Related papers: Approximate computation of projection depths

Generalizable depth completion enables the acquisition of dense metric depth maps for unseen environments, offering robust perception capabilities for various downstream tasks. However, training such models typically requires large-scale…

A new depth-based clustering procedure for directional data is proposed. Such method is fully non-parametric and has the advantages to be flexible and applicable even in high dimensions when a suitable notion of depth is adopted. The…

One fundamental goal of high-dimensional statistics is to detect or recover planted structure (such as a low-rank matrix) hidden in noisy data. A growing body of work studies low-degree polynomials as a restricted model of computation for…

Interesting data often concentrate on low dimensional smooth manifolds inside a high dimensional ambient space. Random projections are a simple, powerful tool for dimensionality reduction of such data. Previous works have studied bounds on…

Many methods in differentially private model training rely on computing the similarity between a query point (such as public or synthetic data) and private data. We abstract out this common subroutine and study the following fundamental…

The regression depth of a hyperplane with respect to a set of n points in R^d is the minimum number of points the hyperplane must pass through in a rotation to vertical. We generalize hyperplane regression depth to k-flats for any k between…

Penetration depth (PD) is essential for robotics due to its extensive applications in dynamic simulation, motion planning, haptic rendering, etc. The Expanding Polytope Algorithm (EPA) is the de facto standard for this problem, which…

The depth of a visible surface of a scene is the distance between the surface and the sensor. Recovering depth information from two-dimensional images of a scene is an important task in computer vision that can assist numerous applications…

We consider discrete optimization problems with interval uncertatinty of objective function coefficients. The interval uncertainty models measurements errors. A pos\-sible optimal solution is a solution that is optimal for some possible…

The approximation of a discrete probability distribution $\mathbf{t}$ by an $M$-type distribution $\mathbf{p}$ is considered. The approximation error is measured by the informational divergence $\mathbb{D}(\mathbf{t}\Vert\mathbf{p})$, which…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

This paper presents a neural network to estimate a detailed depth map of the foreground human in a single RGB image. The result captures geometry details such as cloth wrinkles, which are important in visualization applications. To achieve…

Detecting small and distant objects remains challenging for object detectors due to scale variation, low resolution, and background clutter. Safety-critical applications require reliable detection of these objects for safe planning. Depth…

A powerful data transformation method named guided projections is proposed creating new possibilities to reveal the group structure of high-dimensional data in the presence of noise variables. Utilising projections onto a space spanned by a…

We study the space complexity of estimating the diameter of a subset of points in an arbitrary metric space in the dynamic (turnstile) streaming model. The input is given as a stream of updates to a frequency vector $x \in \mathbb{Z}_{\geq…

Many applications using large datasets require efficient methods for minimizing a proximable convex function subject to satisfying a set of linear constraints within a specified tolerance. For this task, we present a proximal projection…

Point cloud completion is the task of predicting complete geometry from partial observations using a point set representation for a 3D shape. Previous approaches propose neural networks to directly estimate the whole point cloud through…

Monocular depth prediction plays a crucial role in understanding 3D scene geometry. Although recent methods have achieved impressive progress in evaluation metrics such as the pixel-wise relative error, most methods neglect the geometric…

This paper discusses how two classes of approximate computation algorithms can be adapted, in a modular fashion, to achieve exact statistical inference from differentially private data products. Considered are approximate Bayesian…

Neural network width and depth are fundamental aspects of network topology. Universal approximation theorems provide that with increasing width or depth, there exists a neural network that approximates a function arbitrarily well. These…