Monotonicity Constraints Research Articles

A Non-Destructive Measurement Approach for the Internal Temperature of Shiitake Mushroom Sticks Based on a Data–Physics Hybrid-Driven Model

This study aimed to develop a non-destructive measurement method utilizing acoustic sensors for the efficient determination of the internal temperature of shiitake mushroom sticks during the cultivation period. In this research, the sound speed, air temperature, and moisture content of the mushroom sticks were employed as model inputs, while the temperature of the mushroom sticks served as the model output. A data–physics hybrid-driven model for temperature measurement based on XGBoost was constructed by integrating monotonicity constraints between the temperature of the mushroom sticks and sound speed, along with the condition that limited the difference between air temperature and stick temperature to less than 2 °C. The experimental results indicated that the optimal eigenfrequency for applying this model was 850 Hz, the optimal distance between the sound source and the shiitake mushroom sticks was 8.7 cm, and the temperature measurement accuracy was highest when the moisture content of the shiitake mushroom sticks was in the range of 56~66%. Compared to purely data-driven models, our proposed model demonstrated significant improvements in performance; specifically, RMSE, MAE, and MAPE decreased by 74.86%, 77.22%, and 69.30%, respectively, while R2 increased by 1.86%. The introduction of physical knowledge constraints has notably enhanced key performance metrics in machine learning-based acoustic thermometry, facilitating efficient, accurate, rapid, and non-destructive measurements of internal temperatures in shiitake mushroom sticks.

A novel performance prediction method for harmonic reducers based on the trend-enhanced Fisher’s discriminant ratio-Wiener process

Abstract Harmonic reducers, as core components of industrial robots, play a critical role in maintaining robot health. Performance degradation assessment (PDA) and remaining useful life (RUL) prediction are essential for ensuring the operational reliability of such robots. To address the multistage characteristics and stochastic uncertainties in the performance degradation of harmonic reducers, a performance prediction method based on Fisher’s discriminant ratio and Wiener process is proposed. Firstly, the health indicator (HI) construction is defined as an optimization problem based on Fisher’s discriminant ratio and trend monotonicity constraints. By leveraging the sum of the multiplication of frequency amplitudes and optimized weights, precise segmentation of the multistage degradation process over the entire lifecycle is achieved. Notably, the optimized weights can automatically identify the resonance frequency bands caused by damage. Subsequently, a nonlinear Wiener process model with a drift coefficient in the form of a power function is established. The probability density function (PDF) expression for RUL is derived based on the concept of first hit time (FHT). Additionally, a logarithmic likelihood function (Log-LF) for the unknown parameters in the degradation model is constructed. The experimental results indicate that the proposed method surpasses the other two Wiener process models in terms of root mean square error (RMSE), mean absolute percentage error (MAPE), and cumulative relative accuracy (CRA). This provides robust support for preventive maintenance decision-making for harmonic reducers.

Efficient random walks for generating random fuzzy measures in Möbius representation in large universe

Random generation of fuzzy measures plays a pivotal role in large-scale decision-making and optimization. Random walks ensure uniform generation and adequate coverage. The Möbius representation of set functions is a valuable tool for establishing the sparse structure of fuzzy measures, with its non-negativity closely linked to monotonicity and convexity/supermodularity checking. We propose three efficient methods for monotonicity verification and convexity/supermodularity verification applicable to random walks in Möbius representations, specifically tailored for universal sets larger than ten inputs and k-order fuzzy measures. We first present the baseline methods by directly inspecting monotonicity and convexity constraints. Building on the observation that the majority of initially generated values exhibit non-negativity, we intentionally track negative Möbius values to enhance the computational performance of these baseline approaches. Further, we introduce the more agile methods that employ insertion and merge sorting techniques for both monotonicity and convexity checks in random walks that involve small perturbations of fuzzy measures. To address sparsity in large-scale scenarios, we focus on two major types of measures: k-additive and k-interactive measures, demonstrating their effectiveness through theoretical analysis and experimental results.

