Matrix completion has attracted attention in many fields, including statistics, applied mathematics, and electrical engineering. Most of the works focus on the independent sampling models under which the observed entries are sampled independently. Motivated by applications in the integration of multiple Electronic Health Record (EHR) datasets, we propose the method Block-wise missing Embedding Learning Transformer (BELT) to treat rowwise/column-wise missingness. Specifically, BELT can recover block-wise missing matrices efficiently when every pair of matrices has an overlap. Our idea is to exploit the orthogonal Procrustes problem to align the eigenspace of the two sub-matrices using their overlap, then complete the missing blocks by the inner product of the two low-rank components. Besides, we prove the statistical rate for the eigenspace of the underlying matrix, which is comparable to the rate under the independently missing assumption. Simulation studies show that the method performs well under a variety of configurations. In the real data analysis, the method is applied to two tasks: (i) the integrating of several point-wise mutual information matrices built by English EHR and Chinese medical text data, and (ii) the machine translation between English and Chinese medical concepts. Our method shows an advantage over existing methods.

Stochastic gradient descent (SGD) and projected stochastic gradient descent (PSGD) are scalable algorithms to compute model parameters in unconstrained and constrained optimization problems. In comparison with stochastic gradient descent (SGD), PSGD forces its iterative values into the constrained parameter space via projection. The convergence rate of PSGD-type estimates has been exhaustedly studied, while statistical properties such as asymptotic distribution remain less explored. From a purely statistical point of view, this paper studies the limiting distribution of PSGD-based estimate when the true parameters satisfying some linear-equality constraints. Our theoretical findings reveal the role of projection played in the uncertainty of the PSGD estimate. As a byproduct, we propose an online hypothesis testing procedure to test the linear-equality constraints. Simulation studies on synthetic data and an application to a real-world dataset confirm our theory.

Time-series representation learning is a fundamental task for time-series analysis. While significant progress has been made to achieve accurate representations for downstream applications, the learned representations often lack interpretability and do not expose semantic meanings. Different from previous efforts on the entangled feature space, we aim to extract the semantic-rich temporal correlations in the latent interpretable factorized representation of the data. Motivated by the success of disentangled representation learning in computer vision, we study the possibility of learning semantic-rich time-series representations, which remains unexplored due to three main challenges: 1) sequential data structure introduces complex temporal correlations and makes the latent representations hard to interpret, 2) sequential models suffer from KL vanishing problem, and 3) interpretable semantic concepts for time-series often rely on multiple factors instead of individuals. To bridge the gap, we propose Disentangle Time Series (DTS), a novel disentanglement enhancement framework for sequential data. Specifically, to generate hierarchical semantic concepts as the interpretable and disentangled representation of time-series, DTS introduces multi-level disentanglement strategies by covering both individual latent factors and group semantic segments. We further theoretically show how to alleviate the KL vanishing problem: DTS introduces a mutual information maximization term, while preserving a heavier penalty on the total correlation and the dimension-wise KL to keep the disentanglement property. Experimental results on various real-world benchmark datasets demonstrate that the representations learned by DTS achieve superior performance in downstream applications, with high interpretability of semantic concepts.

Efficiently accessing the information contained in non-linear and high dimensional probability distributions remains a core challenge in modern statistics. Traditionally, estimators that go beyond point estimates are either categorized as Variational Inference (VI) or Markov-Chain Monte-Carlo (MCMC) techniques. While MCMC methods that utilize the geometric properties of continuous probability distributions to increase their efficiency have been proposed, VI methods rarely use the geometry. This work aims to fill this gap and proposes geometric Variational Inference (geoVI), a method based on Riemannian geometry and the Fisher information metric. It is used to construct a coordinate transformation that relates the Riemannian manifold associated with the metric to Euclidean space. The distribution, expressed in the coordinate system induced by the transformation, takes a particularly simple form that allows for an accurate variational approximation by a normal distribution. Furthermore, the algorithmic structure allows for an efficient implementation of geoVI which is demonstrated on multiple examples, ranging from low-dimensional illustrative ones to non-linear, hierarchical Bayesian inverse problems in thousands of dimensions.

