Related papers: Chebyshev approximation of exponential data
This paper discusses how two classes of approximate computation algorithms can be adapted, in a modular fashion, to achieve exact statistical inference from differentially private data products. Considered are approximate Bayesian…
We present a new family of min-max optimization algorithms that automatically exploit the geometry of the gradient data observed at earlier iterations to perform more informative extra-gradient steps in later ones. Thanks to this adaptation…
Selecting a good column (or row) subset of massive data matrices has found many applications in data analysis and machine learning. We propose a new adaptive sampling algorithm that can be used to improve any relative-error column selection…
We give an algorithm to compute a one-dimensional shape-constrained function that best fits given data in weighted-$L_{\infty}$ norm. We give a single algorithm that works for a variety of commonly studied shape constraints including…
The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…
Estimators derived from a divergence criterion such as $\varphi-$divergences are generally more robust than the maximum likelihood ones. We are interested in particular in the so-called MD$\varphi$DE, an estimator built using a dual…
Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic…
An energy efficient use of large scale sensor networks necessitates activating a subset of possible sensors for estimation at a fusion center. The problem is inherently combinatorial; to this end, a set of iterative, randomized algorithms…
In this paper, we develop a general approach for probabilistic estimation and optimization. An explicit formula and a computational approach are established for controlling the reliability of probabilistic estimation based on a mixed…
This paper addresses the estimation of parameters of a Bayesian network from incomplete data. The task is usually tackled by running the Expectation-Maximization (EM) algorithm several times in order to obtain a high log-likelihood…
The Expectation Maximisation (EM) algorithm is widely used to optimise non-convex likelihood functions with latent variables. Many authors modified its simple design to fit more specific situations. For instance, the Expectation (E) step…
The ability of many powerful machine learning algorithms to deal with large data sets without compromise is often hampered by computationally expensive linear algebra tasks, of which calculating the log determinant is a canonical example.…
This paper focuses on the further development of the Lie bracket approximation approach for optimization and control via extremum seeking systems. Classical results in this area provide algorithms with exponential convergence rates for…
A local algorithm is a distributed algorithm where each node must operate solely based on the information that was available at system startup within a constant-size neighbourhood of the node. We study the applicability of local algorithms…
We establish the theoretical framework for implementing the maximumn entropy on the mean (MEM) method for linear inverse problems in the setting of approximate (data-driven) priors. We prove a.s. convergence for empirical means and further…
We explore the potential for using a nonsmooth loss function based on the max-norm in the training of an artificial neural network. We hypothesise that this may lead to superior classification results in some special cases where the…
The problem of estimating the pth moment F_p (p nonnegative and real) in data streams is as follows. There is a vector x which starts at 0, and many updates of the form x_i <-- x_i + v come sequentially in a stream. The algorithm also…
The procedure of Least Square-Errors curve fitting is extensively used in many computer applications for fitting a polynomial curve of a given degree to approximate a set of data. Although various methodologies exist to carry out curve…
We present a practical algorithm to approximate the exponential of skew-Hermitian matrices up to round-off error based on an efficient computation of Chebyshev polynomials of matrices and the corresponding error analysis. It is based on…
We study the problem of approximately recovering a probability distribution given noisy measurements of its Chebyshev polynomial moments. This problem arises broadly across algorithms, statistics, and machine learning. By leveraging a…