Academic literature on the topic 'Interpretable coefficients'

The need for ethnic-specific reference values of lung function variables (LFs) is acknowledged. Their estimation requires expensive and laborious examinations, and therefore additional use of results in physiology and epidemiology would be profitable. To this end, we proposed a form of prediction equations with physiologically interpretable coefficients: a baseline, the onset age (A0) and rate (S) of LF decline, and a height coefficient. The form was tested with data from healthy, nonsmoking Poles aged 18–85 yr (1,120 men, 1,625 women) who performed spirometry maneuvers according to American Thoracic Society criteria. The values of all the coefficients (also A0) for several LFs were determined with regression of LF on patient's age and deviation of patient's height from the mean height in the year group of this patient. S values for forced vital capacity (FVC), forced expiratory volume in 1 s (FEV1), peak expiratory flow, and maximal expiratory flow at 75% of FVC (MEF75) were very similar in both sexes (1.03 ± 0.07%/yr). FEV1/FVC declines four to five times slower. S for MEF25 appeared age dependent. A0 was smallest (28–32 yr) for MEF25 and FEV1. About 50% of each age subgroup (18–40, 41–60, 61–85 yr) exhibited LFs below the mean, and 4–6% were below the 5th percentile lower limits of normal, and thus the form of equations proposed in the paper appeared appropriate for spirometry. Additionally, if this form is accepted, epidemiological and physiological comparison of different LFs and populations will be possible by means of direct comparison of the equation coefficients.

Multiple regression's coefficients define change in the dependent variable due to a predictor's change while all other predictors are constant. Rearranging data to paired differences of observations and keeping only biggest changes yield a matrix of a single variable change, which is close to orthogonal design, so there is no impact of multicollinearity on the regression. A similar approach is used for meaningful coefficients of nonlinear regressions with coefficients of half-elasticity, elasticity, and odds' elasticity due the gradients in each predictor. In contrast to regular linear and nonlinear regressions, the suggested technique produces interpretable coefficients not prone to multicollinearity effects.

Clustering is a popular unsupervised learning tool often used to discover groups within a larger population such as customer segments, or patient subtypes. However, despite its use as a tool for subgroup discovery and description few state-of-the-art algorithms provide any rationale or description behind the clusters found. We propose a novel approach for interpretable clustering that both clusters data points and constructs polytopes around the discovered clusters to explain them. Our framework allows for additional constraints on the polytopes including ensuring that the hyperplanes constructing the polytope are axis-parallel or sparse with integer coefficients. We formulate the problem of constructing clusters via polytopes as a Mixed-Integer Non-Linear Program (MINLP). To solve our formulation we propose a two phase approach where we first initialize clusters and polytopes using alternating minimization, and then use coordinate descent to boost clustering performance. We benchmark our approach on a suite of synthetic and real world clustering problems, where our algorithm outperforms state of the art interpretable and non-interpretable clustering algorithms.

This paper proposes a method for deriving interpretable common factors based on canonical correlation analysis applied to the vectors of common factors and manifest variables in the factor analysis model. First, an entropy-based method for measuring factor contributions is reviewed. Second, the entropy-based contribution measure of the common-factor vector is decomposed into those of canonical common factors, and it is also shown that the importance order of factors is that of their canonical correlation coefficients. Third, the method is applied to derive interpretable common factors. Numerical examples are provided to demonstrate the usefulness of the present approach.

This study proposes transformation functions and matrices between coefficients in the original and reparameterized parameter spaces for an existing linear-linear piecewise model to derive the interpretable coefficients directly related to the underlying change pattern. Additionally, the study extends the existing model to allow individual measurement occasions and investigates predictors for individual differences in change patterns. We present the proposed methods with simulation studies and a real-world data analysis. Our simulation study demonstrates that the method can generally provide an unbiased and accurate point estimate and appropriate confidence interval coverage for each parameter. The empirical analysis shows that the model can estimate the growth factor coefficients and path coefficients directly related to the underlying developmental process, thereby providing meaningful interpretation.

Sparse regularization such as [Formula: see text] regularization is a quite powerful and widely used strategy for high-dimensional learning problems. The effectiveness of sparse regularization has been supported practically and theoretically by several studies. However, one of the biggest issues in sparse regularization is that its performance is quite sensitive to correlations between features. Ordinary [Formula: see text] regularization selects variables correlated with each other under weak regularizations, which results in deterioration of not only its estimation error but also interpretability. In this letter, we propose a new regularization method, independently interpretable lasso (IILasso), for generalized linear models. Our proposed regularizer suppresses selecting correlated variables, so that each active variable affects the response independently in the model. Hence, we can interpret regression coefficients intuitively, and the performance is also improved by avoiding overfitting. We analyze the theoretical property of the IILasso and show that the proposed method is advantageous for its sign recovery and achieves almost minimax optimal convergence rate. Synthetic and real data analyses also indicate the effectiveness of the IILasso.

