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Numerous problems of both theoretical and practical interest are related to finding shortest (or otherwise optimal) paths in networks, frequently in the presence of some obstacles or constraints. A somewhat related class of problems focuses…
Functional data analysis is an important research field in statistics which treats data as random functions drawn from some infinite-dimensional functional space, and functional principal component analysis (FPCA) based on…
Principal Component Analysis (PCA) is a fundamental tool for representation learning, but its global linear formulation fails to capture the structure of data supported on curved manifolds. In contrast, manifold learning methods model…
We address the problem of defining a group sparse formulation for Principal Components Analysis (PCA) - or its equivalent formulations as Low Rank approximation or Dictionary Learning problems - which achieves a compromise between…
Analysis of variance (ANOVA) is an extremely important method in exploratory and confirmatory data analysis. Unfortunately, in complex problems (e.g., split-plot designs), it is not always easy to set up an appropriate ANOVA. We propose a…
Principal Component Analysis (PCA) is a transform for finding the principal components (PCs) that represent features of random data. PCA also provides a reconstruction of the PCs to the original data. We consider an extension of PCA which…
This paper considers the estimation and inference of the low-rank components in high-dimensional matrix-variate factor models, where each dimension of the matrix-variates ($p \times q$) is comparable to or greater than the number of…
The methodological contribution in this paper is motivated by biomechanical studies where data characterizing human movement are waveform curves representing joint measures such as flexion angles, velocity, acceleration, and so on. In many…
We study the covariance of the cross-power spectrum of different tracers for the large-scale structure. We develop the counts-in-cells framework for the multi-tracer approach, and use this to derive expressions for the full non-Gaussian…
Solving optimisation problems is a promising near-term application of quantum computers. Quantum variational algorithms leverage quantum superposition and entanglement to optimise over exponentially large solution spaces using an…
Functional data analysis is becoming increasingly popular to study data from real-valued random functions. Nevertheless, there is a lack of multiple testing procedures for such data. These are particularly important in factorial designs to…
In this work we elaborate on two recently discovered invariance principles, according to which transport coefficients are, to a large extent, independent of the microscopic definition of the densities and currents of the conserved…
Many causal estimands are only partially identifiable since they depend on the unobservable joint distribution between potential outcomes. Stratification on pretreatment covariates can yield sharper bounds; however, unless the covariates…
Coupling probability measures lies at the core of many problems in statistics and machine learning, from domain adaptation to transfer learning and causal inference. Yet, even when restricted to deterministic transports, such couplings are…
A multivariate distribution can be described by a triangular transport map from the target distribution to a simple reference distribution. We propose Bayesian nonparametric inference on the transport map by modeling its components using…
Recently, we proposed quantum language (or, measurement theory), which is characterized as the linguistic turn of the Copenhagen interpretation of quantum mechanics. We believe that this language has a great powet of description, and…
Linear principal component analysis (PCA) learns (semi-)orthogonal transformations by orienting the axes to maximize variance. Consequently, it can only identify orthogonal axes whose variances are clearly distinct, but it cannot identify…
The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing…
We extend the principal component analysis (PCA) to second-order stationary vector time series in the sense that we seek for a contemporaneous linear transformation for a $p$-variate time series such that the transformed series is segmented…
The network traffic matrix is widely used in network operation and management. It is therefore of crucial importance to analyze the components and the structure of the network traffic matrix, for which several mathematical approaches such…