Related papers: Identifiability and Error Bound: Metric and Geomet…
We analyse the convergence of the gradient projection algorithm, which is finalized with the Newton method, to a stationary point for the problem of nonconvex constrained optimization $\min_{x \in S} f(x)$ with a proximally smooth set $S =…
Interior-point methods offer a highly versatile framework for convex optimization that is effective in theory and practice. A key notion in their theory is that of a self-concordant barrier. We give a suitable generalization of…
The problem of finding suitable point embedding or geometric configurations given only Euclidean distance information of point pairs arises both as a core task and as a sub-problem in a variety of machine learning applications. In this…
The standard approach to representation learning on attributed graphs -- i.e., simultaneously reconstructing node attributes and graph structure -- is geometrically flawed, as it merges two potentially incompatible metric spaces. This…
Surface comparison and matching is a challenging problem in computer vision. While reparametrization-invariant Sobolev metrics provide meaningful elastic distances and point correspondences via the geodesic boundary value problem, solving…
We propose a method that morphs high-orger meshes such that their boundaries and interfaces coincide/align with implicitly defined geometries. Our focus is particularly on the case when the target surface is prescribed as the zero…
We consider the problem of automatically proving resource bounds. That is, we study how to prove that an integer-valued resource variable is bounded by a given program expression. Automatic resource-bound analysis has recently received…
The pixels in an image, and the objects, scenes, and actions that they compose, determine whether an image will be memorable or forgettable. While memorability varies by image, it is largely independent of an individual observer. Observer…
Traditional manifold learning algorithms assumed that the embedded manifold is globally or locally isometric to Euclidean space. Under this assumption, they divided manifold into a set of overlapping local patches which are locally…
Bayesian optimization (BO) recently became popular in robotics to optimize control parameters and parametric policies in direct reinforcement learning due to its data efficiency and gradient-free approach. However, its performance may be…
The classical approach to system identification is based on stochastic assumptions about the measurement error, and provides estimates that have random nature. Worst-case identification, on the other hand, only assumes the knowledge of…
Bayesian optimization is a principled optimization strategy for a black-box objective function. It shows its effectiveness in a wide variety of real-world applications such as scientific discovery and experimental design. In general, the…
We describe verification techniques for embedded memory systems using efficient memory modeling (EMM), without explicitly modeling each memory bit. We extend our previously proposed approach of EMM in Bounded Model Checking (BMC) for a…
While the expected calibration error (ECE), which employs binning, is widely adopted to evaluate the calibration performance of machine learning models, theoretical understanding of its estimation bias is limited. In this paper, we present…
We study robustness verification of neural networks via metric algebraic geometry. For polynomial neural networks, certifying a robustness radius amounts to computing the distance to the algebraic decision boundary. We use the Euclidean…
We propose an extrinsic Bayesian optimization (eBO) framework for general optimization problems on manifolds. Bayesian optimization algorithms build a surrogate of the objective function by employing Gaussian processes and quantify the…
In order to circumvent statistical and computational hardness results in sequential decision-making, recent work has considered smoothed online learning, where the distribution of data at each time is assumed to have bounded likeliehood…
Manifold learning methods are an invaluable tool in today's world of increasingly huge datasets. Manifold learning algorithms can discover a much lower-dimensional representation (embedding) of a high-dimensional dataset through non-linear…
In the field of remote sensing, we often utilize oriented bounding boxes (OBB) to bound the objects. This approach significantly reduces the overlap among dense detection boxes and minimizes the inclusion of background content within the…
This paper proposes a novel maximum-likelihood (ML) soft-decision decoding framework for linear block codes, termed error-building decoding (EBD). The complete decoding process can be performed using only the parity-check matrix, without…