Simultaneous Measurement Imputation and Outcome Prediction for Achilles Tendon Rupture Rehabilitation

Achilles Tendon Rupture (ATR) is one of the typical soft tissue injuries. Rehabilitation after such a musculoskeletal injury remains a prolonged process with a very variable outcome. Accurately predicting rehabilitation outcome is crucial for treatment decision support. However, it is challenging to train an automatic method for predicting the ATR rehabilitation outcome from treatment data, due to a massive amount of missing entries in the data recorded from ATR patients, as well as complex nonlinear relations between measurements and outcomes. In this work, we design an end-to-end probabilistic framework to impute missing data entries and predict rehabilitation outcomes simultaneously. We evaluate our model on a real-life ATR clinical cohort, comparing with various baselines. The proposed method demonstrates its clear superiority over traditional methods which typically perform imputation and prediction in two separate stages

Scalable Low-Rank Tensor Learning for Spatiotemporal Traffic Data Imputation

Missing value problem in spatiotemporal traffic data has long been a challenging topic, in particular for large-scale and high-dimensional data with complex missing mechanisms and diverse degrees of missingness. Recent studies based on tensor nuclear norm have demonstrated the superiority of tensor learning in imputation tasks by effectively characterizing the complex correlations/dependencies in spatiotemporal data. However, despite the promising results, these approaches do not scale well to large data tensors. In this paper, we focus on addressing the missing data imputation problem for large-scale spatiotemporal traffic data. To achieve both high accuracy and efficiency, we develop a scalable tensor learning model -- Low-Tubal-Rank Smoothing Tensor Completion (LSTC-Tubal) -- based on the existing framework of Low-Rank Tensor Completion, which is well-suited for spatiotemporal traffic data that is characterized by multidimensional structure of location$\times$ time of day $\times$ day. In particular, the proposed LSTC-Tubal model involves a scalable tensor nuclear norm minimization scheme by integrating linear unitary transformation. Therefore, tensor nuclear norm minimization can be solved by singular value thresholding on the transformed matrix of each day while the day-to-day correlation can be effectively preserved by the unitary transform matrix. We compare LSTC-Tubal with state-of-the-art baseline models, and find that LSTC-Tubal can achieve competitive accuracy with a significantly lower computational cost. In addition, the LSTC-Tubal will also benefit other tasks in modeling large-scale spatiotemporal traffic data, such as network-level traffic forecasting

Data analysis and machine learning approaches for time series pre- and post- processing pipelines

157 p.En el ámbito industrial, las series temporales suelen generarse de forma continua mediante sensores quecaptan y supervisan constantemente el funcionamiento de las máquinas en tiempo real. Por ello, esimportante que los algoritmos de limpieza admitan un funcionamiento casi en tiempo real. Además, amedida que los datos evolución, la estrategia de limpieza debe cambiar de forma adaptativa eincremental, para evitar tener que empezar el proceso de limpieza desde cero cada vez.El objetivo de esta tesis es comprobar la posibilidad de aplicar flujos de aprendizaje automática a lasetapas de preprocesamiento de datos. Para ello, este trabajo propone métodos capaces de seleccionarestrategias óptimas de preprocesamiento que se entrenan utilizando los datos históricos disponibles,minimizando las funciones de perdida empíricas.En concreto, esta tesis estudia los procesos de compresión de series temporales, unión de variables,imputación de observaciones y generación de modelos subrogados. En cada uno de ellos se persigue laselección y combinación óptima de múltiples estrategias. Este enfoque se define en función de lascaracterísticas de los datos y de las propiedades y limitaciones del sistema definidas por el usuario

Foundational principles for large scale inference: Illustrations through correlation mining

When can reliable inference be drawn in the "Big Data" context? This paper presents a framework for answering this fundamental question in the context of correlation mining, with implications for general large scale inference. In large scale data applications like genomics, connectomics, and eco-informatics the dataset is often variable-rich but sample-starved: a regime where the number $n$ of acquired samples (statistical replicates) is far fewer than the number $p$ of observed variables (genes, neurons, voxels, or chemical constituents). Much of recent work has focused on understanding the computational complexity of proposed methods for "Big Data." Sample complexity however has received relatively less attention, especially in the setting when the sample size $n$ is fixed, and the dimension $p$ grows without bound. To address this gap, we develop a unified statistical framework that explicitly quantifies the sample complexity of various inferential tasks. Sampling regimes can be divided into several categories: 1) the classical asymptotic regime where the variable dimension is fixed and the sample size goes to infinity; 2) the mixed asymptotic regime where both variable dimension and sample size go to infinity at comparable rates; 3) the purely high dimensional asymptotic regime where the variable dimension goes to infinity and the sample size is fixed. Each regime has its niche but only the latter regime applies to exa-scale data dimension. We illustrate this high dimensional framework for the problem of correlation mining, where it is the matrix of pairwise and partial correlations among the variables that are of interest. We demonstrate various regimes of correlation mining based on the unifying perspective of high dimensional learning rates and sample complexity for different structured covariance models and different inference tasks

Topics in sparse functional data analysis

This dissertation consists of three research papers that address different problems in modeling sparse functional data. The first paper (Chapter 2) focuses on the statistical inference for Analysis of Covariance (ANCOVA) models on sparse functional data. In an analysis of covariance model for sparse functional data, the treatment effects, after adjusting for the effects of subject specific covariates, are represented by functions of time. We apply the seemingly unrelated kernel estimator, which takes the within subject correlation into account, to estimate the nonparametric components of the model, and test treatment effects using a generalized quasi-likelihood ratio test. We derived the asymptotic distribution of the test statistics under both the null and some local alternative hypothesis, and show that the proposed test enjoys the Wilks property and is minimax most powerful when the within-subject correlation structure is correctly specified. The second paper (Chapter 3) develops an algorithm to impute missing values in spatiotemporal satellite images based on sparse functional data analysis methods. We model the satellite images as functional data which is both sparse in temporal domain and spatial domain and assume they are repeated measurements of a latent spatiotemporal process. We assume the latent spatiotemporal process is composed of fixed mean function, random temporal effect and random spatial effect. We propose an algorithm to estimate each component using functional principle component analysis (FPCA) techniques. The proposed imputation algorithm is validated on real data and shows great performance in all aspects compared with its competitors. The third paper (Chapter 4) proposes a hierarchical multiresolution imputation (HMRI) algorithm for imputation of high-resolution spatiotemporal satellite images, which is an extension of the second paper. HMRI is demonstrated by using the Moderate Resolution Imaging Spectrophotometer (MODIS) daily land surfact temperature (LST) data and shows satisfactory imputation results. HMRI shows large improvement in prediction accuracy compared with other existing methods