A quite interpretable linear regression satisfies the following conditions: the signs of its coefficients correspond to the meaningful meaning of the factors; multicollinearity is negligible; coefficients are significant; the quality of the model approximation is high. Previously, to construct such models, estimated using the ordinary least squares, the QInter-1 program was developed. In it, according to the given initial parameters, the mixed integer 0-1 linear programming task is automatically generated, as a result of which the most informative regressors are selected. The mathematical apparatus underlying this program was significantly expanded over time: non-elementary linear regressions were developed, linear restrictions on the absolute values of intercorrelations were proposed to control multicollinearity, assumptions appeared about the possibility of constructing not only linear, but also quasi-linear regressions. This article is devoted to the description of the developed second version of the program for constructing quite interpretable regressions QInter-2. The QInter-2 program allows, depending on the initial parameters selected by the user, to automatically formulate for the LPSolve solver the mixed integer 0-1 linear programming task for constructing both elementary and non-elementary quite interpretable quasi-linear regressions. It is possible to set up to nine elementary functions and control such parameters as the number of regressors in the model, the number of signs in real numbers after the decimal point, the absolute contributions of variables to the overall determination, the number of occurrences of explanatory variables in the model, and the magnitude of intercorrelations. In the process of working with the program, you can also control the number of elementary and non-elementarily transformed variables that affect the speed of solving the mixed integer 0-1 linear programming task. The QInter-2 program is universal and can be used to construct quite interpretable mathematical dependencies in various subject areas.

The difficulty associated with screening and treating colorectal polyps alongside other gastrointestinal pathology presents an opportunity to incorporate computer-aided systems. This paper develops a deep learning pipeline that accurately segments colorectal polyps and various instruments used during endoscopic procedures. To improve transparency, we leverage the Attention U-Net architecture, enabling visualisation of the attention coefficients to identify salient regions. Moreover, we improve performance by incorporating transfer learning using a pre-trained encoder, together with test-time augmentation, softmax averaging, softmax thresholding and connected component labeling to further refine predictions.

The present study analyzed the factor structure of an abbreviated version of Rotter's (1966) locus of control scale. The 11-item scale was administered in both the original forced-choice format and a 4-point rating format. The data were derived from administration of the scale as part of the National Longitudinal Survey (N = 7,407). Maximum likelihood factor analysis with oblique rotation gave a three-factor solution for both the forced-choice and rating formats, but the resulting factors were not easily interpretable, and the subscales had high intercorrelations and unacceptably low reliability coefficients. Subsequent analyses suggested that a single-factor solution was more appropriate. The 4-point rating format appeared to be more interpretable and had the highest reliability coefficient.

In this paper, we propose a vertical federated learning (VFL) structure for logistic regression with bounded constraint for the traditional scorecard, namely FL-LRBC. Under the premise of data privacy protection, FL-LRBC enables multiple agencies to jointly obtain an optimized scorecard model in a single training session. It leads to the formation of scorecard model with positive coefficients to guarantee its desirable characteristics (e.g., interpretability and robustness), while the time-consuming parameter-tuning process can be avoided. Moreover, model performance in terms of both AUC and the Kolmogorov–Smirnov (KS) statistics is significantly improved by FL-LRBC, due to the feature enrichment in our algorithm architecture. Currently, FL-LRBC has already been applied to credit business in a China nation-wide financial holdings group.

