Tensor Robust Principal Component Analysis (TRPCA), which aims to recover a low-rank tensor corrupted by sparse noise, has attracted much attention in many real applications. This paper develops a new Global Weighted TRPCA method (GWTRPCA), which is the first approach simultaneously considers the significance of intra-frontal slice and inter-frontal slice singular values in the Fourier domain. Exploiting this global information, GWTRPCA penalizes the larger singular values less and assigns smaller weights to them. Hence, our method can recover the low-tubal-rank components more exactly. Moreover, we propose an effective adaptive weight learning strategy by a Modified Cauchy Estimator (MCE) since the weight setting plays a crucial role in the success of GWTRPCA. To implement the GWTRPCA method, we devise an optimization algorithm using an Alternating Direction Method of Multipliers (ADMM) method. Experiments on real-world datasets validate the effectiveness of our proposed method.

Diffusion condensation is a dynamic process that yields a sequence of multiscale data representations that aim to encode meaningful abstractions. It has proven effective for manifold learning, denoising, clustering, and visualization of high-dimensional data. Diffusion condensation is constructed as a time-inhomogeneous process where each step first computes and then applies a diffusion operator to the data. We theoretically analyze the convergence and evolution of this process from geometric, spectral, and topological perspectives. From a geometric perspective, we obtain convergence bounds based on the smallest transition probability and the radius of the data, whereas from a spectral perspective, our bounds are based on the eigenspectrum of the diffusion kernel. Our spectral results are of particular interest since most of the literature on data diffusion is focused on homogeneous processes. From a topological perspective, we show diffusion condensation generalizes centroid-based hierarchical clustering. We use this perspective to obtain a bound based on the number of data points, independent of their location. To understand the evolution of the data geometry beyond convergence, we use topological data analysis. We show that the condensation process itself defines an intrinsic condensation homology. We use this intrinsic topology as well as the ambient persistent homology of the condensation process to study how the data changes over diffusion time. We demonstrate both types of topological information in well-understood toy examples. Our work gives theoretical insights into the convergence of diffusion condensation, and shows that it provides a link between topological and geometric data analysis.

Federated Learning (FL) is a paradigm for large-scale distributed learning which faces two key challenges: (i) efficient training from highly heterogeneous user data, and (ii) protecting the privacy of participating users. In this work, we propose a novel FL approach (DP-SCAFFOLD) to tackle these two challenges together by incorporating Differential Privacy (DP) constraints into the popular SCAFFOLD algorithm. We focus on the challenging setting where users communicate with a "honest-but-curious" server without any trusted intermediary, which requires to ensure privacy not only towards a third-party with access to the final model but also towards the server who observes all user communications. Using advanced results from DP theory, we establish the convergence of our algorithm for convex and non-convex objectives. Our analysis clearly highlights the privacy-utility trade-off under data heterogeneity, and demonstrates the superiority of DP-SCAFFOLD over the state-of-the-art algorithm DP-FedAvg when the number of local updates and the level of heterogeneity grow. Our numerical results confirm our analysis and show that DP-SCAFFOLD provides significant gains in practice.

The diversity of terrestrial vascular plants plays a key role in maintaining the stability and productivity of ecosystems. Monitoring species compositional diversity across large spatial scales is challenging and time consuming. The advanced spectral and spatial specification of the recently launched DESIS (the DLR Earth Sensing Imaging Spectrometer) instrument provides a unique opportunity to test the potential for monitoring plant species diversity with spaceborne hyperspectral data. This study provides a quantitative assessment on the ability of DESIS hyperspectral data for predicting plant species richness in two different habitat types in southeast Australia. Spectral features were first extracted from the DESIS spectra, then regressed against on-ground estimates of plant species richness, with a two-fold cross validation scheme to assess the predictive performance. We tested and compared the effectiveness of Principal Component Analysis (PCA), Canonical Correlation Analysis (CCA), and Partial Least Squares analysis (PLS) for feature extraction, and Kernel Ridge Regression (KRR), Gaussian Process Regression (GPR), Random Forest Regression (RFR) for species richness prediction. The best prediction results were r=0.76 and RMSE=5.89 for the Southern Tablelands region, and r=0.68 and RMSE=5.95 for the Snowy Mountains region. Relative importance analysis for the DESIS spectral bands showed that the red-edge, red, and blue spectral regions were more important for predicting plant species richness than the green bands and the near-infrared bands beyond red-edge. We also found that the DESIS hyperspectral data performed better than Sentinel-2 multispectral data in the prediction of plant species richness. Our results provide a quantitative reference for future studies exploring the potential of spaceborne hyperspectral data for plant biodiversity mapping.

