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Surface parameterization is a fundamental concept in fields such as differential geometry and computer graphics. It involves mapping a surface in three-dimensional space onto a two-dimensional parameter space. This process allows for the…
A promising approach to accurate positioning of robots is ground texture based localization. It is based on the observation that visual features of ground images enable fingerprint-like place recognition. We tackle the issue of efficient…
Many tasks in data mining and related fields can be formalized as matching between objects in two heterogeneous domains, including collaborative filtering, link prediction, image tagging, and web search. Machine learning techniques,…
A new Levenberg--Marquardt (LM) method for solving nonlinear least squares problems with convex constraints is described. Various versions of the LM method have been proposed, their main differences being in the choice of a damping…
Least squares is by far the simplest and most commonly applied computational method in many fields. In almost all applications, the least squares objective is rarely the true objective. We account for this discrepancy by parametrizing the…
Parallel tempering is a generic Markov chain Monte Carlo sampling method which allows good mixing with multimodal target distributions, where conventional Metropolis-Hastings algorithms often fail. The mixing properties of the sampler…
The Metropolis-Hastings algorithm allows one to sample asymptotically from any probability distribution $\pi$. There has been recently much work devoted to the development of variants of the MH update which can handle scenarios where such…
Hyperparameter optimization is both a practical issue and an interesting theoretical problem in training of deep architectures. Despite many recent advances the most commonly used methods almost universally involve training multiple and…
In all but the most trivial optimization problems, the structure of the solutions exhibit complex interdependencies between the input parameters. Decades of research with stochastic search techniques has shown the benefit of explicitly…
While classical scaling, just like principal component analysis, is parameter-free, other methods for embedding multivariate data require the selection of one or several tuning parameters. This tuning can be difficult due to the…
We provide a unifying framework for $\mathcal{L}_2$-optimal reduced-order modeling for linear time-invariant dynamical systems and stationary parametric problems. Using parameter-separable forms of the reduced-model quantities, we derive…
We consider the problem of jointly estimating the parameters as well as the structure of binary valued Markov Random Fields, in contrast to earlier work that focus on one of the two problems. We formulate the problem as a maximization of…
Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…
Consider the problem of approximating a given probability distribution on the cube $[0,1]^n$ via the use of a square lattice discretization with mesh-size $1/N$ and the Metropolis algorithm. Here the dimension $n$ is fixed and we focus for…
Texture mapping is a common technology in the area of computer graphics, it maps the 3D surface space onto the 2D texture space. However, the loose texture space will reduce the efficiency of data storage and GPU memory addressing in the…
In parametric design, the geometric model is edited by changing relevant parameters in the parametric model, which is commonly done sequentially on multiple parameters. Without guidance on allowable parameter ranges that can guarantee the…
We consider approximating solutions to parameterized linear systems of the form $A(\mu_1,\mu_2) x(\mu_1,\mu_2) = b$. Here the matrix $A(\mu_1,\mu_2) \in \mathbb{R}^{n \times n}$ is nonsingular, large, and sparse and depends nonlinearly on…
A recent line of research has shown that gradient-based algorithms with random initialization can converge to the global minima of the training loss for over-parameterized (i.e., sufficiently wide) deep neural networks. However, the…
Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the strong convexity parameter remains a challenge; moreover, even…
The geometric constraints of Zhou et al. (2015) are a widely used technique in topology/freeform optimization to impose minimum lengthscales for manufacturability. However, its efficacy degrades as design binarization is increased, and it…