L'essor de l'agriculture numérique permet de plus en plus d'observer de manière automatisée et parfois à haute fréquence des dynamiques d'élaboration de la production et de sa qualité en fonction du climat. Les données issues de ces observations dynamiques peuvent être considérées comme des données fonctionnelles. Analyser ce nouveau type de données nécessite d'étendre les outils statistiques usuels au cas fonctionnel ou d'en proposer de nouveaux.Nous avons proposé dans cette thèse une nouvelle approche (SpiceFP: Sparse and Structured Procedure to Identify Combined Effects of Functional Predictors) permettant d'expliquer les variations d'une variable réponse scalaire par deux ou trois prédicteurs fonctionnels dans un contexte d'influence conjointe de ces derniers. Une attention particulière a été apportée à l'interprétabilité des résultats via l'utilisation de classes d'intervalles combinées définissant une partition du domaine d'observation des facteurs explicatifs. Les développements récents autour des modèles LASSO (Least Absolute Shrinkage and Selection Operator) ont été adaptés pour estimer les régions d'influence dans la partition via une régression pénalisée généralisée. L'approche intègre aussi une double sélection, de modèles (parmi les partitions possibles) et de variables (pour une partition donnée) à partir des critères d'information AIC et BIC. La présentation méthodologique de l'approche, son étude grâce à des simulations ainsi qu'une étude de cas basée sur des données réelles ont été présentés dans le chapitre 2.Les données réelles utilisées au cours de cette thèse proviennent d'une expérimentation viticole visant à mieux comprendre l'impact du changement climatique sur l'accumulation d'anthocyanes dans les baies. L'analyse de ces données dans le chapitre 3 à l'aide de l'approche SpiceFP que nous avons étendue a permis d'identifier un impact négatif des combinaisons matinales de faible irradiance (inférieure à environ 100 µmol/s/m2 ou 45 µmol/s/m2 selon l'état avancé-retardé des baies) et température élevée (supérieure à environ 25°C). Une légère différence induite par la température de la nuit a été observée entre ces effets identifiés en matinée.Dans le chapitre 4 de cette thèse, nous proposons une implémentation de l'approche proposée sous la forme d'un package R. Cette implémentation fournit un ensemble de fonctions permettant de construire les intervalles de classes suivant des échelles linéaire ou logarithmique, de transformer les prédicteurs fonctionnels grâces aux classes d'intervalles combinées puis de mettre en oeuvre l'approche en deux ou trois dimensions. D'autres fonctions facilitent la réalisation de post-traitements ou permettent à l'utilisateur de s'intéresser à d'autres modèles que ceux retenus par l'approche comme par exemple une moyenne de différents modèles.Mots clés: Régressions pénalisées, Interaction, critères d'information, scalar-on-function, coefficients interprétables, microclimat de la vigne
The development of digital agriculture allows to observe at high frequency the dynamics of production according to the climate. Data from these dynamic observations can be considered as functional data. To analyze this new type of data, it is necessary to extend the usual statistical tools to the functional case or develop new ones.In this thesis, we have proposed a new approach (SpiceFP: Sparse and Structured Procedure to Identify Combined Effects of Functional Predictors) to explain the variations of a scalar response variable by two or three functional predictors in a context of joint influence of these predictors. Particular attention was paid to the interpretability of the results through the use of combined interval classes defining a partition of the observation domain of the explanatory factors. Recent developments around LASSO (Least Absolute Shrinkage and Selection Operator) models have been adapted to estimate the areas of influence in the partition via a generalized penalized regression. The approach also integrates a double selection, of models (among the possible partitions) and of variables (areas inside a given partition) based on AIC and BIC information criteria. The methodological description of the approach, its study through simulations as well as a case study based on real data have been presented in chapter 2 of this thesis.The real data used in this thesis were obtained from a vineyard experiment aimed at understanding the impact of climate change on anthcyanins accumulation in berries. Analysis of these data in chapter 3 using SpiceFP and one extension identified a negative impact of morning combinations of low irradiance (lower than about 100 µmol/s/m2 or 45 µmol/s/m2 depending on the advanced-delayed state of the berries) and high temperature (higher than about 25°C). A slight difference associated with overnight temperature occurred between these effects identified in the morning.In chapter 4 of this thesis, we propose an implementation of the proposed approach as an R package. This implementation provides a set of functions allowing to build the class intervals according to linear or logarithmic scales, to transform the functional predictors using the joint class intervals and finally to execute the approach in two or three dimensions. Other functions help to perform post-processing or allow the user to explore other models than those selected by the approach, such as an average of different models.Keywords: Penalized regressions, Interaction, information criteria, scalar-on-function, interpretable coefficients,grapevine microclimate