Predicting the compressive strength of CFRP-confined concrete using deep learning

The application of externally bonded fiber-reinforced polymers (FRP) has revolutionized structural rehabilitation, offering cost-effective and rapid solutions for damaged structures. This study presents a novel deep learning approach for predicting the compressive strength of circular carbon-FRP-confined concrete columns. Leveraging an extensive database of 664 experimental results, the model incorporates monotonicity and smoothness constraints, with hyperparameters optimization using the OPTUNA framework. The proposed model demonstrates exceptional accuracy, achieving R² = 0.93, a20-index = 0.95, and MAPE = 7.89 % on unseen test data, consistently outperforming nine benchmark models including established design guidelines. Scenario-based analysis confirms the model's ability to capture known physical behaviors, such as the effects of concrete strength, column diameter, and FRP thickness on confinement effectiveness. The integration of physical constraints enhances the model's reliability and interpretability, bridging the gap between data-driven and physics-based approaches. This research contributes to the advancement of more accurate, economical, and reliable design guidelines for FRP-strengthened structures, while also demonstrating the potential of constrained deep learning in structural engineering applications.

Bridging spatio-temporal discontinuities in global soil moisture mapping by coupling physics in deep learning

The launch of Soil Moisture Active Passive (SMAP) satellite in 2015 has resulted in significant achievements in global soil moisture mapping. Nonetheless, spatiotemporal discontinuities in the soil moisture products have arisen due to the limitations of its orbit scanning gap and retrieval algorithms. To address these issues, this paper presents a physics-constrained gap-filling method, PhyFill for short. The PhyFill method employs a partial convolutional neural network technique to explore spatial domain features of the original SMAP soil moisture data. Then, it incorporates variations in soil moisture induced by precipitation events and dry-down events as penalty terms in the loss function, thereby accounting for monotonicity and boundary constraints in the physical processes governing the dynamic fluctuations of soil moisture. The PhyFill model was applied to SMAP soil moisture data, resulting in continuous spatially daily soil moisture data on a global scale. Three validation strategies are employed: visual inspection through global pattern, simulated missing-region validation, and soil moisture validation with in situ measurements. The results indicated that the reconstructed soil moisture achieved a higher spatial coverage with satisfactory spatial continuity with neighbouring pixels. The simulated validation of the missing regions revealed that the averaged unbiased root mean square difference (ubRMSD) and correlation coefficient (R) were 0.01 m3/m3 and 0.99, respectively versus the gap filled SMAP product. The core validation sites demonstrated that the reconstructed soil moisture data has a consistent ubRMSD compared with the original SMAP soil moisture data (0.04 m3/m3vs. 0.04 m3/m3). The PhyFill method can generate globally continuous, high accurate soil moisture estimates, providing remarkable support for advanced hydrological applications, e.g., global soil moisture dry-down events and patterns.

Semi-supervised soft sensor method for fermentation processes based on physical monotonicity and variational autoencoders

Data-driven models have shown broad application prospects in soft sensor modeling. However, numerous challenges persist. On the one hand, data-driven soft sensor methods have high requirements on data quality. On the other hand, models relying on limited experimental data often lack physical interpretability. To tackle these challenges, a semi-supervised soft sensor method (PMVAER) for fermentation processes based on physical monotonicity and variational autoencoders (VAEs) is introduced. First, physical monotonicity constraint is incorporated into the loss function of VAEs for regression to ensure that the model's predictions adhere to physical feasibility. Next, considering the disparate sampling frequencies for process and quality variables, this approach is extended to learn from unlabeled data, creating a semi-supervised soft sensor model. The proposed model is validated on simulation and real cases of penicillin fermentation. Comparisons with five other methods verify that the proposed method exhibits exceptional predictive accuracy along with enhanced generalization ability.

REDOMA: Bayesian random-effects dose-optimization meta-analysis using spike-and-slab priors.