Sparse Bayesian learning (SBL) is a powerful framework for tackling the sparse coding problem while also providing uncertainty quantification. However, the most popular inference algorithms for SBL become too expensive for high-dimensional problems due to the need to maintain a large covariance matrix. To resolve this issue, we introduce a new SBL inference algorithm that avoids explicit computation of the covariance matrix, thereby saving significant time and space. Instead of performing costly matrix inversions, our covariance-free method solves multiple linear systems to obtain provably unbiased estimates of the posterior statistics needed by SBL. These systems can be solved in parallel, enabling further acceleration of the algorithm via graphics processing units. In practice, our method can be up to thousands of times faster than existing baselines, reducing hours of computation time to seconds. We showcase how our new algorithm enables SBL to tractably tackle high-dimensional signal recovery problems, such as deconvolution of calcium imaging data and multi-contrast reconstruction of magnetic resonance images. Finally, we open-source a toolbox containing all of our implementations to drive future research in SBL.

Detailed parcel-level crop type mapping for the whole European Union (EU) is necessary for the evaluation of agricultural policies. The Copernicus program, and Sentinel-1 (S1) in particular, offers the opportunity to monitor agricultural land at a continental scale and in a timely manner. However, so far the potential of S1 has not been explored at such a scale. Capitalizing on the unique LUCAS 2018 Copernicus in-situ survey, we present the first continental crop type map at 10-m spatial resolution for the EU based on S1A and S1B Synthetic Aperture Radar observations for the year 2018. Random forest classification algorithms are tuned to detect 19 different crop types. We assess the accuracy of this EU crop map with three approaches. First, the accuracy is assessed with independent LUCAS core in-situ observations over the continent. Second, an accuracy assessment is done specifically for main crop types from farmers declarations from 6 EU member countries or regions totaling >3M parcels and 8.21 Mha. Finally, the crop areas derived by classification are compared to the subnational (NUTS 2) area statistics reported by Eurostat. The overall accuracy for the map is reported as 80.3% when grouping main crop classes and 76% when considering all 19 crop type classes separately. Highest accuracies are obtained for rape and turnip rape with user and produced accuracies higher than 96%. The correlation between the remotely sensed estimated and Eurostat reported crop area ranges from 0.93 (potatoes) to 0.99 (rape and turnip rape). Finally, we discuss how the framework presented here can underpin the operational delivery of in-season high-resolution based crop mapping.

We address in this study the problem of learning a summary causal graph on time series with potentially different sampling rates. To do so, we first propose a new temporal mutual information measure defined on a window-based representation of time series. We then show how this measure relates to an entropy reduction principle that can be seen as a special case of the Probabilistic Raising Principle. We finally combine these two ingredients in a PC-like algorithm to construct the summary causal graph. This algorithm is evaluated on several datasets that shows both its efficacy and efficiency.

Currently, Chronic Kidney Disease (CKD) is experiencing a globally increasing incidence and high cost to health systems. A delayed recognition leads to premature mortality due to progressive loss of kidney function. The employment of data mining to discover subtle patterns in CKD indicators would contribute to an early diagnosis. This work develops a classifier model that would support healthcare professionals in the early diagnosis of CKD patients. Through a data pipeline, an exhaustive search is performed to find the best data mining classifier with different parameters of the data preparation's sub-stages like data missing or feature selection. Therefore, Extra Trees is selected as the best classifier with a 100% and 99% of accuracy with, respectively, cross-validation technique and with new unseen data. Moreover, the 8 features selected are employed to assess the explainability of the model's results denoting which features are more relevant in the model's output.

In this post, I introduce a new Python package to generate clustergrams from clustering solutions. The library has been developed as part of the Urban Grammar research project, and it is compatible with scikit-learn and GPU-enabled libraries such as cuML or cuDF within RAPIDS.AI. When we want to do some cluster analysis to identify groups in our data, we often use algorithms like K-Means, which require the specification of a number of clusters. But the issue is that we usually don't know how many clusters there are. There are many methods on how to determine the correct number, like silhouettes or elbow plot, to name a few.

K-Nearest Neighbors (KNN) is a classification machine learning algorithm. This algorithm is used when the data is discrete in nature. It is a supervised machine learning algorithm. This means we need a set of reference data in order to determine the category of the future data point. This algorithm classifies the given dataset into different groups or categories.