arXiv subjects

Ashkan Panahi

Publications and source records attributed to Ashkan Panahi.

33 records · Page 2Linked to original sources

arXiv2019

Deep Adversarial Belief Networks

We present a novel adversarial framework for training deep belief networks (DBNs), which includes replacing the generator network in the methodology of generative adversarial networks (GANs) with a DBN and developing a highly parallelizable numerical algorithm for training the resulting architecture in a stochastic manner. Unlike the existing techniques, this framework can be applied to the most general form of DBNs with no requirement for back propagation. As such, it lays a new foundation for developing DBNs on a par with GANs with various regularization units, such as pooling and normalization. Foregoing back-propagation, our framework also exhibits superior scalability as compared to other DBN and GAN learning techniques. We present a number of numerical experiments in computer vision as well as neurosciences to illustrate the main advantages of our approach.

cs.LG↗

arXiv2019

Sparse Generative Adversarial Network

We propose a new approach to Generative Adversarial Networks (GANs) to achieve an improved performance with additional robustness to its so-called and well recognized mode collapse. We first proceed by mapping the desired data onto a frame-based space for a sparse representation to lift any limitation of small support features prior to learning the structure. To that end we start by dividing an image into multiple patches and modifying the role of the generative network from producing an entire image, at once, to creating a sparse representation vector for each image patch. We synthesize an entire image by multiplying generated sparse representations to a pre-trained dictionary and assembling the resulting patches. This approach restricts the output of the generator to a particular structure, obtained by imposing a Union of Subspaces (UoS) model to the original training data, leading to more realistic images, while maintaining a desired diversity. To further regularize GANs in generating high-quality images and to avoid the notorious mode-collapse problem, we introduce a third player in GANs, called reconstructor. This player utilizes an auto-encoding scheme to ensure that first, the input-output relation in the generator is injective and second each real image corresponds to some input noise. We present a number of experiments, where the proposed algorithm shows a remarkably higher inception score compared to the equivalent conventional GANs.

cs.CV↗

arXiv2019

Joint Concept Matching based Learning for Zero-Shot Recognition

Zero-shot learning (ZSL) which aims to recognize unseen object classes by only training on seen object classes, has increasingly been of great interest in Machine Learning, and has registered with some successes. Most existing ZSL methods typically learn a projection map between the visual feature space and the semantic space and mainly suffer which is prone to a projection domain shift primarily due to a large domain gap between seen and unseen classes. In this paper, we propose a novel inductive ZSL model based on projecting both visual and semantic features into a common distinct latent space with class-specific knowledge, and on reconstructing both visual and semantic features by such a distinct common space to narrow the domain shift gap. We show that all these constraints on the latent space, class-specific knowledge, reconstruction of features and their combinations enhance the robustness against the projection domain shift problem, and improve the generalization ability to unseen object classes. Comprehensive experiments on four benchmark datasets demonstrate that our proposed method is superior to state-of-the-art algorithms.

cs.CV↗

arXiv2019

Analysis Dictionary Learning based Classification: Structure for Robustness

A discriminative structured analysis dictionary is proposed for the classification task. A structure of the union of subspaces (UoS) is integrated into the conventional analysis dictionary learning to enhance the capability of discrimination. A simple classifier is also simultaneously included into the formulated functional to ensure a more complete consistent classification. The solution of the algorithm is efficiently obtained by the linearized alternating direction method of multipliers. Moreover, a distributed structured analysis dictionary learning is also presented to address large scale datasets. It can group-(class-) independently train the structured analysis dictionaries by different machines/cores/threads, and therefore avoid a high computational cost. A consensus structured analysis dictionary and a global classifier are jointly learned in the distributed approach to safeguard the discriminative power and the efficiency of classification. Experiments demonstrate that our method achieves a comparable or better performance than the state-of-the-art algorithms in a variety of visual classification tasks. In addition, the training and testing computational complexity are also greatly reduced.

cs.CV↗

arXiv2019

Analysis Dictionary Learning: An Efficient and Discriminative Solution

Discriminative Dictionary Learning (DL) methods have been widely advocated for image classification problems. To further sharpen their discriminative capabilities, most state-of-the-art DL methods have additional constraints included in the learning stages. These various constraints, however, lead to additional computational complexity. We hence propose an efficient Discriminative Convolutional Analysis Dictionary Learning (DCADL) method, as a lower cost Discriminative DL framework, to both characterize the image structures and refine the interclass structure representations. The proposed DCADL jointly learns a convolutional analysis dictionary and a universal classifier, while greatly reducing the time complexity in both training and testing phases, and achieving a competitive accuracy, thus demonstrating great performance in many experiments with standard databases.