The rise of cutting-edge precision cancer treatments has led to a growing significance of the optimal biological dose (OBD) in modern oncology trials. These trials now prioritize the consideration of both toxicity and efficacy simultaneously when determining the most desirable dosage for treatment. Traditional approaches in early-phase oncology trials have conventionally relied on the assumption of a monotone relationship between treatment efficacy and dosage. However, this assumption may not hold valid for novel oncology therapies. In reality, the dose-efficacy curve of such treatments may reach a plateau at a specific dose, posing challenges for conventional methods in accurately identifying the OBD. Furthermore, achieving reliable identification of the OBD is typically not possible based on a single small-sample trial. With data from multiple phase I and phase I/II trials, we propose a novel Bayesian random-effects dose-optimization meta-analysis (REDOMA) approach to identify the OBD by synthesizing toxicity and efficacy data from each trial. The REDOMA method can address trials with heterogeneous characteristics. We adopt a curve-free approach based on a Gamma process prior to model the average dose-toxicity relationship. In addition, we utilize a Bayesian model selection framework that uses the spike-and-slab prior as an automatic variable selection technique to eliminate monotonic constraints on the dose-efficacy curve. The good performance of the REDOMA method is confirmed by extensive simulation studies.

A switched system approach to exponential stabilization of interval type-2 fuzzy nonlinear systems with packet dropouts

This paper investigates the exponential stabilization problem for interval type-2 (IT2) fuzzy system with parameter uncertainties and packet dropouts. The sample-and-hold characteristic is simulated by employing an input delay methodology, and we present a model for the packet dropout phenomenon using switched approach. Some novel two-side delay-dependent looped-functionals are proposed by considering state information in the intervals from tr to t and t to tr+1 which relaxes the monotonic constraint of the Lyapunov–Krasovskii functional (LKF) and enhances the utilization of the actual sampling pattern. Additionally, some free-weighting matrices, slack matrices, the bound information in membership functions (MFs) and the signs of the first-order time derivative of fuzzy MFs are used to obtain a novel relaxed sufficient conditions for exponential stabilization of interval type-2 fuzzy systems (IT2 FS). Based on the LKF theory, new relaxed sufficient conditions with linear matrix inequalities (LMIs) constraints are derived. According to the criterion, sampled-data controller is devised to ensure that the closed-loop system is exponential stabilization. Finally, an illustrative example is presented to demonstrate the practicality and effectiveness of the method proposed. Comparative analysis highlights the simplicity and practicality of the suggested algorithm.

A blood-based screening test for colorectal cancer (CRC) using methylation sequencing.

e15089 Background: Diagnosis of CRC is biased towards later stages in India (3.8% Stage I, 16.7% Stage II, 50.7% Stage III, 28.8% Stage IV), and five-year survival at < 40% is one of the lowest in the world. A blood-based non-invasive screening test for CRC using cell-free DNA (cfDNA) methylation sequencing is developed here from the blood of 212 controls and 67 treatment naive CRC patients from 21 sites across India and processed in Strand’s reference lab in Bangalore. Methods: Steps involved cfDNA extraction, NEB Enzymatic Methyl-Seq library preparation, Twist Human Methylome hybridisation capture, 2x150bp sequencing on NovaSeq 6000/X. Methylation + fragmentomic features were calculated for each target region. Samples were split randomly into a leave-in set of 170 controls + 53 cancers (I: 8, II 16, III: 23, IV: 6) and a leave-out set of 42 controls + 14 cancers, (I: 5, II: 4, III: 2, IV: 3) with 20 rounds of 4-fold cross-validation done on the leave-in set (random splits). Feature selection per fold was performed using the KS test without access to ¼ of the leave-in set and to the entire leave-out set. Gradient boosted trees with monotonic constraints reflecting the expected association of the scores with cancer were used to build “explainable” models. Test robustness was assessed using differentially methylated regions (DMRs) from other studies, and by assessing predictability using sample metadata alone. Results: At a 91% specificity level, the ensemble model had a median sensitivity of 62.5% for Stage I (95%CI 38%-86%), 87% for Stage II (95% CI 75%-95%), 87% for Stage III (95% CI 75%-95%) and 83.4% for Stage IV (95% CI 84%-100%) in cross-validation, and 60% for Stage I (95%CI 60%-80%), 100% for Stage II (95% CI 80%-100%), 100% for Stage III (95% CI 100%-100%) and 100% for Stage IV (95% CI 100%-100%) on the leave-out set. At a ~98% specificity level, the model had a median sensitivity of 37.5% for Stage I (95%CI 37%-50%), 69% for Stage II (95% CI 56%-75%), 69% for Stage III (95% CI 60%-84%) and 67% for Stage IV (95% CI 50%-84%) in cross-validation, and 40% for Stage I (95%CI 20%-60%), 75% for Stage II (95% CI 75%-100%), 100% for Stage III (95% CI 100%-100%) and 100% for Stage IV (95% CI 66%-100%) with a slight decrease in specificity to 95.2% on the leave-out set. Using DMRs derived from TCGA data and other publications, yielded a comparable (to our models) cross-validation area under the curve (AUC: 0.93-0.95). Cross-validation performance using only the sample metadata in table 1 and without access to the data was significantly poorer (AUC 0.75-0.81). Conclusions: cfDNA-based methylation profiles are consistent across studies and ethnicities, leading to robust and “explainable” CRC screening predictions. [Table: see text]

