Forecasting of non-linear time series is a relevant problem in control. Furthermore, an estimate of the uncertainty of the prediction is useful for constructing robust controllers. Multiple-step ahead forecasting has recently been addressed using Gaussian processes, but direct implementations are restricted to small data sets. In this paper we consider multiple-step forecasting for sparse Gauss...

In the present article, we introduce Chlodowsky variant of $(p,q)$-Bernstein operators and compute the moments for these operators which are used in proving our main results. Further, we study some approximation properties of these new operators, which include the rate of convergence using usual modulus of continuity and also the rate of convergence when the function $f$ belongs to the class Li...

In this paper, we study the concept of S-approximation spaces in fuzzy set theory and investigate its properties. Along introducing three pairs of lower and upper approximation operators for fuzzy S-approximation spaces, their properties under different assumptions, e.g. monotonicity and weak complement compatibility are studied. By employing two thresholds for minimum acceptance accuracy and m...

A new procedure based on partition of the unity has been developed to construct spatial approximation-prediction functions for discrete density functions. This Partition of the Unity Procedure (PUP) provides a family of approximation-prediction functions which depends on several parameters. In order to find the best function we have considered error estimators induced by the Vietoris simplicial...

Deep Learning predictions with measurable confidence are increasingly desirable for real-world problems, especially in high-risk settings. The Conformal Prediction (CP) framework is a versatile solution that guarantees maximum error rate given minimal constraints [1]. In this paper, we propose novel conformal loss function approximates the traditionally two-step CP approach single step. By eval...

The problem of real time prediction blood glucose (BG) levels based on the readings from a continuous monitoring (CGM) device is great importance in diabetes care, and therefore, has attracted lot research recent years, especially machine learning. An accurate with 30, 60, or 90 min horizon potential saving millions dollars emergency care costs. In this paper, we treat as one function approxima...

The linear theory of prediction is capable of performing long term forecasting when the observed time series is linear. For the chaotic signals, where linear modeling techniques are insufficient, nonlinear approximation theory can be used effectively for predicting. Long-term prediction however, is always difficult to achieve for such signals because of the amplification of errors in each predi...