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1. Stacked LSTM based deep recurrent neural network with kalman smoothing for blood glucose prediction

   https://doi.org/10.1186/s12911-021-01462-5  

   Rabby, Md Fazle ; Tu, Yazhou ; Hossen, Md Imran ; Lee, Insup ; Maida, Anthony S. ; Hei, Xiali ( December 2021 , BMC Medical Informatics and Decision Making)

   Abstract Background Blood glucose (BG) management is crucial for type-1 diabetes patients resulting in the necessity of reliable artificial pancreas or insulin infusion systems. In recent years, deep learning techniques have been utilized for a more accurate BG level prediction system. However, continuous glucose monitoring (CGM) readings are susceptible to sensor errors. As a result, inaccurate CGM readings would affect BG prediction and make it unreliable, even if the most optimal machine learning model is used. Methods In this work, we propose a novel approach to predicting blood glucose level with a stacked Long short-term memory (LSTM) based deep recurrent neural network (RNN) model considering sensor fault. We use the Kalman smoothing technique for the correction of the inaccurate CGM readings due to sensor error. Results For the OhioT1DM (2018) dataset, containing eight weeks’ data from six different patients, we achieve an average RMSE of 6.45 and 17.24 mg/dl for 30 min and 60 min of prediction horizon (PH), respectively. Conclusions To the best of our knowledge, this is the leading average prediction accuracy for the ohioT1DM dataset. Different physiological information, e.g., Kalman smoothed CGM data, carbohydrates from the meal, bolus insulin, and cumulative step counts in a fixed time interval, are crafted to represent meaningful features used as input to the model. The goal of our approach is to lower the difference between the predicted CGM values and the fingerstick blood glucose readings—the ground truth. Our results indicate that the proposed approach is feasible for more reliable BG forecasting that might improve the performance of the artificial pancreas and insulin infusion system for T1D diabetes management. 

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2. Sharper Model-free Reinforcement Learning for Average-reward Markov Decision Processes

   Zhang, Zihan ; Xie, Qiaomin ( July 2023 , Conference on Learning Theory)

   We study model-free reinforcement learning (RL) algorithms for infinite-horizon average-reward Markov decision process (MDP), which is more appropriate for applications that involve continuing operations not divided into episodes. In contrast to episodic/discounted MDPs, theoretical understanding of model-free RL algorithms is relatively inadequate for the average-reward setting. In this paper, we consider both the online setting and the setting with access to a simulator. We develop computationally efficient model-free algorithms that achieve sharper guarantees on regret/sample complexity compared with existing results. In the online setting, we design an algorithm, UCB-AVG, based on an optimistic variant of variance-reduced Q-learning. We show that UCB-AVG achieves a regret bound $\widetilde{O}(S^5A^2sp(h^*)\sqrt{T})$ after $T$ steps, where $S\times A$ is the size of state-action space, and $sp(h^*)$ the span of the optimal bias function. Our result provides the first computationally efficient model-free algorithm that achieves the optimal dependence in $T$ (up to log factors) for weakly communicating MDPs, which is necessary for low regret. In contrast, prior results either are suboptimal in $T$ or require strong assumptions of ergodicity or uniformly mixing of MDPs. In the simulator setting, we adapt the idea of UCB-AVG to develop a model-free algorithm that finds an $\epsilon$-optimal policy with sample complexity $\widetilde{O}(SAsp^2(h^*)\epsilon^{-2} + S^2Asp(h^*)\epsilon^{-1}).$ This sample complexity is near-optimal for weakly communicating MDPs, in view of the minimax lower bound $\Omega(SAsp(^*)\epsilon^{-2})$. Existing work mainly focuses on ergodic MDPs and the results typically depend on $t_{mix},$ the worst-case mixing time induced by a policy. We remark that the diameter $D$ and mixing time $t_{mix}$ are both lower bounded by $sp(h^*)$, and $t_{mix}$ can be arbitrarily large for certain MDPs. On the technical side, our approach integrates two key ideas: learning an $\gamma$-discounted MDP as an approximation, and leveraging reference-advantage decomposition for variance in optimistic Q-learning. As recognized in prior work, a naive approximation by discounted MDPs results in suboptimal guarantees. A distinguishing feature of our method is maintaining estimates of value-difference between state pairs to provide a sharper bound on the variance of reference advantage. We also crucially use a careful choice of the discounted factor $\gamma$ to balance approximation error due to discounting and the statistical learning error, and we are able to maintain a good-quality reference value function with $O(SA)$ space complexity. 

