相关论文: Accumulated Random Distances in High Dimensions --…
In this paper, we derive the distribution of a two-dimensional (complex) random walk in which the angle of each step is restricted to a subset of the circle. This setting appears in various domains, such as in over-the-air computation in…
This paper develops efficient algorithms for distributed average consensus with quantized communication using the alternating direction method of multipliers (ADMM). We first study the effects of probabilistic and deterministic…
Accurate maps are a prerequisite for virtually all mobile robot tasks. Most state-of-the-art maps assume a static world; therefore, dynamic objects are filtered out of the measurements. However, this division ignores movable but non-moving…
Statistical models with constrained probability distributions are abundant in machine learning. Some examples include regression models with norm constraints (e.g., Lasso), probit, many copula models, and latent Dirichlet allocation (LDA).…
Several convergence results in Hilbert scales under different source conditions are proved and orders of convergence and optimal orders of convergence are derived. Also, relations between those source conditions are proved. The concept of a…
Binary segmentation, which is sequential in nature is thus far the most widely used method for identifying multiple change points in statistical models. Here we propose a top down methodology called arbitrary segmentation that proceeds in a…
Adaptive sampling theory has shown that, with proper assumptions on the signal class, algorithms exist to reconstruct a signal in $\mathbb{R}^{d}$ with an optimal number of samples. We generalize this problem to the case of spatial signals,…
This paper establishes sharp dimension-free concentration inequalities and expectation bounds for the deviation of the sum of simple random tensors from its expectation. As part of our analysis, we use generic chaining techniques to obtain…
Minimizing a convex function of a measure with a sparsity-inducing penalty is a typical problem arising, e.g., in sparse spikes deconvolution or two-layer neural networks training. We show that this problem can be solved by discretizing the…
Barycentric averaging is a principled way of summarizing populations of measures. Existing algorithms for estimating barycenters typically parametrize them as weighted sums of Diracs and optimize their weights and/or locations. However,…
Although the \emph{residual method}, or \emph{constrained regularization}, is frequently used in applications, a detailed study of its properties is still missing. This sharply contrasts the progress of the theory of Tikhonov…
We analyze the behavior of stochastic approximation algorithms where iterates, in expectation, progress towards an objective at each step. When progress is proportional to the step size of the algorithm, we prove exponential concentration…
We consider the problem of rank aggregation based on new distance measures derived through axiomatic approaches and based on score-based methods. In the first scenario, we derive novel distance measures that allow for discriminating between…
Deep neural networks, when optimized with sufficient data, provide accurate representations of high-dimensional functions; in contrast, function approximation techniques that have predominated in scientific computing do not scale well with…
We explore the features of two methods of stabilization, aggregation and supremizer methods, for reduced-order modeling of parametrized optimal control problems. In both methods, the reduced basis spaces are augmented to guarantee…
This paper introduces new parameter-free first-order methods for convex optimization problems in which the objective function exhibits H\"{o}lder smoothness. Inspired by the recently proposed distance-over-gradient (DOG) technique, we…
Over-parameterized deep models usually over-fit to a given training distribution, which makes them sensitive to small changes and out-of-distribution samples at inference time, leading to low generalization performance. To this end, several…
Data normalization is an essential task when modeling a classification system. When dealing with data streams, data normalization becomes especially challenging since we may not know in advance the properties of the features, such as their…
Many problems in science and engineering involve, as part of their solution process, the consideration of a separable function which is the sum of two convex functions, one of them possibly non-smooth. Recently a few works have discussed…
Some prominent discretisation methods such as finite elements provide a way to approximate a function of $d$ variables from $n$ values it takes on the nodes $x_i$ of the corresponding mesh. The accuracy is $n^{-s_a/d}$ in $L^2$-norm, where…