cs.LG↗

arXiv2018

Structured Analysis Dictionary Learning for Image Classification

We propose a computationally efficient and high-performance classification algorithm by incorporating class structural information in analysis dictionary learning. To achieve more consistent classification, we associate a class characteristic structure of independent subspaces and impose it on the classification error constrained analysis dictionary learning. Experiments demonstrate that our method achieves a comparable or better performance than the state-of-the-art algorithms in a variety of visual classification tasks. In addition, our method greatly reduces the training and testing computational complexity.

cs.CV↗

arXiv2018

Demystifying Deep Learning: A Geometric Approach to Iterative Projections

Parametric approaches to Learning, such as deep learning (DL), are highly popular in nonlinear regression, in spite of their extremely difficult training with their increasing complexity (e.g. number of layers in DL). In this paper, we present an alternative semi-parametric framework which foregoes the ordinarily required feedback, by introducing the novel idea of geometric regularization. We show that certain deep learning techniques such as residual network (ResNet) architecture are closely related to our approach. Hence, our technique can be used to analyze these types of deep learning. Moreover, we present preliminary results which confirm that our approach can be easily trained to obtain complex structures.

cs.LG↗

arXiv2018

Deep Dictionary Learning: A PARametric NETwork Approach

Deep dictionary learning seeks multiple dictionaries at different image scales to capture complementary coherent characteristics. We propose a method for learning a hierarchy of synthesis dictionaries with an image classification goal. The dictionaries and classification parameters are trained by a classification objective, and the sparse features are extracted by reducing a reconstruction loss in each layer. The reconstruction objectives in some sense regularize the classification problem and inject source signal information in the extracted features. The performance of the proposed hierarchical method increases by adding more layers, which consequently makes this model easier to tune and adapt. The proposed algorithm furthermore, shows remarkably lower fooling rate in presence of adversarial perturbation. The validation of the proposed approach is based on its classification performance using four benchmark datasets and is compared to a CNN of similar size.

cs.CV↗

arXiv2015

Performance Analysis of Parameter Estimation Using LASSO

The Least Absolute Shrinkage and Selection Operator (LASSO) has gained attention in a wide class of continuous parametric estimation problems with promising results. It has been a subject of research for more than a decade. Due to the nature of LASSO, the previous analyses have been non-parametric. This ignores useful information and makes it difficult to compare LASSO to traditional estimators. In particular, the role of the regularization parameter and super-resolution properties of LASSO have not been well-understood yet. The objective of this work is to provide a new insight into this context by introducing LASSO as a parametric technique of a varying order. This provides us theoretical expressions for the LASSO-based estimation error and false alarm rate in the asymptotic case of high SNR and dense grids. For this case, LASSO is compared to maximum likelihood and conventional beamforming. It is found that LASSO loses performance due to the regularization term, but the amount of loss is practically negligible with a proper choice of the regularization parameter. Thus, we provide suggestions on the selection of the regularization parameter. Without loss of generality, we present the comparative numerical results in the context of Direction of Arrival (DOA) estimation using a sensor array.

stat.CO↗

arXiv2015

A Novel Sparsity-Based Approach to Recursive Estimation of Dynamic Parameter Sets

We consider the problem of estimating a variable number of parameters with a dynamic nature. A familiar example is finding the position of moving targets using sensor array observations. The problem is challenging in cases where either the observations are not reliable or the parameters evolve rapidly. Inspired by the sparsity based techniques, we introduce a novel Bayesian model for the problems of interest and study its associated recursive Bayesian filter. We propose an algorithm approximating the Bayesian filter, maintaining a reasonable amount of calculations. We compare by numerical evaluation the resulting technique to state-of-the-art algorithms in different scenarios. In a scenario with a low SNR, the proposed method outperforms other complex techniques.