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3. Embedding properties of network realizations of dissipative reduced order models

   Druskin, Guddati ( July 2022 , HOUSEHOLDER SYMPOSIUM XXI)

   Embedding properties of network realizations of dissipative reduced order models Jörn Zimmerling, Mikhail Zaslavsky,Rob Remis, Shasri Moskow, Alexander Mamonov, Murthy Guddati, Vladimir Druskin, and Liliana Borcea Mathematical Sciences Department, Worcester Polytechnic Institute https://www.wpi.edu/people/vdruskin Abstract Realizations of reduced order models of passive SISO or MIMO LTI problems can be transformed to tridiagonal and block-tridiagonal forms, respectively, via dierent modications of the Lanczos algorithm. Generally, such realizations can be interpreted as ladder resistor-capacitor-inductor (RCL) networks. They gave rise to network syntheses in the rst half of the 20th century that was at the base of modern electronics design and consecutively to MOR that tremendously impacted many areas of engineering (electrical, mechanical, aerospace, etc.) by enabling ecient compression of the underlining dynamical systems. In his seminal 1950s works Krein realized that in addition to their compressing properties, network realizations can be used to embed the data back into the state space of the underlying continuum problems. In more recent works of the authors Krein's ideas gave rise to so-called nite-dierence Gaussian quadrature rules (FDGQR), allowing to approximately map the ROM state-space representation to its full order continuum counterpart on a judicially chosen grid. Thus, the state variables can be accessed directly from the transfer function without solving the full problem and even explicit knowledge of the PDE coecients in the interior, i.e., the FDGQR directly learns" the problem from its transfer function. This embedding property found applications in PDE solvers, inverse problems and unsupervised machine learning. Here we show a generalization of this approach to dissipative PDE problems, e.g., electromagnetic and acoustic wave propagation in lossy dispersive media. Potential applications include solution of inverse scattering problems in dispersive media, such as seismic exploration, radars and sonars. To x the idea, we consider a passive irreducible SISO ROM fn(s) = Xn j=1 yi s + σj , (62) assuming that all complex terms in (62) come in conjugate pairs. We will seek ladder realization of (62) as rjuj + vj − vj−1 = −shˆjuj , uj+1 − uj + ˆrj vj = −shj vj , (63) for j = 0, . . . , n with boundary conditions un+1 = 0, v1 = −1, and 4n real parameters hi, hˆi, ri and rˆi, i = 1, . . . , n, that can be considered, respectively, as the equivalent discrete inductances, capacitors and also primary and dual conductors. Alternatively, they can be viewed as respectively masses, spring stiness, primary and dual dampers of a mechanical string. Reordering variables would bring (63) into tridiagonal form, so from the spectral measure given by (62 ) the coecients of (63) can be obtained via a non-symmetric Lanczos algorithm written in J-symmetric form and fn(s) can be equivalently computed as fn(s) = u1. The cases considered in the original FDGQR correspond to either (i) real y, θ or (ii) real y and imaginary θ. Both cases are covered by the Stieltjes theorem, that yields in case (i) real positive h, hˆ and trivial r, rˆ, and in case (ii) real positive h,r and trivial hˆ,rˆ. This result allowed us a simple interpretation of (62) as the staggered nite-dierence approximation of the underlying PDE problem [2]. For PDEs in more than one variables (including topologically rich data-manifolds), a nite-dierence interpretation is obtained via a MIMO extensions in block form, e.g., [4, 3]. The main diculty of extending this approach to general passive problems is that the Stieltjes theory is no longer applicable. Moreover, the tridiagonal realization of a passive ROM transfer function (62) via the ladder network (63) cannot always be obtained in port-Hamiltonian form, i.e., the equivalent primary and dual conductors may change sign [1]. 100 Embedding of the Stieltjes problems, e.g., the case (i) was done by mapping h and hˆ into values of acoustic (or electromagnetic) impedance at grid cells, that required a special coordinate stretching (known as travel time coordinate transform) for continuous problems. Likewise, to circumvent possible non-positivity of conductors for the non-Stieltjes case, we introduce an additional complex s-dependent coordinate stretching, vanishing as s → ∞ [1]. This stretching applied in the discrete setting induces a diagonal factorization, removes oscillating coecients, and leads to an accurate embedding for moderate variations of the coecients of the continuum problems, i.e., it maps discrete coecients onto the values of their continuum counterparts. Not only does this embedding yields an approximate linear algebraic algorithm for the solution of the inverse problems for dissipative PDEs, it also leads to new insight into the properties of their ROM realizations. We will also discuss another approach to embedding, based on Krein-Nudelman theory [5], that results in special data-driven adaptive grids. References [1] Borcea, Liliana and Druskin, Vladimir and Zimmerling, Jörn, A reduced order model approach to inverse scattering in lossy layered media, Journal of Scientic Computing, V. 89, N1, pp. 136,2021 [2] Druskin, Vladimir and Knizhnerman, Leonid, Gaussian spectral rules for the three-point second dierences: I. A two-point positive denite problem in a semi-innite domain, SIAM Journal on Numerical Analysis, V. 37, N 2, pp.403422, 1999 [3] Druskin, Vladimir and Mamonov, Alexander V and Zaslavsky, Mikhail, Distance preserving model order reduction of graph-Laplacians and cluster analysis, Druskin, Vladimir and Mamonov, Alexander V and Zaslavsky, Mikhail, Journal of Scientic Computing, V. 90, N 1, pp 130, 2022 [4] Druskin, Vladimir and Moskow, Shari and Zaslavsky, Mikhail LippmannSchwingerLanczos algorithm for inverse scattering problems, Inverse Problems, V. 37, N. 7, 2021, [5] Mark Adolfovich Nudelman The Krein String and Characteristic Functions of Maximal Dissipative Operators, Journal of Mathematical Sciences, 2004, V 124, pp 49184934 Go back to Plenary Speakers Go back to Speakers Go back 

