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.
New algorithms extract Koopman invariant subspaces from large-scale data.
Paper develops a method to learn optimal sparsity-promoting regularizers for linear inverse problems.
We present a family of expectation-maximization (EM) algorithms for binary and negative-binomial logistic regression, drawing a sharp connection with the variational-Bayes algorithm of Jaakkola and Jordan (2000). Indeed, our results allow a version of this variational-Bayes approach to be re-interpreted as a true EM al…
Medical image reconstruction is typically an ill-posed inverse problem. In order to address such ill-posed problems, the prior distribution of the sought after object property is usually incorporated by means of some sparsity-promoting regularization. Recently, prior distributions for images estimated using generative …
Sparsity-promoting priors have become increasingly popular over recent years due to an increased number of regression and classification applications involving a large number of predictors. In time series applications where observations are collected over time, it is often unrealistic to assume that the underlying spar…
New Bayesian method for joint sparse parameter inference.
In this paper, we introduce a new sparsity-promoting prior, namely, the "normal product" prior, and develop an efficient algorithm for sparse signal recovery under the Bayesian framework. The normal product distribution is the distribution of a product of two normally distributed variables with zero means and possibly …
Convex optimization with sparsity-promoting convex regularization is a standard approach for estimating sparse signals in noise. In order to promote sparsity more strongly than convex regularization, it is also standard practice to employ non-convex optimization. In this paper, we take a third approach. We utilize a no…
We consider an important class of signal processing problems where the signal of interest is known to be sparse, and can be recovered from data given auxiliary information about how the data was generated. For example, a sparse Green's function may be recovered from seismic experimental data using sparsity optimization…
Dynamic Mode Decomposition (DMD) yields a linear, approximate model of a system's dynamics that is built from data. We seek to reduce the order of this model by identifying a reduced set of modes that best fit the output. We adopt a model selection algorithm from statistics and machine learning known as Least Angle Reg…
In this paper, Bayesian parameter estimation through the consideration of the Maximum A Posteriori (MAP) criterion is revisited under the prism of the Expectation-Maximization (EM) algorithm. By incorporating a sparsity-promoting penalty term in the cost function of the estimation problem through the use of an appropri…
Recently, there has been focus on penalized log-likelihood covariance estimation for sparse inverse covariance (precision) matrices. The penalty is responsible for inducing sparsity, and a very common choice is the convex norm. However, the best estimator performance is not always achieved with this penalty. The …
Sparse-mode DMD disambiguates local and global modes in spatiotemporal data.
The paper studies how regularization parameters affect sparsity in deep neural networks.
We consider factoring low-rank tensors in the presence of outlying slabs. This problem is important in practice, because data collected in many real-world applications, such as speech, fluorescence, and some social network data, fit this paradigm. Prior work tackles this problem by iteratively selecting a fixed number …
The potential of recovering the topology of a grid using solely publicly available market data is explored here. In contemporary whole-sale electricity markets, real-time prices are typically determined by solving the network-constrained economic dispatch problem. Under a linear DC model, locational marginal prices (LM…
Large-scale recurrent networks have drawn increasing attention recently because of their capabilities in modeling a large variety of real-world phenomena and physical mechanisms. This paper studies how to identify all authentic connections and estimate system parameters of a recurrent network, given a sequence of node …
We propose a modification of linear discriminant analysis, referred to as compressive regularized discriminant analysis (CRDA), for analysis of high-dimensional datasets. CRDA is specially designed for feature elimination purpose and can be used as gene selection method in microarray studies. CRDA lends ideas from $\el…
In hyperspectral images, some spectral bands suffer from low signal-to-noise ratio due to noisy acquisition and atmospheric effects, thus requiring robust techniques for the unmixing problem. This paper presents a robust supervised spectral unmixing approach for hyperspectral images. The robustness is achieved by writi…
Online method learns sparse models efficiently in large scale settings.
Recently, a number of mostly -norm regularized least squares type deterministic algorithms have been proposed to address the problem of \emph{sparse} adaptive signal estimation and system identification. From a Bayesian perspective, this task is equivalent to maximum a posteriori probability estimation under a …
This work shows how disentangled and sparse representations improve multi-task learning.