stat.CO↗

arXiv2015

Asymptotically Exact Error Analysis for the Generalized $\ell_2^2$-LASSO

Given an unknown signal $\mathbf{x}_0\in\mathbb{R}^n$ and linear noisy measurements $\mathbf{y}=\mathbf{A}\mathbf{x}_0+σ\mathbf{v}\in\mathbb{R}^m$, the generalized $\ell_2^2$-LASSO solves $\hat{\mathbf{x}}:=\arg\min_{\mathbf{x}}\frac{1}{2}\|\mathbf{y}-\mathbf{A}\mathbf{x}\|_2^2 + σλf(\mathbf{x})$. Here, $f$ is a convex regularization function (e.g. $\ell_1$-norm, nuclear-norm) aiming to promote the structure of $\mathbf{x}_0$ (e.g. sparse, low-rank), and, $λ\geq 0$ is the regularizer parameter. A related optimization problem, though not as popular or well-known, is often referred to as the generalized $\ell_2$-LASSO and takes the form $\hat{\mathbf{x}}:=\arg\min_{\mathbf{x}}\|\mathbf{y}-\mathbf{A}\mathbf{x}\|_2 + λf(\mathbf{x})$, and has been analyzed in [1]. [1] further made conjectures about the performance of the generalized $\ell_2^2$-LASSO. This paper establishes these conjectures rigorously. We measure performance with the normalized squared error $\mathrm{NSE}(σ):=\|\hat{\mathbf{x}}-\mathbf{x}_0\|_2^2/σ^2$. Assuming the entries of $\mathbf{A}$ and $\mathbf{v}$ be i.i.d. standard normal, we precisely characterize the "asymptotic NSE" $\mathrm{aNSE}:=\lim_{σ\rightarrow 0}\mathrm{NSE}(σ)$ when the problem dimensions $m,n$ tend to infinity in a proportional manner. The role of $λ,f$ and $\mathbf{x}_0$ is explicitly captured in the derived expression via means of a single geometric quantity, the Gaussian distance to the subdifferential. We conjecture that $\mathrm{aNSE} = \sup_{σ>0}\mathrm{NSE}(σ)$. We include detailed discussions on the interpretation of our result, make connections to relevant literature and perform computational experiments that validate our theoretical findings.

math.ST↗

arXiv2015

Precise Error Analysis of the $\ell_2$-LASSO

A classical problem that arises in numerous signal processing applications asks for the reconstruction of an unknown, $k$-sparse signal $x_0\in R^n$ from underdetermined, noisy, linear measurements $y=Ax_0+z\in R^m$. One standard approach is to solve the following convex program $\hat x=\arg\min_x \|y-Ax\|_2 + λ\|x\|_1$, which is known as the $\ell_2$-LASSO. We assume that the entries of the sensing matrix $A$ and of the noise vector $z$ are i.i.d Gaussian with variances $1/m$ and $σ^2$. In the large system limit when the problem dimensions grow to infinity, but in constant rates, we \emph{precisely} characterize the limiting behavior of the normalized squared-error $\|\hat x-x_0\|^2_2/σ^2$. Our numerical illustrations validate our theoretical predictions.

math.ST↗

arXiv2014

Wideband Waveform Design for Robust Target Detection

Future radar systems are expected to use waveforms of a high bandwidth, where the main advantage is an improved range resolution. In this paper, a technique to design robust wideband waveforms for a Multiple-Input-Single-Output system is developed. The context is optimal detection of a single object with partially unknown parameters. The waveforms are robust in the sense that, for a single transmission, detection capability is maintained over an interval of time-delay and time-scaling (Doppler) parameters. A solution framework is derived, approximated, and formulated as an optimization by means of basis expansion. In terms of probabilities of detection and false alarm, numerical evaluation shows the efficiency of the proposed method when compared with a Linear Frequency Modulated signal and a Gaussian pulse.

stat.AP↗

arXiv2013

Calculation of the Performance of Communication Systems from Measured Oscillator Phase Noise

Oscillator phase noise (PN) is one of the major problems that affect the performance of communication systems. In this paper, a direct connection between oscillator measurements, in terms of measured single-side band PN spectrum, and the optimal communication system performance, in terms of the resulting error vector magnitude (EVM) due to PN, is mathematically derived and analyzed. First, a statistical model of the PN, considering the effect of white and colored noise sources, is derived. Then, we utilize this model to derive the modified Bayesian Cramer-Rao bound on PN estimation, and use it to find an EVM bound for the system performance. Based on our analysis, it is found that the influence from different noise regions strongly depends on the communication bandwidth, i.e., the symbol rate. For high symbol rate communication systems, cumulative PN that appears near carrier is of relatively low importance compared to the white PN far from carrier. Our results also show that 1/f^3 noise is more predictable compared to 1/f^2 noise and in a fair comparison it affects the performance less.

cs.IT↗

arXiv2012

A robust l_1 penalized DOA estimator

The SPS-LASSO has recently been introduced as a solution to the problem of regularization parameter selection in the complex-valued LASSO problem. Still, the dependence on the grid size and the polynomial time of performing convex optimization technique in each iteration, in addition to the deficiencies in the low noise regime, confines its performance for Direction of Arrival (DOA) estimation. This work presents methods to apply LASSO without grid size limitation and with less complexity. As we show by simulations, the proposed methods loose a negligible performance compared to the Maximum Likelihood (ML) estimator, which needs a combinatorial search We also show by simulations that compared to practical implementations of ML, the proposed techniques are less sensitive to the source power difference.

cs.IT↗