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A deep learning approach to diabetic blood glucose prediction
H. N. Mhaskar, S. V. Pereverzyev, M. D. van der Walt
TL;DR
Predicting glucose 30 minutes ahead from continuous-monitoring data is important, but prior work commonly trains patient by patient. This paper uses domain knowledge to build a two-layer deep predictor and tests transfer across patients. Its deep method has fewer erroneous predictions than the compared methods in nearly all reported experiments, with one stated exception.
Problem
Method
The method uses domain knowledge to build three range-specific predictors and a judge network, with training on some patients and prediction on the others.
Source: §1 · p. 2, §4.4 · p. 9Results
Erroneous predictions were substantially lower with deep networks than with the two other tested methods, except for the hyperglycemic range with 30% training data and flat low-pass filtering.
Source: §5 · p. 12Takeaways & Limitations
The results demonstrate that a domain-knowledge-guided deep representation can support cross-patient blood-glucose prediction in this data set.
Source: §1 · p. 2, §4.4 · p. 9, §6 · p. 15The paper uses a cross-patient training setup and does not evaluate the separate patient-by-patient training approach.
Source: §4.4 · p. 9
Abstract
from arXiv · showhide
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.
1 Introduction
Deep networks can efficiently represent hierarchical target functions, but their learned features may not be uniquely interpretable. This paper uses domain knowledge to construct a parsimonious deep network for blood-glucose prediction and evaluates training on some patients and prediction on the remainder.
1 Introduction
- Deep networks can approximate hierarchical target functions more efficiently than shallow networks, but the resulting features may not be uniquely defined.For a bounded-gradient hierarchical function, the cited theory gives accuracy O(n^-1/2) for a deep network versus at most O(n^-1/8) for a shallow network.Source: §1 · p. 2
- The paper constructs a parsimonious deep network by using domain knowledge to suggest the target function's compositional structure and constituent functions.Source: §1 · p. 2
- Three range-specific networks make 5-minute trend-based predictions, and a judge network combines their outputs into a final prediction.The approach uses diffusion geometry because the readings and constituent-network outputs are not dense in a Euclidean cube.Source: §1 · p. 2
- Unlike patient-by-patient studies, the paper trains on all data from 30% of patients and predicts blood glucose for the remaining 70%.The paper describes this as transferring learned knowledge between data sets, while still requiring knowledge of both data sets.Source: §1 · pp. 2–3
2 Problem statement and evaluation
The task is to predict blood glucose from recent continuous-monitoring readings, with clinical accuracy assessed separately across glucose ranges and prediction dimensions.
2 Problem statement and evaluation
- For 30-minute prediction, the model uses seven readings spanning 30 minutes to predict the glucose level six 5-minute intervals ahead.Source: §2 · p. 3
- PRED-EGA reports accurate, benign, and erroneous predictions by glucose range, using both glucose estimates and directions and rates of change.The paper treats clinical accuracy, rather than numerical accuracy alone, as the central objective.Source: §2 · p. 3
3 Prior work
Prior blood-glucose prediction work includes linear predictors and supervised-learning methods, including kernel, neural-network, and time-series approaches.
3 Prior work
- Linear predictors estimate the glucose derivative from recent readings, with polynomial fitting methods addressing numerical conditioning and error control.The paper identifies the approach in as the state of the art in short-term blood-glucose prediction using linear prediction technology.Source: §3 · p. 4
- Kernel methods adapt their kernel and regularization choices, while neural-network methods have used additional inputs such as meals and insulin dosage.The cited neural-network study evaluated a 75-minute prediction with the classical EGA grid, which compares glucose concentrations but not rates of change.Source: §3 · p. 4
- Autoregressive methods are another supervised-learning group, and some patient-by-patient approaches have been reported as sensitive to gaps in input data.Source: §3 · pp. 4–5
4 Methodology in the current paper
The method uses diffusion-polynomial function approximation on data manifolds in a two-layer predictor. Its first layer builds three range-specific predictors, while a judge selects among them for the final output.
4 Methodology in the current paper
- The method formats each sample as recent glucose readings paired with a future reading, then constructs a diffusion matrix from the input data.Source: §4 · p. 5
4.1 First layer: Three networks in different clusters
- A 5-minute linear prediction divides training measurements into three glucose-range clusters, each used to form a range-specific predictor.The judge is trained on the full training set to choose which of the three predictions is best for each input.Source: §4.1 · p. 6
4.2 Second layer (judge): Final output
- The final layer compares each range-specific prediction with the judge reference using PRED-EGA placements and selects the best-placed prediction.If placements tie, it selects the prediction closest to the judge reference; at each patient's first and last samples, it uses that closeness rule.Source: §4.2 · pp. 6–7
4.3 Evaluation
- Evaluation repeats the training and prediction procedure for fixed trials and averages PRED-EGA placements over inputs and trials.Source: §4.3 · p. 7
4.4 Remarks
- The paper allows optional low-pass smoothing, but does not pursue the alternative of training separate networks for each patient.That alternative draws training data from each patient's own measurements and is described as a different problem.Source: §4.4 · pp. 7, 9
5 Results and discussion
Across 100 trials, deep networks generally yielded fewer erroneous predictions than shallow networks and Tikhonov regularization, while more training patients improved performance; filtered hyperglycemic prediction with 30% training was the exception.