A new flexible and partially monotonic discrete choice model

The poor predictability and the misspecification arising from hand-crafted utility functions are common issues in theory-driven discrete choice models (DCMs). Data-driven DCMs improve predictability through flexible utility specifications, but they do not address the misspecification issue and provide untrustworthy behavioral interpretations (e.g., biased willingness to pay estimates). Improving interpretability at the minimum loss of flexibility/predictability is the main challenge in the data-driven DCM. To this end, this study proposes a flexible and partially monotonic DCM by specifying the systematic utility using the Lattice networks (i.e., DCM-LN). DCM-LN ensures the monotonicity of the utility function relative to the selected attributes while learning attribute-specific non-linear effects through piecewise linear functions and interaction effects using multilinear interpolations in a data-driven manner. Partial monotonicity could be viewed as domain-knowledge-based regularization to prevent overfitting, consequently avoiding incorrect signs of the attribute effects. The light architecture and an automated process to write monotonicity constraints make DCM-LN scalable and translatable to practice. The proposed DCM-LN is benchmarked against deep neural network-based DCM (i.e., DCM-DNN) and a DCM with a hand-crafted utility in a simulation study. While DCM-DNN marginally outperforms DCM-LN in predictability, DCM-LN highly outperforms all considered models in interpretability, i.e., recovering willingness to pay at individual and population levels. The empirical study verifies the balanced interpretability and predictability of DCM-LN. With superior interpretability and high predictability, DCM-LN lays out new pathways to harmonize the theory-driven and data-driven paradigms.

On Constrained Mixed-Integer DR-Submodular Minimization

Diminishing returns (DR)–submodular functions encompass a broad class of functions that are generally nonconvex and nonconcave. We study the problem of minimizing any DR-submodular function with continuous and general integer variables under box constraints and, possibly, additional monotonicity constraints. We propose valid linear inequalities for the epigraph of any DR-submodular function under the constraints. We further provide the complete convex hull of such an epigraph, which, surprisingly, turns out to be polyhedral. We propose a polynomial-time exact separation algorithm for our proposed valid inequalities with which we first establish the polynomial-time solvability of this class of mixed-integer nonlinear optimization problems. Funding: This work was supported by the Office of Naval Research Global [Grant N00014-22-1-2602].

Smoothness and monotonicity constraints for neural networks using ICEnet

Abstract Deep neural networks have become an important tool for use in actuarial tasks, due to the significant gains in accuracy provided by these techniques compared to traditional methods, but also due to the close connection of these models to the generalized linear models (GLMs) currently used in industry. Although constraining GLM parameters relating to insurance risk factors to be smooth or exhibit monotonicity is trivial, methods to incorporate such constraints into deep neural networks have not yet been developed. This is a barrier for the adoption of neural networks in insurance practice since actuaries often impose these constraints for commercial or statistical reasons. In this work, we present a novel method for enforcing constraints within deep neural network models, and we show how these models can be trained. Moreover, we provide example applications using real-world datasets. We call our proposed method ICEnet to emphasize the close link of our proposal to the individual conditional expectation model interpretability technique.