Questa tesi è volta ad investigare due importanti fenomeni, uno naturale ed uno umano. Il primo riguarda i terremoti, mentre il secondo è legato al contenuto dei discorsi ufficiali dei presidenti americani. Per il primo caso, il nostro obiettivo è quello di definire un indicatore dei danni economici causati dai terremoti, proponendo un indice calibrato su una lunga serie di magnitudo rilevate in lunghi periodi di tempo. Mentre per il caso dei discorsi presidenziali, vogliamo quantificare il loro impatto sul mercato finanziario, in particolare studiamo l’effetto che essi hanno sull’indice “Standard and Poor’s 500”. Il nostro obiettivo principale è quello di contribuire nell’ambito delle scelte di politica economica prendendo in considerazione tali fenomeni ed analizzandoli con un approccio diverso ed innovativo. L’analisi esposta in questa tesi è sviluppata per mezzo di strumenti econofisici strettamente collegati all’ambito dell’analisi “rank-size”. Tale analisi consiste nell’uso di una serie di funzioni particolarmente utili per l’esplorazione delle proprietà di grandi dataset, anche quando essi sono distribuiti nel tempo e hanno bande di errore non perfettamente definite per via di particolari condizioni di campionamento. Nei capitoli che riguardano i terremoti così come in quelli dedicati all’analisi dei discorsi dei presidenti americani sono mostrati e commentati i risultati di regressioni non lineari impiegate per stimare i coefficienti di varie leggi “rank-size”. Tali stime sono state manipolate in modo tale da poter giungere a conclusioni dal rilievo economico. I risultati più robusti sono stati raggiunti grazie alla straordinaria capacità di interpretare i dati da parte delle leggi “rank-size”. Nell’ambito della valutazione dell’impatto economico dei discorsi presidenziali, un’analisi aggiuntiva è stata svolta valutando diverse distanze tra serie storiche. In particolare considerando la serie storica delle parole semanticamente legate all’economica e pronunciate dai presidenti americani nel corso della storia e le serie storiche del volume, dei prezzi e dei rendimenti dell’indice “Standard & Poor's 500”. Per questa analisi abbiamo impiegato un approccio probabilistico ed anche uno meramente topologico. Infatti abbiamo misurato l’entropia delle serie storiche e comparato le conclusioni valutando le differenze fra diverse misure di distanza vettoriale.

AbstractData-driven machine learning (ML) models are attracting increasing interest in chemical engineering and already partly outperform traditional physical simulations. Previous work in this field has mainly focused on improving the models’ statistical performance while the thereby imparted knowledge has been taken for granted. However, also the structures learned by the model during the training are fascinating yet non-trivial to assess as they are usually high-dimensional. As such, the interpretable communication of the relationship between the learned model and domain knowledge is vital for its evaluation by applying engineers. Specifically, visual analytics enables the interactive exploration of data sets and can thus reveal structures in otherwise too large-scale or too complex data. This chapter focuses on the thermodynamic modeling of mixtures of substances using the so-called activity coefficients as exemplary measures. We present and apply two visualization techniques that enable analyzing high-dimensional learned substance descriptors compared to chemical domain knowledge. We found explanations regarding chemical classes for most of the learned descriptor structures and striking correlations with physicochemical properties.

Automatic classification of ECG signals has been a longtime research area with large progress having been made recently. However these advances have been achieved with increasingly complex models at the expense of model’s interpretability. In this research, a new model based on multivariate autoregressive model (MAR) coefficients combined with a tree-based model to classify bundle branch blocks is proposed. The advantage of the presented approach is to build a lightweight model which combined with post-hoc interpretability can bring new insights into important cross-lead dependencies which are indicative of the diseases of interest.

ABSTRACT Formation pressure is a key parameter in the process of oilfield exploration and development. In this study, a novel deep learning model is proposed for accurate calculation of formation pressure. Particularly, making use of the long short-term memory (LSTM) network in solving sequential-data based regression problems, this paper considers the specific domain knowledge of logging and develops a self-interpretable LSTM (SI-LSTM) to calculate the formation pressure. It can dynamically capture the potential correlation between the formation pressure and input variables, and interpretability analysis is conducted for weighting coefficient of characteristics and temporal. Field logging datasets are adopted to evaluate the accuracy and effectiveness of the proposed models. The results indicate that the model embedded mechanism knowledge has greatly improved the prediction accuracy and stability with a mean absolute percentage error of 1.223%. The interpretation results show that the formation pressure has short-term auto-correlation. The proposed method provides a new idea for field calculation of formation pressure, and can be a useful and high-precision scientific alternative to the traditional methods. INTRODUCTION Formation pore pressure is a crucial parameter in the process of exploring and developing oilfields, and accurate prediction of this parameter is essential to reduce the occurrence of wellbore instability, such as overflow (Song et al., 2022). Currently, formation pore pressure prediction methods can be broadly classified into four categories: (1) under-compaction theory-based methods, such as the equivalent depth method (Hottman and Johnson, 1965; Walter and George, 1988; Song et al., 2011) and the Eaton method (Bektas et al., 2015; Ernanda et al., 2018; Yi et al., 2019), which construct the normal compaction trend equation through the mud shale layer and consider only the under-compaction effect; (2) rock mechanics theory-based methods, such as the effective stress method (Sun et al., 2011; Wang et al., 2019) the Bowers formula method (Bowers, 1995; Etminan et al., 2012; Qiang et al., 2020). These methods require a large amount of logging data, experimental data, and statistical regression analysis to determine the empirical coefficients; (3) empirical statistical model methods, such as multiple regression method (Deng et al., 2015) which involves more empirical parameters. The errors of each parameter are superimposed on each other, making the calculation accuracy of formation pore pressure limited; (4) artificial intelligence prediction methods, which have been a hot research topic in recent years, such as the gray prediction model with drilling (Zhang and Gao, 2005; He et al., 2008), artificial neural networks (S et al., 2018; Rashidi and Asadi, 2018; Hadi et al., 2019; Hutomo et al., 2019), support vector machines (Wei et al., 2007). Although these intelligent methods effectively improve the prediction accuracy, they do not integrate with empirical knowledge, which leads to the instability of the prediction results. Moreover, the black-box nature of the internal decision making of the model also makes the results weakly interpretable.

