arXiv subjects

Lawrence Carin

Publications and source records attributed to Lawrence Carin.

At least 199 records · Page 11Linked to original sources

arXiv2015

A Generative Model for Deep Convolutional Learning

A generative model is developed for deep (multi-layered) convolutional dictionary learning. A novel probabilistic pooling operation is integrated into the deep model, yielding efficient bottom-up (pretraining) and top-down (refinement) probabilistic learning. Experimental results demonstrate powerful capabilities of the model to learn multi-layer features from images, and excellent classification results are obtained on the MNIST and Caltech 101 datasets.

stat.ML↗

arXiv2015

Generative Deep Deconvolutional Learning

A generative Bayesian model is developed for deep (multi-layer) convolutional dictionary learning. A novel probabilistic pooling operation is integrated into the deep model, yielding efficient bottom-up and top-down probabilistic learning. After learning the deep convolutional dictionary, testing is implemented via deconvolutional inference. To speed up this inference, a new statistical approach is proposed to project the top-layer dictionary elements to the data level. Following this, only one layer of deconvolution is required during testing. Experimental results demonstrate powerful capabilities of the model to learn multi-layer features from images. Excellent classification results are obtained on both the MNIST and Caltech 101 datasets.

stat.ML↗

arXiv2015

Compressive Hyperspectral Imaging with Side Information

A blind compressive sensing algorithm is proposed to reconstruct hyperspectral images from spectrally-compressed measurements.The wavelength-dependent data are coded and then superposed, mapping the three-dimensional hyperspectral datacube to a two-dimensional image. The inversion algorithm learns a dictionary {\em in situ} from the measurements via global-local shrinkage priors. By using RGB images as side information of the compressive sensing system, the proposed approach is extended to learn a coupled dictionary from the joint dataset of the compressed measurements and the corresponding RGB images, to improve reconstruction quality. A prototype camera is built using a liquid-crystal-on-silicon modulator. Experimental reconstructions of hyperspectral datacubes from both simulated and real compressed measurements demonstrate the efficacy of the proposed inversion algorithm, the feasibility of the camera and the benefit of side information.

cs.CV↗

arXiv2014

Tree-Structure Bayesian Compressive Sensing for Video

A Bayesian compressive sensing framework is developed for video reconstruction based on the color coded aperture compressive temporal imaging (CACTI) system. By exploiting the three dimension (3D) tree structure of the wavelet and Discrete Cosine Transformation (DCT) coefficients, a Bayesian compressive sensing inversion algorithm is derived to reconstruct (up to 22) color video frames from a single monochromatic compressive measurement. Both simulated and real datasets are adopted to verify the performance of the proposed algorithm.

cs.CV↗

arXiv2014

Reconstruction of Signals Drawn from a Gaussian Mixture from Noisy Compressive Measurements

This paper determines to within a single measurement the minimum number of measurements required to successfully reconstruct a signal drawn from a Gaussian mixture model in the low-noise regime. The method is to develop upper and lower bounds that are a function of the maximum dimension of the linear subspaces spanned by the Gaussian mixture components. The method not only reveals the existence or absence of a minimum mean-squared error (MMSE) error floor (phase transition) but also provides insight into the MMSE decay via multivariate generalizations of the MMSE dimension and the MMSE power offset, which are a function of the interaction between the geometrical properties of the kernel and the Gaussian mixture. These results apply not only to standard linear random Gaussian measurements but also to linear kernels that minimize the MMSE. It is shown that optimal kernels do not change the number of measurements associated with the MMSE phase transition, rather they affect the sensed power required to achieve a target MMSE in the low-noise regime. Overall, our bounds are tighter and sharper than standard bounds on the minimum number of measurements needed to recover sparse signals associated with a union of subspaces model, as they are not asymptotic in the signal dimension or signal sparsity.

cs.IT↗

arXiv2014

Low-Cost Compressive Sensing for Color Video and Depth

A simple and inexpensive (low-power and low-bandwidth) modification is made to a conventional off-the-shelf color video camera, from which we recover {multiple} color frames for each of the original measured frames, and each of the recovered frames can be focused at a different depth. The recovery of multiple frames for each measured frame is made possible via high-speed coding, manifested via translation of a single coded aperture; the inexpensive translation is constituted by mounting the binary code on a piezoelectric device. To simultaneously recover depth information, a {liquid} lens is modulated at high speed, via a variable voltage. Consequently, during the aforementioned coding process, the liquid lens allows the camera to sweep the focus through multiple depths. In addition to designing and implementing the camera, fast recovery is achieved by an anytime algorithm exploiting the group-sparsity of wavelet/DCT coefficients.