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4. Overcoming the Long Horizon Barrier for Sample-Efficient Reinforcement Learning with Latent Low-Rank Structure

   https://doi.org/10.1145/3589973  

   Sam, Tyler ; Chen, Yudong ; Yu, Christina Lee ( May 2023 , Proceedings of the ACM on Measurement and Analysis of Computing Systems)

   The practicality of reinforcement learning algorithms has been limited due to poor scaling with respect to the problem size, as the sample complexity of learning an ε-optimal policy is Ω(|S||A|H/ ε2) over worst case instances of an MDP with state space S, action space A, and horizon H. We consider a class of MDPs for which the associated optimal Q* function is low rank, where the latent features are unknown. While one would hope to achieve linear sample complexity in |S| and |A| due to the low rank structure, we show that without imposing further assumptions beyond low rank of Q*, if one is constrained to estimate the Q function using only observations from a subset of entries, there is a worst case instance in which one must incur a sample complexity exponential in the horizon H to learn a near optimal policy. We subsequently show that under stronger low rank structural assumptions, given access to a generative model, Low Rank Monte Carlo Policy Iteration (LR-MCPI) and Low Rank Empirical Value Iteration (LR-EVI) achieve the desired sample complexity of Õ((|S|+|A|)poly (d,H)/ε2) for a rank d setting, which is minimax optimal with respect to the scaling of |S|, |A|, and ε. In contrast to literature on linear and low-rank MDPs, we do not require a known feature mapping, our algorithm is computationally simple, and our results hold for long time horizons. Our results provide insights on the minimal low-rank structural assumptions required on the MDP with respect to the transition kernel versus the optimal action-value function. 

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5. A Machine Learning Model for Week-Ahead Hypoglycemia Prediction From Continuous Glucose Monitoring Data

   https://doi.org/10.1177/19322968241236208  

   Giammarino, Flavia ; Senanayake, Ransalu ; Prahalad, Priya ; Maahs, David M. ; Scheinker, David ( March 2024 , Journal of Diabetes Science and Technology)

   Remote patient monitoring (RPM) programs augment type 1 diabetes (T1D) care based on retrospective continuous glucose monitoring (CGM) data. Few methods are available to estimate the likelihood of a patient experiencing clinically significant hypoglycemia within one week.

   We developed a machine learning model to estimate the probability that a patient will experience a clinically significant hypoglycemic event, defined as CGM readings below 54 mg/dL for at least 15 consecutive minutes, within one week. The model takes as input the patient’s CGM time series over a given week, and outputs the predicted probability of a clinically significant hypoglycemic event the following week. We used 10-fold cross-validation and external validation (testing on cohorts different from the training cohort) to evaluate performance. We used CGM data from three different cohorts of patients with T1D: REPLACE-BG (226 patients), Juvenile Diabetes Research Foundation (JDRF; 355 patients) and Tidepool (120 patients).

   In 10-fold cross-validation, the average area under the receiver operating characteristic curve (ROC-AUC) was 0.77 (standard deviation [SD]: 0.0233) on the REPLACE-BG cohort, 0.74 (SD: 0.0188) on the JDRF cohort, and 0.76 (SD: 0.02) on the Tidepool cohort. In external validation, the average ROC-AUC across the three cohorts was 0.74 (SD: 0.0262).

   We developed a machine learning algorithm to estimate the probability of a clinically significant hypoglycemic event within one week. Predictive algorithms may provide diabetes care providers using RPM with additional context when prioritizing T1D patients for review.

    

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