Related papers: Optimal Algorithms for $L_1$-subspace Signal Proce…
In this paper, we study the communication and (sub)gradient computation costs in distributed optimization and give a sharp complexity analysis for the proposed distributed accelerated gradient methods. We present two algorithms based on the…
New algorithms are devised for finding the maxima of multidimensional point samples, one of the very first problems studied in computational geometry. The algorithms are very simple and easily coded and modified for practical needs. The…
The problem of minimizing the maximum of $N$ convex, Lipschitz functions plays significant roles in optimization and machine learning. It has a series of results, with the most recent one requiring $O(N\epsilon^{-2/3} + \epsilon^{-8/3})$…
We construct an adaptive asymptotically optimal in the classical norm of the space L(2) of square integrable functions non - parametrical multidimensional time defined signal regaining (adaptive filtration, noise canceller) on the…
This paper presents a novel L1-norm semi-supervised learning algorithm for robust image analysis by giving new L1-norm formulation of Laplacian regularization which is the key step of graph-based semi-supervised learning. Since our L1-norm…
Motivated by the observation that a given signal $\boldsymbol{x}$ admits sparse representations in multiple dictionaries $\boldsymbol{\Psi}_d$ but with varying levels of sparsity across dictionaries, we propose two new algorithms for the…
We consider the problem of finding optimal piecewise constant approximations of one-dimensional signals. These approximations should consist of a specified number of segments (samples) and minimise the mean squared error to the original…
We present an amelioration of current known algorithms for optimal spectral partitioning problems. The idea is to use the advantage of a representation using density functions while decreasing the computational time. This is done by…
Excellent variational approximations to Gaussian process posteriors have been developed which avoid the $\mathcal{O}\left(N^3\right)$ scaling with dataset size $N$. They reduce the computational cost to $\mathcal{O}\left(NM^2\right)$, with…
Compressed sensing has shown that it is possible to reconstruct sparse high dimensional signals from few linear measurements. In many cases, the solution can be obtained by solving an L1-minimization problem, and this method is accurate…
We study a two-dimensional generalization of the classical Bin Packing problem, denoted as 2D Demand Bin Packing. In this context, each bin is a horizontal timeline, and rectangular tasks (representing electric appliances or computational…
This work studies the linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). Searching this approximation in a data-driven approach is formalised as attempting to solve a low-rank…
This paper introduces a novel approach for recovering sparse signals using sorted L1/L2 minimization. The proposed method assigns higher weights to indices with smaller absolute values and lower weights to larger values, effectively…
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
In this work, we consider a class of differentiable criteria for sparse image computing problems, where a nonconvex regularization is applied to an arbitrary linear transform of the target image. As special cases, it includes…
The problem of maximizing the $p$-th power of a $p$-norm over a halfspace-presented polytope in $\R^d$ is a convex maximization problem which plays a fundamental role in computational convexity. It has been shown in 1986 that this problem…
In recent years, non-convex optimization problems are more often described by generalized $(L_0, L_1)$-smoothness assumption rather than standard one. Meanwhile, severely corrupted data used in these problems has increased the demand for…
In this technical report, we discuss several sampling algorithms for Determinantal Point Processes (DPP). DPPs have recently gained a broad interest in the machine learning and statistics literature as random point processes with negative…
Template matching is widely used for many applications in image and signal processing and usually is time-critical. Traditional methods usually focus on how to reduce the search locations by coarse-to-fine strategy or full search combined…
Signal estimation from incomplete observations improves as more signal structure can be exploited in the inference process. Classic algorithms (e.g., Kalman filtering) have exploited strong dynamic structure for time-varying signals while…