相关论文: Adversarial Manifold Estimation

Supervised 3D reconstruction has witnessed a significant progress through the use of deep neural networks. However, this increase in performance requires large scale annotations of 2D/3D data. In this paper, we explore inexpensive 2D…

We solve a regularized weighted low-rank approximation problem by a stochastic gradient descent on a manifold. To guarantee the convergence of our stochastic gradient descent, we establish a convergence theorem on manifolds for…

We propose a stochastic variance-reduced cubic regularized Newton algorithm to optimize the finite-sum problem over a Riemannian submanifold of the Euclidean space. The proposed algorithm requires a full gradient and Hessian update at the…

In this paper, we consider the composite optimization problems over the Stiefel manifold. A successful method to solve this class of problems is the proximal gradient method proposed by Chen et al. Motivated by the proximal Newton-type…

A solution manifold is the collection of points in a $d$-dimensional space satisfying a system of $s$ equations with $s<d$. Solution manifolds occur in several statistical problems including hypothesis testing, curved-exponential families,…

Despite extensive progress in point cloud robustness, existing methods primarily rely on augmentation strategies or defense mechanisms while overlooking the geometric nature of adversarial fragility. We hypothesize that adversarial…

Fitting an unknown number of hyperplanes to data is a fundamental yet challenging problem in machine learning, characterized by its non-convexity, non-differentiability, and unknown model order. Existing approaches often struggle with local…

In the thesis, we use a recently developed tight characterisation of quantum query complexity, the adversary bound, to develop new quantum algorithms and lower bounds. Our results are as follows: * We develop a new technique for the…

Nonlinear dimensionality reduction methods provide a valuable means to visualize and interpret high-dimensional data. However, many popular methods can fail dramatically, even on simple two-dimensional manifolds, due to problems such as…

Riemannian optimization is a principled framework for solving optimization problems where the desired optimum is constrained to a smooth manifold $\mathcal{M}$. Algorithms designed in this framework usually require some geometrical…

Dueling optimization considers optimizing an objective with access to only a comparison oracle of the objective function. It finds important applications in emerging fields such as recommendation systems and robotics. Existing works on…

Consider the task of locating an unknown target point using approximate distance queries: in each round, a reconstructor selects a query point and receives a noisy version of its distance to the target. This problem arises naturally in…

Manifold learning approaches seek the intrinsic, low-dimensional data structure within a high-dimensional space. Mainstream manifold learning algorithms, such as Isomap, UMAP, $t$-SNE, Diffusion Map, and Laplacian Eigenmaps do not use data…

We study the problem of estimating a manifold from random samples. In particular, we consider piecewise constant and piecewise linear estimators induced by k-means and k-flats, and analyze their performance. We extend previous results for…

Large-scale multiobjective optimization problems (LSMOPs) are characterized as involving hundreds or even thousands of decision variables and multiple conflicting objectives. An excellent algorithm for solving LSMOPs should find…

We consider optimization problems on Riemannian manifolds with equality and inequality constraints, which we call Riemannian nonlinear optimization (RNLO) problems. Although they have numerous applications, the existing studies on them are…

Std $Q$-target is a conservative, actor-critic, ensemble, $Q$-learning-based algorithm, which is based on a single key $Q$-formula: $Q$-networks standard deviation, which is an "uncertainty penalty", and, serves as a minimalistic solution…

Envelopes were recently proposed as methods for reducing estimative variation in multivariate linear regression. Estimation of an envelope usually involves optimization over Grassmann manifolds. We propose a fast and widely applicable…

Consensus algorithms are popular distributed algorithms for computing aggregate quantities, such as averages, in ad-hoc wireless networks. However, existing algorithms mostly address the case where the measurements lie in a Euclidean space.…

This paper reports the design of a high-accuracy spatial location estimation method using ultrasound waves by exploiting the fixed geometry of the transmitters. Assuming an isosceles triangle antenna configuration, where three antennas are…