cs.CV↗

arXiv2014

Multiscale Shrinkage and Lévy Processes

A new shrinkage-based construction is developed for a compressible vector $\boldsymbol{x}\in\mathbb{R}^n$, for cases in which the components of $\xv$ are naturally associated with a tree structure. Important examples are when $\xv$ corresponds to the coefficients of a wavelet or block-DCT representation of data. The method we consider in detail, and for which numerical results are presented, is based on increments of a gamma process. However, we demonstrate that the general framework is appropriate for many other types of shrinkage priors, all within the Lévy process family, with the gamma process a special case. Bayesian inference is carried out by approximating the posterior with samples from an MCMC algorithm, as well as by constructing a heuristic variational approximation to the posterior. We also consider expectation-maximization (EM) for a MAP (point) solution. State-of-the-art results are manifested for compressive sensing and denoising applications, the latter with spiky (non-Gaussian) noise.

stat.ML↗

arXiv2014

Finite sample posterior concentration in high-dimensional regression

We study the behavior of the posterior distribution in high-dimensional Bayesian Gaussian linear regression models having $p\gg n$, with $p$ the number of predictors and $n$ the sample size. Our focus is on obtaining quantitative finite sample bounds ensuring sufficient posterior probability assigned in neighborhoods of the true regression coefficient vector, $β^0$, with high probability. We assume that $β^0$ is approximately $S$-sparse and obtain universal bounds, which provide insight into the role of the prior in controlling concentration of the posterior. Based on these finite sample bounds, we examine the implied asymptotic contraction rates for several examples showing that sparsely-structured and heavy-tail shrinkage priors exhibit rapid contraction rates. We also demonstrate that a stronger result holds for the Uniform-Gaussian\footnote[2]{A binary vector of indicators ($γ$) is drawn from the uniform distribution on the set of binary sequences with exactly $S$ ones, and then each $β_i\sim\mathcal{N}(0,V^2)$ if $γ_i=1$ and $β_i=0$ if $γ_i=0$.} prior. These types of finite sample bounds provide guidelines for designing and evaluating priors for high-dimensional problems.

math.ST↗

arXiv2013

Latent protein trees

Unbiased, label-free proteomics is becoming a powerful technique for measuring protein expression in almost any biological sample. The output of these measurements after preprocessing is a collection of features and their associated intensities for each sample. Subsets of features within the data are from the same peptide, subsets of peptides are from the same protein, and subsets of proteins are in the same biological pathways, therefore, there is the potential for very complex and informative correlational structure inherent in these data. Recent attempts to utilize this data often focus on the identification of single features that are associated with a particular phenotype that is relevant to the experiment. However, to date, there have been no published approaches that directly model what we know to be multiple different levels of correlation structure. Here we present a hierarchical Bayesian model which is specifically designed to model such correlation structure in unbiased, label-free proteomics. This model utilizes partial identification information from peptide sequencing and database lookup as well as the observed correlation in the data to appropriately compress features into latent proteins and to estimate their correlation structure. We demonstrate the effectiveness of the model using artificial/benchmark data and in the context of a series of proteomics measurements of blood plasma from a collection of volunteers who were infected with two different strains of viral influenza.

stat.AP↗

arXiv2013

Dynamic Clustering via Asymptotics of the Dependent Dirichlet Process Mixture

This paper presents a novel algorithm, based upon the dependent Dirichlet process mixture model (DDPMM), for clustering batch-sequential data containing an unknown number of evolving clusters. The algorithm is derived via a low-variance asymptotic analysis of the Gibbs sampling algorithm for the DDPMM, and provides a hard clustering with convergence guarantees similar to those of the k-means algorithm. Empirical results from a synthetic test with moving Gaussian clusters and a test with real ADS-B aircraft trajectory data demonstrate that the algorithm requires orders of magnitude less computational time than contemporary probabilistic and hard clustering algorithms, while providing higher accuracy on the examined datasets.

cs.LG↗

arXiv2013

Adaptive Temporal Compressive Sensing for Video

This paper introduces the concept of adaptive temporal compressive sensing (CS) for video. We propose a CS algorithm to adapt the compression ratio based on the scene's temporal complexity, computed from the compressed data, without compromising the quality of the reconstructed video. The temporal adaptivity is manifested by manipulating the integration time of the camera, opening the possibility to real-time implementation. The proposed algorithm is a generalized temporal CS approach that can be incorporated with a diverse set of existing hardware systems.

stat.AP↗

arXiv2013

Negative Binomial Process Count and Mixture Modeling

The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability measure for mixture modeling and whose marginalization leads to an NB process for count modeling. A draw from the NB process consists of a Poisson distributed finite number of distinct atoms, each of which is associated with a logarithmic distributed number of data samples. We reveal relationships between various count- and mixture-modeling distributions and construct a Poisson-logarithmic bivariate distribution that connects the NB and Chinese restaurant table distributions. Fundamental properties of the models are developed, and we derive efficient Bayesian inference. It is shown that with augmentation and normalization, the NB process and gamma-NB process can be reduced to the Dirichlet process and hierarchical Dirichlet process, respectively. These relationships highlight theoretical, structural and computational advantages of the NB process. A variety of NB processes, including the beta-geometric, beta-NB, marked-beta-NB, marked-gamma-NB and zero-inflated-NB processes, with distinct sharing mechanisms, are also constructed. These models are applied to topic modeling, with connections made to existing algorithms under Poisson factor analysis. Example results show the importance of inferring both the NB dispersion and probability parameters.

