Related papers: Approximation with Random Bases: Pro et Contra
Interest in the random-order model (ROM) leads us to initiate a study of utilizing random-order arrivals to extract random bits with the goal of derandomizing algorithms. Besides producing simple algorithms, simulating random bits through…
The statistical problem of parameter estimation in partially observed hypoelliptic diffusion processes is naturally occurring in many applications. However, due to the noise structure, where the noise components of the different coordinates…
We provide finite-sample analysis of a general framework for using k-nearest neighbor statistics to estimate functionals of a nonparametric continuous probability density, including entropies and divergences. Rather than plugging a…
Given a Hilbert space $\mathcal H$ and a finite measure space $\Omega$, the approximation of a vector-valued function $f: \Omega \to \mathcal H$ by a $k$-dimensional subspace $\mathcal U \subset \mathcal H$ plays an important role in…
We enhance the approximation capabilities of algebraic polynomials by composing them with homeomorphisms. This composition yields families of functions that remain dense in the space of continuous functions, while enabling more accurate…
The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…
The computational complexity of reasoning within the Dempster-Shafer theory of evidence is one of the main points of criticism this formalism has to face. To overcome this difficulty various approximation algorithms have been suggested that…
Neural networks are usually not the tool of choice for nonparametric high-dimensional problems where the number of input features is much larger than the number of observations. Though neural networks can approximate complex multivariate…
Increasing amounts of available data have led to a heightened need for representing large-scale probabilistic knowledge bases. One approach is to use a probabilistic database, a model with strong assumptions that allow for efficiently…
We consider models for multivariate point processes where the intensity is given nonparametrically in terms of functions in a reproducing kernel Hilbert space. The likelihood function involves a time integral and is consequently not given…
Probabilistic conditioning is concerned with the identification of a distribution of a random variable $X$ given a random variable $Y$. It is a cornerstone of scientific and engineering applications where modeling uncertainty is key. This…
In supervised learning using kernel methods, we often encounter a large-scale finite-sum minimization over a reproducing kernel Hilbert space (RKHS). Large-scale finite-sum problems can be solved using efficient variants of Newton method,…
The A* algorithm is commonly used to solve NP-hard combinatorial optimization problems. When provided with a completely informed heuristic function, A* solves many NP-hard minimum-cost path problems in time polynomial in the branching…
Variational mean field approximations tend to struggle with contemporary overparametrized deep neural networks. Where a Bayesian treatment is usually associated with high-quality predictions and uncertainties, the practical reality has been…
In biomedical studies, researchers are often interested in assessing the association between one or more ordinal explanatory variables and an outcome variable, at the same time adjusting for covariates of any type. The outcome variable may…
Incorporating domain knowledge into the modeling process is an effective way to improve learning accuracy. However, as it is provided by humans, domain knowledge can only be specified with some degree of uncertainty. We propose to…
Recommender systems present a customized list of items based upon user or item characteristics with the objective of reducing a large number of possible choices to a smaller ranked set most likely to appeal to the user. A variety of…
Being able to reason in an environment with a large number of discrete actions is essential to bringing reinforcement learning to a larger class of problems. Recommender systems, industrial plants and language models are only some of the…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
We present bounds on the maximal gain of adaptive and randomized algorithms over non-adaptive, deterministic ones for approximating linear operators on convex sets. If the sets are additionally symmetric, then our results are optimal. For…