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This paper describes a novel approach to change-point detection when the observed high-dimensional data may have missing elements. The performance of classical methods for change-point detection typically scales poorly with the…
Modeling continuous-time dynamics from sparse and irregularly-sampled time series remains a fundamental challenge. Neural controlled differential equations provide a principled framework for such tasks, yet their performance is highly…
In the machine learning field, dimensionality reduction is an important task. It mitigates the undesired properties of high-dimensional spaces to facilitate classification, compression, and visualization of high-dimensional data. During the…
Transformation-invariant analysis of signals often requires the computation of the distance from a test pattern to a transformation manifold. In particular, the estimation of the distances between a transformed query signal and several…
Manifold Learning is a class of algorithms seeking a low-dimensional non-linear representation of high-dimensional data. Thus manifold learning algorithms are, at least in theory, most applicable to high-dimensional data and sample sizes to…
Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…
This paper considers the problem of finding a meaningful template function that represents the common pattern of a sample of curves. To address this issue, a novel algorithm based on a robust version of the isometric featuring mapping…
In many engineered systems, optimization is used for decision making at time-scales ranging from real-time operation to long-term planning. This process often involves solving similar optimization problems over and over again with slightly…
Dripping water from a faucet is a typical example exhibiting rich nonlinear phenomena. For such a system, the time stamps at which water drops separate from the faucet can be directly observed in real experiments, and the time series of…
Moving object segmentation based on LiDAR is a crucial and challenging task for autonomous driving and mobile robotics. Most approaches explore spatio-temporal information from LiDAR sequences to predict moving objects in the current frame.…
Manifold learning (ML), known also as non-linear dimension reduction, is a set of methods to find the low dimensional structure of data. Dimension reduction for large, high dimensional data is not merely a way to reduce the data; the new…
Real world data often lie on low-dimensional Riemannian manifolds embedded in high-dimensional spaces. This motivates learning degenerate normalizing flows that map between the ambient space and a low-dimensional latent space. However, if…
Diffusion maps are a nonlinear manifold learning technique based on harmonic analysis of a diffusion process over the data. Out-of-sample extensions with computational complexity $\mathcal{O}(N)$, where $N$ is the number of points…
spectral-based subspace learning is a common data preprocessing step in many machine learning pipelines. The main aim is to learn a meaningful low dimensional embedding of the data. However, most subspace learning methods do not take into…
In this work, we present data stream algorithms to compute optimal splits for decision tree learning. In particular, given a data stream of observations \(x_i\) and their corresponding labels \(y_i\), without the i.i.d. assumption, the…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
This paper addresses the problem of segmenting a stream of graph signals: we aim to detect changes in the mean of a multivariate signal defined over the nodes of a known graph. We propose an offline method that relies on the concept of…
Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is…
Linear subspace models are pervasive in computational sciences and particularly used for large datasets which are often incomplete due to privacy issues or sampling constraints. Therefore, a critical problem is developing an efficient…
Online multiple-output regression is an important machine learning technique for modeling, predicting, and compressing multi-dimensional correlated data streams. In this paper, we propose a novel online multiple-output regression method,…