Related papers: Laplace's formula: an approach by nonstandard anal…
Implicit samplers are algorithms for producing independent, weighted samples from multi-variate probability distributions. These are often applied in Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to analyze two…
We give an overview of basic methods that can be used for obtaining asymptotic expansions of integrals: Watson's lemma, Laplace's method, the saddle point method, and the method of stationary phase. Certain developments in the field of…
A common problem in astronomy is the determination of the time shift between two otherwise identical time series of measured flux from a variable source, in short the determination of a time lag. Two examples of where this problem occurs…
Consider estimating a structured signal $\mathbf{x}_0$ from linear, underdetermined and noisy measurements $\mathbf{y}=\mathbf{A}\mathbf{x}_0+\mathbf{z}$, via solving a variant of the lasso algorithm: $\hat{\mathbf{x}}=\arg\min_\mathbf{x}\{…
The method to derive uniform bounds with Gaussian and Rademacher complexities is extended to the case where the sample average is replaced by a nonlinear statistic. Tight bounds are obtained for U-statistics, smoothened L-statistics and…
One advantage of paraconsistent logic is that it can deal with inconsistencies without making the system trivial. However, unlike classical propositional calculus, its deductive system is limited, and the meaning of paraconsistent negation…
An approximation method is presented for probabilistic inference with continuous random variables. These problems can arise in many practical problems, in particular where there are "second order" probabilities. The approximation, based on…
We present a principled approach for designing stochastic Newton methods for solving finite sum optimization problems. Our approach has two steps. First, we re-write the stationarity conditions as a system of nonlinear equations that…
The notion of a Laplace ladder for a discrete analogue of the Laplace equation is presented. The adjoint of the discrete Moutard equation and a discrete counterpart of the nonlinear form of Goursat equation are introduced.
Given an ODE and its perturbation, the Alekseev formula expresses the solutions of the latter in terms related to the former. By exploiting this formula and a new concentration inequality for martingale-differences, we develop a novel…
In this paper we describe NPSA, the first parallel nonparametric global maximum likelihood optimization algorithm using simulated annealing (SA). Unlike the nonparametric adaptive grid search method NPAG, which is not guaranteed to find a…
We consider an inverse problem of recovering the non-linearity in the one dimensional variable exponent $p(x)$-Laplace equation from the Dirichlet-to-Neumann map. The variable exponent can be recovered up to the natural obstruction of…
We present a novel approach to the formulation and the resolution of sparse Linear Discriminant Analysis (LDA). Our proposal, is based on penalized Optimal Scoring. It has an exact equivalence with penalized LDA, contrary to the multi-class…
Classical linear discriminant analysis (LDA) is based on squared Frobenious norm and hence is sensitive to outliers and noise. To improve the robustness of LDA, in this paper, we introduce capped l_{2,1}-norm of a matrix, which employs…
Due to their quantitative nature, probabilistic programs pose non-trivial challenges for designing compositional and efficient program analyses. Many analyses for probabilistic programs rely on iterative approximation. This article presents…
We define an equivalence relation on propositions and a proof system where equivalent propositions have the same proofs. The system obtained this way resembles several known non-deterministic and algebraic lambda-calculi.
Linear regression is a basic and widely-used methodology in data analysis. It is known that some quantum algorithms efficiently perform least squares linear regression of an exponentially large data set. However, if we obtain values of the…
Many mainstream robust control/estimation algorithms for power networks are designed using the Lyapunov theory as it provides performance guarantees for linear/nonlinear models of uncertain power networks but comes at the expense of…
An analytical method is advanced for constructing interpolation formulae for complicated problems of statistical mechanics, in which just a few terms of asymptotic expansions are available. The method is based on the self-similar…
For basic machine learning problems, expected error is used to evaluate model performance. Since the distribution of data is usually unknown, we can make simple hypothesis that the data are sampled independently and identically distributed…