMF.

In this article, we address the problem of federated learning in the presence of stragglers. For this problem, a coded federated learning framework has been proposed, where the central server aggregates gradients received from the non-stragglers and gradient computed from a privacy-preservation global coded dataset to mitigate the negative impact of the stragglers. However, when aggregating these gradients, fixed weights are consistently applied across iterations, neglecting the generation process of the global coded dataset and the dynamic nature of the trained model over iterations. This oversight may result in diminished learning performance. To overcome this drawback, we propose a new method named adaptive coded federated learning (ACFL). In ACFL, before the training, each device uploads a coded local dataset with additive noise to the central server to generate a global coded dataset under privacy preservation requirements. During each iteration of the training, the central server aggregates the gradients received from the non-stragglers and the gradient computed from the global coded dataset, where an adaptive policy for varying the aggregation weights is designed. Under this policy, we optimize the performance in terms of privacy and learning, where the learning performance is analyzed through convergence analysis and the privacy performance is characterized via mutual information differential privacy. Finally, we perform simulations to demonstrate the superiority of ACFL compared with the non-adaptive methods.

Early detection plays a crucial role in the treatment of depression. Therefore, numerous studies have focused on social media platforms, where individuals express their emotions, aiming to achieve early detection of depression. However, the majority of existing approaches often rely on specific features, leading to limited scalability across different types of social media datasets, such as text, images, or videos. To overcome this limitation, we introduce a Multimodal Object-Oriented Graph Attention Model (MOGAM), which can be applied to diverse types of data, offering a more scalable and versatile solution. Furthermore, to ensure that our model can capture authentic symptoms of depression, we only include vlogs from users with a clinical diagnosis. To leverage the diverse features of vlogs, we adopt a multimodal approach and collect additional metadata such as the title, description, and duration of the vlogs. To effectively aggregate these multimodal features, we employed a cross-attention mechanism. MOGAM achieved an accuracy of 0.871 and an F1-score of 0.888. Moreover, to validate the scalability of MOGAM, we evaluated its performance with a benchmark dataset and achieved comparable results with prior studies (0.61 F1-score). In conclusion, we believe that the proposed model, MOGAM, is an effective solution for detecting depression in social media, offering potential benefits in the early detection and treatment of this mental health condition.

This study employs the Causal Machine Learning (CausalML) statistical method to analyze the influence of electricity pricing policies on carbon dioxide (CO2) levels in the household sector. Investigating the causality between potential outcomes and treatment effects, where changes in pricing policies are the treatment, our analysis challenges the conventional wisdom surrounding incentive-based electricity pricing. The study's findings suggest that adopting such policies may inadvertently increase CO2 intensity. Additionally, we integrate a machine learning-based meta-algorithm, reflecting a contemporary statistical approach, to enhance the depth of our causal analysis. The study conducts a comparative analysis of learners X, T, S, and R to ascertain the optimal methods based on the defined question's specified goals and contextual nuances. This research contributes valuable insights to the ongoing dialogue on sustainable development practices, emphasizing the importance of considering unintended consequences in policy formulation.

Audio-Visual Segmentation (AVS) aims to identify, at the pixel level, the object in a visual scene that produces a given sound. Current AVS methods rely on costly fine-grained annotations of mask-audio pairs, making them impractical for scalability. To address this, we introduce unsupervised AVS, eliminating the need for such expensive annotation. To tackle this more challenging problem, we propose an unsupervised learning method, named Modality Correspondence Alignment (MoCA), which seamlessly integrates off-the-shelf foundation models like DINO, SAM, and ImageBind. This approach leverages their knowledge complementarity and optimizes their joint usage for multi-modality association. Initially, we estimate positive and negative image pairs in the feature space. For pixel-level association, we introduce an audio-visual adapter and a novel pixel matching aggregation strategy within the image-level contrastive learning framework. This allows for a flexible connection between object appearance and audio signal at the pixel level, with tolerance to imaging variations such as translation and rotation. Extensive experiments on the AVSBench (single and multi-object splits) and AVSS datasets demonstrate that our MoCA outperforms strongly designed baseline methods and approaches supervised counterparts, particularly in complex scenarios with multiple auditory objects. Notably when comparing mIoU, MoCA achieves a substantial improvement over baselines in both the AVSBench (S4: +17.24%; MS3: +67.64%) and AVSS (+19.23%) audio-visual segmentation challenges.

Extracting meaningful features from complex, high-dimensional datasets across scientific domains remains challenging. Current methods often struggle with scalability, limiting their applicability to large datasets, or make restrictive assumptions about feature-property relationships, hindering their ability to capture complex interactions. BoUTS's general and scalable feature selection algorithm surpasses these limitations to identify both universal features relevant to all datasets and task-specific features predictive for specific subsets. Evaluated on seven diverse chemical regression datasets, BoUTS achieves state-of-the-art feature sparsity while maintaining prediction accuracy comparable to specialized methods. Notably, BoUTS's universal features enable domain-specific knowledge transfer between datasets, and suggest deep connections in seemingly-disparate chemical datasets. We expect these results to have important repercussions in manually-guided inverse problems. Beyond its current application, BoUTS holds immense potential for elucidating data-poor systems by leveraging information from similar data-rich systems. BoUTS represents a significant leap in cross-domain feature selection, potentially leading to advancements in various scientific fields.

We identify reduced order models (ROM) of forced systems from data using invariant foliations. The forcing can be external, parametric, periodic or quasi-periodic. The process has four steps: 1. identify an approximate invariant torus and the linear dynamics about the torus; 2. identify a globally defined invariant foliation about the torus; 3. identify a local foliation about an invariant manifold that complements the global foliation 4. extract the invariant manifold as the leaf going through the torus and interpret the result. We combine steps 2 and 3, so that we can track the location of the invariant torus and scale the invariance equations appropriately. We highlight some fundamental limitations of invariant manifolds and foliations when fitting them to data, that require further mathematics to resolve.

Artificial intelligence has recently experienced remarkable advances, fueled by large models, vast datasets, accelerated hardware, and, last but not least, the transformative power of differentiable programming. This new programming paradigm enables end-to-end differentiation of complex computer programs (including those with control flows and data structures), making gradient-based optimization of program parameters possible. As an emerging paradigm, differentiable programming builds upon several areas of computer science and applied mathematics, including automatic differentiation, graphical models, optimization and statistics. This book presents a comprehensive review of the fundamental concepts useful for differentiable programming. We adopt two main perspectives, that of optimization and that of probability, with clear analogies between the two. Differentiable programming is not merely the differentiation of programs, but also the thoughtful design of programs intended for differentiation. By making programs differentiable, we inherently introduce probability distributions over their execution, providing a means to quantify the uncertainty associated with program outputs.