High-Fidelity Specular SVBRDF Acquisition From Flash Photographs.

Obtaining accurate SVBRDFs from 2D photographs of shiny, heterogeneous 3D objects is a highly sought-after goal for domains like cultural heritage archiving, where it is critical to document color appearance in high fidelity. In prior work such as the promising framework by Nam et al., the problem is simplified by assuming that specular highlights exhibit symmetry and isotropy about an estimated surface normal. The present work builds on this foundation with several significant modifications. Recognizing the importance of the surface normal as an axis of symmetry, we compare nonlinear optimization for normals with a linear approximation proposed by Nam et al. and find that nonlinear optimization is superior to the linear approximation, while noting that the surface normal estimates generally have a very significant impact on the reconstructed color appearance of the object. We also examine the use of a monotonicity constraint for reflectance and develop a generalization that also enforces continuity and smoothness when optimizing continuous monotonic functions like a microfacet distribution. Finally, we explore the impact of simplifying from an arbitrary 1D basis function to a traditional parametric microfacet distribution (GGX), and we find this to be a reasonable approximation that trades some fidelity for practicality in certain applications. Both representations can be used in existing rendering architectures like game engines or online 3D viewers, while retaining accurate color appearance for fidelity-critical applications like cultural heritage or online sales.

Metric learning for monotonic classification: turning the space up to the limits of monotonicity

This paper presents, for the first time, a distance metric learning algorithm for monotonic classification. Monotonic datasets arise in many real-world applications, where there exist order relations in the input and output variables, and the outputs corresponding to ordered pairs of inputs are also expected to be ordered. Monotonic classification can be addressed through several distance-based classifiers that are able to respect the monotonicity constraints of the data. The performance of distance-based classifiers can be improved with the use of distance metric learning algorithms, which are able to find the distances that best represent the similarities among each pair of data samples. However, learning a distance for monotonic data has an additional drawback: the learned distance may negatively impact the monotonic constraints of the data. In our work, we propose a new model for learning distances that does not corrupt these constraints. This methodology will also be useful in identifying and discarding non-monotonic pairs of samples that may be present in the data due to noise. The experimental analysis conducted, supported by a Bayesian statistical testing, demonstrates that the distances obtained by the proposed method can enhance the performance of several distance-based classifiers in monotonic problems.

Learning bayesian network parameters from limited data by integrating entropy and monotonicity

High-accuracy parameter learning in Bayesian Networks (BNs) is a key challenge in real-time decision support applications, particularly when the available data are limited. Prior/Expert knowledge was introduced to eliminate the drawbacks of insufficient information; however, this method is subjective. In this study, we explored the use of monotonicity constraints to control the causal relationships between the nodes and their parents-nodes in BNs and proposed a new learning algorithm called global domain monotonicity based on maximum information entropy (GDM-MIE), which was designed for parameter learning in uncertain discrete BNs with nonlinear equality constraints when only finite data are available. In the proposed algorithm, a class of monotonicity is encoded as a constraint on information entropy and the parameter learning problem is transformed into constraints among the node parameters based on a known network. Furthermore, we considered the parameters as uncertain entropy information and discussed the monotonicity among parameters in the global spatial domain, proving the accuracy of the logical relationships of the model, system reliability, and time complexity. Finally, the proposed method was validated using standard BNs, and its performance was analyzed by comparing the proposed method with the existing learning algorithms. The results showed that the proposed method is more accurate and has better Kullback–Leibler divergence. To revalidate the rationality of the proposed method, the Alarm and Asia networks were employed as special cases. The GDM-MIE was found to achieve the intended goal of observing the estimated parameters by closely approximating the original real parameters with a small sample size, indicating that the proposed algorithm can served as an efficient and feasible method for learning Bayesian parameter.

