A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
We consider the problem of signal recovery on graphs as graphs model data with complex structure as signals on a graph. Graph signal recovery implies recovery of one or multiple smooth graph signals from noisy, corrupted, or incomplete measurements. We propose a graph signal model and formulate signal recovery as a cor…
Various problems in data analysis and statistical genetics call for recovery of a column-sparse, low-rank matrix from noisy observations. We propose ReFACTor, a simple variation of the classical Truncated Singular Value Decomposition (TSVD) algorithm. In contrast to previous sparse principal component analysis (PCA) al…
Suppose that we observe noisy linear measurements of an unknown signal that can be modeled as the sum of two component signals, each of which arises from a nonlinear sub-manifold of a high dimensional ambient space. We introduce SPIN, a first order projected gradient method to recover the signal components. Despite the…
In the past decade, sparse and low-rank recovery have drawn much attention in many areas such as signal/image processing, statistics, bioinformatics and machine learning. To achieve sparsity and/or low-rankness inducing, the ℓ1 norm and nuclear norm are of the most popular regularization penalties due to their co…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise. The maximum likelihood solution for the model is an eigenvalue problem on the sample covariance matrix. In this paper we consider the situation where the data v…
Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and functional (smooth) aspects and may benefit from a regularization scheme that can captur…
High-dimensional tensors or multi-way data are becoming prevalent in areas such as biomedical imaging, chemometrics, networking and bibliometrics. Traditional approaches to finding lower dimensional representations of tensor data include flattening the data and applying matrix factorizations such as principal component…
The measurement and analysis of Electrodermal Activity (EDA) offers applications in diverse areas ranging from market research, to seizure detection, to human stress analysis. Unfortunately, the analysis of EDA signals is made difficult by the superposition of numerous components which can obscure the signal informatio…
In this paper, we consider the Tensor Robust Principal Component Analysis (TRPCA) problem, which aims to exactly recover the low-rank and sparse components from their sum. Our model is based on the recently proposed tensor-tensor product (or t-product). Induced by the t-product, we first rigorously deduce the tensor sp…
We study signal recovery on graphs based on two sampling strategies: random sampling and experimentally designed sampling. We propose a new class of smooth graph signals, called approximately bandlimited, which generalizes the bandlimited class and is similar to the globally smooth class. We then propose two recovery s…
This paper establishes conditions for sparse signal recovery with sparse measurements.
problem Recovering the support of a sparse signal using noisy projections with sparse measurement matrices.
method Establishes sufficient conditions for successful sparse recovery using sparse measurement matrices.
result A phase transition threshold for sparse recovery in the sparse setting is discovered, revealing a trade-off between sampling complexity and measurement sparsity.
In this paper, we propose majority voting neural networks for sparse signal recovery in binary compressed sensing. The majority voting neural network is composed of several independently trained feedforward neural networks employing the sigmoid function as an activation function. Our empirical study shows that a choice…
CPCR mitigates bias in PCR for overparameterized models.
problem Bias in Principal Component Regression (PCR) for overparameterized models.
method Calibrated Principal Component Regression (CPCR) learns a low-variance prior in the PC subspace and calibrates the model in the original feature space.
result CPCR outperforms standard PCR in overparameterized settings, improving prediction across multiple problems.
Independent Component Analysis (ICA) is a popular model for blind signal separation. The ICA model assumes that a number of independent source signals are linearly mixed to form the observed signals. We propose a new algorithm, PEGI (for pseudo-Euclidean Gradient Iteration), for provable model recovery for ICA with Gau…
HPPCA improves imputation of longitudinal data with missing values.
problem Handling incomplete, high-dimensional longitudinal data with nested sources of variation and temporal dependency.
method Hierarchical probabilistic principal component analysis (HPPCA) with a two-level latent factor model and Gaussian process.
result HPPCA outperforms standard PPCA and multivariate functional PCA in imputation accuracy, even under heavy missingness and model misspecification.
We introduce a new convex formulation for stable principal component pursuit (SPCP) to decompose noisy signals into low-rank and sparse representations. For numerical solutions of our SPCP formulation, we first develop a convex variational framework and then accelerate it with quasi-Newton methods. We show, via synthet…
High throughput biomedical measurements normally capture multiple overlaid biologically relevant signals and often also signals representing different types of technical artefacts like e.g. batch effects. Signal identification and decomposition are accordingly main objectives in statistical biomedical modeling and data…
Recently, the principal component pursuit has received increasing attention in signal processing research ranging from source separation to video surveillance. So far, all existing formulations are real-valued and lack the concept of phase, which is inherent in inputs such as complex spectrograms or color images. Thus,…
Robust principal component analysis (RPCA) can recover low-rank matrices when they are corrupted by sparse noises. In practice, many matrices are, however, of high-rank and hence cannot be recovered by RPCA. We propose a novel method called robust kernel principal component analysis (RKPCA) to decompose a partially cor…