Bayesian neural networks improve deep learning's accuracy and uncertainty estimation.
In this paper, we consider the problem of recovering a sparse signal based on penalized least squares formulations. We develop a novel algorithm of primal-dual active set type for a class of nonconvex sparsity-promoting penalties, including , bridge, smoothly clipped absolute deviation, capped and mini…
Item response theory (IRT) is a non-linear generative probabilistic paradigm for using exams to identify, quantify, and compare latent traits of individuals, relative to their peers, within a population of interest. In pre-existing multidimensional IRT methods, one requires a factorization of the test items. For this t…
Level-set optimization formulations with data-driven constraints minimize a regularization functional subject to matching observations to a given error level. These formulations are widely used, particularly for matrix completion and sparsity promotion in data interpolation and denoising. The misfit level is typically …
We propose a novel approach for nonlinear regression using a two-layer neural network (NN) model structure with sparsity-favoring hierarchical priors on the network weights. We present an expectation propagation (EP) approach for approximate integration over the posterior distribution of the weights, the hierarchical s…
In this paper, we study the effect of different regularizers and their implications in high dimensional image classification and sparse linear unmixing. Although kernelization or sparse methods are globally accepted solutions for processing data in high dimensions, we present here a study on the impact of the form of r…
Parsimonious Dynamic Mode Decomposition selects sparse modes robustly.
New framework learns physics from output measurements only.
New algorithm finds sparse matrices on Stiefel manifold for optimisation.
Automated PDE discovery from multiple noisy experiments.
Sparsity promoting norms are frequently used in high dimensional regression. A limitation of such Lasso-type estimators is that the optimal regularization parameter depends on the unknown noise level. Estimators such as the concomitant Lasso address this dependence by jointly estimating the noise level and the regressi…
Randomized feature models learn interaction kernels from agent paths.
High dimensional regression benefits from sparsity promoting regularizations. Screening rules leverage the known sparsity of the solution by ignoring some variables in the optimization, hence speeding up solvers. When the procedure is proven not to discard features wrongly the rules are said to be \emph{safe}. In this …
We propose to optimize the activation functions of a deep neural network by adding a corresponding functional regularization to the cost function. We justify the use of a second-order total-variation criterion. This allows us to derive a general representer theorem for deep neural networks that makes a direct connectio…
Our goal is to estimate causal interactions in multivariate time series. Using vector autoregressive (VAR) models, these can be defined based on non-vanishing coefficients belonging to respective time-lagged instances. As in most cases a parsimonious causality structure is assumed, a promising approach to causal discov…
Regularized least-squares approaches have been successfully applied to linear system identification. Recent approaches use quadratic penalty terms on the unknown impulse response defined by stable spline kernels, which control model space complexity by leveraging regularity and bounded-input bounded-output stability. T…
Bayesian framework for robust model discovery from noisy data.
Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. This problem finds numerous applications in signal processing, computer vision, and inverse problems. However…
In this paper, the task-related fMRI problem is treated in its matrix factorization formulation, focused on the Dictionary Learning (DL) approach. The new method allows the incorporation of a priori knowledge associated both with the experimental design as well as with available brain Atlases. Moreover, the proposed me…
Paper improves Tm prediction of protein fragments using sparsity and probabilistic models.
A new method for high-dimensional data classification reduces misclassification errors.
A new filter adapts to heavy-tailed data without tuning, improving performance in challenging conditions.
To improve the compressive sensing MRI (CS-MRI) approaches in terms of fine structure loss under high acceleration factors, we have proposed an iterative feature refinement model (IFR-CS), equipped with fixed transforms, to restore the meaningful structures and details. Nevertheless, the proposed IFR-CS still has some …
ISR creates analytical relationships from data via invertible maps.
Least squares fitting is in general not useful for high-dimensional linear models, in which the number of predictors is of the same or even larger order of magnitude than the number of samples. Theory developed in recent years has coined a paradigm according to which sparsity-promoting regularization is regarded as a n…
The standard approach for dealing with the ill-posedness of the training problem in machine learning and/or the reconstruction of a signal from a limited number of measurements is regularization. The method is applicable whenever the problem is formulated as an optimization task. The standard strategy consists in augme…