An interpretable neural network-based non-proportional odds model for ordinal regression

This study proposes an interpretable neural network-based non-proportional odds model (N3POM) for ordinal regression. N3POM is different from conventional approaches to ordinal regression with non-proportional models in several ways: (1) N3POM is defined for both continuous and discrete responses, whereas standard methods typically treat the continuous variables as if they were discrete, (2) instead of estimating response-dependent finite-dimensional coefficients of linear models from discrete responses as is done in conventional approaches, we train a non-linear neural network to serve as a coefficient function. Thanks to the neural network, N3POM offers flexibility while preserving the interpretability of conventional ordinal regression. We establish a sufficient condition under which the predicted conditional cumulative probability locally satisfies the monotonicity constraint over a user-specified region in the covariate space. Additionally, we provide a monotonicity-preserving stochastic (MPS) algorithm for effectively training the neural network. We apply N3POM to several real-world datasets.

Nonparametric estimation and forecasting of interval-valued time series regression models with constraints

Nowadays information technology advances allow the collecting and storage of large complex datasets in many areas. Modeling and forecasting interval-valued time series (ITS) has drawn much attention over the last two decades because interval-valued observations contain more information than point-valued observations over the same period and remove undesirable noises in high-frequency data. However, most work mainly focuses on modeling a linear univariate ITS or bivariate point process. This paper proposes nonparametric regression models for interval-valued time series with imposing constraints, e.g., monotonicity. This setting with a monotonic constraint is consistent with the existing literature, which focuses on incorporating valuable empirical information in modeling and forecasts. Two constraint estimators are developed and asymptotic properties are established. Monte Carlo simulation is conducted to show the finite sample performance. An empirical application to equity premium documents that the proposed model yields a better forecast performance than some popular models in the literature.

Prediction for distributional outcomes in high-performance computing input/output variability

Abstract Although high-performance computing (HPC) systems have been scaled to meet the exponentially growing demand for scientific computing, HPC performance variability remains a major challenge in computer science. Statistically, performance variability can be characterized by a distribution. Predicting performance variability is a critical step in HPC performance variability management. In this article, we propose a new framework to predict performance distributions. The proposed framework is a modified Gaussian process that can predict the distribution function of the input/output (I/O) throughput under a specific HPC system configuration. We also impose a monotonic constraint so that the predicted function is nondecreasing, which is a property of the cumulative distribution function. Additionally, the proposed model can incorporate both quantitative and qualitative input variables. We predict the HPC I/O distribution using the proposed method for the IOzone variability data. Data analysis results show that our framework can generate accurate predictions, and outperform existing methods. We also show how the predicted functional output can be used to generate predictions for a scalar summary of the performance distribution, such as the mean, standard deviation, and quantiles. Our prediction results can further be used for HPC system variability monitoring and optimization. This article has online supplementary materials.

Ground motion models for regions with limited data: Data‐driven approach

AbstractThe ground motion model (GMM) for response spectra is crucial to hazard studies and structural design. GMM developed for regions with abundant data can capture appropriate spectral attenuation characteristics. However, several seismically active regions, such as the Himalayas, have limited recorded data, and thus, traditionally, simulated, or other regional data are supplemented with the available data for developing a GMM. Despite data augmentation, GMMs developed for such regions cannot appropriately depict attenuation characteristics. Therefore, the paper presents a comprehensive study encompassing the development of data‐driven approaches to obtain GMM for response spectra using the Himalayan crustal data with inputs: magnitude, distance, site class, depth, and a flag corresponding to the horizontal and vertical components. In this regard, GMM using transfer learning is initially developed from a pre‐trained model using global crustal data. Additionally, GMM using the XGBoost approach with monotonic constraints enforced on inputs is developed. These approaches could not capture trends appropriately. Finally, a monotonic constrained transfer learning model is developed to appropriately depict magnitude saturation and scaling, magnitude‐dependent geometric spreading, anelastic attenuation, depth scaling, site amplification, and other desired characteristics.

Single-index mixture cure model under monotonicity constraints

Single-index mixture cure model under monotonicity constraints