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This work presents a geometrical analysis of the Large Step Gradient Descent (LGD) dictionary learning algorithm. LGD updates the atoms of the dictionary using a gradient step with a step size equal to twice the optimal step size. We show that the large step gradient descent can be understood as a maximal exploration step where one goes as far away as possible without increasing the error. We also...
Statistical factor models based on principal component analysis (PCA) have been widely used to reduce the dimensionality of financial time-series. We investigate the sensitivity of PCA to peculiarities of financial data, such as heavy tails and asymmetry and suggest to use alternatives to PCA. We investigate a recent reformulation of principal components as a search for projections which allows to...
A regularized stochastic version of the Broyden-Fletcher- Goldfarb-Shanno (BFGS) quasi-Newton method is proposed to solve optimization problems with stochastic objectives that arise in large scale machine learning. Stochastic gradient descent is the currently preferred solution methodology but the number of iterations required to approximate optimal arguments can be prohibitive in high dimensional...
We consider the problem of in-network compressed sensing, where the goal is to recover a global, sparse signal from local measurements using only local computation and communication. Our approach to this distributed compressed sensing problem is based on the centralized Iterative Hard Thresholding algorithm (IHT). In time-varying networks, the network dynamics necessarily introduce inaccuracies that...
The main result of this paper is providing a tight convex envelope to row sparse and rank one matrices which is of major interest in signal recovery applications. The resulting convexification turns out to be the ℓ1 norm of the matrix. This result highlights the fact that a joint convexification approach may not significantly improve the signal recovery process.
We propose a parametric dictionary learning algorithm to design structured dictionaries that sparsely represent graph signals. We incorporate the graph structure by forcing the learned dictionaries to be concatenations of subdictionaries that are polynomials of the graph Laplacian matrix. The resulting atoms capture the main spatial and spectral components of the graph signals of interest, leading...
We consider a non-parametric perspective of analyzing network data. Our goal is to seek a limiting object of a sequence of exchangeable random arrays called the graphon. We propose a numerically efficient algorithm for estimating graphons and we show that the proposed algorithm yields a consistent estimate as the size of the graph grows. Preliminary experiments show that the algorithm is effective...
Graphs are quickly emerging as a leading abstraction for the representation of data. One important application domain originates from an emerging discipline called “connectomics”. Connectomics studies the brain as a graph; vertices correspond to neurons (or collections thereof) and edges correspond to structural or functional connections between them. To explore the variability of connectomes—to address...
In this paper, we consider the problem of quickest change detection and identification over a linear array of N sensors, in which a change could first occur at any of these sensors and then propagate to other sensors. Our goal is not only to detect the presence of such a change as quickly as possible, but also to identify the sensor that the change pattern first reaches. We jointly design two decision...
In this paper, we investigate threshold effects associated with swapping of signal and noise subspaces in estimating signal parameters from compressed noisy data. The term threshold effect refers to a catastrophic increase in mean-squared error when the signal-to-noise ratio falls below a threshold SNR. In many cases, the threshold effect is caused by a subspace swap event, when the measured data...
In this paper, we propose a new wavelet-based image deconvolution algorithm to restore blurred images based on a Gaussian scale mixture model within the variational Bayesian framework. Our sparsity-regularized model approximates an l0 norm by reweighting an l2 norm iteratively. We derive a hierarchial Bayesian estimation with the use of subband adaptive majorization-minimization which simplifies computation...
We consider the problem of classification under the multi-view learning setting referred to as surrogate supervision multi-view learning (SSML). In this setting, training data is provided for two parts of the feature vector (views) in the following format (i) labeled first view examples and (ii) unlabeled first and second view examples. The goal in this setting is to obtain a classifier for the unlabeled...
We consider an application of adaptive compressive sensing for estimating time-varying sparse signals. The scenario entails the corruption of the sparse signal by additive observational noise and erasure. We formulate the problem as a partially observable Markov decision process (POMDP) and apply a multi-step lookahead solution technique, rollout. To reduce computations involved in the posterior distribution...
Group-based sparsity models [1], [2] are proven instrumental in linear regression problems for recovering signals from much fewer measurements than standard compressive sensing. A promise of these models is to lead to “interpretable” signals for which we identify its constituent groups, however we show that, in general, claims of correctly identifying the groups with convex relaxations would lead...
We extend the proximal mapping property of soft thresholding to a general class of shrinkage mappings. We give an example and demonstrate improved reconstruction performance.
Estimating an image M* ∈ ℝ+m1×m2 from its linear measurements under Poisson noise is an important problem arises from applications such as optical imaging, nuclear medicine and x-ray imaging [1]. When the image M* has a low-rank structure, we can use a small number of linear measurements to recover M*, also known as low-rank matrix recovery. This is related to compressed sensing, where the goal is...
In this paper, we propose an algorithm to maximize the total throughput in an energy harvesting two-hop amplify and forward (AF) relay network in finite signal-to-noise ratio (SNR) regimes. This algorithm is for the off-line case, assuming non-causal knowledge of the energy harvesting profiles of the source and the relay in the network. Furthermore, using the method of Lagrangian multipliers, we present...
We consider the problem of quickest localization of anomaly in a resource-constrained cyber network consisting of multiple components. Due to resource constraints, only one component can be probed at each time. The observations are random realizations drawn from two different distributions depending on whether the component is normal or anomalous. Components are assigned priorities. Components with...
Biomarker discovery and classification in medical applications both typically involve feature selection applied to a small-sample high-dimensional dataset. Recent work has proposed a framework to integrate a prior over an uncertainty class of parameterized feature-label distributions with training data to obtain optimal classifiers, MMSE classifier error estimates, and evaluate the MSE of error estimates...
This paper extends our previous effort in employing transitivity attributes of graphs for social network analysis. Specifically, here we focus on the problem of network community detection. We propose spectral analysis of the transitivity gradient matrix and compare our framework to the modularity based community detection that attracted many network researchers' attention recently. Previously, we...
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