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Found 10 papers, 0 papers with code
Weighted least-squares approximation with determinantal point processes and generalized volume sampling
We first provide a generalized version of volume-rescaled sampling yielding quasi-optimality results in expectation with a number of samples $n = O(m\log(m))$, that means that the expected $L^2$ error is bounded by a constant times the best approximation error in $L^2$.
Approximation Theory of Tree Tensor Networks: Tensorized Multivariate Functions
To answer the latter: as a candidate model class we consider approximation classes of TNs and show that these are (quasi-)Banach spaces, that many types of classical smoothness spaces are continuously embedded into said approximation classes and that TN approximation classes are themselves not embedded in any classical smoothness space.
A PAC algorithm in relative precision for bandit problem with costly sampling
This paper considers the problem of maximizing an expectation function over a finite set, or finite-arm bandit problem.
Approximation of Smoothness Classes by Deep Rectifier Networks
We consider approximation rates of sparsely connected deep rectified linear unit (ReLU) and rectified power unit (RePU) neural networks for functions in Besov spaces $B^\alpha_{q}(L^p)$ in arbitrary dimension $d$, on general domains.
Learning with tree tensor networks: complexity estimates and model selection
We propose and analyze a complexity-based model selection method for tree tensor networks in an empirical risk minimization framework and we analyze its performance over a wide range of smoothness classes.
Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions -- Part II
The considered approximation tool combines a tensorization of functions in $L^p([0, 1))$, which allows to identify a univariate function with a multivariate function (or tensor), and the use of tree tensor networks (the tensor train format) for exploiting low-rank structures of multivariate functions.
Approximation Theory of Tree Tensor Networks: Tensorized Univariate Functions -- Part I
The results of this work are both an analysis of the approximation spaces of TNs and a study of the expressivity of a particular type of neural networks (NN) -- namely feed-forward sum-product networks with sparse architecture.
Learning high-dimensional probability distributions using tree tensor networks
These algorithms exploit the multilinear parametrization of the formats to recast the nonlinear minimization problem into a sequence of empirical risk minimization problems with linear models.
Learning with tree-based tensor formats
For a given tree, the selection of the tuple of tree-based ranks that minimize the risk is a combinatorial problem.
A least-squares method for sparse low rank approximation of multivariate functions
In this paper, we propose a low-rank approximation method based on discrete least-squares for the approximation of a multivariate function from random, noisy-free observations.