Nowadays, a tremendous amount of human communications occur on Internet-based communication infrastructures, like social networks, email, forums, organizational communication platforms, etc. Indeed, the automatic prediction or assessment of individuals' personalities through their written or exchanged text would be advantageous to ameliorate their relationships. To this end, this paper aims to propose KGrAt-Net, which is a Knowledge Graph Attention Network text classifier. For the first time, it applies the knowledge graph attention network to perform Automatic Personality Prediction (APP), according to the Big Five personality traits. After performing some preprocessing activities, it first tries to acquire a knowing-full representation of the knowledge behind the concepts in the input text by building its equivalent knowledge graph. A knowledge graph collects interlinked descriptions of concepts, entities, and relationships in a machine-readable form. Practically, it provides a machine-readable cognitive understanding of concepts and semantic relationships among them. Then, applying the attention mechanism, it attempts to pay attention to the most relevant parts of the graph to predict the personality traits of the input text. We used 2,467 essays from the Essays Dataset. The results demonstrated that KGrAt-Net considerably improved personality prediction accuracies (up to 70.26% on average). Furthermore, KGrAt-Net also uses knowledge graph embedding to enrich the classification, which makes it even more accurate (on average, 72.41%) in APP.

While GPT-2 generates sentences that are remarkably human-like, longer documents can ramble and do not follow human-like writing structure. We study the problem of imposing structure on long-range text. We propose a novel controlled text generation task, sequentially controlled text generation, and identify a dataset, NewsDiscourse as a starting point for this task. We develop a sequential controlled text generation pipeline with generation and editing. We test different degrees of structural awareness and show that, in general, more structural awareness results in higher control-accuracy, grammaticality, coherency and topicality, approaching human-level writing performance.

The empirical risk minimization approach to data-driven decision making assumes that we can learn a decision rule from training data drawn under the same conditions as the ones we want to deploy it in. However, in a number of settings, we may be concerned that our training sample is biased, and that some groups (characterized by either observable or unobservable attributes) may be under- or over-represented relative to the general population; and in this setting empirical risk minimization over the training set may fail to yield rules that perform well at deployment. We propose a model of sampling bias called $\Gamma$-biased sampling, where observed covariates can affect the probability of sample selection arbitrarily much but the amount of unexplained variation in the probability of sample selection is bounded by a constant factor. Applying the distributionally robust optimization framework, we propose a method for learning a decision rule that minimizes the worst-case risk incurred under a family of test distributions that can generate the training distribution under $\Gamma$-biased sampling. We apply a result of Rockafellar and Uryasev to show that this problem is equivalent to an augmented convex risk minimization problem. We give statistical guarantees for learning a model that is robust to sampling bias via the method of sieves, and propose a deep learning algorithm whose loss function captures our robust learning target. We empirically validate our proposed method in simulations and a case study on ICU length of stay prediction.

Everyone has probably heard of machine learning, but how exactly does it work? Does it mean that an intelligent machine makes decisions on behalf of humans? You might want to replace the term "intelligent machine" with "efficient algorithm" and add that this algorithm works with data. In doing so, it delivers a view that captures the essence of the data. Simply put, machine learning focuses on building models that learn from existing data and then uses those models to make logical decisions without requiring human intervention.

This article represents the continuation of a series of dedicated articles that began some time ago. This series proposes the reader to understand the basic concepts leading to Machine Learning for biomedical data, like the difference between Linear and logistic regression, the Cost Function, Regularized Logistic Regression, and Gradient (see the Reference section). Each implementation is intended from scratch, and we will not use optimized machine learning packages like Scikit-learn, PyTorch, or TensorFlow. The only requirement is an updated version of Python 3, some fundamental libraries, and the desire to read this post to the end! Regressions (linear, logistic, for single and multiple variables) are statistical models helpful in finding correlations between observed dataset variables and answering whether those correlations are statistically significant.

Developments in sequencing technology allow us to obtain more and more genomic data since the publication of the first human genome sequence. Computational techniques can help us to mine meaningful information from raw data and understand how gene expression is regulated in cells. In general, these problems include identifying cancer gene co-expression (co-expression: simultaneous expression of two or more genes) modules, determining SNP-gene relationships through eQTL (expression quantitative trait locus) mapping and determining gene-gene relationships by estimating gene network structure, etc (Rockman and Kruglyak, 2006; Gardner and Faith, 2005). Given a dataset containing single nucleotide polymorphisms (SNPs) and mRNA expression, the problem is to understand the SNP-gene and gene-gene relationships.