Standard convolution operations can effectively perform feature extraction and representation but result in high computational cost, largely due to the generation of the original convolution kernel corresponding to the channel dimension of the feature map, which will cause unnecessary redundancy. In this paper, we focus on kernel generation and present an interpretable span strategy, named SpanConv, for the effective construction of kernel space. Specifically, we first learn two navigated kernels with single channel as bases, then extend the two kernels by learnable coefficients, and finally span the two sets of kernels by their linear combination to construct the so-called SpanKernel. The proposed SpanConv is realized by replacing plain convolution kernel by SpanKernel. To verify the effectiveness of SpanConv, we design a simple network with SpanConv. Experiments demonstrate the proposed network significantly reduces parameters comparing with benchmark networks for remote sensing pansharpening, while achieving competitive performance and excellent generalization. Code is available at https://github.com/zhi-xuan-chen/IJCAI-2022 SpanConv.

Abstract Model testing is common in coastal and offshore engineering. The design of such model tests is important such that the maximal information of the underlying physics can be extrapolated with a limited amount of test cases. The optimal design of experiments also requires considering the previous similar experimental results and the typical sea-states of the ocean environments. In this study, we develop a model test design strategy based on Bayesian sampling for a classic problem in ocean engineering — nonlinear wave loading on a vertical cylinder. The new experimental design strategy is achieved through a GP-based surrogate model, which considers the previous experimental data as the prior information. The metocean data are further incorporated into the experimental design through a modified acquisition function. We perform a new experiment, which is mainly designed by data-driven methods including several critical parameters such as the size of the cylinder and all the wave conditions. We examine the performance of such a method when compared to traditional experimental design based on manual decisions. This method is a step forward to a more systematic way of approaching test designs with marginally better performance in capturing the higher-order force coefficients. The current surrogate model also made several ‘interpretable’ decisions which can be explained with physical insights.

This paper introduces the Lasso and Ridge Regression methods, which are two popular regularization approaches. The method they give a penalty to the coefficients differs in both of them. L1 Regularization refers to Lasso linear regression, while L2 Regularization refers to Ridge regression. As we all know, regression models serve two main purposes: explanation and prediction of scientific phenomena. Where prediction accuracy will be optimized by balancing each of the bias and variance of predictions, while explanation will be gained by constructing interpretable regression models by variable selection. The penalized regression method, also known as Lasso regression, adds bias to the model's estimates and reduces variance to enhance prediction. Ridge regression, on the other hand, introduces a minor amount of bias in the data to get long-term predictions. In the presence of multicollinearity, both regression methods have been offered as an alternative to the least square approach (LS). Because they deal with multicollinearity, they have the appropriate properties to reduce numerical instability caused by overfitting. As a result, prediction accuracy can be improved. For this study, the Corona virus disease (Covid-19) dataset was used, which has had a significant impact on global life. Particularly in our region (Kurdistan), where life has altered dramatically and many people have succumbed to this deadly sickness. Our data is utilized to analyze the benefits of each of the two regression methods. The results show that the Lasso approach produces more accurate and dependable or reliable results in the presence of multicollinearity than Ridge and LS methods when compared in terms of accuracy of predictions by using NCSS10, EViews 12 and SPSS 25.

Understanding driver’s maneuver behavior is an important prerequisite for providing drivers with different levels of assistance in the collaborative driving system. Aiming at establishing a general and interpretable model of driver steering styles, 38 drivers’ data are collected by a driving simulator platform, where a U-shaped experimental scene is built. To reduce data redundancy, Principal Component Analysis (PCA) is utilized to extract key features. Vali-dated by both Elbow Method and Silhouette Coefficient, the features are classified by k-means cluster. Finally, three driving styles with different characteristics are defined, and the corresponding original data are compared to make a reasonable explanation. The results can be used as a design basis for customizing shared steering controllers in collaborative driving.