Related papers: Ziv-Zakai-type error bounds for general statistica…
We study the estimation of $\beta$ for the nonlinear model $y = f(X\sp{\top}\beta) + \epsilon$ when $f$ is a nonlinear transformation that is known, $\beta$ has sparse nonzero coordinates, and the number of observations can be much smaller…
Motivated by the learned iterative soft thresholding algorithm (LISTA), we introduce a general class of neural networks suitable for sparse reconstruction from few linear measurements. By allowing a wide range of degrees of weight-sharing…
Suppose that we have two training sequences generated by parametrized distributions $P_{\theta^*}$ and $P_{\xi^*}$, where $\theta^*$ and $\xi^*$ are unknown true parameters. Given training sequences, we study the problem of classifying…
Initial-boundary value problem for the generalized Zakharov-Kuznetsov equation posed on a bounded rectangle is considered. Critical and subcritical powers in nonlinearity are studied.
In this paper we have introduced a generalized version of alpha beta skew normal distribution in the same line of Sharafi et al. (2017) and investigated some of its basic properties. The extensions of the proposed distribution have also…
In a meta-analysis, it is important to specify a model that adequately describes the effect-size distribution of the underlying population of studies. The conventional normal fixed-effect and normal random-effects models assume a normal…
In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the…
Nested error regression models are useful tools for analysis of grouped data, especially in the case of small area estimation. This paper suggests a nested error regression model using uncertain random effects in which the random effect in…
New upper and lower bounds for the error probability over an erasure channel are provided, making use of Wei's generalized weights, hierarchy and spectra. In many situations the upper and lower bounds coincide and this allows improvement of…
Squared error loss remains the most commonly used loss function for constructing a Bayes estimator of the parameter of interest. However, it can lead to sub-optimal solutions when a parameter is defined in a restricted space. It can also be…
In this article we consider theta-expanded noncommutative gauge field theory, constructed at the first order in noncommutative parameter theta, as an effective, anomaly free theory, with one-loop renormalizable gauge sector. Related…
In this paper we derive a PAC-Bayesian error bound for autonomous stochastic LTI state-space models. The motivation for deriving such error bounds is that they will allow deriving similar error bounds for more general dynamical systems,…
Algorithm- and data-dependent generalization bounds are required to explain the generalization behavior of modern machine learning algorithms. In this context, there exists information theoretic generalization bounds that involve (various…
We derive generalization error bounds for traditional time-series forecasting models. Our results hold for many standard forecasting tools including autoregressive models, moving average models, and, more generally, linear state-space…
This work performs a non-asymptotic analysis of the generalized Lasso under the assumption of sub-exponential data. Our main results continue recent research on the benchmark case of (sub-)Gaussian sample distributions and thereby explore…
For one-parameter continuous exponential families, we identify an unbiased estimator of the inverse of the natural parameter $\theta$ for cases where $\theta > 0$, extending an earlier result of \cite{voinov1985unbiased} applicable to a…
Univariate and multivariate general linear regression models, subject to linear inequality constraints, arise in many scientific applications. The linear inequality restrictions on model parameters are often available from phenomenological…
This paper builds on recent research that focuses on regression modeling of continuous bounded data, such as proportions measured on a continuous scale. Specifically, it deals with beta regression models with mixed effects from a Bayesian…
Some computations made about the Riemann Hypothesis and in particular, the verification that zeroes of zeta belong on the critical line and the extension of zero-free region are useful to get better effective estimates of number theory…
We introduce a generalization of the method of S. P. Zaitsev. This generalization allows us to prove omega-theorems for the Riemann zeta function and its derivatives in some regions near the line $\mathrm{Re}\,s=1$.