Dekun Zhou

Jun Wang, Sixian Wang, Jincheng Dai et al.

As one novel approach to realize end-to-end wireless image semantic transmission, deep learning-based joint source-channel coding (deep JSCC) method is emerging in both deep learning and communication communities. However, current deep JSCC image transmission systems are typically optimized for traditional distortion metrics such as peak signal-to-noise ratio (PSNR) or multi-scale structural similarity (MS-SSIM). But for low transmission rates, due to the imperfect wireless channel, these distortion metrics lose significance as they favor pixel-wise preservation. To account for human visual perception in semantic communications, it is of great importance to develop new deep JSCC systems optimized beyond traditional PSNR and MS-SSIM metrics. In this paper, we introduce adversarial losses to optimize deep JSCC, which tends to preserve global semantic information and local texture. Our new deep JSCC architecture combines encoder, wireless channel, decoder/generator, and discriminator, which are jointly learned under both perceptual and adversarial losses. Our method yields human visually much more pleasing results than state-of-the-art engineered image coded transmission systems and traditional deep JSCC systems. A user study confirms that achieving the perceptually similar end-to-end image transmission quality, the proposed method can save about 50\% wireless channel bandwidth cost.

Alberto Del Pia, Dekun Zhou

In this paper, we study the \emph{sparse integer least squares problem} (SILS), an NP-hard variant of least squares with sparse $\{0, \pm 1\}$-vectors. We propose an $\ell_1$-based SDP relaxation, and a randomized algorithm for SILS, which computes feasible solutions with high probability with an asymptotic approximation ratio $1/T^2$ as long as the sparsity constant $σ\ll T$. Our algorithm handles large-scale problems, delivering high-quality approximate solutions for dimensions up to $d = 10,000$. The proposed randomized algorithm applies broadly to binary quadratic programs with a cardinality constraint, even for non-convex objectives. For fixed sparsity, we provide sufficient conditions for our SDP relaxation to solve SILS, meaning that any optimal solution to the SDP relaxation yields an optimal solution to SILS. The class of data input which guarantees that SDP solves SILS is broad enough to cover many cases in real-world applications, such as privacy preserving identification and multiuser detection. We validate these conditions in two application-specific cases: the \emph{feature extraction problem}, where our relaxation solves the problem for sub-Gaussian data with weak covariance conditions, and the \emph{integer sparse recovery problem}, where our relaxation solves the problem in both high and low coherence settings under certain conditions.

Alberto Del Pia, Dekun Zhou, Yinglun Zhu

Sparse Principal Component Analysis (Sparse PCA) is a pivotal tool in data analysis and dimensionality reduction. However, Sparse PCA is a challenging problem in both theory and practice: it is known to be NP-hard and current exact methods generally require exponential runtime. In this paper, we propose a novel framework to efficiently approximate Sparse PCA by (i) approximating the general input covariance matrix with a re-sorted block-diagonal matrix, (ii) solving the Sparse PCA sub-problem in each block, and (iii) reconstructing the solution to the original problem. Our framework is simple and powerful: it can leverage any off-the-shelf Sparse PCA algorithm and achieve significant computational speedups, with a minor additive error that is linear in the approximation error of the block-diagonal matrix. Suppose $g(k, d)$ is the runtime of an algorithm (approximately) solving Sparse PCA in dimension $d$ and with sparsity constant $k$. Our framework, when integrated with this algorithm, reduces the runtime to $\mathcal{O}\left(\frac{d}{d^\star} \cdot g(k, d^\star) + d^2\right)$, where $d^\star \leq d$ is the largest block size of the block-diagonal matrix. For instance, integrating our framework with the Branch-and-Bound algorithm reduces the complexity from $g(k, d) = \mathcal{O}(k^3\cdot d^k)$ to $\mathcal{O}(k^3\cdot d \cdot (d^\star)^{k-1})$, demonstrating exponential speedups if $d^\star$ is small. We perform large-scale evaluations on many real-world datasets: for exact Sparse PCA algorithm, our method achieves an average speedup factor of 100.50, while maintaining an average approximation error of 0.61%; for approximate Sparse PCA algorithm, our method achieves an average speedup factor of 6.00 and an average approximation error of -0.91%, meaning that our method oftentimes finds better solutions.

Alberto Del Pia, Dekun Zhou

Sparse Principal Component Analysis (SPCA) is a fundamental technique for dimensionality reduction, and is NP-hard. In this paper, we introduce a randomized approximation algorithm for SPCA, which is based on the basic SDP relaxation. Our algorithm has an approximation ratio of at most the sparsity constant with high probability, if called enough times. Under a technical assumption, which is consistently satisfied in our numerical tests, the average approximation ratio is also bounded by $\mathcal{O}(\log{d})$, where $d$ is the number of features. We show that this technical assumption is satisfied if the SDP solution is low-rank, or has exponentially decaying eigenvalues. We then present a broad class of instances for which this technical assumption holds. We also demonstrate that in a covariance model, which generalizes the spiked Wishart model, our proposed algorithm achieves a near-optimal approximation ratio. We demonstrate the efficacy of our algorithm through numerical results on real-world datasets.