Related papers: Fast implementation of the Tukey depth
We derive an algorithm of optimal complexity which determines whether a given matrix is a Cauchy matrix, and which exactly recovers the Cauchy points defining a Cauchy matrix from the matrix entries. Moreover, we study how to approximate a…
Omnidirectional depth estimation has received much attention from researchers in recent years. However, challenges arise due to camera soiling and variations in camera layouts, affecting the robustness and flexibility of the algorithm. In…
Measuring how quickly iterative methods converge is essential in computational mathematics, but current approaches have significant limitations. Q-order analysis requires strict smoothness conditions, while R-order analysis lacks precision…
Multi-view depth estimation plays a critical role in reconstructing and understanding the 3D world. Recent learning-based methods have made significant progress in it. However, multi-view depth estimation is fundamentally a…
Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an…
Tightness is a generalisation of the notion of convexity: a space is tight if and only if it is "as convex as possible", given its topological constraints. For a simplicial complex, deciding tightness has a straightforward exponential time…
Fixed-point solvers are ubiquitous in nonlinear PDEs, yet their progress collapses whenever the Jacobian at the solution carries an eigenvalue arbitrarily close to one. We ask whether such stagnation can be removed without storing long…
Small depth networks arise in a variety of network related applications, often in the form of maximum flow and maximum weighted matching. Recent works have generalized such methods to include costs arising from concave functions. In this…
We develop a new algorithm for factoring a bivariate polynomial $F\in \mathbb{K}[x,y]$ which takes fully advantage of the geometry of the Newton polygon of $F$. Under a non degeneracy hypothesis, the complexity is…
Monocular 3D object detection has attracted widespread attention due to its potential to accurately obtain object 3D localization from a single image at a low cost. Depth estimation is an essential but challenging subtask of monocular 3D…
A collection of algorithms is described for numerically computing with smooth functions defined on the unit sphere. Functions are approximated to essentially machine precision by using a structure-preserving iterative variant of Gaussian…
Several methods for solving efficiently the one-dimensional deconvolution problem are proposed. The problem is to solve the Volterra equation ${\mathbf k} u:=\int_0^t k(t-s)u(s)ds=g(t),\quad 0\leq t\leq T$. The data, $g(t)$, are noisy. Of…
A deep approximation is an approximating function defined by composing more than one layer of simple functions. We study deep approximations of functions of one variable using layers consisting of low-degree polynomials or simple conformal…
Estimating the depth of omnidirectional images is more challenging than that of normal field-of-view (NFoV) images because the varying distortion can significantly twist an object's shape. The existing methods suffer from troublesome…
Depth-adaptive neural networks can dynamically adjust depths according to the hardness of input words, and thus improve efficiency. The main challenge is how to measure such hardness and decide the required depths (i.e., layers) to conduct.…
The paper is devoted to the efficient computation of high-order cubature formulas for volume potentials obtained within the framework of approximate approximations. We combine this approach with modern methods of structured tensor product…
In appropriate frameworks, automatic differentiation is transparent to the user at the cost of being a significant computational burden when the number of operations is large. For iterative algorithms, implicit differentiation alleviates…
The efficiency of exact subset sum problem algorithms which compute individual subset sums is defined as $e=min(T/z, 1)$, where $z$ is the number of subset sums computed. $e$ is related to these algorithms' computational complexity. This…
Submodular Functions are a special class of set functions, which generalize several information-theoretic quantities such as entropy and mutual information [1]. Submodular functions have subgradients and subdifferentials [2] and admit…
Multipoint evaluation is the computational task of evaluating a polynomial given as a list of coefficients at a given set of inputs. And while \emph{nearly linear time} algorithms have been known for the univariate instance of multipoint…