Related papers: Some remarks on regularized Shannon sampling formu…
We study the problem of estimating the parameters of a Gaussian distribution when samples are only shown if they fall in some (unknown) subset $S \subseteq \R^d$. This core problem in truncated statistics has long history going back to…
In this paper, we propose a new discriminative model named \emph{nonextensive information theoretical machine (NITM)} based on nonextensive generalization of Shannon information theory. In NITM, weight parameters are treated as random…
Motivated by a recent result of Daskalakis et al. 2018, we analyze the population version of Expectation-Maximization (EM) algorithm for the case of \textit{truncated} mixtures of two Gaussians. Truncated samples from a $d$-dimensional…
Large scale optimization problems are ubiquitous in machine learning and data analysis and there is a plethora of algorithms for solving such problems. Many of these algorithms employ sub-sampling, as a way to either speed up the…
Stochastic processes wherein the size of the state space is changing as a function of time offer models for the emergence of scale-invariant features observed in complex systems. I consider such a sample-space reducing (SSR) stochastic…
Compressed sensing is a signal processing technique whereby the limits imposed by the Shannon--Nyquist theorem can be exceeded provided certain conditions are imposed on the signal. Such conditions occur in many real-world scenarios, and…
The effectiveness of non-parametric, kernel-based methods for function estimation comes at the price of high computational complexity, which hinders their applicability in adaptive, model-based control. Motivated by approximation techniques…
A new sampling methodology based on incomplete cosine expansion series is presented as an alternative to the traditional sinc function approach. Numerical integration shows that this methodology is efficient and practical. Applying the…
In this note we present a fully information theoretic approach to renormalization inspired by Bayesian statistical inference, which we refer to as Bayesian Renormalization. The main insight of Bayesian Renormalization is that the Fisher…
In this paper, we consider an unconstrained optimization model where the objective is a sum of a large number of possibly nonconvex functions, though overall the objective is assumed to be smooth and convex. Our bid to solving such model…
We consider the numerical evaluation of the Evans function, a Wronskian-like determinant that arises in the study of the stability of travelling waves. Constructing the Evans function involves matching the solutions of a linear ordinary…
In non-linear estimations, it is common to assess sampling uncertainty by bootstrap inference. For complex models, this can be computationally intensive. This paper combines optimization with resampling: turning stochastic optimization into…
In the coming years, strong gravitational lens discoveries are expected to increase in frequency by two orders of magnitude. Lens-modelling techniques are being developed to prepare for the coming massive influx of new lens data, and blind…
We provide a novel statistical perspective on a classical problem at the intersection of computer science and information theory: recovering the empirical frequency of a symbol in a large discrete dataset using only a compressed…
Reconstructing an infinite-dimensional signal from a finite set of measurements is a fundamental problem in approximation theory and signal processing. While the generalized sampling (GS) framework provides a robust methodology for…
Many data-fitting applications require the solution of an optimization problem involving a sum of large number of functions of high dimensional parameter. Here, we consider the problem of minimizing a sum of $n$ functions over a convex…
This PhD thesis is devoted to show that differential renormalization is a simple and useful renormalization method that we can use when dealing with gauge theories. In this work, it is shown how the one-loop results of Constraint…
Assume that samples of a filtered version of a function in a shift-invariant space are avalaible. This work deals with the existence of a sampling formula involving these samples and having reconstruction functions with compact support.…
Since the celebrated works of Russo and Zou (2016,2019) and Xu and Raginsky (2017), it has been well known that the generalization error of supervised learning algorithms can be bounded in terms of the mutual information between their input…
The motivation of this paper is the development of an optimisation method for solving optimisation problems appearing in Chebyshev rational and generalised rational approximation problems, where the approximations are constructed as ratios…