In this talk, we discuss two problems: the sampling problem for a given class of functions on $\mathbb{R}$ (direct problem) and the 
 reconstruction of a function from finite samples (inverse problem). In the sampling problem, we are given a class of functions $V\subset 
 L^2(\mathbb{R}) $ and one seeks to find sets of discrete samples such that any $f$ in $V$ can be completely recovered from its values at 
 the sample points. Here we address the sampling problem for the class of functions $V = V(\varphi)$, the (integer) shift invariant space 
 defined by a generator $\varphi$ with some general assumption. In the second problem, we discuss the problem of reconstruction of a real-
 valued function $f$ on $X\subset \mathbb{R}^d$ from the given data $\{(x_i,y_i)\}_{i=1}^n\subset X\times\mathbb{R}$, where it is assumed 
 that $y_i=f(x_i)+\xi_i$ and $(\xi_1,...,\xi_n)$ is a noise vector. In particular, we are interested in reconstructing the function at points 
 outside the closed convex hull of $\{x_1,...,x_n\}$, which is the so-called extrapolation problem. We consider this problem in the framework 
 of statistical learning theory and regularization networks. In this framework, we address the major issues: how to choose an appropriate 
 hypothesis space and regularized predictor for given data through a meta-learning approach. We employ the proposed method for blood glucose 
 prediction in diabetes patients. Further, using real clinical data, we demonstrate that the proposed method outperforms the state-of-art 
 (time series and neural-network-based models).