Sergei V. Pereverzyev

A meta-learning approach to the regularized learning-Case study: Blood glucose prediction

In this paper we present a new scheme of a kernel-based regularization learning algorithm, in which the kernel and the regularization parameter are adaptively chosen on the base of previous experience with similar learning tasks. The construction of such a scheme is motivated by the problem of prediction of the blood glucose levels of diabetic patients. We describe how the proposed scheme can be used for this problem and report the results of the tests with real clinical data as well as comparing them with existing literature.

Extrapolation in variable RKHSs with application to the blood glucose reading

In this paper we present a new scheme of a kernel adaptive regularization algorithm, where the kernel and the regularization parameter are adaptively chosen within the regularization procedure. The construction of such a fully adaptive regularization algorithm is motivated by the problem of reading the blood glucose concentration of diabetic patients. We describe how the proposed scheme can be used for this purpose and report the results of numerical experiments with real clinical data.

A linear functional strategy for regularized ranking

Regularization schemes are frequently used for performing ranking tasks. This topic has been intensively studied in recent years. However, to be effective a regularization scheme should be equipped with a suitable strategy for choosing a regularization parameter. In the present study we discuss an approach, which is based on the idea of a linear combination of regularized rankers corresponding to different values of the regularization parameter. The coefficients of the linear combination are estimated by means of the so-called linear functional strategy. We provide a theoretical justification of the proposed approach and illustrate them by numerical experiments. Some of them are related with ranking the risk of nocturnal hypoglycemia of diabetes patients.

Adaptive parameter choice for one-sided finite difference schemes and its application in diabetes technology

In this paper we discuss the problem of approximation of the first derivative of a function at the endpoint of its definition interval. This problem is motivated by diabetes therapy management, where it is important to provide estimations of the future blood glucose trend from current and past measurements. A natural way to approach the problem is to use one-sided finite difference schemes for numerical differentiation, but, following this way, one should be aware that the values of the function to be differentiated are noisy and available only at given fixed points. Then (as we argue in the paper) the number of used point values is the only parameter to be employed for regularization of the above mentioned ill-posed problem of numerical differentiation. In this paper we present and theoretically justify an adaptive procedure for choosing such a parameter. We also demonstrate some illustrative tests, as well as the results of numerical experiments with simulated clinical data.

On the convergence rate and some applications of regularized ranking algorithms

This paper studies the ranking problem in the context of the regularization theory that allows a simultaneous analysis of a wide class of ranking algorithms. Some of them were previously studied separately. For such ones, our analysis gives a better convergence rate compared to the reported in the literature. We also supplement our theoretical results with numerical illustrations and discuss the application of ranking to the problem of estimating the risk from errors in blood glucose measurements of diabetic patients.

Reading blood glucose from subcutaneous electric current by means of a regularization in variable Reproducing Kernel Hilbert Spaces

In this paper we propose an adaptive kernel regularization algorithm for blood glucose reading from subcutaneous electric current. We illustrate the proposed algorithm with clinical data and quantify its clinical accuracy by means of the Clarke error grid analysis (EGA) and by the number of detected hypoglycemic events. We show that the proposed algorithm provides more accurate blood glucose reading than a commercially available system.

Nyström type subsampling analyzed as a regularized projection

In the statistical learning theory the Nyström type subsampling methods are considered as tools for dealing with big data. In this paper we consider Nyström subsampling as a special form of the projected Lavrentiev regularization, and study it using the approaches developed in the regularization theory. As a result, we prove that the same capacity independent learning rates that are quaranteed for standard algorithms running with quadratic computational complexity can be obtained with subquadratic complexity by the Nyström subsampling approach, provided that the subsampling size is chosen properly. We propose a priori rule for choosing the subsampling size and a posteriori strategy for dealing with uncertainty in the choice of it. The theoretical results are illustrated by numerical experiments.

A Deep Learning Approach to Diabetic Blood Glucose Prediction

We consider the question of 30-minute prediction of blood glucose levels measured by continuous glucose monitoring devices, using clinical data. While most studies of this nature deal with one patient at a time, we take a certain percentage of patients in the data set as training data, and test on the remainder of the patients; i.e., the machine need not re-calibrate on the new patients in the data set. We demonstrate how deep learning can outperform shallow networks in this example. One novelty is to demonstrate how a parsimonious deep representation can be constructed using domain knowledge.

Prediction of nocturnal hypoglycemia by an aggregation of previously known prediction approaches

BACKGROUND AND OBJECTIVE Nocturnal hypoglycemia (NH) is common in patients with insulin-treated diabetes. Despite the risk associated with NH, there are only a few methods aiming at the prediction of such events based on intermittent blood glucose monitoring data and none has been validated for clinical use. Here we propose a method of combining several predictors into a new one that will perform at the level of the best involved one, or even outperform all individual candidates. METHODS The idea of the method is to use a recently developed strategy for aggregating ranking algorithms. The method has been calibrated and tested on data extracted from clinical trials, performed in the European FP7-funded project DIAdvisor. Then we have tested the proposed approach on other datasets to show the portability of the method. This feature of the method allows its simple implementation in the form of a diabetic smartphone app. RESULTS On the considered datasets the proposed approach exhibits good performance in terms of sensitivity, specificity and predictive values. Moreover, the resulting predictor automatically performs at the level of the best involved method or even outperforms it. CONCLUSION We propose a strategy for a combination of NH predictors that leads to a method exhibiting a reliable performance and the potential for everyday use by any patient who performs self-monitoring of blood glucose.

Two-parameter regularization of ill-posed spherical pseudo-differential equations in the space of continuous functions

In this paper, a two-step regularization method is used to solve an ill-posed spherical pseudo-differential equation in the presence of noisy data. For the first step of regularization we approximate the data by means of a spherical polynomial that minimizes a functional with a penalty term consisting of the squared norm in a Sobolev space. The second step is a regularized collocation method. An error bound is obtained in the uniform norm, which is potentially smaller than that for either the noise reduction alone or the regularized collocation alone. We discuss an a posteriori parameter choice, and present some numerical experiments, which support the claimed superiority of the two-step method.