5 Results and discussion
- The evaluation used 25 patients under 18 with type 1 diabetes, each with more than 160 five-minute BG measurements.The dataset was designed to study CGM devices in children; the paper describes the algorithm as general-purpose.Source: §5 · p. 9
- At 30% training, accurate/benign predictions were 84.32% hypoglycemic, 97.63% euglycemic, and 82.89% hyperglycemic; at 50%, they were 93.21%, 97.68%, and 86.78%.Average PRED-EGA scores across the experiments.Source: §5 · p. 9, Table 1 · p. 10
- Boxplots summarize 100 trials by glucose range for no-smoothing and filtered settings, each with 30% or 50% training data.Methods shown are deep network, shallow network, and Tikhonov regularization.Source: Figure 2 · p. 10, Figure 3 · p. 11, Figure 4 · p. 13
- With flat low-pass filtering, accurate/benign predictions were 88.92%, 97.64%, and 77.58% at 30% training, and 96.43%, 97.96%, and 85.29% at 50%, across hypoglycemic, euglycemic, and hyperglycemic ranges.These are the average PRED-EGA scores reported for the filtered time series.Source: §5 · p. 12, Table 2 · p. 12
- Deep networks had fewer errors than shallow networks across all ranges and outperformed Tikhonov regularization especially in hypoglycemia, except in filtered hyperglycemia with 30% training.Source: §5 · pp. 9, 12
- Increasing training data from 30% to 50% reduced erroneous predictions in every glucose range across all experiments.Source: §5 · p. 12
- Sparse hyperglycemic spikes may have affected results: one patient had only 5 readings above 180 mg/dL among 194 measurements.The DirecNet study covered roughly 26 hours and involved children with type 1 diabetes.Source: §5 · p. 15
6 Conclusions
The paper uses domain knowledge to design a parsimonious deep learning model for 30-minute blood glucose prediction. It presents this as an example of building a suitable compositional structure for deep learning.
6 Conclusions
- The paper demonstrates how domain knowledge can guide the construction of an appropriate compositional structure for a parsimonious deep learning design.The conclusion notes that compositional structure is not unique and can be difficult to identify for a target function.Source: §6 · p. 15
- The proposed paradigm combines domain knowledge with mathematical theory to predict blood glucose 30 minutes ahead from continuous glucose monitoring data.The paper assesses prediction accuracy with the glucose-specific PRED-EGA grid.Source: §6 · p. 15
- The conclusion relates deep networks’ expressiveness advantage to targets with compositional structure, describing this as the blessing of compositionality curing the curse of dimensionality.The paper presents its design as an example of using domain knowledge to build that structure.Source: §6 · p. 15
A Filtered Legendre expansion method
This appendix summarizes a method for estimating a function’s endpoint derivative from noisy measurements of its past values. It describes the Legendre-polynomial setup and refers readers to for the detailed proof.
A Filtered Legendre expansion method
- The method estimates f′(1) from noisy measurements of a continuously differentiable function at points in the past interval.The appendix frames this as the mathematical problem underlying short-term blood glucose prediction.Source: A Filtered Legendre expansion method · p. 18
- The appendix summarizes the method developed in and directs readers to that work for the detailed mathematical proof.It also states that the estimate of f′(1) is based on the noisy values yj=f(tj)+ϵj.Source: A Filtered Legendre expansion method · p. 18
- The Legendre polynomials are defined recursively, with P0(x)=1 and P1(x)=x as the initial polynomials.The recurrence is introduced to support the method’s polynomial-based estimation.Source: A Filtered Legendre expansion method · p. 18
- The stated constant A need not be determined, but is guaranteed to be proportional to the system’s condition number.Source: A Filtered Legendre expansion method · p. 18
B Function approximation on data defined spaces
This appendix motivates function approximation on data-defined spaces by contrasting machine-learning data with classical approximation on known domains. It outlines a manifold-based spectral approach and its approximation guarantee under technical conditions.
B Function approximation on data defined spaces
- Classical approximation often assumes data dense on a known domain, whereas machine-learning data may instead be viewed as sampled from an unknown manifold or other measured space.The appendix gives lagged CGM readings as an example of vectors unlikely to be dense in a cube.Source: B Function approximation on data… · p. 19
- The spectral subspace Πλ is spanned by eigenfunctions whose eigenvalues satisfy λk<λ, providing the basis for the approximation defined in this appendix.Source: B Function approximation on data… · p. 19
- The method learns f from its values on training points by solving an underdetermined system and choosing the largest λ for which the system remains well conditioned.The resulting approximation is described as analogous to classical radial basis function networks.Source: B Function approximation on data… · p. 19
- Under technical conditions, the approximation σλ(f) is described as asymptotically best possible given the training data for uniformly continuous, bounded functions.The appendix characterizes it as a “good approximation.”Source: B Function approximation on data… · p. 19
- The data point cloud P is assumed to lie on a compact, low-dimensional submanifold of a possibly high-dimensional Euclidean space, and the graph Laplacian is built from P using a weight matrix.Source: B Function approximation on data… · p. 20