Data visualization via dimensionality reduction is an important tool in exploratory data analysis. However, when the data are noisy, many existing methods fail to capture the underlying structure of the data. The method called Empirical Intrinsic Geometry (EIG) was previously proposed for performing dimensionality reduction on high dimensional dynamical processes while theoretically eliminating all noise. However, implementing EIG in practice requires the construction of high-dimensional histograms, which suffer from the curse of dimensionality. Here we propose a new data visualization method called Functional Information Geometry (FIG) for dynamical processes that adapts the EIG framework while using approaches from functional data analysis to mitigate the curse of dimensionality. We experimentally demonstrate that the resulting method outperforms a variant of EIG designed for visualization in terms of capturing the true structure, hyperparameter robustness, and computational speed. We then use our method to visualize EEG brain measurements of sleep activity.
The aim of this work is to estimate a quadratic functional of a unknown Wigner function from noisy tomographic data. The Wigner function can be seen as the representation of the quantum state of a light beam. The estimation of a quadratic functional is done from result of quantum homodyne measurement performed on identically prepared quantum systems. We start by constructing an estimator of a quadratic functional of the Wigner function. We show that the proposed estimator is optimal or nearly optimal in a minimax sense over a class of infinitely differentiable functions. Parametric rates are a…
When collections of functional data are too large to be exhaustively observed, survey sampling techniques provide an effective way to estimate global quantities such as the population mean function. Assuming functional data are collected from a finite population according to a probabilistic sampling scheme, with the measurements being discrete in time and noisy, we propose to first smooth the sampled trajectories with local polynomials and then estimate the mean function with a Horvitz-Thompson estimator. Under mild conditions on the population size, observation times, regularity of the trajec…
This paper presents the nonparametric inference for nonlinear volatility functionals of general multivariate Itô semimartingales, in high-frequency and noisy setting. Pre-averaging and truncation enable simultaneous handling of noise and jumps. Second-order expansion reveals explicit biases and a pathway to bias correction. Estimators based on this framework achieve the optimal convergence rate. A class of stable central limit theorems are attained with estimable asymptotic covariance matrices. This paper form a basis for infill asymptotic results of, for example, the realized Laplace transfor…
The R add-on package FDboost is a flexible toolbox for the estimation of functional regression models by model-based boosting. It provides the possibility to fit regression models for scalar and functional response with effects of scalar as well as functional covariates, i.e., scalar-on-function, function-on-scalar and function-on-function regression models. In addition to mean regression, quantile regression models as well as generalized additive models for location scale and shape can be fitted with FDboost. Furthermore, boosting can be used in high-dimensional data settings with more covari…
This work is concerned with tests on structural breaks in the spot volatility process of a general Itô semimartingale based on discrete observations contaminated with i.i.d. microstructure noise. We construct a consistent test building up on infill asymptotic results for certain functionals of spectral spot volatility estimates. A weak limit theorem is established under the null hypothesis relying on extreme value theory. We prove consistency of the test and of an associated estimator for the change point. A simulation study illustrates the finite-sample performance of the method and efficienc…
In this work, we provide a new formulation for Graph Convolutional Neural Networks (GCNNs) for link prediction on graph data that addresses common challenges for biomedical knowledge graphs (KGs). We introduce a regularized attention mechanism to GCNNs that not only improves performance on clean datasets, but also favorably accommodates noise in KGs, a pervasive issue in real-world applications. Further, we explore new visualization methods for interpretable modelling and to illustrate how the learned representation can be exploited to automate dataset denoising. The results are demonstrated o…