stat.ME↗

arXiv2013

Multichannel Electrophysiological Spike Sorting via Joint Dictionary Learning & Mixture Modeling

We propose a construction for joint feature learning and clustering of multichannel extracellular electrophysiological data across multiple recording periods for action potential detection and discrimination ("spike sorting"). Our construction improves over the previous state-of-the art principally in four ways. First, via sharing information across channels, we can better distinguish between single-unit spikes and artifacts. Second, our proposed "focused mixture model" (FMM) elegantly deals with units appearing, disappearing, or reappearing over multiple recording days, an important consideration for any chronic experiment. Third, by jointly learning features and clusters, we improve performance over previous attempts that proceeded via a two-stage ("frequentist") learning process. Fourth, by directly modeling spike rate, we improve detection of sparsely spiking neurons. Moreover, our Bayesian construction seamlessly handles missing data. We present state-of-the-art performance without requiring manually tuning of many hyper-parameters on both a public dataset with partial ground truth and a new experimental dataset.

q-bio.QM↗

arXiv2013

Generalized Bregman Divergence and Gradient of Mutual Information for Vector Poisson Channels

We investigate connections between information-theoretic and estimation-theoretic quantities in vector Poisson channel models. In particular, we generalize the gradient of mutual information with respect to key system parameters from the scalar to the vector Poisson channel model. We also propose, as another contribution, a generalization of the classical Bregman divergence that offers a means to encapsulate under a unifying framework the gradient of mutual information results for scalar and vector Poisson and Gaussian channel models. The so-called generalized Bregman divergence is also shown to exhibit various properties akin to the properties of the classical version. The vector Poisson channel model is drawing considerable attention in view of its application in various domains: as an example, the availability of the gradient of mutual information can be used in conjunction with gradient descent methods to effect compressive-sensing projection designs in emerging X-ray and document classification applications.

cs.IT↗

arXiv2013

Augment-and-Conquer Negative Binomial Processes

By developing data augmentation methods unique to the negative binomial (NB) distribution, we unite seemingly disjoint count and mixture models under the NB process framework. We develop fundamental properties of the models and derive efficient Gibbs sampling inference. We show that the gamma-NB process can be reduced to the hierarchical Dirichlet process with normalization, highlighting its unique theoretical, structural and computational advantages. A variety of NB processes with distinct sharing mechanisms are constructed and applied to topic modeling, with connections to existing algorithms, showing the importance of inferring both the NB dispersion and probability parameters.

stat.ML↗

arXiv2013

Coded aperture compressive temporal imaging

We use mechanical translation of a coded aperture for code division multiple access compression of video. We present experimental results for reconstruction at 148 frames per coded snapshot.

cs.CV↗

arXiv2013

Bayesian Gaussian Copula Factor Models for Mixed Data

Gaussian factor models have proven widely useful for parsimoniously characterizing dependence in multivariate data. There is a rich literature on their extension to mixed categorical and continuous variables, using latent Gaussian variables or through generalized latent trait models acommodating measurements in the exponential family. However, when generalizing to non-Gaussian measured variables the latent variables typically influence both the dependence structure and the form of the marginal distributions, complicating interpretation and introducing artifacts. To address this problem we propose a novel class of Bayesian Gaussian copula factor models which decouple the latent factors from the marginal distributions. A semiparametric specification for the marginals based on the extended rank likelihood yields straightforward implementation and substantial computational gains, critical for scaling to high-dimensional applications. We provide new theoretical and empirical justifications for using this likelihood in Bayesian inference. We propose new default priors for the factor loadings and develop efficient parameter-expanded Gibbs sampling for posterior computation. The methods are evaluated through simulations and applied to a dataset in political science. The methods in this paper are implemented in the R package bfa.

stat.ME↗

arXiv2012

Nested Dictionary Learning for Hierarchical Organization of Imagery and Text

A tree-based dictionary learning model is developed for joint analysis of imagery and associated text. The dictionary learning may be applied directly to the imagery from patches, or to general feature vectors extracted from patches or superpixels (using any existing method for image feature extraction). Each image is associated with a path through the tree (from root to a leaf), and each of the multiple patches in a given image is associated with one node in that path. Nodes near the tree root are shared between multiple paths, representing image characteristics that are common among different types of images. Moving toward the leaves, nodes become specialized, representing details in image classes. If available, words (text) are also jointly modeled, with a path-dependent probability over words. The tree structure is inferred via a nested Dirichlet process, and a retrospective stick-breaking sampler is used to infer the tree depth and width.

cs.LG↗