University of Warwick（华威大学）；Helsinki Institute for Information Technology HIIT（赫尔辛基信息技术研究所（HIIT））；Aalto University（阿尔托大学）
A main goal of data visualization is to find, from among all the available alternatives, mappings to the 2D/3D display which are relevant to the user. Assuming user interaction data, or other auxiliary data about the items or their relationships, the goal is to identify which aspects in the primary data support the userś input and, equally importantly, which aspects of the userś potentially noisy input have support in the primary data. For solving the problem, we introduce a multi-view embedding in which a latent factorization identifies which aspects in the two data views (primary data and us…
We study the problem of discovering functional dependencies (FD) from a noisy dataset. We focus on FDs that correspond to statistical dependencies in a dataset and draw connections between FD discovery and structure learning in probabilistic graphical models. We show that discovering FDs from a noisy dataset is equivalent to learning the structure of a graphical model over binary random variables, where each random variable corresponds to a functional of the dataset attributes. We build upon this observation to introduce AutoFD a conceptually simple framework in which learning functional depen…
EmbedOR: Provable Cluster-Preserving Visualizations with Curvature-Based Stochastic Neighbor Embeddings
Department of Computer Science, Columbia University（哥伦比亚大学计算机科学系）；Department of Statistics & Data Science, Wu Tsai Institute, Yale University（耶鲁大学统计与数据科学系、吴氏研究所）；Department of Machine Learning, University of Fribourg（弗里堡大学机器学习系）；Department of Mathematics, Columbia University（哥伦比亚大学数学系）；Irving Institute for Cancer Dynamics, Columbia University（哥伦比亚大学癌症动力学研究所）
University of Cambridge（剑桥大学）；Cambridge University（剑桥大学）
Classification of whole-brain functional connectivity MRI data with convolutional neural networks (CNNs) has shown promise, but the complexity of these models impedes understanding of which aspects of brain activity contribute to classification. While visualization techniques have been developed to interpret CNNs, bias inherent in the method of encoding abstract input data, as well as the natural variance of deep learning models, detract from the accuracy of these techniques. We introduce a stochastic encoding method in an ensemble of CNNs to classify functional connectomes by gender. We appli…
Helmholtz-Zentrum Dresden-Rossendorf（亥姆霍兹德累斯顿罗森多夫研究中心）；University Hospital Carl Gustav Carus（卡尔·古斯塔夫·卡鲁斯大学医院）
Multimodal medical image fusion helps in combining contrasting features from two or more input imaging modalities to represent fused information in a single image. One of the pivotal clinical applications of medical image fusion is the merging of anatomical and functional modalities for fast diagnosis of malignant tissues. In this paper, we present a novel end-to-end unsupervised learning-based Convolutional Neural Network (CNN) for fusing the high and low frequency components of MRI-PET grayscale image pairs, publicly available at ADNI, by exploiting Structural Similarity Index (SSIM) as the …
University of Göttingen（哥廷根大学）；Clausthal University of Technology（克劳斯塔尔工业大学）
We present Twitmo, a package that provides a broad range of methods to collect, pre-process, analyze and visualize geo-tagged Twitter data. Twitmo enables the user to collect geo-tagged Tweets from Twitter and and provides a comprehensive and user-friendly toolbox to generate topic distributions from Latent Dirichlet Allocations (LDA), correlated topic models (CTM) and structural topic models (STM). Functions are included for pre-processing of text, model building and prediction. In addition, one of the innovations of the package is the automatic pooling of Tweets into longer pseudo-documents …
Dataflow visualization systems enable flexible visual data exploration by allowing the user to construct a dataflow diagram that composes query and visualization modules to specify system functionality. However learning dataflow diagram usage presents overhead that often discourages the user. In this work we design FlowSense, a natural language interface for dataflow visualization systems that utilizes state-of-the-art natural language processing techniques to assist dataflow diagram construction. FlowSense employs a semantic parser with special utterance tagging and special utterance placehol…
Latent Manifold Reconstruction and Representation with Topological and Geometrical Regularization
Southern University of Science and Technology（南方科技大学）；Shenzhen University of Advanced Technology（深圳先进技术大学）；Shenzhen Institute of Advanced Technology, Chinese Academy of Sciences（深圳先进技术研究所，中国科学院）
